CN107579941B

CN107579941B - Mechanism for I/Q impairment correction, and transmitter impairment measurement using an offset local oscillator

Info

Publication number: CN107579941B
Application number: CN201710967762.2A
Authority: CN
Inventors: S·L·达克; D·J·贝克; C·J·比恩克
Original assignee: National Instruments Corp
Current assignee: National Instruments Corp
Priority date: 2012-02-24
Filing date: 2013-02-18
Publication date: 2020-05-19
Anticipated expiration: 2033-02-18
Also published as: WO2013126302A2; CN104040982B; CN107579941A; CN104040982A; WO2013126302A3

Abstract

The present disclosure relates to mechanisms for I/Q impairment correction, and transmitter impairment measurements using an offset local oscillator. Mechanisms for measuring transmitter and/or receiver I/Q impairments are disclosed, including iterative methods of measuring transmitter I/Q impairments with a shared local oscillator or with an intentionally offset local oscillator, and methods of measuring receiver I/Q impairments. Methods for calculating I/Q impairments from a sampled complex signal, for calculating DC properties of a signal path between a transmitter and a receiver, and for transforming I/Q impairments by a linear system are also disclosed.

Description

Mechanism for I/Q impairment correction, and transmitter impairment measurement using an offset local oscillator

The present application is a divisional application of the inventive patent application having application number 201380004425.3, filing date 2013, 2/18/h, entitled "mechanism for I/Q impairment correction, and transmitter impairment measurement using an offset local oscillator".

Technical Field

The present invention relates to the field of signal processing, and more particularly, to a system and method for measurement and correction of I/Q impairments (impairments) in a receiving device or a transmitting device.

Background

The transmitter receives a complex digital signal I (n) + jQ (n), converts the complex digital signal to an analog signal I (t) + jQ (t), and upconverts the analog signal using an I/Q modulator. The upconverted signal is transmitted onto a channel. Ideally, a pure complex exponential tone (tone) provided to the I/Q modulator would result in a pure tone being transmitted. However, in reality, I/Q impairments in the transmitter will cause the I and Q channels to have different gains and different phase shifts. This distortion implies, among other things, that the transmitted signal will have undesirable energy at a frequency equal to the negative of the pitch frequency. Depending on the communication standard, this undesirable "mirroring" leads to potential distortions on the constellation diagram (constellation diagram) or the artificial noise floor (artifical noise floor). Receivers have similar problems. When the receiver is stimulated by pure audio at frequency f, the complex signal appearing at the output of the I/Q demodulator of the receiver will include undesired signal energy at frequency-f in addition to the energy at frequency f. In both cases (transmitter and receiver), difficulties arise due to gain and phase imbalance between the I and Q signals. Thus, there is a need for a mechanism that can correct for I/Q impairments in a transmitter and/or receiver.

Furthermore, to achieve high quality correction of the I/Q impairments, high quality measurements that can take advantage of the I/Q impairments are needed. However, quality measurements may be difficult to obtain. For example, measuring the I/Q impairments of a transmitter involves directing the transmitter to transmit a signal to a receiver. The receiver estimates the I/Q impairments of the transmitter based on the signals it receives. However, the I/Q demodulator of the receiver corrupts the estimate with its own I/Q impairments. Furthermore, the signal path between the I/Q modulator of the transmitter and the I/Q demodulator of the receiver also introduces distortion to the estimation. Thus, there is a need for the following mechanisms: mechanisms that can estimate or measure I/O impairments of a transmitter and/or receiver, mechanisms that can accurately measure I/Q impairments implied in a sampled signal, mechanisms that can determine properties of a signal path, and mechanisms that can predict how an I/Q impairment is transformed by a system, such as a signal path.

Disclosure of Invention

This patent discloses, among other things, mechanisms that can compensate for I/Q impairments in a transmitter and/or receiver. The parameters used to perform the compensation are calculated based on measured or estimated values of the I/Q impairments. For example, the parameters used to compensate for the I/Q impairments of the transmitter (or receiver) are calculated based on measured or estimated values of those impairments. Any known technique may be used to measure or estimate the I/Q impairments of the transmitter or receiver, or a series combination of transmitter and receiver, including but not limited to the techniques disclosed herein.

In one embodiment, a system and method for compensating for I/Q impairments of a receiver may involve the following operations.

An analog input signal is received from a transmission medium. I/Q demodulation is performed on the analog input signal to produce an analog in-phase (I) signal and an analog quadrature (Q) signal. The analog I signal and the analog Q signal are then digitized to produce a digital I signal and a digital Q signal, respectively. The digital I signal and the digital Q signal are filtered according to a 2x2 matrix of digital filters to produce filtered digital I signals and filtered digital Q signals. (filtering may be performed in a programmable hardware element such as a FGPA, or in a dedicated digital circuit such as an ASIC, or in software on a processor, etc..) the 2x2 matrix of digital filters at least partially compensates for the I/Q impairments of the receiver over a frequency range. The frequency response of at least one diagonal component of the 2x2 matrix is calculated based on a measure of I/Q impairment as a function of frequency and a measure as a function of the negative of frequency. (the measure of the I/Q impairment of the receiver may be obtained by any known method the document describes various methods for obtaining such a measure.) furthermore, the frequency response of at least one off-diagonal component of the 2x2 matrix is calculated based on the measure as a function of frequency and the measure as a function of the negative of frequency.

In some embodiments, it may be assumed that the I/Q impairments of the receiver above positive frequencies and the I/Q impairments of the receiver above negative frequencies are functionally related. (A) In one such embodiment, the frequency response of the 2x2 matrix may be calculated as follows. The frequency response of at least one diagonal component of the 2x2 matrix at any frequency f may be calculated based only on the measurement of the I/Q impairments at frequency f (or alternatively, based only on the measurement of the I/Q impairments at frequency-f). Further, the frequency response of at least one off-diagonal component of the 2x2 matrix at frequency f may be calculated based solely on the measurement of the I/Q impairments at frequency f (or alternatively, based solely on the measurement of the I/Q impairments at frequency-f). (B) In another such embodiment, the gain imbalance is assumed to be even and the phase skew is assumed to be odd. Thus, both off-diagonal components of the 2x2 matrix may be set to zero; one of the diagonal components may correspond to a pure pass filter (i.e., unity frequency response); and the frequency response of the other diagonal component at any frequency f may be calculated based solely on the measurement of the I/Q impairments at frequency f (or alternatively, solely on the measurement of the I/Q impairments at frequency-f). (C) In another such embodiment, both diagonal components of the 2x2 matrix may correspond to pure pass filters; one of the off-diagonal components may be set to zero; and the frequency response of another off-diagonal component at any frequency f may be calculated based solely on the measurement of the I/Q impairments at frequency f (or alternatively, based solely on the measurement of the I/Q impairments at frequency-f).

In another embodiment, a system and method for configuring a receiver to at least partially compensate for I/Q impairments of the receiver may involve the following operations.

A measurement of I/Q impairments of the receiver over one frequency band is received (or accessed from memory). Based on this measurement, a 2x2 matrix of digital filters is calculated. A 2x2 matrix of digital filters is calculated to at least partially compensate for the I/Q impairments of the receiver over that frequency band. The frequency response of at least one diagonal component of the 2x2 matrix is calculated based on the measurement as a function of frequency and the measurement as a function of the negative of frequency. Further, the frequency response of at least one off-diagonal component of the 2x2 matrix is calculated based on the measurement as a function of frequency and the measurement as a function of the negative of frequency. The digital circuit is then programmed to implement a 2x2 matrix of digital filters. When so programmed, the digital circuit is configured to at least partially compensate for the I/Q impairments of the receiver over that frequency band. Digital circuitry may be implemented in any of a variety of forms. For example, digital circuitry may be implemented by programmable hardware elements, or by special purpose digital circuitry, such as an ASIC, or by a processor in response to execution of program instructions. (digital circuitry may be incorporated as part of the receiver or as part of another system, such as a host computer or controller board).

In another embodiment, a system and method for operating a transmitter to implement I/Q impairment compensation may involve the following operations.

A digital in-phase (I) signal and a digital quadrature (Q) signal are received. The digital I signal and the digital Q signal are filtered according to a 2x2 matrix of digital filters to produce filtered digital I signals and filtered digital Q signals. The 2x2 matrix of the digital filter at least partially pre-compensates for the I/Q impairments of the transmitter over a range of frequencies. The frequency response of at least one diagonal component of the 2x2 matrix is calculated based on a measure of the I/Q impairments as a function of frequency and a measure as a function of the negative of frequency. (the measurement of the I/Q impairment of the transmitter may be obtained by any known method-this document describes various methods for obtaining such a measurement.) furthermore, the frequency response of at least one off-diagonal component of the 2x2 matrix is calculated based on the measurement as a function of frequency and the measurement as a function of the negative of frequency. The filtered digital I and Q signals are then converted into analog form to obtain corresponding analog I and Q signals. I/Q modulation may be performed on the analog I signal and the analog Q signal to produce a modulated analog signal.

In some embodiments, it may be assumed that the I/Q impairments of the transmitter at positive frequencies and the I/Q impairments of the transmitter at negative frequencies are functionally related. (A) In one such embodiment, the computation of the 2x2 matrix of the digital filter may be simplified as follows. The frequency response of at least one diagonal component of the 2x2 matrix at any frequency f within the frequency range may be calculated based solely on the measurement of the I/Q impairments at frequency f (or alternatively, solely on the measurement of the I/Q impairments at frequency-f). Further, the frequency response of at least one off-diagonal component of the 2x2 matrix at frequency f may be calculated based solely on the measurement of the I/Q impairments at frequency f (or alternatively, based solely on the measurement of the I/Q impairments at frequency-f). (B) In another such embodiment, the gain imbalance is assumed to be even and the phase skew is assumed to be odd. Thus, both off-diagonal components of the 2x2 matrix may be set to zero; one of the diagonal components may correspond to a pure pass filter (i.e., unity frequency response); and the frequency response of the other diagonal component at any frequency f may be calculated based solely on the measurement of the I/Q impairments at frequency f (or alternatively, solely on the measurement of the I/Q impairments at frequency-f). (C) In another such embodiment, both diagonal components of the 2x2 matrix may correspond to pure pass filters; one of the off-diagonal components may be set to zero; and the frequency response of the other non-diagonal component at any frequency f may be calculated based solely on the measurement of the I/Q impairments at frequency f (or alternatively, based solely on the measurement of the I/Q impairments at frequency-f).

In another embodiment, a system and method for configuring a transmitter to at least partially compensate for I/Q impairments of the transmitter may involve the following operations.

A measurement of I/Q impairments of a transmitter over a range of frequencies is received (or accessed from memory). A 2x2 matrix of digital filters is calculated based on the measurements. A 2x2 matrix of digital filters is calculated to at least partially pre-compensate for the I/Q impairments of the transmitter. The frequency response of at least one diagonal component of the 2x2 matrix is calculated based on the measurement as a function of frequency and the measurement as a function of the negative of frequency. Further, the frequency response of at least one off-diagonal component of the 2x2 matrix is calculated based on the measurement as a function of frequency and the measurement as a function of the negative of frequency. The digital circuit is then programmed to implement a 2x2 matrix of digital filters. When so programmed, the digital circuit is configured to at least partially pre-compensate for the I/Q impairments of the transmitter.

In another embodiment, a system and method for operating a transmitter to at least partially compensate for I/Q impairments of the transmitter at a given frequency f may involve the following operations.

A digital in-phase (I) signal and a digital quadrature (Q) signal are received. The digital I signal and the digital Q signal are transformed according to a constant 2x2 matrix to produce a resulting digital I signal and a resulting digital Q signal. (in other words, a vector signal including a digital I signal and a digital Q signal is multiplied by the 2 × 2 matrix). The resulting digital I signal and digital Q signal are converted into analog form to obtain corresponding analog I signal and analog Q signal. I/Q modulation is performed on the analog I signal and the analog Q signal to produce a modulated analog signal. The 2x2 matrix is configured to at least partially pre-compensate for the I/Q impairments at frequency f. The first constant corresponding to a diagonal element of the 2x2 matrix is calculated based on the measurement of the I/Q impairments at frequency f and the measurement of the I/Q impairments at frequency-f. In addition, a second constant corresponding to an off-diagonal element of the 2x2 matrix is calculated based on the measurement at frequency f and the measurement at frequency-f.

In another embodiment, a method for determining (i.e., measuring) an I/Q impairment of a transmitter may involve the following actions.

The method involves performing a set of operations. This set of operations includes: (a) directing complex exponential tones at a frequency f to be provided to a transmitter; (b) a pre-compensation circuit that provides a pre-compensation transform to the transmitter, wherein the pre-compensation circuit is configured to apply the pre-compensation transform to the complex exponential tones to obtain an adjusted complex signal, wherein the pre-compensation transform is configured to pre-compensate a current estimate of I/Q impairments of the transmitter, wherein the transmitter is configured to transmit a transmit signal based on the adjusted complex signal, wherein the receiver is configured to receive the transmit signal and capture a sampled complex signal representative of the received transmit signal; (c) calculating an original I/Q impairment based on the sampled complex signal; (d) transforming the original I/Q impairments to determine transformed I/Q impairments, wherein the transforming removes the measured I/Q impairments of the receiver from the original I/Q impairments; (e) removing a current estimate of a signal path from the transformed I/Q impairments to obtain path-compensated I/Q impairments, wherein the signal path comprises a path from an I/Q modulator of the transmitter to a demodulator of the receiver; and (f) updating the current estimate of the I/Q impairments of the transmitter based on the path-compensated I/Q impairments. (depending on the architecture of the receiver, the demodulator may or may not be an I/Q demodulator).

In another embodiment, a method for determining I/Q impairments of a transmitter may involve the following actions.

The method may include configuring a Local Oscillator (LO) of the transmitter and a Local Oscillator (LO) of the receiver to be phase-locked to a common reference, and causing a frequency of the LO of the receiver minus a frequency of the LO of the transmitter to be equal to (e.g., substantially equal to) an amount alo.

The method may further include performing a set of operations, wherein the set of operations includes: (a) directing complex exponential tones at a frequency f to be provided to a transmitter; (b) a pre-compensation circuit that provides a pre-compensation transform to the transmitter, wherein the pre-compensation circuit is configured to apply the pre-compensation transform to the complex exponential tones to obtain an adjusted complex signal, wherein the pre-compensation transform is configured to pre-compensate a current estimate of I/Q impairments of the transmitter, wherein the transmitter is configured to transmit a transmit signal based on the adjusted complex signal, wherein the receiver is configured to receive the transmit signal and capture a sampled complex signal representative of the received transmit signal; (c) frequency shifting the sampled complex signal by an amount Δ LO to obtain a frequency shifted signal; (d) calculating an original I/Q impairment at a frequency f based on the frequency shifted signal; (e) removing a current estimate of a signal path from the original I/Q impairments at the frequency f to obtain path-compensated I/Q impairments at the frequency f, wherein the signal path comprises a path from an I/Q modulator of the transmitter to a demodulator of the receiver; and (f) updating the current estimate of the I/Q impairments of the transmitter at frequency f based on the path-compensated I/Q impairments at frequency f. (depending on the architecture of the receiver, the demodulator may or may not be an I/Q demodulator).

In another embodiment, a method for determining (i.e., measuring) an I/Q impairment of a receiver may involve the following actions.

The method may involve directing an input signal to be provided to a receiver, wherein the input signal includes an isolated tone at a displacement frequency f and includes a void interval (void interval) around the displacement frequency-f. (in one embodiment, the receiver includes a calibrated tone generator configured to generate the input signal). The receiver is configured to demodulate the input signal to obtain a sampled complex signal. The displacement frequencies f and-f are displacements relative to the local oscillator frequency of the receiver.

The method may also involve calculating an I/Q impairment of the receiver at frequency f based on the sampled complex signal.

The method may also involve repeating the acts of directing and calculating for values of frequency f that span a specified frequency band.

The method may also involve storing in memory the I/Q impairments of the receiver for the values of the frequency f.

In another embodiment, a method for estimating I/Q impairments associated with a sampled complex signal generated by a receiver may involve the following acts.

The device is directed to stimulate the receiver with a stimulation signal having an isolated tone at a displacement frequency f and an invalid interval at the displacement frequency-f. (the displacement frequencies f and-f are displacements about the local oscillator frequency of the receiver. Calculating a discrete-time Fourier transform value C at frequency f for the I component of a sampled complex signal_I. Calculating a discrete-time Fourier transform value C at frequency f for the Q component of a sampled complex signal_Q. The gain imbalance g of the sampled complex signal at frequency f is based on the value C_IAnd C_QIs calculated. The gain imbalance g comprises at least a gain imbalance of the receiver. Phase skew of sampled complex signal at frequency f

Is based on the value C_IAnd C_QOf phase calculation, wherein the phase is skewed

Including at least the phase skew of the receiver.

In another embodiment, a method for estimating DC scaling of a signal path between an I/Q modulator of a transmitter and an I/Q demodulator of a receiver may involve the following operations. To facilitate this estimation method, the output of the transmitter may be coupled to the input of the receiver, e.g. via a cable.

The transmitter is directed to provide a null signal as an input to the I/Q modulator. Receiving a first response signal that has been captured from the I/Q demodulator in response to providing the null signal. The transmitter is directed to provide a constant signal equal to a non-zero complex constant as an input to the I/Q modulator. Receiving a second response signal that has been captured from the I/Q demodulator in response to providing the constant signal. The first response signal is averaged to obtain a first average value and the second response signal is averaged to obtain a second average value. The difference between the second average and the first average is calculated. A DC scaling is calculated based on the difference and the non-zero complex constant. Further, a DC rotation of the signal path may be calculated based on the phase of the difference and the phase of the non-zero complex constant. DC scaling and DC rotation can be used to remove the effects of the signal path from the I/Q impairments measured at the receiver to obtain an estimate of the I/Q impairments of the transmitter.

In an alternative embodiment of the above described DC scaling/rotation estimation method, the transmitter has no (or negligible) local oscillator leakage. (this may be the case, for example, when the transmitter has other RF architectures than the direct conversion architecture). Thus, the transmission of the null signal, the capture of the first response signal, the calculation of the first average value, and the calculation of the difference value may be omitted. Then, a DC scaling is calculated based on the second average and the non-zero complex constant. The DC rotation is calculated based on the phase of the second average and the phase of the non-zero complex constant.

In another embodiment, a method for calculating an I/Q impairment at a complex output (i.e., an I/Q output pair) of an electronic system based on I/Q impairments at complex inputs (i.e., I/Q input pairs) of the electronic system may comprise the following operations.

The spectrum a (f) is calculated according to the following expression,

where H (f) is the frequency spectrum of a linear system model of the electronic system, where g (f) is the gain imbalance at the complex input, where

Is the phase skew in the complex input. The frequency spectrum B (f) is calculated according to the following expression.

The sum of the spectra a (f) and B (f) and the difference between the spectra a (f) and B (f) are calculated. Gain imbalance and phase skew in the complex output are calculated based on the real and imaginary parts of the sum and the real and imaginary parts of the difference.

In some embodiments, the electronic system modeled by the frequency spectrum H (f) is the inverse of the signal path from the I/Q modulator of the transmitter to the demodulator of the receiver, e.g., as described in various different manners herein. The gain imbalance and phase skew in the complex input of the electronic system may represent the gain imbalance and phase skew in the input of the demodulator (or alternatively, in the output of the demodulator). The gain imbalance and phase skew in the complex output of the electronic system may represent the gain imbalance and phase skew at the output of the I/Q modulator.

Various embodiments of a communication device and associated methods for reducing I/Q impairments in a signal used by the communication device are described herein. According to one embodiment, a receiving device may receive a transmit signal over a communication medium and may perform I/Q demodulation on the received transmit signal to produce a pair of analog I (in-phase) and Q (quadrature) signals. The receiving device may perform analog-to-digital conversion of each of the analog I signal and the analog Q signal to generate corresponding digital I signal and digital Q signal. The resulting digital I and Q signals may have I/Q impairments caused by I/Q demodulation and/or analog-to-digital conversion and/or other processing. The receiving device may be configured to perform wideband I/Q impairment correction on the digital I signal and the digital Q signal to correct I/Q impairment. The wideband I/Q impairment correction may compensate for frequency-dependent variations in gain imbalance and phase imbalance in the digital I signal and the digital Q signal, e.g., may compensate for gain imbalance and phase imbalance in the digital I signal and the digital Q signal at multiple frequency offsets across the instantaneous bandwidth of the receiving device.

Performing wideband I/Q impairment correction on the digital I signal and the digital Q signal may include filtering one or more of the digital I signal and the digital Q signal to produce a resulting digital I signal and a resulting digital Q signal. The resulting digital I and Q signals represent the corrected signal. In some embodiments, the resulting digital I signal is identical to the digital I signal, and the resulting digital Q signal is generated by filtering one or more of the digital I signal and the digital Q signal to obtain one or more corresponding filtered signals and by adding the one or more filtered signals. In other embodiments, the resulting digital Q signal is identical to the digital Q signal, and the resulting digital I signal is generated by filtering one or more of the digital I signal and the digital Q signal to obtain one or more corresponding filtered signals and by adding the one or more filtered signals. In yet other embodiments, the resulting digital I signal is generated by filtering one or more of the digital I signal and the digital Q signal to obtain one or more corresponding filtered signals and by adding the one or more filtered signals; and the resulting digital Q signal is generated by filtering one or more of the digital I signal and the digital Q signal to obtain one or more corresponding additional filtered signals and by adding the one or more additional filtered signals.

In other embodiments, the calibration system (or the receiving device itself) may determine the correction information by providing a plurality of known test signals to the receiving device and measuring the I/Q impairments introduced by the receiving device in response to the known test signals. (in one embodiment, the receiving device may include a calibrated tone generator that generates a known test signal). The wideband I/Q impairment correction may utilize the correction information to compensate for frequency-dependent variations in gain imbalance and phase imbalance in the digital I signal and the digital Q signal.

In some embodiments, the calibration system may operate in an off-line calibration phase and an on-line operation phase. Performing the offline calibration phase may include providing a plurality of known test signals to the receiving device, measuring I/Q impairments introduced by the receiving device in response to the known test signals, and determining correction information based on the measured I/Q impairments. Performing the on-line operational phase may include receiving a transmission signal via a communication medium, performing I/Q demodulation on the received transmission signal to generate an analog I signal and an analog Q signal, performing analog-to-digital conversion on each of the analog I signal and the analog Q signal to generate a digital I signal and a digital Q signal, and performing wideband I/Q impairment correction on the digital I signal and the digital Q signal. The wideband I/Q impairment correction may use correction information determined in an off-line calibration stage to compensate for frequency-dependent variations in gain imbalance and phase imbalance in the digital I signal and the digital Q signal.

In some embodiments, the offline calibration phase may be performed in response to the receiving device being powered on. In some embodiments, the receiving device may automatically enter the online operation phase in response to determining that the offline calibration phase is complete. In some embodiments, the receiving device may automatically switch from the online operation phase to the offline calibration phase in response to determining that the receiver is not busy processing a transmission signal received in the online operation phase. In some embodiments, the offline calibration phase may be initiated in response to user input.

According to other embodiments, a transmitting device may receive digital I (in-phase) and Q (quadrature) signals to be transmitted. The transmitting device may perform wideband I/Q impairment pre-correction on the digital I signal and the digital Q signal. The act of performing wideband I/Q impairment pre-correction may involve filtering one or more of the digital I signal and the digital Q signal to produce a resulting digital I signal and a resulting digital Q signal to pre-compensate for frequency-dependent variations of gain imbalance and phase imbalance that will be subsequently introduced during synthesis of the transmission signal. The transmission signal may be synthesized using the resulting digital I signal and the resulting digital Q signal.

The act of combining the transmit signals may include performing digital-to-analog conversion on the resulting digital I signal and the resulting digital Q signal to produce analog I signals and analog Q signals, and performing I/Q modulation using the analog I signals and the analog Q signals to produce the transmit signals. The resulting digital I signal and the resulting digital Q signal may pre-compensate for frequency-dependent variations in gain imbalance and phase imbalance caused by one or more of digital-to-analog conversion and I/Q modulation.

In some embodiments, the resulting digital I signal is identical to the digital I signal, and the resulting digital Q signal is generated by filtering one or more of the digital I signal and the digital Q signal to obtain one or more corresponding filtered signals and by adding the one or more filtered signals. In other embodiments, the resulting digital Q signal is identical to the digital Q signal, and the resulting digital I signal is generated by filtering one or more of the digital I signal and the digital Q signal to obtain one or more corresponding filtered signals and by adding the one or more filtered signals. In still other embodiments, the resulting digital I signal is generated by filtering one or more of the digital I signal and the digital Q signal to obtain one or more filtered signals, respectively, and by adding the one or more filtered signals; and the resulting digital Q signal is generated by filtering one or more of the digital I signal and the digital Q signal to obtain one or more additional filtered signals, respectively, and by adding the one or more additional filtered signals.

In still other embodiments, the calibration system may determine the correction information by providing a plurality of known digital test signals to the transmitting device and measuring the I/Q impairments introduced by the transmitting device in response to the known test signals. The wideband I/Q impairment pre-correction may utilize the correction information to generate a resultant digital signal.

In some embodiments, the sending device may operate in an offline calibration phase and an online operation phase. The offline calibration phase may include providing a plurality of known test signals to the transmitting device, measuring I/Q impairments introduced by the transmitting device in response to the known test signals, and determining correction information based on the measured I/Q impairments.

In some embodiments, the offline calibration phase may be performed in response to the sending device being powered on. In some embodiments, the sending device may automatically enter the online operation phase in response to determining that the offline calibration phase is complete. In some embodiments, the transmitting device may automatically switch from the online operation phase to the offline calibration phase in response to determining that the transmitter is not busy transmitting signals in the online operation phase. In some embodiments, the offline calibration phase may be initiated in response to user input.

The online operation phase may include receiving a digital I signal and a digital Q signal to be transmitted, and performing wideband I/Q impairment pre-correction on the digital I signal and the digital Q signal. The act of performing wideband I/Q impairment pre-correction may filter one or more of the digital I signal and the digital Q signal using correction information determined in an off-line calibration stage to produce a resulting digital I signal and a resulting digital Q signal to pre-compensate for frequency-dependent variations of gain imbalance and phase imbalance that would be subsequently introduced in the transmission signal synthesis process. The transmission signal may be synthesized using the resulting digital I signal and the resulting digital Q signal.

According to another embodiment, a measurement system may include a receiving device and a device under test. The receiving device may be configured to receive a transmission signal including measurement data acquired from a device under test, perform I/Q demodulation on the received transmission signal to generate analog I (in-phase) and Q (quadrature) signals, perform analog-to-digital conversion of each of the analog I signal and the analog Q signal to generate a digital I signal and a digital Q signal, and perform wideband I/Q impairment correction on the digital I signal and the digital Q signal. The wideband I/Q impairment correction may compensate for frequency-dependent variations in gain imbalance and phase imbalance in the digital I signal and the digital Q signal.

In other embodiments, the measurement system may further include a transmitting device. The transmitting device may be configured to receive a digital I signal and a digital Q signal to be transmitted. The digital I signal and the digital Q signal may specify information to be sent to the device under test. The transmitting device may also be configured to perform wideband I/Q impairment pre-correction on the digital I signal and the digital Q signal. The act of performing wideband I/Q impairment pre-correction may involve filtering one or more of the digital I signal and the digital Q signal to produce a resulting digital I signal and a resulting digital Q signal to pre-compensate for frequency-dependent variations in gain imbalance and phase imbalance that will be subsequently introduced during transmit signal synthesis. The transmitting device may synthesize a transmission signal using the resultant digital I signal and the resultant digital Q signal, and transmit the transmission signal to the device under test.

According to another embodiment, a method for determining I/Q impairments of a transmitter may comprise the operations of: configuring a Local Oscillator (LO) of the transmitter and a Local Oscillator (LO) of the receiver to be phase-locked to a common reference and such that a frequency of the LO of the receiver minus a frequency of the LO of the transmitter is equal to an amount alo; performing a set of operations, wherein the set of operations comprises: (a) directing complex exponential tones at a frequency f to be provided to a transmitter; (b) a pre-compensation circuit that provides a pre-compensation transform to the transmitter, wherein the pre-compensation circuit is configured to apply the pre-compensation transform to the complex exponential tones to obtain an adjusted complex signal, wherein the pre-compensation transform is configured to pre-compensate a current estimate of I/Q impairments of the transmitter, wherein the transmitter is configured to transmit the transmitted signal based on the adjusted complex signal, wherein the receiver is configured to receive the transmitted signal and capture a sampled complex signal representative of the received transmitted signal; (c) frequency shifting the sampled complex signal by an amount Δ LO to obtain a frequency shifted signal; (d) calculating an original I/Q impairment at a frequency f based on the frequency shifted signal; (e) removing a current estimate of a signal path from the original I/Q impairments at the frequency f to obtain path-compensated I/Q impairments at the frequency f, wherein the signal path comprises a path from an I/Q modulator of the transmitter to a demodulator of the receiver; and (f) updating the current estimate of the I/Q impairments of the transmitter at the frequency f based on the path-compensated I/Q impairments at the frequency f.

In other embodiments, the transmitter adheres to a direct conversion architecture, wherein the demodulator is an I/Q demodulator.

Drawings

A better understanding of the present invention may be obtained when the following detailed description is considered in conjunction with the following drawings.

Fig. 1A illustrates one possible application of the compensation methods disclosed herein, in which mobile device 10 and/or transceiver station 15 apply digital pre-compensation to signals they transmit and/or apply digital post-compensation to signals they receive.

FIG. 1B illustrates another possible application of the compensation method disclosed herein, in which test instrument 20 applies a digital pre-compensation to the signal it sends to receiver-under-test 25 to remove the effects of its I/Q impairments.

FIG. 1C illustrates yet another possible application of the compensation method disclosed herein, wherein the test instrument 35 applies digital post-compensation to the signal it receives from the transmitter under test to remove the effects of its I/Q impairments.

Fig. 2A illustrates one embodiment of a method for operating a receiver to implement at least partial I/Q impairment compensation.

Fig. 2B illustrates an embodiment of a receiver configured to implement at least partial I/Q impairment compensation.

Fig. 3 illustrates one embodiment of a method for configuring a receiver to enable the receiver to at least partially compensate for I/Q impairments.

Fig. 4 illustrates one embodiment of a method for operating a transmitter to implement at least partial I/Q impairment compensation.

Fig. 5 illustrates one embodiment of a transmitter configured to implement at least partial I/Q impairment compensation.

Fig. 6 illustrates one embodiment of a method for configuring a transmitter to enable the transmitter to at least partially compensate for I/Q impairments.

Fig. 7 illustrates one embodiment of a system configured to provide I/Q impairment compensation. The I/Q impairments are modeled as occurring entirely on the Q channel.

Fig. 8 illustrates another embodiment of a system configured to provide I/Q impairment compensation. The I/Q impairments are modeled as occurring entirely on the I channel.

Fig. 9 illustrates yet another embodiment of a system configured to provide I/Q impairment compensation. The I/Q impairments are modeled to occur in part on both channels.

Fig. 10 illustrates one embodiment of a method for operating a receiver to at least partially compensate for I/Q impairments at frequency f.

Fig. 11 illustrates one embodiment of a receiver configured to at least partially compensate for I/Q impairments at frequency f.

Fig. 12 illustrates one embodiment of a method for configuring a receiver to enable the receiver to at least partially compensate for I/Q impairments at frequency f.

Fig. 13 illustrates one embodiment of a method for operating a transmitter to at least partially compensate for I/Q impairments at a frequency f.

Fig. 14 illustrates one embodiment of a transmitter configured to at least partially compensate for I/Q impairments at a frequency f.

Fig. 15 illustrates a system stimulated by complex exponential tones appearing at the system output and complex exponential tones distorted, wherein the distortion is characterized by gain imbalance and phase skew.

Fig. 16 illustrates a system in which gain imbalance and phase skew are fully present on the Q channel.

Fig. 17 illustrates an embodiment of a system for performing impairment compensation at a single frequency.

Fig. 18 illustrates a 2x2 system model for performing I/Q impairment compensation.

Fig. 19 illustrates an embodiment in which the impairment model G precedes the compensation model H.

Fig. 20A and 20B illustrate an embodiment in which an impairment model G follows a compensation model H.

FIG. 21 illustrates one embodiment for compensating model H with respect to a pair of digital filters having frequency responses U (f) and V (f), respectively.

Fig. 22 illustrates a modified view of fig. 21, wherein U and V are represented by their even and odd parts.

Fig. 23 illustrates an equivalent representation of the system of fig. 22, in which the odd spectra B and D are replaced by corresponding even spectra followed by a Hilbert transform.

Fig. 24A and 24B illustrate the response of the system of fig. 23 to two corresponding inputs.

Fig. 25 gives equations derived from fig. 24A and 24B, respectively.

Fig. 26A and 26B illustrate a vector diagram (phasor diagram) corresponding to the equation of fig. 25.

FIG. 27 shows that specifying A, E a compensation spectrum based on information about I/Q impairments_BC and E_DIs described in the equation of (1).

FIG. 28 illustrates a 2x2 model H representing the I/Q impairments of the system.

FIG. 29 illustrates one embodiment of model H with respect to frequencies U and V.

Fig. 30 illustrates a modified view of fig. 29, in which U and V are represented by their even and odd parts.

Fig. 31 illustrates an equivalent representation of the system of fig. 30, in which the odd spectra B and D are replaced by corresponding even spectra, followed by a Hilbert transform.

Fig. 32A and 32B illustrate the response of the system of fig. 31 to two corresponding inputs.

Fig. 33 gives equations derived from fig. 32A and 32B, respectively.

Fig. 34A and 34B illustrate vector diagrams corresponding to the equations of fig. 33.

Fig. 35 shows a matrix equation derived from the vector diagrams of fig. 34A and 34B.

Fig. 36 gives a solution to the matrix equation of fig. 35.

Fig. 37 illustrates an embodiment of a system for measuring properties of a signal path between I/Q modulator 3710 and I/Q demodulator 3735.

Fig. 38 illustrates LO leakage vector a, intentionally injected DC vector B, and their sum C.

Fig. 39 illustrates response vectors a ', B ', and C ' corresponding to vectors A, B and C, respectively.

Fig. 40 illustrates one embodiment of a method for calculating DC mapping values for signal paths.

FIG. 41 illustrates a system having a frequency response H (f) that is provided with a gain imbalance g (f) and phase skew

Input signal s_input(f, t) stimulation and generation of a signal with gain imbalance g' (f) and phase skew

Is output signal s_output(f，t)。

Fig. 42 gives the equations derived from fig. 41.

FIG. 43 illustrates one embodiment of a method for transforming I/Q impairments through a linear system H (f).

FIG. 44 illustrates one embodiment of a method for determining I/Q impairments of a transmitter.

Fig. 45 illustrates one embodiment of a method for determining I/Q impairments of a transmitter using an intentionally shifted local oscillator.

FIG. 46 illustrates one embodiment of a method for determining I/Q impairments of a receiver.

FIG. 47 illustrates one embodiment of a method for estimating I/Q impairments associated with a complex signal.

Fig. 48 illustrates an embodiment of a system for measuring transmitter and/or receiver I/Q impairments, wherein the system includes a transmitter and receiver whose local oscillator frequency is intentionally shifted.

Fig. 49 illustrates the spectrum of a signal received by a receiver in response to a transmitter transmitting a tone at 31 MHz. The local oscillator frequency of the transmitter is 6MHz higher than the local oscillator frequency of the receiver. Thus, in the received spectrum, the tone appears at 37 MHz.

Fig. 50 illustrates the received spectrum after the I/Q impairments of the receiver are removed.

Fig. 51 illustrates the spectrum of fig. 50 after frequency shifting.

Fig. 52 illustrates a frequency shifted spectrum without first removing receiver impairments.

FIG. 53A illustrates a single point vector calibration correction 5310 followed by a two point vector destruction model 5320.

FIG. 53B shows a modified view of FIG. 53A, wherein the single point vector calibration correction is determined by constants α and β, and wherein the two point vector violation is determined by a constant A, E_BC and E_DAnd (4) determining.

Fig. 54 illustrates a vector diagram corresponding to the right-hand portion of fig. 53B (i.e., to the right of the dashed line).

Fig. 55A illustrates a receiver including a receiver filter 5525 and an I/Q demodulator 5530.

Fig. 55B illustrates a system including a transmitter and a receiver coupled together. The system may be used to determine I/Q impairments of a transmitter and/or receiver.

Fig. 55C illustrates the relative magnitudes of tones at frequency f and images at-f at three points along the path from the I/Q modulator of the transmitter to the I/Q demodulator of the receiver.

Fig. 56A illustrates the rate of convergence as a function of magnitude estimation error.

Fig. 56B illustrates the rate of convergence as a function of the rotation (phase) estimation error.

FIG. 57 illustrates the complex amplitude α for a tone and the complex amplitude α that has been passed through the gain imbalance g (f) and phase skew

and a notation of the complex amplitude β of the image carried by the distorted complex signal.

FIGS. 58A and 58B derive the gain imbalance g (f) and phase skew

Equations characterizing pitch and mirror.

FIG. 59 illustrates gain imbalance g (f) and phase skew in terms of distortion of a Q-channel signal ("Qactual") relative to an I-channel signal ("Iref")

Fig. 60 and 61 show magnitude spectra for in-phase and quadrature signal components (i.e., the "I reference" and "Q actual" signals for fig. 59).

Fig. 62 illustrates a LabVIEW graph routine for calculating local oscillator leakage, signal amplitude, gain imbalance, image rejection, and phase skew, according to one embodiment.

Fig. 63 illustrates LabVIEW graphics program (VI) that receives data computed by a programmable hardware element (e.g., the FPGA of the receiver) and computes LO leakage, amplitude gain imbalance, and phase skew from the data.

Fig. 64 and 65 show plots of the amplitude spectra of rectangular window functions with different acquisition lengths and with a common sampling rate of 120 MHz.

FIG. 66 illustrates a complex input signal having I/Q impairments g_in(ω) and

and the complex output signal has I/Q loss g_out(ω) and

the system model of (1).

FIG. 67 shows the input-dependent I/Q impairments g_in(omega) and

and output I/Q impairments g_out(omega) and

the equations of the frequency response functions U (ω) and V (ω) of fig. 66 are specified.

FIG. 68 illustrates one embodiment of a computer system 6800 that may be used to perform any of the method embodiments described herein.

While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof have been shown by way of example in the drawings and are herein described in detail. It should be understood, however, that the drawings and detailed description thereto are not intended to limit the invention to the particular form disclosed, but on the contrary, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the present invention as defined by the appended claims. It should be noted that the section headings in the following detailed description are for organizational purposes only and are not meant to be used to limit the claims.

Detailed Description

Term(s) for

The following is a glossary of terms used in this application.

Memory medium-any of various types of memory devices or storage devices. The term "memory medium" is intended to include: mounting media such as CD-ROM, floppy disk 105, or tape device; computer system memory or random access memory such as DRAM, DDR RAM, SRAM, EDO RAM, Rambus RAM, etc.; non-volatile memory, such as flash memory, magnetic media (e.g., hard drives), or optical storage; registers, or other similar types of memory elements, etc. The memory medium may include other types and combinations of memory. Further, the memory medium may be located in a first computer in which the program is executed, or may be located in a different second computer connected to the first computer via a network such as the internet. In the latter case, the second computer may provide the program instructions to be executed to the first computer. The term "memory medium" may include two or more memory media that may reside in different locations, such as different computers connected via a network.

Programmable hardware element-includes various hardware devices that include a plurality of programmable functional blocks connected via programmable interconnects. Examples include FPGAs (field programmable gate arrays), PLDs (programmable logic devices), FPOAs (field programmable object arrays), and CPLDs (complex PLDs). Programmable function blocks can vary from fine grained (combinational logic or look-up tables) to coarse grained (arithmetic logic units or processor cores). The programmable hardware elements may also be referred to as "reconfigurable logic".

Computer system-any of various types of computing or processing systems, including a personal computer system (PC), mainframe computer system, workstation, network appliance, internet appliance, Personal Digital Assistant (PDA), television system, grid computing system, or other device or combination of devices. In general, the term "computer system" may be broadly defined as any device (or combination of devices) having at least one processor that executes instructions from a memory medium.

Local Oscillator (LO) -a circuit configured to generate a periodic signal at a specified frequency and amplitude. The periodic signal may be purely sinusoidal and may be programmable in frequency and/or amplitude. The periodic signal may or may not be phase or frequency locked to another periodic signal.

Embodiments of the invention may be implemented in any of various forms. For example, in some embodiments, the invention may be implemented as a computer-implemented method, a computer-readable storage medium, or a computer system. In other embodiments, the invention may be implemented using one or more custom designed hardware devices, such as ASICs. In other embodiments, the invention may be implemented using one or more programmable hardware elements, such as FPGAs.

In some embodiments, a computer-readable memory medium may be configured such that it stores program instructions and/or data, wherein the program instructions, if executed by a computer system, cause the computer system to perform a method, e.g., any of the method embodiments described herein, or any combination of the method embodiments described herein, or any subset of any of the method embodiments described herein, or any combination of such subsets.

In some embodiments, a computer system may be configured to include a processor (or a set of processors) and a memory medium, where the memory medium stores program instructions, where the processor is configured to read and execute the program instructions from the memory medium, where the program instructions are executable to implement any of the various method embodiments described herein (or, any combination of the method embodiments described herein, or any subset of any of the method embodiments described herein, or any combination of such subsets). The computer system may be implemented in any of various forms. For example, the computer system may be a personal computer (in any of its various forms of implementation), a workstation, a computer on a card (computer on a card), a special-purpose computer in a box (application-specific computer in a box), a server computer, a client computer, a handheld device, a tablet computer, a wearable computer, and so forth.

In some embodiments, a group of computers distributed across a network may be configured to partition the work of performing a computational method (e.g., any of the method embodiments disclosed herein). In some embodiments, the first computer may be configured to receive an O-QPSK modulated signal and capture samples of the signal. The first computer may send the sample to the second computer over the network. The second computer may operate on the sample according to any of the method embodiments described herein, or any combination of the method embodiments described herein, or any subset of any of the method embodiments described herein, or any combination of such subsets.

FIG. 1A illustrates one possible application (among many possible applications) of the inventive concepts described herein. A mobile device 10 (e.g., a mobile telephone) communicates wirelessly with a radio transceiver station 15. The mobile device 10 may include digital pre-correction as described herein to improve the quality of the signal it transmits, i.e., to correct for so-called "I/Q impairments" in its transmission hardware (e.g., in its I/Q modulator). Similarly, radio transceiver station 15 may apply digital post-correction to signals it receives to correct I/Q impairments in its receive hardware (e.g., in its I/Q demodulator). Furthermore, the radio transceiver station and the mobile device may apply the same pre-calibration and post-calibration, i.e., for transmissions in opposite directions, interchangeably.

FIG. 1B illustrates another possible application of the inventive concepts described herein. The test transmitter 20 transmits a signal to the receiver under test 25. Test transmitter 20 may perform the digital pre-correction described herein to correct its own I/Q impairments and thus improve the quality of its transmission. For example, test transmitter 20 may implement a higher standard for image rejection due to the use of digital pre-correction. Thus, distortion (e.g., I/Q impairments) measured in the signal captured by the receiver may be attributed to imperfections of the receiver.

FIG. 1C illustrates yet another possible application of the inventive concepts described herein. The test receiver 35 receives the signal transmitted by the transmitter under test 30. The test receiver employs the digital post-correction described herein to correct its own I/Q impairments. Thus, the receiver can meet a higher criterion for image rejection than without post-correction. Thus, any distortion (e.g., I/Q impairments) measured in the signal captured by the receiver can be clearly directed to the imperfections of the transmitter.

Wideband correction method for receiver

In one set of embodiments, the method 100 for compensating for I/Q impairments of a receiver over a range of frequencies may involve the operations shown in fig. 2A.

At 110, a receiver may receive an analog input signal. The analog input signal may be received from a transmission medium. A transmission medium is a medium that allows the transmission of signal energy. For example, the transmission medium may be free space, the atmosphere, the earth or some part of the earth's surface, an electrical power cable, a fiber optic cable, a body of water such as the ocean.

At 115, the receiver may perform I/Q demodulation on the analog input signal to generate an analog in-phase (I) signal and an analog quadrature (Q) signal. The process of I/Q demodulation is well known in the communications arts. In general, I/Q demodulation involves mixing an analog input signal with a pair of quadrature carriers. For example, the mixing can be explained according to the following model:

I(t)＝y(t)cos(ωt)

Q(t)＝y(t)sin(ωt)

in some embodiments, the analog I signal and the analog Q signal may be interpreted as baseband signals, i.e., as components of a complex baseband signal. In other embodiments, the analog I signal and the analog Q signal may be interpreted as Intermediate Frequency (IF) signals.

At 120, the receiver may digitize the analog I signal and the analog Q signal to produce a digital I signal and a digital Q signal, respectively. (the term "digital signal" is intended to imply a sampled signal, not a two-state signal). Thus, the receiver may comprise a pair of analog-to-digital converters (ADCs).

At 125, a digital I signal and a digital Q signalThe signal may be filtered according to a 2x2 matrix of digital filters to produce a filtered digital I signal and a filtered digital Q signal. The filtering may involve applying a 2x2 matrix (h) of digital filters according to the following relationship_ij)：

I_F(n)＝h₁₁(n)*I(n)+h₁₂(n)*Q(n)

Q_F(n)＝h₂₁(n)*I(n)+h₂₂(n)*Q(n)

wherein the symbol "＊" represents convolution (note that, elsewhere in this patent disclosure, the symbol "＊" may refer to convolution or multiplication, depending on the particular situation, as a superscript, "＊" represents a complex conjugate.)

The 2x2 matrix of the digital filter may compensate (or at least partially compensate) for I/Q impairments of the receiver over a range of frequencies, such as a range of frequencies wide enough to cover the bandwidth of the transmitted communication signal or the instantaneous bandwidth of the receiver. (the process for measuring I/Q impairments is discussed in detail later in this patent disclosure.) in other words, the digital filter causes the input-output behavior of the receiver to more closely approximate an ideal receiver without I/Q impairments. In response to applying a pure sinusoidal tone at an arbitrary frequency ω as input, an ideal receiver will produce signals I (n) and Q (n) that are equal in amplitude and 90 degrees apart in phase, i.e., no gain imbalance and no phase skew.

The 2x2 matrix of the digital filter may have the following properties. The frequency response of at least one diagonal component of the 2x2 matrix may be calculated based on a measure of I/Q impairments as a function of frequency and a measure of I/Q impairments as a function of the negative of frequency. For example, if a gain imbalance function g (f) and a phase skew function are utilized

To characterize the I/Q impairments, where f covers the frequency range, then the component h₂₂(or component h)₁₁Or the component h₁₁And h₂₂Each of) may be based on functions g (f), g (-f),

And

to calculate.

Further, the frequency response of at least one off-diagonal component of the 2x2 matrix may be calculated based on a measure of I/Q impairment as a function of frequency and a measure of I/Q impairment as a function of the negative of frequency.

It is not intended to imply that the filtering of the digital I and Q signals is performed "according to a 2 × 2 matrix of digital filters": the receiver (or any device for implementing the filtering) must comprise a filtering circuit implementing a simple multiplication with zero (when the corresponding element of the 2 × 2 matrix is identical to zero), or an adder implementing a simple addition with zero (a trivisual addition by zero). By way of example, if h₁₂When the value is 0, then I_F(n) may be based on the simplified expression I using only one convolution circuit_F(n)＝h₁₁(n) I (n). Similarly, if one component of the 2x2 matrix is a unit pulse at time n-0, the receiver need not include a multiplier to perform a simple convolution (trivialconvolution). For example, if h₁₁(n) is 0, then I_F(n) may be based on expression I using only one convolution unit and one adder_F(n)＝I(n)+h₁₂(n) Q (n) is simply calculated. Thus, a "2 x2 matrix according to digital filter" filtering does not necessarily require a full 2x2 array of convolution circuits in all cases.

In some embodiments, the filtered digital I signal and the filtered digital Q signal can be used to recover a stream of information bits. The receiver (or another processing agent such as a host computer) may recover the information bit stream by performing symbol demodulation on the filtered digital I signal and the filtered digital Q signal. In symbol demodulation, the vector signal (I)_F(n)，Q_F(n)) may be decimated to determine a sequence of complex symbols, and each complex symbol may be mapped to the closest constellation point in a given constellation (constellation) (a set of points in the complex plane). Result generationDetermines the stream of information bits.

In some embodiments, the receiver includes a digitizer, wherein the digitizer performs the digitizing and filtering acts described above. The term "digitizer" is intended to imply an instrument that is calibrated to a known standard. For example, the relationship between the analog input and the digital output is calibrated to a known standard for both the I and Q channels.

In some embodiments, the receiver is a test instrument such as a Vector Signal Analyzer (VSA). (the term "vector signal" is synonymous with complex signal or I/Q signal). The test instrument may receive an analog input signal from a transmitter (e.g., a transmitter under test). The analog input signal is received in response to the act of the transmitter transmitting a transmission signal onto the transmission medium. The test instrument may be configured to compensate its own I/Q impairments, but not the I/Q impairments of the transmitter. In the case of testing and measurement, it is important to be able to accurately measure and report the impairments of the device under test rather than compensate for the impairments of the device. Thus, for a test instrument, it is preferred that the measurement of the I/Q impairments of the receiver (on which the impairments compensation of the receiver is based) does not include the I/Q impairments of the transmitter. This patent disclosure describes a method for testing receiver impairments only.

Test instruments are generally used to perform testing of a Device Under Test (DUT) or a System Under Test (SUT). The test instrument generally includes one or more inputs and outputs for connecting to the SUT. The inputs and outputs may be analog, digital, radio frequency, etc., for example, at various voltage levels and frequencies. The test instruments are generally capable of performing one or more tests or features. For example, the test instrument may be configured to capture and analyze waveforms, calculate measured power, generate tones at programmed frequencies, and so forth. The test instrument is also typically calibrated to achieve a specified level of accuracy with respect to its I/O. Finally, the test instrument typically includes a user interface to specify how the test instrument should function.

In other cases, it may be desirable for the receiver to compensate for the transmitter impairments and its own impairments. Thus, a 2x2 matrix for the digital filter may be calculated based on a measure of the I/Q impairments of the transmitter and receiver combination. The same principle with respect to calculating the frequency response based on the impairment as a function of f and the impairment as a function of-f is also applicable here.

In some embodiments, the filtering operation 125 may be performed on programmable hardware elements, such as an FPGA, or in dedicated digital circuitry, such as an Application Specific Integrated Circuit (ASIC). The same sampling clock that drives the ADC conversion may be provided to programmable hardware elements or dedicated digital circuitry.

In some embodiments, the filtering operation 125 may be performed by a processor in response to execution of program instructions. The processor may be incorporated as part of the receiver or as part of another system such as a host computer or controller board.

As described above, at least one diagonal component of the 2x2 matrix is calculated based on a measure of I/Q impairments as a function of f and a measure of I/Q impairments as a function of-f. In some embodiments, "at least one diagonal" should be interpreted as "exactly one diagonal" and the other diagonal component of the 2x2 matrix is a discrete time unit pulse function (e.g., taking a value of one at time zero and zero elsewhere).

As described above, at least one off-diagonal component of the 2x2 matrix is calculated based on a measure of I/Q impairment as a function of f and a measure of I/Q impairment as a function of-f. In some embodiments, "at least one off-diagonal" should be interpreted as "exactly one off-diagonal" and the other off-diagonal component of the 2x2 matrix is a zero function.

Constraint between receiver impairments at frequency f and frequency-f

In some embodiments, it may be assumed that the I/Q impairments of the receiver at positive frequencies and the I/Q impairments of the receiver at negative frequencies are functionally related. In one such embodiment, the computation of the 2x2 matrix of the digital filter may be simplified as follows. The frequency response of a diagonal component of the 2x2 matrix at any frequency f in the frequency range may be based solely on a measure of the I/Q impairments at frequency f (or alternatively, solely onBased on a measurement of I/Q impairments at frequency-f). For example, if the I/Q impairments are defined by the gain imbalance function g (f) and the phase skew function

Characterizing, then the component h₂₂Frequency response H of₂₂(f) May be based on the sum of measurements of g (f) only

Wherein f comprises the frequency at which the measurement was obtained. Furthermore, the frequency response of one off-diagonal component of the 2x2 matrix at frequency f may be calculated based only on the measurement of the I/Q impairments at frequency f (or alternatively, based only on the measurement of the I/Q impairments at frequency-f).

In some embodiments, the I/Q impairments at frequency f and the I/Q impairments at frequency-f are constrained such that the I/Q impairments at f are determined by the I/Q impairments at-f, or such that the I/Q impairments at frequency-f are determined by the I/Q impairments at f. For example, the gain imbalance at frequency f and the gain imbalance at frequency-f may be constrained to be equal, and the phase skew at frequency f and the phase skew at frequency-f may be constrained to be equal (or negative of each other).

In some embodiments, the gain imbalance is assumed to be even and the phase skew is assumed to be odd. In these embodiments, the two off-diagonal components of the 2x2 matrix may be set to zero; one diagonal component may correspond to a pure pass filter (i.e., unity frequency response); and the frequency response of the other diagonal component at any frequency f may be calculated based solely on the measurement of the I/Q impairments at frequency f (or alternatively, solely on the measurement of the I/Q impairments at frequency-f).

In some embodiments, both diagonal components of the 2x2 matrix may correspond to pure pass filters; one off-diagonal component may be set to zero; and the frequency response of the other non-diagonal component at any frequency f may be calculated based solely on the measurement of the I/Q impairments at frequency f (or alternatively, based solely on the measurement of the I/Q impairments at frequency-f).

Receiver configured for wideband correction

In one set of embodiments, the receiver 200 may be configured as shown in FIG. 2B. (the receiver 200 may include any subset of the features described above in connection with the method 100). Receiver 200 may include an I/Q demodulator 210, a digitizing unit 215, and a digital circuit 220.

I/Q demodulator 210 may be configured to receive an analog input signal y (t) and perform I/Q demodulation on the analog input signal to generate an analog in-phase (I) signal and an analog quadrature (Q) signal, denoted as I (t) and Q (t). The I/Q demodulator may receive a pair of quadrature carriers from a local oscillator circuit.

The digitizing unit 215 may be configured to digitize the analog I signal and the analog Q signal to produce digital I and Q signals, denoted as I (n) and Q (n), respectively. The digitizing unit 215 may receive the converted clock from the clock generation circuit. The digitizing unit includes an I-channel ADC and a Q-channel ADC, each driven by the same conversion clock.

The digital circuit 220 may be configured to filter the digital I signal and the digital Q signal (as described above) according to a 2x2 matrix of digital filters to produce filtered digital I signals and filtered digital Q signals. The 2x2 matrix of the digital filter may be configured to compensate (or at least partially compensate) for I/Q impairments of the receiver over a range of frequencies. When programmed with the 2x2 matrix of digital filters, the digital circuit causes the receiver 200 to behave more like a mathematically ideal receiver, i.e., a receiver with an ideal I/Q demodulator and an ideal digitizing unit.

In some embodiments, digital circuit 220 is implemented by (or as part of) a programmable hardware element or special-purpose digital circuitry such as an ASIC.

In some embodiments, digital circuitry 220 is (or includes or is implemented by) a processor configured to execute program instructions. In one embodiment, the processor is part of a computer system, such as a host computer, or a controller board.

In some embodiments, receiver 200 may include means for recovering an information bit stream by performing symbol demodulation on the filtered digital I signal and the filtered digital Q signal. The recovery means may comprise any one or more of: a processor executing on the receiver, a processor executing on a host computer, a processor executing on a controller board (e.g., a controller board mounted on an instrumentation chassis (instrumentation chassis) along with the receiver), a programmable hardware element, an ASIC.

In some embodiments, the receiver 200 is (or includes) a test instrument. See the discussion above of the concept of the test instrument.

Method for configuring a receiver to perform impairment correction

In one set of embodiments, the method 300 for configuring a receiver may involve the operations shown in fig. 3. The method 300 may be used to configure a receiver to at least partially compensate for I/Q impairments of the receiver. The method 300 may be implemented by a computer system in response to execution of program instructions. (the method 300 may include any subset of the features described above).

At 310, the computer system may receive a measurement of the I/Q impairments of the receiver over a frequency band. (by "over a frequency band" is meant a measurement that measures a plurality of different frequencies included within the frequency band, e.g., the different frequencies cover the frequency band uniformly or non-uniformly). The receiver may include an I/Q demodulator, a pair of analog-to-digital converters (ADCs), and digital circuitry, e.g., as described above. The I/Q demodulator may be configured to generate an analog I signal and an analog Q signal from an analog input signal. The ADC may be configured to sample the analog I signal and the analog Q signal to obtain a digital I signal and a digital Q signal, respectively. The digital circuit may be configured to filter the digital I signal and the digital Q signal to obtain a filtered digital I signal and a filtered digital Q signal. (see discussion of various ways to implement digital circuitry above).

At 315, the computer system may calculate a 2x2 matrix of digital filters based on the measurements. A 2x2 matrix of digital filters may be calculated to achieve at least partial compensation of the I/Q impairments of the receiver over that band. The frequency response of at least one diagonal component of the 2x2 matrix may be calculated based on the measurement as a function of frequency and the measurement as a function of the negative of frequency. Further, the frequency response of at least one off-diagonal component of the 2x2 matrix may be calculated based on the measurement as a function of frequency and the measurement as a function of the negative of frequency.

At 320, the computer system may program the digital circuit to implement a 2x2 matrix of digital filters, wherein when so programmed, the digital circuit is configured to at least partially compensate for the I/Q impairments of the receiver over the frequency band. The act of programming the digital circuit involves transferring a 2x2 matrix of digital filters (or parameters that specify those filters) to the digital circuit or to a memory used by the digital circuit.

Wideband correction method for transmitter

In one set of embodiments, the method 400 for compensating for I/Q impairments of a transmitter may involve the operations shown in fig. 4.

At 410, a digital in-phase (I) signal and a digital quadrature (Q) signal may be received. The digital I signal and the digital Q signal may be interpreted as components of a complex-valued signal I (n) + jQ (n). For example, the digital I signal and the digital Q signal may carry one or more information bit streams as a result of symbol modulation according to a given constellation. In some embodiments, the digital I signal and the digital Q signal may be interpreted as components of a complex baseband signal or an Intermediate Frequency (IF) signal.

At 415, the digital I signal and the digital Q signal may be filtered according to a 2x2 matrix of digital filters to produce filtered digital I signals and filtered digital Q signals. (the filtering operation may be performed by the transmitter or some other agent). The filtering operation may involve applying a 2x2 matrix (h) of digital filters according to the following relationship_ij)：

I_F(n)＝h₁₁(n)*I(n)+h₁₂(n)*Q(n)，

Q_F(n)＝h₂₁(n)*I(n)+h₂₂(n)*Q(n).

The 2x2 matrix of digital filters may pre-compensate (or, at least partially pre-compensate) for I/Q impairments of the transmitter over a frequency range (e.g., over a frequency range wide enough to cover the bandwidth of the communication signal to be transmitted).

The 2x2 matrix of the digital filter may have the following properties. The frequency response of at least one diagonal component of the 2x2 matrix may be calculated based on a measure of I/Q impairments as a function of frequency and a measure of I/Q impairments as a function of the negative of frequency. For example, if the I/Q impairments are defined by the gain imbalance function g (f) and the phase skew function

Wherein f covers the frequency range, then the digital filter h₂₂(or a digital filter h₁₁Or a digital filter h₁₁And h₂₂Each of) may be based on g (f), g (-f),

And

to calculate.

In the description of the receiver 100 we carefully define (qualify) "filtering according to the 2x2 matrix" of digital filters. Those same definitions apply here for transmitter compensation.

At 420, the transmitter may convert the filtered digital I signal and the filtered digital Q signal to analog form to obtain an analog I signal and an analog Q signal, respectively.

At 425, the transmitter may perform I/Q modulation on the analog I signal and the analog Q signal to produce a modulated analog signal. The modulated analog signal may be transmitted over a transmission medium, such as the transmission medium described above. The receiver may receive the modulated analog signal, possibly in the form of noise disturbances and channel distortions.

In the above, we describe the 2 × 2 matrix of the digital filter as the I/Q impairments of the "precompensated" transmitter. This is because the I/Q impairments occur after the application of the digital filter, especially in the I/Q modulation phase. Thus, a 2x2 matrix may be interpreted as applying an inverse distortion that, together with the following distortions, will give an approximation to the overall identity map.

In some embodiments, the filtering operation 415 may be performed in a Programmable Hardware Element (PHE), such as an FPGA, or in dedicated digital circuitry, such as an Application Specific Integrated Circuit (ASIC).

In some embodiments, filtering operation 415 may be performed by a processor (e.g., a processor of a host computer system or instrument controller board) in response to execution of program instructions.

In some embodiments, the transmitter is a test instrument (e.g., an arbitrary waveform generator or a vector signal generator). The test instrument may send the modulated analog signal to a receiver (e.g., a receiver under test). In the case of testing and measurement, it is important that the test instrument correct for its own impairments but not for the receiver impairments. Thus, in this case, the above-mentioned measurement of the I/Q impairments of the transmitter (on which the pre-compensation of the transmitter is based) preferably does not comprise the I/Q impairments of the receiver. This patent disclosure describes a method for measuring only the transmitter impairments (clearly separated from the receiver impairments).

In some cases, it may be desirable for the transmitter to correct for impairments of the receiver and its own impairments. Thus, a 2x2 matrix for the digital filter may be calculated based on a measure of the I/Q impairments of the transmitter and receiver combination. The same principle with respect to calculating the frequency response based on impairments as a function of f and impairments as a function of-f is also applicable here.

Constraint between transmitter impairments at frequency f and frequency-f

In some embodiments, it may be assumed that the I/Q impairments of the transmitter at positive frequencies and the I/Q impairments of the transmitter at negative frequencies areThe functions are related. In one such embodiment, the computation of the 2x2 matrix of the digital filter may be simplified as follows. The frequency response of at least one diagonal component of the 2x2 matrix at any frequency f within the frequency range may be calculated based solely on the measurement of the I/Q impairments at frequency f (or alternatively, solely on the measurement of the I/Q impairments at frequency-f). For example, if the I/Q impairments are defined by the gain imbalance function g (f) and the phase skew function

Characterizing, then the component h₂₂Frequency response value H of₂₂(f) May be based on the sum of measurements of g (f) only

Wherein f comprises the frequency at which the measurement has been obtained. Furthermore, the frequency response of at least one off-diagonal component of the 2x2 matrix at frequency f may be calculated based solely on the measurement of the I/Q impairments at frequency f (or alternatively, solely on the measurement of the I/Q impairments at frequency-f).

In some embodiments, the I/Q impairments at frequency f and the I/Q impairments at frequency-f are constrained such that the I/Q impairments at f are determined by the I/Q impairments at-f, or such that the I/Q impairments at frequency-f are determined by the I/Q impairments at f. For example, the gain imbalance at frequency f and the gain imbalance at frequency-f may be constrained to be equal, and the phase skew at frequency f and the phase skew at frequency-f may be constrained to be equal (or alternatively, negative numbers of each other).

In some embodiments, the gain imbalance is assumed to be even and the phase skew is assumed to be odd. Thus, the two off-diagonal components of the 2x2 matrix may be set to zero; one diagonal component may correspond to a pure pass filter (i.e., unity frequency response); and the frequency response of the other diagonal component at any frequency f may be calculated based solely on the measurement of the I/Q impairments at frequency f (or alternatively, solely on the measurement of the I/Q impairments at frequency-f).

Transmitter configured for wideband correction

In one set of embodiments, the transmitter 500 may be configured as shown in FIG. 5. (the transmitter 500 may incorporate any subset of the features described above in connection with the method 400). Transmitter 500 may include digital circuitry 510, a digital-to-analog converter (DAC) unit 515, and an I/Q modulator 520.

Digital circuit 510 may be configured to receive a digital in-phase (I) signal and a digital quadrature (Q) signal and filter the digital I signal and the digital Q signal using a 2x2 matrix of digital filters to produce a filtered digital I signal and a filtered digital Q signal. (filtering can be performed as described in various different ways above). The digital I signal and the digital Q signal may carry one or more information bit streams.

A 2x2 matrix of digital filters may be calculated to pre-compensate (or at least partially pre-compensate) for I/Q impairments of the transmitter over a range of frequencies. The frequency response of at least one diagonal component of the 2x2 matrix may be calculated based on a measure of I/Q impairments as a function of frequency and a measure of I/Q impairments as a function of the negative of frequency. Further, the frequency response of at least one off-diagonal component of the 2x2 matrix may be calculated based on a measure of I/Q impairment as a function of frequency and a measure of I/Q impairment as a function of the negative of frequency.

The digital circuit 510 is said to "pre-compensate" for the I/Q impairments of the transmitter because the I/Q impairments occur in the transmitter stage after the digital circuit, particularly in the I/Q modulator 520. Thus, the digital circuit introduces predistortion (by applying a 2x2 matrix of digital filters) to the complex signal I (n) + jQ (n) so that the net effect of the predistortion followed by subsequent impairments will approximate an ideal transmitter without I/Q impairments. In other words, the digital circuit applies an inverse distortion that, in combination with the subject distortion, approximates an identity map (i.e., a frequency response function that is identical to a unity function).

DAC cell 515 may be configured to convert the filtered I and Q signals to analog form to obtain corresponding analog I and Q signals. DAC cell 515 may receive the conversion clock from the clock generation cell. Digital circuit 510 may receive the same conversion clock so that it generates complex samples (I (t), Q (t)) at the same rate that the DAC unit converts the samples to analog form (I (t), Q (t))_F(n)，Q_F(n))。

I/Q modulator 520 may be configured to perform I/Q modulation on the analog I signal and the analog Q signal to produce a modulated analog signal. The modulated analog signal may be transmitted over a transmission medium to a receiver. The concept of I/Q modulation is well known in the field of communications. For example, the I/Q modulation can be modeled by the following expression:

x(t)＝I(t)cos(ωt)-Q(t)sin(ωt)

＝Re{(I(t)+jQ(t))exp(jωt)}，

where ω is the carrier frequency.

In some embodiments, digital circuit 510 is implemented by (or as part of) a programmable hardware element or dedicated digital circuitry such as an ASIC.

In some embodiments, digital circuitry 510 is (or includes or is implemented by) a processor configured to execute program instructions. In one embodiment, the processor is part of a computer system, such as a host computer system, or a controller board.

In some embodiments, the transmitter 500 may be a test instrument. See the discussion above of the test instrument in the context of method 400.

Method for configuring a transmitter for impairment correction

In one set of embodiments, the method 600 for configuring a transmitter may involve the operations shown in FIG. 6. The method 600 may be used to configure a transmitter to at least partially compensate for I/Q impairments of (or introduced by) the transmitter. The method 600 may be performed by a computer system in response to execution of program instructions.

At 610, the computer system may receive a measurement of the I/Q impairments of the transmitter over a range of frequencies. ("within a frequency range" implies that measurements of I/Q impairments are obtained at a plurality of frequencies within the frequency range (e.g., frequencies that uniformly or non-uniformly cover the frequency range)). The transmitter may include digital circuitry, a pair of digital-to-analog converters (DACs), and an I/Q modulator. The digital circuit may be configured to filter the digital I signal and the digital Q signal to obtain a filtered digital I signal and a filtered digital Q signal, respectively. The pair of DACs may be configured to convert the filtered digital I signal and the filtered digital Q signal to analog form to obtain an analog I signal and an analog Q signal, respectively. The I/Q modulator may be configured to modulate the carrier signal with the analog I signal and the analog Q signal to obtain a modulated carrier signal. The modulated bearer signal may be transmitted to a receiver over a transmission channel.

At 615, the computer system may calculate a 2x2 matrix of digital filters based on the measurements. A 2x2 matrix of digital filters may be calculated to achieve pre-compensation (or, at least partial pre-compensation) of the I/Q impairments of the receiver over the frequency range. The frequency response of at least one diagonal component of the 2x2 matrix may be calculated based on the measurement as a function of frequency and the measurement as a function of the negative of frequency. Further, the frequency response of at least one off-diagonal component of the 2x2 matrix may be calculated based on the measurement as a function of frequency and the measurement as a function of the negative of frequency.

At 620, the computer system may program the digital circuit to implement a 2x2 matrix of digital filters, wherein when so programmed, the digital circuit is configured to at least partially pre-compensate for I/Q impairments in the frequency range. The act of programming the digital circuit involves transferring the digital filter (or parameters specifying the filter) to the digital circuit or to a parameter memory used by the digital circuit.

In various embodiments, the digital circuits may be programmable hardware elements, Application Specific Integrated Circuits (ASICs), processors executing under the control of program instructions, or any combinations thereof.

Derivation of digital filters for wideband impairment compensation

As described above, a 2x2 matrix of digital filters can be used to compensate for I/Q impairments at the receiver or transmitter. (in practice, both the transmitter and receiver may employ matrix compensation, each with its own 2x2 compensation matrix. This section will derive the frequency response for the digital filter in the special case where the 2x2 matrix has the special form shown in fig. 7.

Due to gain imbalance g and phase skew

Is a correlation measure, we are free to model the gain imbalance and phase skew as distortion due to one channel (I or Q) only, while the other channel is ideal. Fig. 7 represents an option to model both gain imbalance and phase skew as due to distortion on the Q channel only. The opposite option is illustrated in fig. 8. (thus, the frequency response H₁₁And H₁₂For effecting compensation, and H ₂₂1 and H₂₁0). It is also possible to model the gain imbalance as due to amplitude distortion on one channel only and the phase skew as due to phase distortion on the opposite channel only. As yet another alternative, gain imbalance and/or phase skew may be modeled as a partial distortion due to both channels, e.g., as suggested by fig. 9. Thus, digital compensation can utilize all four frequency responses H₁₁、 H₁₂、H₂₁And H₂₂To be executed. After understanding the following derivation based on fig. 7, those skilled in the art will find it simple to apply the same mathematical principles to all other cases.

Fig. 7 may be interpreted as a filtering operation performed by the digital circuit 220 of the receiver or a filtering operation performed by the digital circuit 510 of the transmitter. Thus, the following derivation applies to both the compensation matrix of the transmitter and the compensation matrix of the receiver.

Although the compensation is applied digitally, for simplicity, the following derivation will be expressed with respect to successive times t. To achieve compensation, we look for the frequency responses U (ω) and V (ω) such that impairments g (ω) and V (ω) are available for all frequencies ω within a frequency band (e.g., a frequency band symmetric about zero) or at least at

At the selected frequency of the measurement, the distorted signal

Is converted into a corrected signal cos (ω t) + jsin (ω t). g (ω) is the gain imbalance corresponding to frequency ω, and

is the phase skew corresponding to frequency omega. Thus, we obtain the equation:

where "＊" denotes convolution, where U (t) and V (t) are impulse responses corresponding to frequency responses U (ω) and V (ω), respectively.

By making a substitution

cos(θ)＝(1/2){exp(jθ)+exp(-jθ)}

sin(θ)＝(-j/2){exp(jθ)-exp(-jθ)}，

We obtain the equation

Due to the linear independence of exp (j ω t) and exp (-j ω t), we obtain the following two equations:

since equation (b) holds for all ω, we can replace ω with- ω, thus obtaining the following equation (b').

Equations (a) and (b') specify the unknown vector [ U (ω), V (ω)]^TThe solution of the matrix equation in (1) is given by:

it was observed that both U (ω) and V (ω) depend on g (ω), g (- ω), respectively,

And

this property of the frequency response (of the digital filter) being dependent on impairment information at ω and- ω is generally more applicable than with the special matrix form of fig. 7. In fact, it applies to any form of compensation matrix. It is also observed that U and V are conjugate symmetric with respect to frequency: u (-omega) U (omega)^*and V(-ω)＝V(ω)^*As would be expected for a filter whose impulse response is purely real.

To simplify the process of designing digital filters (impulse responses) corresponding to the frequency responses U (ω) and V (ω), it may be useful to represent those frequency responses in terms of their even and odd parts:

U(ω)＝A(ω)+B(ω)

A(ω)＝(1/2){U(ω)+U(-ω)}

B(ω)＝(1/2){U(ω)-U(-ω)}

V(ω)＝C(ω)+D(ω)

C(ω)＝(1/2){V(ω)+V(-ω)}

D(ω)＝(1/2){V(ω)-V(-ω)}.

in the time domain, the corresponding representation is:

u(t)＝a(t)+b(t)

a(t)＝(1/2){u(t)+u(-t)}

b(t)＝(1/2){u(t)-u(-t)}

v(t)＝c(t)+d(t)

c(t)＝(1/2){v(t)+v(-t)}

d(t)＝(1/2){v(t)-v(-t)}，

where u, a, b, v, c, and D are impulse responses corresponding to frequency responses U, A, B, V, C and D, respectively.

Using the above derived expressions for U (ω) and V (ω), followed by:

the above expression can be used to base measured or estimated impairment functions g and

the frequency responses U and V are calculated. These expressions apply equally to post-compensation at the receiver or pre-compensation at the transmitter. In other words, for pre-correcting the I/Q impairments g (f) and

are the same as those used to post-compensate those same I/Q impairments.

The calculated frequency responses U and V may be used to determine the corresponding impulse responses U (n) and V (n) using any of a variety of known filter design algorithms.

Considerations regarding filters having an odd frequency response

Given a filter with an odd frequency response B (ω), the basic fact is represented by E_BFunction E given by (ω) ═ jB (ω) sgn (ω)_B(ω) is even and has the following properties:

b(t)*x(t)＝HT(e_B(t)*x(t))，

where HT is the Hilbert transform operator, where B (t) is the impulse response corresponding to B (ω), and x (t) is an arbitrary input function where sgn (ω) is 1 when ω is greater than zero and-1 when ω is less than zero.

If we apply this fact to the odd functions B (ω) and D (ω) from the discussion above, we will get the corresponding even functions:

with respect to even numbers g (ω) and odd numbers

Attention to the particular situation of

In many cases, the gain imbalance function may be modeled as an even number and the phase skew function may be modeled as an odd number, i.e., g (ω) g (- ω) and

under these constraints, U (ω) is 0 and V (ω) is a complex number.

With respect to even numbers g (ω) and even numbers

Attention to the particular situation of

The expressions derived above for U (ω) and V (ω) are typically complex values. However, when the gain imbalance and phase skew functions are even numbers, i.e., g (ω) is g (- ω) and

u (ω) and V (ω) become real values:

constant matrix for post-correction receiver impairments at a single frequency

In one set of embodiments, a method 1000 for operating a receiver (or operating a system including a receiver) may involve the operations shown in fig. 10.

At 1010, a receiver may receive an analog input signal. The analog input signal may be received from a transmission medium, for example, as described above.

At 1015, the receiver may perform I/Q demodulation on the analog input signal to generate an analog in-phase (I) signal and an analog quadrature (Q) signal, e.g., as described above.

At 1020, the receiver may digitize the analog I signal and the analog Q signal to produce a digital I signal and a digital Q signal, respectively.

At 1025, the receiver may get (c) from the constant 2x2 matrix c ═ c_ij) The digital I signal and the digital Q signal are transformed to produce a resultant digital I signal and a resultant digital Q signal. The transformation may be performed by applying the following matrix multiplication:

wherein I_R(n) and Q_R(n) represent the resulting digital I signal and the resulting digital Q signal, respectively. The 2x2 matrix c may be configured to post-compensate (or, at least partially post-compensate) the measured I/Q impairments of the receiver at a particular frequency f.

The matrix c may have the following properties. Diagonal element c₁₁And c₂₂At least one of which may be calculated based on the measured I/Q impairments of the receiver at frequency f. For example, coefficient c₂₂Can be used as the measured value g (f) and/or the measured value

Is calculated as a function of, where g is a gain imbalance function, and

is a phase skew function. Similarly, the off-diagonal element c₁₂And c₂₁At least one of which may be calculated based on the measured I/Q impairments of the receiver at frequency f. For example, coefficient c₂₁Can be used as the measured value g (f) and/or the measured value

Is calculated as a function of (c). In some embodiments, each of these four matrix elements is calculated similarly (i.e., based on the impairments measured at f).

For one possible embodiment of the matrix c, see the section "perform conventional impairment compensation at a single frequency".

Let c_ij(f) Representation for determining the coefficient c from the I/Q impairment at frequency f_ijIs used for the functional expression of (1). Due to functional expression c_ij(f) Regarding the continuity of the frequency f, the matrix c (f) is therefore a good approximation to the matrix c (f + Δ f), provided Δ f is sufficiently small. Thus, when the receiver performs transform operation 1025 using matrix c (f), the receiver will achieve at least partial compensation around the frequencies around f. The quality of the compensation will generally degrade as the absolute value of Δ f increases.

In some embodiments, the analog input signal is a pure sinusoidal tone, e.g., a tone at frequency fTuned or at frequency f + f_LOTone of where f_LOIs the frequency of the local oscillator of the receiver. In other embodiments, the analog input signal is a communication signal carrying a stream of binary information.

In some embodiments, matrix c has the additional property that one diagonal element is one. In some embodiments, matrix c has the additional property that one off-diagonal element is zero. In some embodiments, the matrix c has one of the following special forms:

as described above, the transform operation 1025 is performed "according to a 2x2 matrix". That defined phrase does not imply that the receiver is required to include a multiplier (or adder) that implements a simple multiplication with one (or a simple addition with zero). For example, in the first special form given above, the resulting digital I signal is equal to the digital I signal: i is_R(n) is I (n). This requires no computation at all. The I (n) input can simply be passed to I_R(n) outputting.

In one set of embodiments, receiver 1100 may be configured as shown in FIG. 11. (receiver 1100 may incorporate any subset of the features described above in connection with method 1000). Receiver 1100 may include I/Q demodulator 1110, digitizing unit 1115, and digital circuitry 1120.

I/Q demodulator 1110 may be configured to receive an analog input signal and perform I/Q demodulation on the analog input signal to generate an analog in-phase (I) signal and an analog quadrature (Q) signal. The analog input signal may be received from a transmission medium, as described above.

The digitization unit 1115 may be configured to digitize the analog I signal and the analog Q signal to generate a digital I signal and a digital Q signal, respectively.

Digital circuit 1120 may be configured to matrix convert the digital I signal and the digital Q signal according to a constant of 2x2 to produce a resulting digital I signal and a resulting digital Q signal. The 2x2 matrix may be configured to at least partially compensate for the I/Q impairments of the receiver at a particular frequency f. The first constant corresponding to the first diagonal element of the 2x2 matrix may be calculated based on the measured I/Q impairments of the receiver at frequency f. Furthermore, a second constant corresponding to the first off-diagonal element of the 2x2 matrix may be calculated based on the measured I/Q impairments of the receiver at frequency f. In some embodiments, each of these four constants is calculated similarly (i.e., based on the measured impairment at f).

In one set of embodiments, the method 1200 for configuring a receiver may involve the operations shown in fig. 12. The method 1200 may be used to configure a receiver to at least partially compensate for the I/Q impairments of the receiver at a given frequency f. The method 1200 may be implemented by a computer system in response to execution of program instructions. (the method 1200 may include any subset of the features described above in connection with fig. 10 and 11).

At 1210, the computer system may receive a measured I/Q impairment for the receiver at frequency f. The receiver may include an I/Q demodulator, an analog-to-digital conversion (ADC) unit, and digital circuitry, e.g., as described above in connection with fig. 10 and 11. The I/Q demodulator may be configured to generate an analog I signal and an analog Q signal from an analog input signal. The ADC unit may be configured to sample the analog I signal and the analog Q signal to obtain a digital I signal and a digital Q signal, respectively. The digital circuit may be configured to transform the digital I signal and the digital Q signal to obtain a resulting digital I signal and a resulting digital Q signal. (see discussion of various ways to implement digital circuitry above).

At 1215, the computer system may calculate a 2x2 matrix of constants based on the I/Q impairments measured at frequency f. The 2x2 matrix may be calculated to achieve at least partial compensation for the I/Q impairments measured at frequency f. At least one diagonal component of the 2x2 matrix may be calculated based on the I/Q impairments measured at frequency f. Further, at least one off-diagonal component of the 2x2 matrix may be calculated based on the I/Q impairments measured at frequency f.

At 1220, the computer system may program the digital circuit to implement a constant 2x2 matrix, wherein when so programmed, the digital circuit is configured to at least partially compensate for the I/Q impairments measured at the frequency f. The act of programming the digital circuit involves transferring the 2x2 matrix (or information specifying the matrix) to the digital circuit or to a memory used by the digital circuit.

True matrix pre-correction at a single frequency

In one set of embodiments, the method 1300 for compensating for I/Q impairments of a transmitter at a particular frequency f may involve the operations shown in fig. 13.

At 1310, a digital in-phase (I) signal and a digital quadrature (Q) signal may be received (e.g., as described in various forms above). In some embodiments, the digital I signal and the digital Q signal together may represent a complex exponential tone at a frequency f. In other embodiments, the digital I signal and the digital Q signal may carry respective streams of binary information. The digital I signal and the digital Q signal may be components of a complex baseband signal or a complex intermediate frequency signal.

At 1315, the digital I signal and the digital Q signal may be based on a 2x2 matrix c ═ of constants (c_ij) To produce a resulting digital I signal and a resulting digital Q signal. (the transformation may be performed by the sender or some other agent). The transformation can be described by the following matrix multiplication:

wherein I_R(n) and Q_R(n) represent the resulting digital I signal and the resulting digital Q signal, respectively. The 2x2 matrix may be configured to pre-compensate (or, at least partially pre-compensate) for the I/Q impairments of the transmitter at frequency f. See the discussion above regarding the nature of "pre-compensation". In short, the application of the transformation introduces an inverse distortion which, in combination with the distortion of the following transmitter stage, makes the input-output behavior of the transmitter look more ideal. It should be noted that the above discussion of the meaning of "transforming according to a 2x2 matrix" is hereThe method is also applicable.

The 2x2 matrix c may have the following properties. Diagonal element c₁₁And c₂₂May be calculated based on a measurement of I/Q impairments at frequency f and a measurement of I/Q impairments at frequency-f. For example, diagonal element c₂₂May be based on g (f), g (-f),

And

is calculated, where g is a gain imbalance function, and

is a phase skew function. For example, diagonal element c₂₂May be based on g (f), g (-f),

And

is calculated, where g is a gain imbalance function, and

is a phase skew function. In addition, the off-diagonal element c₁₂And c₂₁May be calculated based on the measurement at frequency f and the measurement at frequency-f. In some embodiments, each of these four coefficients may be calculated based on a measurement at frequency f and a measurement at frequency-f. For one possible embodiment of the matrix c, see the "calculate true single point vector alignment constant" part.

The measured impairments may be impairments measured at the corrupted output (i.e., the I/Q modulator) and, if measurable at the input, may be different from the impairments. Alternatively, the method may include transforming output impairments at + f and-f to input impairments at only + f, howeverThe matrix constants are then calculated from the simplified formula using the input impairments at only + f. The transformation may be derived as follows. First, a specific expression for U (f) and V (f) is derived based on the output impairments at + f and-f using equations (7.9) and (7.10), where g is_in(f) ＝g_in(-f) ═ 1 and

then, the input impairment g is calculated based on equation (7.7)_in(f) And

wherein g is_out(f) 1 and

the matrix constants may then be based on g_in(f) And

to determine, for example, according to a relationship

And

the quality of the compensation achieved by operation 1315 will be limited by the quality of the impairment measurements. This patent disclosure describes a method for obtaining a quality measure of the I/Q impairments of the transmitter at any given frequency, or over the entire frequency range.

Let c_ij(f) Means for determining coefficient c from I/Q impairments at frequency f and I/Q impairments at frequency-f_ijIs used for the functional expression of (1). Due to functional expression c_ij(f) Regarding the continuity of the frequency f, the matrix c (f) is therefore a good approximation to the matrix c (f + Δ f), provided Δ f is sufficiently small. Thus, the number of the first and second electrodes,when the transmitter performs transform operation 1315 using matrix c (f), the transmitter will implement at least partial compensation around frequencies around f. The quality of the compensation will generally degrade as the absolute value of Δ f increases.

At 1320, the transmitter may convert the resulting digital I signal and digital Q signal to analog form to obtain corresponding analog I signal and analog Q signal.

At 1325, the transmitter may perform I/Q modulation on the analog I signal and the analog Q signal to produce a modulated analog signal, e.g., as described above.

In some embodiments, the matrix c has one of the following special forms:

in the above first special form, the constant c₂₁And c₂₂Can be based on the values A (f), E_B(f) C (f) and E_D(f) As described in the "calculate true single point vector calibration constants" section, particularly in equations (1.81) and (1.82).

In some embodiments, the transformation 1315 can be performed on programmable hardware elements such as an FPGA or in special purpose digital circuitry such as an Application Specific Integrated Circuit (ASIC). The same sampling clock that drives the ADC conversion may be provided to programmable hardware elements or dedicated digital circuitry.

In some embodiments, the transformation 1315 may be performed by a processor in response to execution of program instructions. The processor may be incorporated as part of the transmitter or as part of another system such as a host computer or controller board.

In one set of embodiments, the transmitter 1400 may be configured as shown in FIG. 14. (the transmitter 1400 may include any subset of the features described above in connection with the method 1300). Transmitter 1400 may include digital circuitry 1410, DAC unit 1415, and I/Q modulator 1420.

The digital circuit 1410 may be configured to receive a digital in-phase (I) signal and a digital quadrature (Q) signal and transform the digital I signal and the digital Q signal according to a constant 2x2 matrix to produce a resulting digital I signal and a resulting digital Q signal. Digital circuitry 1410 may be implemented in any of various forms, for example, as described above in various different ways in connection with method 1300.

The DAC cell 1415 may be configured to convert the resulting digital I signal and the resulting digital Q signal into analog form to obtain an analog I signal and an analog Q signal, respectively.

I/Q modulator 1420 may be configured to perform I/Q modulation on the analog I signal and the analog Q signal to produce a modulated analog signal. The 2x2 matrix is configured to at least partially pre-compensate for the I/Q impairments of the transmitter at frequency f. The first constant corresponding to the first diagonal element of the 2x2 matrix may be calculated based on a measure of the I/Q impairments at frequency f and a measure of the I/Q impairments at frequency-f. The second constant corresponding to the first off-diagonal element of the 2x2 matrix may be calculated based on the measurement at frequency f and the measurement at frequency-f.

By "impairment at frequency f

The present disclosure repeatedly uses the term "I/Q impairments at frequency f". Whether this term is used for a transmitter, a receiver or a serial combination comprising a transmitter, a transmission path and a receiver, it includes within its meaning the I/Q impairments at frequency f caused by the system in question being stimulated with complex exponential tones exp (j2 pi ft) ═ cos (2 pi ft) + jsin (2 pi ft), as shown in fig. 15. The real and imaginary outputs of the system can be expressed as:

the I/Q impairments at frequency f may includeGain imbalance g (f) and phase skew given by

g(f)＝g_Q(f)/g_I(f)

Here we use the convention of using the I channel as a reference for gain imbalance and phase skew. However, the inventive principles described herein are equally applicable to any other reference convention. For example, the opposite convention (i.e., selecting the Q channel as a reference for gain imbalance and phase skew) may also be used, or the convention where gain imbalance references one channel and phase skew references another channel.

Because we are interested in compensating for gain imbalance and phase difference between two channels, we can model gain imbalance and phase skew as appearing to be all on the I channel or all on the Q channel. For example, fig. 16 illustrates the latter option. Thus, the Q channel output has the form:

physical consequences of I/Q impairments

The consequence of I/Q impairments at frequency f is the occurrence of undesired signal energy at frequency-f. To see this, we analyze the complex output signal as follows:

(we switch from f to ω ═ 2 π f, simply for notation simplicity). Thus, in response to the stimulus signal exp (j ω t), the system produces a signal having a complex amplitude A at the frequency ω_TONE(omega) complex exponential tones and producing at a frequency-omega a complex amplitude A_IMAGEComplex exponential pitch of (ω).

The complex exponential tones at frequency ω are often referred to simply as "tones", while the complex exponential tones at frequency- ω are often referred to as "mirror images". As expected, when g (. omega.) → 1 and

when, A_TONE(ω) → 1 and A_IMAGE(ω) → 0. It is desirable to let g (ω) be as close to one as possible and let

As close to zero as possible. (Linear scale is assumed here for gain imbalance may also be expressed in logarithmic scale, e.g., in dB, in which case 0dB represents the case of no gain imbalance.)

From the above discussion, it can be readily seen that the series combination of the two systems, the first with a gain imbalance g₁(omega) and phase skew

And the second with gain imbalance g₂(omega) and phase skew

Does not give a net gain imbalance g (ω) ═ g₁(ω)g₂(omega) and net phase skew

(since the second system is not stimulated by pure complex exponentials exp j ω t). The true relationship is more complex.

Image Rejection (Image Rejection)

Image rejection isFor complex amplitude A_TONE(omega) and A_IMAGE(ω) measurement of relative magnitude. For example, according to one conventional definition:

image rejection of 20 log (| a)_IMAGE|/|A_TONE|).

Because of | A_IMAGEI is usually less than A_TONEL, so the image rejection is usually negative. The more negative the image rejection, the better.

Post-compensation and pre-compensation

The concept of post-compensation involves coupling a compensation block to the output of a system that exhibits I/Q impairments. The compensation block is configured such that the series combination of the systems followed by the compensation block exhibits (or, approximately exhibits) an ideal model with unity gain imbalance and zero phase skew. When the system is stimulated by complex exponential tones at frequency ω, it will generate a signal that can be modeled as

Wherein g (ω) and

is the I/Q impairment of the system at frequency ω. The compensation block operates on the distorted complex signal to generate a corrected output signal equal to the original complex exponential pitch at frequency ω. Thus, the compensation block is said to be an "compensation" or "post-compensation" system I/Q impairments at frequency ω. Broadband post-compensation of the I/Q impairments means post-compensation of the I/Q impairments at each frequency ω within a frequency range or band.

The concept of pre-compensation involves placing a compensation block in front of the system, i.e. the output of the compensation block is coupled to the input of the system. The compensation blocks are configured such that the series combination of compensation blocks followed by the system exhibits (or, approximately exhibits) an ideal model with unity gain imbalance and zero phase skew. The compensation block will produce a predistorted complex signal in response to the complex exponential tone at frequency ω. The system receives the predistorted complex signal and further distorts the signal (by introducing I/Q impairments) thereby producing a complex output signal. The compensation block generates a predistorted complex signal such that the complex output signal from the system is equal to the original complex exponential pitch at frequency ω. Thus, the compensation block is said to "compensate" or "pre-compensate" the system's I/Q impairments at frequency ω. Wideband pre-compensation of I/Q impairments means pre-compensation of I/Q impairments at each frequency within a frequency range or band.

Performing conventional impairment compensation at a single frequency

If the pair is at a specific frequency ω₀of interest in post-compensation of the underlying I/Q impairments, the block diagram of FIG. 17 with real constants α and β can be used

Will map to the corrected output signal cos (ω)₀t)+jsin(ω₀t), as desired. Suitable values are:

this compensation method is referred to herein as "conventional single point compensation".

Due to gain imbalance g and phase skew

with respect to the continuity of the frequency ω, the real constants α and β will therefore be aligned at ω₀Partial compensation is achieved for I/Q impairments at nearby frequencies, with distance from ω₀Compensating for the quality degradation. However, because of g (ω)₀) Usually different from g (-omega)₀) And is

Is usually different from

So aim at supplementingCompensating for frequency omega₀appropriate pairs of I/Q impairments (α, β) below are generally associated with compensation at frequency- ω₀The appropriate values for the following I/Q impairments are different. Thus, unfortunately, the simultaneous pairs ω cannot usually be found₀And-omega₀A single value pair that both work.

the values of α and β derived above are for a single frequency ω₀While post-compensation of the lower I/Q impairments works ideally, they can also be used at a single frequency ω₀The following pre-compensation of the I/Q impairments is generally less than ideal. (while it gives less than ideal results, the various methods described herein can employ such pre-compensation, in part because it does not require knowledge at the frequency- ω₀I/Q impairments below). To achieve ideal pre-compensation of I/Q impairments at a single frequency, see the section "calculate true single point vector calibration constants".

Wideband I/Q impairment equalization

Fig. 18 depicts a basic model of a system H that will be reused throughout this patent disclosure, for example, to represent the equalization filtering performed by the receiver and the equalization filtering performed by the transmitter. (equalization is used herein as a synonym for I/Q impairment compensation).

In the case where system H represents the equalization filtering of the receiver, the complex input signal I (t) + jQ (t) represents the distorted signal provided by the preceding system G, as illustrated in fig. 19. System G generates a distorted signal in response to being stimulated at frequency f by a complex exponential signal i (t) + jq (t) ═ exp (j2 π ft)

Gain imbalance g (f) and phase skew

Is the I/Q impairment of the system G at frequency f. System G may represent the baseband equivalent of the receiver front-end, i.e. the part of the receiver from its RF input to the output of the I/Q digitizing unit. Instead, system G is expected to compensate for the transmitter's I/Q impairments and its own I/Q impairmentsMay represent the path from the input of the I/Q DAC unit of the transmitter to the output of the I/Q digitizing unit of the receiver.

System H operates on the distorted input to produce a corrected output signal I ' (t) + jQ ' (t) ═ exp (j2 pi ft) for all f's in the desired frequency band. Note, however, that the output from { exp (j2 π ft): the set B given by f within a given frequency range forms the basis of a function space x (t) that is band limited to the given frequency range. Since the series combination of G followed by H is an identity mapping to each function of the basis set B, it will be an identity mapping to all band-limiting functions x (t) due to linearity.

The equalization system H may be implemented by the digital circuitry 220 of the receiver as described in various different ways above.

Where system H represents the equalization filtering of the transmitter, we interpret H as the receive basis function

And, in response to the basis function, a pre-compensated complex signal I '(t) + jQ' (t) ═ exp (j2 pi ft) as shown in fig. 20A is generated. It should be noted that

The set X given by f in a given frequency range also forms the basis of the function space X (t) band-limited to the given frequency range.

The pre-compensated signal is distorted by the following system G. System G generates a distorted signal

Wherein g (f) and

representing the gain imbalance and phase skew of the system G at frequency f. Since the series combination of H followed by G is an identity map for each function of the basis set X, it will be an identity map for all band limiting functions X (t). Thus, when being multiplexed at any frequency f within the frequency bandThis series combination will produce the same complex exponential tone at its output when stimulated by the exponential tone exp (j2 π ft), as shown in FIG. 20B.

System G may represent the baseband equivalent of the RF front end of the transmitter, i.e. the part of the transmitter from the input of the DAC cell of the transmitter to the RF output. Alternatively, the system G may represent a path from at the input of the DAC of the transmitter to the output of the digitizing unit of the receiver, in case the transmitter is expected to compensate for the I/Q impairments of the receiver and its own I/Q impairments. System H may be implemented by digital circuitry 510 as described in a variety of different ways above.

The complex exponential is used throughout the analysis because any band-limited signal can be represented by a fourier analysis as a superposition of the population of complex exponentials. When comparing in-phase (I) and quadrature-phase (Q) channels, the I/Q impairments may include gain imbalance and phase skew occurs due to imperfect quadrature mixing. (the phase skew perturbs the ideal 90 degree phase relationship between the I and Q channels). While phase skew is generally modeled as an imperfection in the quadrature mixing, it can also be modeled as phase skew between the I (t) and Q (t) signals. In both cases discussed above, the input to the distortion model G is a complex exponential signal. Since the I/Q impairments are relative, we can assume that the I/Q impairments are fully present at the Q (t) output, which is ideal. This assumption will simplify the following mathematical derivation, although other assumptions may be made.

The equalization system H may be represented by a 2x2 frequency response matrix H (f) — (H)_ij(f) Or equivalently from a 2x2 matrix of real-valued impulse responses h (t) — (h)_ij(t)) to model. However, under the assumptions identified above regarding how impairments are represented at the output of the distortion model G, the matrix H can be reduced to the structure shown in FIG. 21, i.e., H₁₁(f) 1 and H₁₂(f) 0. For notation efficiency, we define U (f) ═ H₂₁(f) And V (f) ═ H₂₂(f) In that respect Thus, the number of the first and second electrodes,

I’(t)＝I(t)

Q’(t)＝u(t)*I(t)+v(t)*Q(t)，

where U (t) and V (t) are impulse responses corresponding to U (f) and V (f), respectively.

Any real-valued filter necessarily has a symmetric magnitude response and an antisymmetric phase response. In other words, x (t) is a real number implying that for all f,

|X(f)|＝|X(-f)|

Phase{X(-f)}＝-Phase{X(f)}

where X (f) is the Fourier transform of X (t). Therefore, the frequency response V (f) cannot apply independent impairment corrections at frequencies f and-f. Typically, g (f) is different from g (-f), and

and

different. Thus, the filter V acting by itself (i.e., U is always equal to zero) is not sufficient to provide correction at f and-f. The filter V will be sufficient if the goal is to correct only the wideband I/Q impairments above only positive frequencies or only negative frequencies. (note: as long as the impairment is constrained to g (f) ═ g (-f) and

v acting on itself can correct the + f and-f impairments, as evidenced in the "add constraints" section). However, since it is desired to correct both sides of the spectrum, a second filter U (f) is introduced. Applying another filter from the in-phase component and adding it to the quadrature-phase channel provides the degrees of freedom needed to control both sides of the complex frequency. This is due to the fact that the in-phase component I (t) ═ cos (2 pi ft) is the same for frequencies f and-f while the phase of the quadrature-phase component changes 180 degrees when going from f to-f.

In order to solve for U (f) and V (f), their respective output signals need to be known. To simplify the mathematical derivation, both U (f) and V (f) are divided into their even and odd parts, as shown in fig. 22. Thus, A (f) and B (f) are the even and odd portions of U (f), while C (f) and D (f) are the even and odd portions of V (f).

Since any real-valued filter necessarily has a symmetric magnitude response, we can reduce complexity by solving for only the positive frequency portion of each spectrum A, B, C and D. However, to achieve impairment compensation for negative as well as positive frequencies, the input I (t) + jQ (t) corresponding to negative frequencies cannot be simply ignored. Instead, depending on the odd symmetry of the sine function and the even symmetry of the cosine function, we consider such inputs by representing them as equivalent positive frequency inputs:

thus, we will derive two equations for the positive frequency portions of A, B, C and D, the first based on the input

And the second based on the input

Where f > 0 for both equations.

If the filter is constrained to have a symmetric impulse response, the filter will exhibit a symmetric magnitude response and a zero phase response. This is the case for filters a (t) and c (t). However, if the impulse response of the filter is anti-symmetric, it will exhibit a symmetric magnitude response, but will exhibit a phase response equal to- (π/2) sgn (f).

Thus, an anti-symmetric impulse response is equivalent to an even impulse response followed by a Hilbert transform. This is the case for filters b (t) and d (t). Thus, the filter b (t) can be represented as an even impulse response e followed by a Hilbert Transform (HT)_B(t) as shown in FIG. 23. Similarly, the filter d (t) can be represented as an even impulse response e followed by a Hilbert Transform (HT)_D(t)。E_B(f) And E_D(f) Are respectively corresponding to e_B(t) and e_DFrequency of (t)And (6) responding. The exact output of the original filters A, B, C and D can now be easily determined. FIG. 24A shows four filters A, B, C and D responsive to signal I₁(t)+jQ₁(t) output. FIG. 24B shows four filters responding to signal I₂(t)+jQ₂(t) output.

Each of FIGS. 24A and 24B can be directly converted to A (f), E for positive f (or non-negative f)_B(f) C (f) and E_D(f) Corresponding linear equation in (1). We use the following notation:

g₁(f)＝g(f) for f＞0

g₂(f)＝g(-f) for f＞0

fig. 24A and 24B give equations (1.1) and (1.2), respectively, which are shown in fig. 25. Fig. 26A and 26B show corresponding vector diagrams. (recall that cos (2 π ft) maps to 1 and sin (2 π ft) maps to-j in the vector map).

The horizontal projection of the vector in fig. 26A gives the following equation (1.3); the vertical projection gives equation (1.4). Similarly, the horizontal projection of the vector in fig. 26B gives equation (1.5); the vertical projection gives equation (1.6):

the system of equations is an unknown vector (A, E)_B，C，E_D) 4x4 linear system in (1):

wherein

And is

The determination of the matrix P is given by:

Det(P)＝w²+x²+y²+z²-2wy+2xz. (1.13)

as long as

There is a unique solution vector (A (f), E)_B(f)，C(f)，E_D(f) ). As an example, the equation cannot be skewed in phase

And the gain imbalance g (f) are solved when both are completely odd. However, it does not make sense for the gain imbalance g (f) to be completely odd, since the gain imbalance is usually close to unity for all f, or at least bounded by some positive constant.

Using the Cramer rule, we found

A(f)＝-2(wz+xy)/Det(P). (1.16)

E_B(f)＝(-w²-x²+y²+z²)/Det(P) (1.17)

C(f)＝2(x+z)/Det(P) (1.18)

E_D(f)＝2(w-y)/Det(P). (1.19)

Substituting equations (1.9) through (1.14) into equations (1.16) through (1.19) will yield equations (1.20) through (1.23), shown in fig. 27.

Adding constraints

In many cases, gain imbalance and phase skew approximate common constraints. This part simplifies equations (1.20) to (1.23) for some typical real world conditions. For optimal compensation, equations (1.20-1.23) may be used. However, adding some constraints reduces the computational requirements if the compensation performance can be relaxed.

Case 1: odd phase skew

In the case of odd phase skew, i.e., for f > 0,

equations (1.20) to (1.23) are specific to (specularize to):

A(f)＝0 (1.24)

E_B(f)＝{g₂(f)-g₁(f)}/{g₁(f)+g₂(f)} (1.25)

case 2: even gain imbalance

In the case of even gain imbalance, i.e. for f > 0, g (f) is g₁(f)＝-g₂(f) Equations (1.20) to (1.23) are specific to:

E_B(f)＝0 (1.29)

case 3: odd phase skew and even gain imbalance

In the case of odd phase skew and even gain imbalance, equations (1.20) to (1.23) are specific to:

A(f)＝0 (1.32)

E_B(f)＝0 (1.33)

case 4: zero phase skew and arbitrary gain imbalance

In the case of zero phase skew and arbitrary gain imbalance, equations (1.20) to (1.23) are specific to:

A(f)＝0 (1.36)

E_B(f)＝{g₂(f)-g₁(f)}/{g₂(f)+g₁(f)} (1.37)

C(f)＝2/{g₂(f)+g₁(f)} (1.38)

E_D(f)＝0. (1.39)

case 5: arbitrary phase skew and unity gain imbalance

In the case of arbitrary phase skew and unity gain imbalance, equations (1.20) to (1.23) are specific to:

E_B(f)＝0 (1.41)

case 6: constant gain imbalance and phase skew

In the case where the gain imbalance and phase skew functions are constant functions, i.e., g (f) ═ g for all f and

equations (1.20) to (1.23) are specific to:

E_B(f)＝0 (1.45)

E_D(f)＝0. (1.47)

filter design

In one embodiment, a symmetric linear phase FIR filter

And

designed based on magnitude responses | A (f) | and | C (f) |, respectively, and an anti-symmetric linear phase FIR filter

And

are designed based on magnitude responses | B (f) | and | D (f) |, respectively. Note that for all f, | B (f) | E_B(f) And | D (f) | ═ E_D(f) L. The Remez algorithm can be used to design these filters. Thus, the equalization system of FIG. 22 may utilize a filter

And

to design. By creating four filters, each with a symmetric or anti-symmetric filter valve (tap), and summing the filters shown in fig. 22, we can effectively match two arbitrary frequency responses U (f) and V (f). (Note: depending on the filter design tool, the summation may actually be a subtraction.

In another embodiment, a symmetric linear phase FIR filter

And

based on magnitude responses | A (f) |, | E |, respectively_B(f) I, | C (f) | and | E_D(f) Of. Also, the Remez algorithm can be used to design these filters. Thus, the equalization system of FIG. 23 mayUsing filters

And

to be implemented.

In yet another embodiment, the filter

And

may be designed based on the frequency responses U (f) and V (f). L is_pA range (L)_pNorm) design method can be used to design these filters based on the magnitude and phase response of U (f) and the magnitude and phase response of V (f). Thus, the equalization system of FIG. 21 may utilize a filter

And

to be implemented.

Breaking I/Q impairments

As described above, FIG. 15 illustrates the I/Q impairments (i.e., gain imbalance g (f) and phase skew)

) A system of received complex exponential signals exp (j2 π ft). In general, the 2x2 frequency response matrix H characterizing the system can be derived from the impairment functions g (f) and

and (6) exporting. To simplify this derivation, we consider the gain imbalance g (f) and phase skew of the system

Modeling was done to appear entirely on the Q channel output as shown in fig. 28. This model is such thatIt is convenient to use a special form of the matrix shown in fig. 29, where U (f) and V (f) are the frequency responses corresponding to the real filters U (t) and V (t). The response U (f) can be expressed as the sum of its even part a (f) and odd part B (f), as shown in fig. 30. Similarly, V (f) can be represented as the sum of its even portion C (f) and odd portion D (f). A filter with an odd spectrum B (f) may be composed of a filter with an even spectrum E followed by a Hilbert transform HT_B(f) As shown in fig. 31. (see above "attention on filters with odd frequency response"). Similarly, a filter with an odd spectrum D (f) may be composed of a filter with an even spectrum E followed by a Hilbert transform HT_D(f) Is shown. Note that B and E_BThe magnitude response of (c) is equal, | B (f) | E |_B(f) L, as D (f) and E_D(f) The magnitude response of.

We will address A (f), E_B(f) C (f) and E_D(f) The positive frequency part of (a) gives an equation because the negative frequency part is determined by the respective positive frequency part. One equation would come from using a positive frequency input I₁(t)+jQ₁(t) ═ exp (j2 π ft) (for f > 0) stimulation system, as shown in FIG. 32A. Another equation would result from stimulating the system with a negative frequency input (for f > 0) as follows expressed in terms of an equivalent positive frequency input, as shown in fig. 32B.

I₂(t)+jQ₂(t)＝exp(-j2πft)

＝cos(-2πft)+jsin(-2πft)

＝cos(2πft)-jsin(2πft)

Fig. 33 shows two equations. Equation (1.48) is based on fig. 32A. Equation (1.49) is based on fig. 32B.

Fig. 34A and 34B show the corresponding vector diagrams, depending on the notation:

g₁(f)＝g(f) for f＞0

g₂(f)＝g(-f) for f＞0

the vector diagram gives the following equation:

these equations include unknown A (f), E_B(f) C (f) and E_D(f) The 4x4 matrix equation (1.54) in (1), as shown in fig. 35. By inverting the 4x4 coefficient matrix, we obtain a solution. See the matrix equation (1.55) in fig. 36. It follows that:

due to A, E_BC and E_DIs an even function of the frequency f. Thus, their negative frequency part is dictated by the even symmetry. Further, the odd frequency responses B (f) and D (f) are given by:

B(f)＝-jE_B(f) sgn (f) and

D(f)＝-jE_D(f)sgn(f).

special cases are as follows: even gain imbalance and odd phase skew

In case the gain imbalance is an even function and the phase skew is an odd function, i.e. g (f) ═ g (-f) and

equations (1.56) to (1.59) are specific to:

A(f)＝0

E_B(f)＝0

special cases are as follows: even gain imbalance and even phase skew

In the case where the gain imbalance and phase skew are even functions, i.e., g (f) ═ g (-f) and

equations (1.56) to (1.59) are specific to:

E_B(f)＝0

E_D(f)＝0.

special cases are as follows: constant gain imbalance and phase skew

In the case where the gain imbalance and phase skew are constant functions, i.e., g (f) ═ g and

equations (1.56) to (1.59) are specific to:

E_B(f)＝0 (1.61)

E_D(f)＝0. (1.63)

calculating a mapping between Rx and Tx

In some embodiments, the transmitter predistorts the digital I/Q signal to compensate for the I/Q impairments of the compensator itself, as described in various different manners above. To achieve this compensation, it is necessary to have an estimate of the I/Q impairments of the transmitter. The quality of the compensation will be limited by the quality of the estimate (the degree of matching with the fact). While high quality estimation is desirable, it is difficult to directly measure the I/Q impairments of the transmitter. Instead, the measurements are obtained indirectly, for example, using a receiver as shown in fig. 37.

Fig. 37 shows a transmitter 3700 coupled to a receiver 3725 via a channel (e.g., a cable 3720 or wireless channel). The transmitter may include a digital compensation unit 3702, a DAC unit 3705, an I/Q modulator 3710, and a front end 3715. The compensation unit 3702 may perform pre-compensation (pre-distortion) on the digital signal I (n) + jQ (n) to obtain a pre-compensated signal I '(n) + jQ' (n), e.g., as described in various different manners above. DAC cell 3705 may convert the pre-compensated signal to an analog signal s (t) ═ I '(n) + jQ' (n). The analog signal s (t) may be up-converted to RF using I/Q modulator 3710. The upconverted signal is conditioned by TX front end 3715 to obtain a transmit signal. The transmit signal may be conveyed to the receiver by cable 3720.

Receiver 3725 may include a front end 3730, an I/Q demodulator 3735, and a digitizing unit 3740. The front end 3830 may receive the transmitted signals from the cable 3720 and perform operations on the received signals to generate conditioned signals. The conditioned signal may be down-converted by an I/Q demodulator to produce a complex down-converted signal. The complex down-converted signal may be sampled by a digitizing unit 3740 to obtain a sampled complex signal. The sampled complex signal can be used to make I/Q impairment measurements. In some embodiments, the receiver is a spectrum analyzer, e.g., a vector signal analyzer.

It is important to understand how the I/Q impairment measurements taken at the receiver 3725 correlate to the I/Q impairment of the transmitter. They are not the same. This is because the I/Q impairments at the transmitter (e.g., I/Q impairments at the I/Q modulator) are blurred (obscure) (distorted) by the signal path including TX front-end 3715, cable 3720, and receiver front-end 3730. The signal path may be characterized by a frequency response H (f) m (f) exp (j θ (f)), where H (f) is a complex number. The amplitude m (f) refers herein to the "scaling" of the signal path at the frequency f. Phase θ (f) refers herein to the "rotation" of the signal path at frequency f.

The problem of estimating the I/Q impairments of the transmitter from receiver-based measurements is not trivial. The solution of which is disclosed in the present patent disclosure. (see the iterative method disclosed below). Part of the solution includes obtaining an initial estimate for the signal path response function H (f). This part will focus on obtaining an initial estimate of the form H (0), i.e. the frequency response of the signal path at DC (zero frequency). The amplitude m (0) of H (0) is referred to as the "DC scaling" of the signal path. The phase θ (0) of H (0) is referred to as the "DC rotation" of the signal path.

One approach to estimating the I/Q impairments of a transmitter involves performing an iterative process with a spectrum analyzer. (a spectrum analyzer is a device configured to measure the magnitude and frequency of an input signal over the instrument's frequency range). The spectrum analyzer measures the I/Q impairments of its demodulated signal and then applies compensation at the transmitter based on the measurement. The measurement can only roughly approximate the I/Q impairments of the transmitter, but it can be good enough to achieve at least partial compensation. The spectrum analyzer then makes a second measurement of the I/Q impairments of its demodulated signal. This second measurement can be used to adjust the compensation applied at the transmitter, etc. The measurement sequence will converge, i.e. the measured gain imbalance will converge to one and the measured phase skew will converge to zero, indicating that proper compensation has been achieved at the transmitter. Because the spectrum analyzer does not capture phase information, multiple iterations may be required to achieve convergence.

In some embodiments, the I/Q impairments of the transmitter may be determined using a measurement device (such as a vector signal analyzer) capable of making phase measurements and locking the measured phase to the transmitter. In this case, the I/Q impairments of the transmitter may be determined at the measurement device using two measurements or less.

The method described below makes two measurements, but requires that the I/Q modulator of the transmitter and the I/Q demodulator of the receiver be locked together in frequency (via a phase-locked loop with a common reference). Unlike other approaches, this approach is resistant to synchronous excitation (spurs), i.e., excitation such as LO leakage of the LO phase locked to the transmitter. While this technique can be used at any frequency, the main applications are to determine the DC scaling m (0) and DC rotation θ (0) of the signal path in order to calibrate the LO leakage impairments of the transmitter.

In fig. 38, vector a ═ a_I+jA_QRepresents the LO leakage of the transmitter when the transmitter is stimulated with a constant zero signal I '(n) ═ Q' (n) ═ 0 (the term "vector" is used herein as a synonym for "complex"). The amplitude and phase of vector a represent the amplitude and phase of the LO leakage. When this LO leakage signal moves from the I/Q modulator of the transmitter to the I/Q demodulator of the receiver, it scales by m (0) and rotates by θ (0) so that vector a is transformed into vector a' at the receiver. See fig. 39. The vector a' is measured by, for example, averaging sampled complex signals captured from the output of the I/Q demodulator.

Then, we stimulate the transmitter with the known non-zero vector B:

I’(n)＝B_I

Q’(n)＝B_Q.

(vector B need not be real as shown in FIG. 38, however, it need not be non-zero). This deliberately applied LO leakage B is superimposed on the intrinsic LO leakage a of the transmitter so that the total leakage of the transmitter is the vector C. (the choice of B (primarily its magnitude) will affect the accuracy of the measurement. This total leakage signal undergoes the same scaling m (0) and rotation θ (0) as it traverses the signal path, so that vector C is transformed into vector C' at the receiver. Referring to fig. 39, it is observed that vector C ' is the sum of vectors a ' and B '. Vector B' is the vector that would result if vector B itself traversed the signal path.

At the receiver, vector C' is measured by, for example, averaging sampled complex signals captured from the output of the I/Q demodulator during stimulation by vector B. Since both a ' and C ' are known from the measurement, the vector B ' can be calculated by subtraction. The DC scaling m (0) and the DC rotation θ (0) may be calculated from vector B' and vector B:

the mapping is m (0) exp (j θ (0)) ═ B'/B

Similarly, the inverse mapping that will undo the effect of the signal path may be determined from an inverse expression:

inverse mapping exp (-j θ (0))/m (0) = B/B'

The LO leakage vector a may then be calculated by multiplying the vector a' with the inverse mapping. In practice, it is advisable to keep the magnitude of B on the order of a. It is also a good practice to not transmit the vector B itself but the sum of the vector B and another signal K, where the signal K has more energy than the vector B signal and a frequency component defined away from DC, since the LO leakage of the transmitter is likely to vary with power in the instantaneous bandwidth. For example, the signal K may be a tone.

In some embodiments, the sampled complex signal is windowed. If no window is applied, there is a constraint on the frequency of tone K. In addition to the tone K, if other signal tones are present, they may also leak into the measurement. Thus, if no windowing is used, tones (intentional or not) are preferably constrained to certain frequencies to avoid leakage.

Method for determining LO leakage of transmitter

1. The transmitter is stimulated with a constant zero signal.

2. The vector a' generated at the receiver is measured.

3. The transmitter is stimulated with a non-zero complex constant B.

4. The vector C' is measured at the receiver.

5. The LO leakage vector a of the transmitter is calculated according to the following equation:

B’＝C’-A’ (1.64)

InvMap＝B/B’ (1.65)

A＝A，*InvMap. (1.66)

once the LO leakage vector a of the transmitter is calculated, the transmitter may remove (or substantially compensate for) the LO leakage by applying a translation vector-a to the following transmitted signals.

I’(n)＝I(n)-A_I

Q’(n)＝Q(n)-A_Q

In addition to the I/Q impairment precompensation described above, the compensation unit 3702 may also apply such a translation. For example, the complex signals (I (n), Q (n)) may be subjected to a 2 × 2 matrix of digital filters to pre-compensate for I/Q impairments and then shifted to pre-compensate for LO leakage.

In some embodiments, the calculation of the DC map may include the following additional calculations. As described herein, the iterative method may diverge if the estimation error of the phase rotation is too large. In case of large phase skew, this extra step can be used to obtain a more accurate estimate and to converge the iterative method: (1) the mapping from RX to TX is calculated as already described. (2) A measurement of the phase skew is made. (3) The mapping from #1 was used to calculate "modify gain imbalance and phase skew by linear system". (4) The rotation measurement of #1 is added to the calculated phase skew of #3 to obtain a more accurate rotation estimate.

Method for calculating a DC-map and a DC-rotation for a signal path

In one set of embodiments, method 4000 may involve the acts illustrated in FIG. 40. Method 4000 may be used to estimate the DC scaling m (0) of the signal path between the I/Q modulator of the transmitter and the demodulator of the receiver. (method 4000 may incorporate any subset of the features described above in the "calculate mapping between Rx and Tx" section). Method 4000 is described below as being performed by a "processing agent". The processing agent may be any system of digital circuitry, such as a processor (executing under control of program instructions), a programmable hardware element, an ASIC, or any combination thereof.

In some embodiments, the receiver adheres to a direct conversion architecture, and the demodulator is an analog I/Q demodulator. In other embodiments, the receiver may adhere to a different architecture (e.g., a superheterodyne architecture) that performs analog down-conversion followed by digital I/Q demodulation. Thus, in this case, the demodulator is implemented by digital circuitry, e.g., on programmable hardware elements, in dedicated digital circuitry, in software on a processor, or any combination thereof.

At 4010, the processing agent may direct the transmitter to provide a null signal as an input to the I/Q modulator. The zero signal is a constant zero signal. The null signal may be a digital null signal provided to the complex input of a DAC cell (e.g., DAC cell 3705 of fig. 37) of the transmitter. Thus, I '(n) ═ 0 and Q' (n) ═ 0.

At 4105, the processing agent can receive a first response signal that has been captured from the demodulator in response to the act of providing a null signal. The first response signal may be captured from an output of an ADC unit of the receiver. (see, e.g., digitizing unit 215 of FIG. 2B).

At 4020, the processing agent may direct the transmitter to provide a non-zero complex constant B ═ B to the I/Q modulator_I+jB_QAs an input. Also, the constant signal may be provided to the complex input of the DAC cell of the transmitter. Thus, I' (n) ═ B_IAnd Q' (n) ═ B_Q. In some embodiments, B is entirely real, i.e., B_Q＝0。

At 4025, the processing agent may receive a second response signal that has been captured from the demodulator in response to the act of providing the constant signal. The second response signal may be captured from an output of an ADC unit of the receiver.

At 4030, the processing agent may average the first response signal to obtain a first average value and average the second response signal to obtain a second average value. Averaging helps to reduce noise in the measurement.

At 4035, the processing agent may calculate a difference between the second average and the first average, e.g., according to the expression:

difference value-second average value-first average value

At 4040, the processing agent may calculate a DC scaling based on the difference and the non-zero complex constant, e.g., as described above. The processing agent may store the DC scaling in memory.

In some embodiments, method 4000 may further include calculating a DC rotation θ (0) of the signal path based on the phase of the difference and the phase of the non-zero complex constant B, e.g., according to the expression:

θ (0) is phase (difference)/phase (B)

In some embodiments, DC scaling and DC rotation are used to remove the effect of the signal path from the I/Q impairments measured at the receiver in order to obtain an estimate of the I/Q impairments at the transmitter.

In some embodiments, the signal path includes a cable coupling between the transmitter and the receiver. In other embodiments, the signal path includes a wireless channel between the transmitter and the receiver.

As an alternative to calculating the difference between the averages, the processing agent may instead calculate a difference signal by subtracting the first response signal from the second response signal and then averaging the difference signal. DC scaling may then be calculated based on the average and a non-zero complex constant.

In one set of embodiments, a computer system, including a processor and a memory, is used to estimate a DC scaling m (0) of a signal path between an I/Q modulator of a transmitter and a demodulator of a receiver. The memory stores program instructions that, when executed by the processor, cause the processor to: directing the transmitter to provide a null signal as an input to the I/Q modulator; receiving a first response signal that has been captured from a demodulator in response to providing the null signal; directing the transmitter to provide as an input a constant signal equal to a non-zero complex constant to the I/Q modulator; receiving a second response signal that has been captured from the demodulator in response to providing the constant signal; averaging the first response signal to obtain a first average value and averaging the second response signal to obtain a second average value; calculating the difference between the second average value and the first average value; a DC scaling is calculated based on the difference and a non-zero complex constant. The program instructions may incorporate any subset of the features described above in the "calculate mapping between Rx and Tx" section and in connection with method 4000.

Modifying gain imbalance and phase skew by a linear system

This part of the method can be used to remove the influence of the signal path between the I/Q modulator of the transmitter and the I/Q demodulator of the receiver from the measurement of the I/Q impairments of the receiver when calibrating the transmitter or measuring the I/Q impairments of the transmitter. Those effects may include effects of the front end of the transmitter, the transmission channel, and the front end of the receiver. For example, the front end of the transmitter may include an RF filter that operates on the frequency response of the signal path. Similarly, the front end of the receiver may include an RF filter that operates on the frequency response of the signal path.

In some embodiments, the magnitude response m (f) of the signal path may be calibrated while the phase rotation θ (f) is not calibrated. (calibration may be achieved by performing pre-compensation at the transmitter using digital circuitry 510 and/or post-compensation at the receiver using digital circuitry 220). This part of the calculation allows a correct measurement of the I/Q impairments of the transmitter without first calibrating the phase response of the signal path.

In some embodiments, the overall frequency response (including magnitude and phase rotation) of the signal is calibrated.

Given a system with a frequency response H (f) and with gain imbalance g (f) and phase skew

Input signal s_input(f, t), as shown in FIG. 41, we will get a signal that allows us to determine the output s at the system_outputGain imbalance g' (f) and phase skew of (f, t)

Equation (c) of (c). We assume input gain imbalance g (f) and input phase skew

Appearing completely on the Q input channel. However, we cannot make the same assumptions at the system output at the same time. In general, the output components I '(t) and Q' (t) will have the form:

thus, the output gain imbalance g' (f) and the output phase skew

Can be determined by the following equation:

g’(f)＝g_Q(f)/g_I(f)

dependent on s_output(f，t)＝h(t)＊s_input(f, t), the derivation begins with equations (1.60) through (1.62) given in FIG. 42, where H (t) is the impulse response corresponding to H (f). Equations 1.61 and 1.62 imply:

definitions a (f) and B (f) are the right-hand sides of equations (1.63) and (1.64), respectively:

also, w (f), x (f), y (f), and z (f) are defined based on the left-hand sides of equations (1.63) and (1.64):

this follows from

w(f)+jx(f)+y(f)+jz(f)＝A(f) (1.69)

w(f)-jx(f)-y(f)+jz(f)＝B(f)， (1.70)

And thus

w(f)＝(1/2)Re{A(f)+B(f)}

x(f)＝(1/2)Im{A(f)-B(f)}

y(f)＝(1/2)Re{A(f)-B(f)}

z(f)＝(1/2)Im{A(f)+B(f)}.

Note that if H (f) has an even magnitude response and an odd phase response, i.e., H (-f) ═ H (f)^＊Then the impulse response corresponding to H (f) is purely real. Thus, in this particular case, the filter H (f) does not change the measurement of the I/Q impairments:

w(f)＝Re(H(f))，x(f)＝Im(H(f))

the following method describes how the TX impairments are iteratively measured when the magnitude and phase of the signal path transfer function H (f) are only approximately known. Part of the iterative measurement method involves using the equations derived in this section to calculate the I/Q impairments at the output of the I/Q modulator at the transmitter based on the I/Q impairments at the input (or alternatively at the output) of the I/Q demodulator at the receiver. To perform this calculation, the frequency response H (f) is set equal to the inverse of the estimate of the frequency response of the signal path. Different estimates of the signal path frequency response may be used in different situations.

I/Q impairment by linear system H (f) transformation

In one set of embodiments, the method 4300 may involve the operations shown in FIG. 43. The method 4300 may be used to base a complex input z at an electronic system_INThe I/Q impairment calculation of (z) is performed at the complex output of the electronic system_OUTI/Q impairments of (1). The complex input is an input comprising an in-phase channel and a quadrature channel. Also, the complex output is an output including an in-phase channel and a quadrature channel. (the method 4300 may include any subset of the features described above in the section "altering gain imbalance and phase skew by linear system"). The method 4300 may be performed by a processing agentLines, as described above.

At 4310, the processing agent may act according to an expression

Computing a spectrum A (f), where H (f) is a spectrum of a linear system model of an electronic system, where g (f) is at a complex input z_INIs not balanced, wherein

Is at a complex input z_INIs skewed.

At 4315, the processing agent may act according to the expression

The spectrum B (f) is calculated.

At 4320, the processing agent may calculate a sum of spectra a (f) and B (f), and a difference between spectra a (f) and B (f), for example, according to the relationship:

Sum(f)＝A(f)+B(f)，

Diff(f)＝A(f)-B(f).

at 4325, the processing agent may compute the complex output z based on the real and imaginary parts of the sum and the real and imaginary parts of the difference_OUTGain imbalance and phase skew. In particular, as described above, the function g_I(f)、g_Q(f)、

And

can be calculated based on the spectrum of the sum and the spectrum of the difference and then at the complex output z_OUTThe gain imbalance and phase skew may be based on g_I(f)、g_Q(f)、

And

to calculate the time of the calculation of the time of the calculation,as shown in fig. 41. The output gain imbalance and phase skew constitute useful information, in part because they can be used to perform I/Q impairment compensation or calibration, as described in various different ways herein.

The processing agent may store the output gain imbalance and the output phase skew in a memory.

In some embodiments, the electronic system modeled by the frequency spectrum H (f) is the inverse of the signal path from the I/Q modulator of the transmitter to the demodulator of the receiver, e.g., as described in various different manners herein. Plural inputs z in electronic systems_INMay represent the gain imbalance and phase skew of the input (or alternatively, the output) of the demodulator. Complex output z in electronic system_OUTMay represent gain imbalance and phase skew of the output of the I/Q modulator.

In some embodiments, the processing agent may also include computing an inverse of the spectrum of the signal path to determine the spectrum H (f), e.g., as described in various different manners herein.

In some embodiments, the frequency spectrum H (f) may be determined (or estimated) based on DC scaling and DC rotation of the signal path, e.g., according to a relationship

H(f)＝exp{-jθ(0)}/m(0).

In some embodiments, the processing agent may calculate the DC scaling and DC rotation by: providing a zero signal as an input to the I/Q modulator; capturing a first response signal from an I/Q demodulator in response to providing the null signal; providing a constant signal equal to a non-zero complex constant as an input to the I/Q modulator; capturing a second response signal from the I/Q demodulator in response to providing the constant signal; averaging the first response signal to obtain a first average value and averaging the second response signal to obtain a second average value; calculating the difference between the second average value and the first average value; and calculating a DC scaling based on the difference and a non-zero complex constant.

In some embodiments, the processing agent may also measure gain imbalance g (f) and phase skew of the electronic device at multiple frequencies

(e.g., directing gain imbalance g (f) and phase skew to an electronic device

Measurement of (d). The electronic device may be a transmitter, a receiver, or a series combination of a transmitter and a receiver, as described in various different ways herein.

In some embodiments, the processing agent may be a programmable hardware element. In other embodiments, the processing agent may be a processor configured to perform the method 4300 in response to execution of program instructions.

Transmitter I/Q impairment determination with shared LO

In one set of embodiments, the method 4400 for determining I/Q impairments of a sender may involve the acts illustrated in fig. 44. (furthermore, method 4400 may include any subset of the features described in the "iterative technique for measuring Tx impairments" section, in the "iterative estimation of transmitter impairments with shared LO" section, and in the "iterative estimation-optimization of transmitter impairments with shared LO" section). The method 4400 may be enacted by a processing agent (enact), e.g., as described herein in a variety of different manners.

At 4410, the processing agent may perform a set of operations. This set of operations may include operations 4415 through 4440 as shown in fig. 44.

At 4415, the processing agent may direct the complex exponential tones at frequency f to be provided to the transmitter. For example, the processing agent may issue a command to cause the complex exponential tones to be provided to (or generated by) the transmitter. The frequency f may be interpreted as a shifted frequency relative to the local oscillator frequency of the transmitter. The frequency f may be non-zero.

At 4420, the processing agent may provide a pre-compensation transformation to pre-compensation circuitry of the transmitter. The pre-compensation circuit may be configured to apply a pre-compensation transformation to the complex exponential tones to obtain an adjusted complex signal. (e.g., the pre-compensation circuit may be the digital circuit 510 of FIG. 5 or the compensation circuit 3702 of FIG. 37). The pre-compensation transform may be configured to pre-compensate a current estimate of the I/Q impairments of the transmitter. The transmitter may be configured to transmit the transmit signal based on the adjusted complex signal, e.g., as described in various different manners above. The receiver may be configured to receive a transmitted signal and capture a sampled complex signal representative of the received transmitted signal, e.g., as described in various different manners above. (the act of "sampling" the complex signal involves sampling its I component and sampling its Q component. thus, a "sampled complex signal" includes both a sampled I signal and a sampled Q signal.)

At 4425, the processing agent may calculate the original I/Q impairments based on the sampled complex signals. For example, the original I/Q impairments may include gain imbalance and phase skew of the sampled complex signal. For information on how to calculate the raw I/Q impairments, see the section "precision measurement techniques".

At 4430, the processing agent may transform the original I/Q impairments to determine transformed I/Q impairments. The transformation may remove the measured I/Q impairments of the receiver from the original I/Q impairments. For more information on how to perform such a transformation, see section "remove receiver impairments from measured output impairments".

As an alternative to operations 4425 and 4430, the processing agent may apply a 2x2 matrix of digital filters to the sampled complex signal to remove the measured I/Q impairments of the receiver, e.g., as described above in connection with fig. 2A, 2B, and 3 and in the "wideband I/Q impairment equalization" and "filter design" sections. Applying the 2x2 matrix of digital filters to the sampled complex signal will produce a filtered complex signal. The filtered complex signal may be used to calculate a transformed I/Q impairment. The method described in the section "precision measurement techniques" can be used to determine transformed I/Q impairments based on a filtered complex signal.

At 4435, the processing agent may remove the current estimate of the signal path from the transformed I/Q impairments to obtain path-compensated I/Q impairments, wherein the signal path comprises a path from an I/Q modulator of the transmitter to a demodulator of the receiver. (the signal path estimate can be removed by using the method described in the section "altering gain imbalance and phase skew by linear system"). The path-compensated I/Q impairments may represent estimates of the residual I/Q impairments of the transmitter, i.e., "residual" in the sense that they are residual impairments after the partial correction implemented by the pre-compensation transform of 4420.

In some embodiments, the receiver may adhere to a direct conversion architecture and the demodulator is an analog I/Q demodulator, in which case the sampled complex signal may be captured by digitizing the complex analog output of the analog I/Q demodulator. In other embodiments, the receiver may comply with a different kind of architecture, for example, a super-heterodyne architecture. Thus, the receiver may generate a real analog signal (e.g., a real intermediate frequency signal) representative of the received transmit signal. The real analog signal may be digitized to obtain a sampled real signal. The sampled complex signals may then be generated by calculations, for example, by digitally mixing the sampled real signals with the quadrature pair of digital sinusoids to obtain the I and Q components of the sampled complex signals, respectively.

At 4440, the processing agent may update the current estimate of the transmitter's I/Q impairments based on the path-compensated I/Q impairments, e.g., by combining the path-compensated I/Q impairments with corresponding impairments of the current estimate.

In some embodiments, method 4400 may include repeating the set of operations to determine an estimate of convergence (stable estimate) of the I/Q impairments of the transmitter at frequency f. (the estimate of this convergence comprises a measure of the I/Q impairment of the transmitter at frequency f). The set of operations may be repeated until the quality measurement based on the path compensated I/Q impairments is greater than the threshold. The converged estimate may be used to at least partially compensate for I/Q impairments of the transmitter at frequency f, e.g., as described in various different manners herein.

In some embodiments, the above-described act of repeating the set of operations may itself be performed multiple times to determine a convergence estimate at multiple different values for frequency f. The above-described act of repeating this set of operations to determine a convergence estimate at frequency f is referred to herein as a "measure of I/Q impairment of the transmitter at frequency f". Thus, multiple measurements of transmitter I/Q impairments can be made, covering multiple frequency values.

In some embodiments, the plurality of frequency values are symmetric about zero. Further, measurements of the I/Q impairments of the transmitter may be made such that frequency values are accessed in a symbol-alternating manner and absolute values are not reduced, e.g., as described in various different manners herein.

In some embodiments, the local oscillator of the transmitter and the local oscillator of the receiver are phase locked to the same frequency reference (implying frequency locking).

In some embodiments, the current estimate of the signal path is based on DC scaling and DC rotation of the signal path, at least for the first transmitter I/Q impairment measurement.

In some embodiments, the DC scaling and DC rotation may be determined by: providing a zero vector signal to a transmitter; providing a non-zero DC vector signal to a transmitter; and calculating a DC scaling and DC rotation based on a first DC vector response and a second DC vector response, wherein the first DC vector response is measured at the receiver in response to a zero vector signal, wherein the second DC vector response is measured at the receiver in response to a non-zero DC vector signal. For more information on how to compute the DC scaling and DC rotation, see the "compute mapping between RX and TX" section.

In some embodiments, the pre-compensation transform has the form of a 2x2 matrix, wherein at least a first diagonal element of the matrix is computed from a current estimate of the I/Q impairments of the transmitter at frequencies f and-f, and wherein at least a first off-diagonal element of the matrix is computed from a current estimate of the I/Q impairments of the transmitter at frequencies f and-f.

In some embodiments, the current estimate of the signal path comprises a measured amplitude of the sampled complex signal at frequency f. The amplitude can be measured as described in the section "precision measurement technique".

In some embodiments, the current estimate of the signal path further comprises a measured rotation of the sampled complex signal at frequency f.

Determination of transmitter I/Q impairments with offset LO

In one set of embodiments, a method 4500 for determining I/Q impairments of a transmitter may involve the acts illustrated in fig. 45. (furthermore, method 4500 may include any subset of the features described in the iterative technique for measuring Tx impairment section). Method 4500 can be performed by a processing agent (e.g., a processing agent as described in various different manners above).

At 4510, the processing agent may configure a Local Oscillator (LO) of the transmitter and a Local Oscillator (LO) of the receiver to be phase-locked to a common reference and such that a frequency of the LO of the receiver minus a frequency of the LO of the transmitter equals a non-zero amount, Δ LO. The quantity Δ LO may be positive or negative.

At 4520, the processing agent may perform a set of operations So. This set So may include operations 4525 through 4550, as shown in fig. 45.

At 4525, the processing agent may direct the complex exponential tones at frequency f to be provided to the transmitter. (frequency f can be interpreted as a displacement from the LO frequency of the transmitter). The complex exponential tones may be provided in digital form, for example, as described in various different ways above. In some embodiments, the transmitter may be coupled to (or include) a programmable hardware element configured to generate complex exponential tones. To facilitate this generation, the PHE may receive a sampling clock used by the DAC cell of the transmitter.

At 4530, the processing agent may provide a pre-compensation transformation to pre-compensation circuitry of the transmitter. The pre-compensation circuit may be configured to apply a pre-compensation transformation to the complex exponential tones to obtain an adjusted complex signal. (e.g., the pre-compensation circuit may be the digital circuit 510 of FIG. 5 or the compensation unit 3702 of FIG. 37). The pre-compensation transform may be configured to pre-compensate a current estimate of the I/Q impairments of the transmitter. The transmitter may be configured to transmit the transmit signal (or transmit a transmit signal derived from the adjusted complex signal) based on the adjusted complex signal, e.g., as described in various different manners above. The receiver may be configured to receive the transmitted signal and capture a sampled complex signal representative of the received transmitted signal, e.g., as described in various different manners above. The transmitter may transmit a transmission signal onto a transmission channel (e.g., a cable), and the receiver may receive the transmission signal from the channel.

At 4535, the processing agent may frequency shift the sampled complex signal by an amount Δ LO to obtain a frequency shifted signal, for example, by multiplying the sampled complex signal by a discrete-time complex exponential signal operating at a frequency Δ LO.

At 4540, the processing agent may calculate the original I/Q impairment at frequency f based on the frequency shifted signal. The raw I/Q impairments may include a gain imbalance g_R(f) And phase skew

(the process of calculating the I/Q impairments from the complex signal is discussed above).

At 4545, the processing agent may remove the current estimate of the signal path from the original I/Q impairment at frequency f to obtain a path-compensated I/Q impairment at frequency f (e.g., as described above in the "transform I/Q impairment by linear system" section, or in the "alter gain imbalance and phase skew by linear system" section). The signal path may include a path from an I/O modulator of the transmitter to a demodulator of the receiver. The path compensated I/Q impairments at frequency f may represent an estimate of the residual I/Q impairments of the transmitter at frequency f.

In some embodiments, the receiver may adhere to a direct conversion architecture, and the demodulator may be an analog I/Q demodulator, in which case the sampled complex signal may be captured by digitizing the complex analog output of the analog I/Q demodulator. In other embodiments, the receiver may comply with a different kind of architecture, for example, a super-heterodyne architecture. Thus, the receiver may generate a real analog signal (e.g., a real intermediate frequency signal) representative of the received transmit signal. The real analog signal may be digitized to obtain a sampled real signal. The sampled complex signals may then be generated by calculations, for example, by digitally mixing the sampled real signals with the quadrature pair of digital sinusoids to obtain the I and Q components of the sampled complex signals, respectively.

At 4550, the processing agent may update the estimate of the I/Q impairments of the transmitter at frequency f based on the path compensated I/Q impairments at frequency f.

In some embodiments, method 4500 may include repeating operational group So to determine a convergence estimate (or stable estimate) of the I/Q impairments of the transmitter at frequency f. (this convergence estimate can be interpreted as a measure of the I/Q impairment of the transmitter at frequency f). For example, the set of operations may be repeated until the quality measure based on the path-compensated I/Q impairments is greater than a threshold. (the quality measure may be the negative of the image rejection at frequency f). The convergence estimate can be used to at least partially compensate for the I/Q impairments of the transmitter at frequency f. The above-described frequency shifting action may be performed using a frequency shifted signal that is phase continuous between successive repetitions of the operational group.

In some embodiments, method 4500 may further include performing the repeating operation (of operational group So) multiple times to determine a converged estimate at multiple different frequency values f (e.g., values covering a desired transmission (or communication) band).

In some embodiments, operational set So may further include removing the measured I/Q impairments of the receiver at frequency f- Δ LO from the sampled complex signal prior to the frequency shifting operation. The measured I/Q impairments of the receiver at frequency f- Δ LO can be determined by using a constant 2x2 matrix M ═ M (M_ij) Multiplying and samplingThe sampled complex signal is removed, for example, according to the relationship:

where I (n) and Q (n) represent the in-phase and quadrature components, respectively, of the sampled complex signal. In one embodiment, the matrix M may have a special form

And constant m₂₁And m₂₂The gain imbalance g of the receiver at the frequency f- Δ LO can be based on the following expression_RX(f- Δ LO) and phase skew of receiver

Angle determination:

see the section entitled "performing conventional impairment compensation at a single frequency".

In an alternative embodiment, the constant m₂₁And m₂₂It can be determined based on the measured I/Q impairments of the receiver at the frequency f- Δ LO and its negative- (f- Δ LO), as described in the "calculate true single point vector calibration constant" section, and in particular in equations (1.81) and (1.82).

In some embodiments, the I/Q impairments of the receiver may be measured as part of method 4500, i.e., based on the sampled complex signal prior to frequency shifting. For example, operational group So may include measuring the I/Q impairments of the receiver at frequency f- Δ LO based on the sampled complex signal. One technique for performing such measurements involves: (a) calculating sampled complex signalsIs a discrete-time Fourier transform value C of the I component of (1) at a frequency f- Δ LO_I(ii) a (b) Calculating a discrete-time Fourier transform C of the Q component of the sampled complex signal at a frequency f- Δ LO_Q(ii) a (c) Based on the value C_IAnd C_QCalculates the receiver gain imbalance at frequency f- Δ LO; and (d) based on the value C_IAnd C_QCalculates the receiver phase skew at the frequency f- Δ LO. For more information on embodiments of this technique, see the section "precision measurement technique".

In some embodiments, method 4500 may also include calculating value C_IAnd C_QA time domain window was previously applied to the sampled complex signal. The time domain window may be a rectangular (uniform) window or any of various standard non-uniform windows. For more information about the use of rectangular windows, see the "rectangular window optimization" section.

In some embodiments, the measurement of receiver I/Q impairments and the estimation of transmitter I/Q impairments described above may be performed at least partially in parallel. For example, in one embodiment, a programmable hardware element (or possibly a multi-core processor) may be configured to perform measurements of receiver I/Q impairments in parallel with frequency shifting operations on the sampled complex signal.

In some embodiments, the set of operations may include measuring the I/Q impairments of the receiver at the frequency f- Δ LO as described above, computing a 2x2 matrix of correction constants based on the measured I/Q impairments as described above, and then applying a 2x2 matrix to the sampled complex signal prior to the frequency shifting operation. In other words, the frequency shift operation is applied to the modified complex signal (I '(n), Q' (n)) resulting from the application of the 2x2 matrix.

In some embodiments, it is assumed that the I/Q impairments of the receiver have been measured over the band of interest before method 4500 is performed. Thus, the 2x2 matrix of the digital filter may be designed based on the I/Q impairments of the receiver, as described above in connection with fig. 2A, 2B, and 3 and in the "wideband I/Q impairment equalization" and "filter design" sections. The set of operations may include an operation of applying a 2x2 matrix of digital filters to the sampled complex signal prior to the frequency shifting operation. The resulting filtered complex signal may then be subjected to a frequency shift.

In some embodiments, the pre-compensation transform has the form of a 2x2 matrix, and the matrix has properties that at least one diagonal element of the matrix is computed based on a current estimate of the I/Q impairments of the transmitter at frequency f and a current estimate of the I/Q impairments of the transmitter at frequency-f, and properties that at least one off-diagonal element of the matrix is computed based on a current estimate of the I/Q impairments of the transmitter at frequency f and a current estimate of the I/Q impairments of the transmitter at frequency-f. In some embodiments, each of the four matrix elements is calculated in this manner.

As described above, the processing agent may remove the current estimate of the signal path from the original I/Q impairments at frequency f to obtain path-compensated I/Q impairments at frequency f. In some embodiments, the current estimate of the signal path may include a measurement and amplitude of the frequency shifted signal at frequency f. In one embodiment, the current estimate of the signal path may also include a measured rotation of the frequency shifted signal at frequency f.

In some embodiments, the current estimate of the signal path may be based on DC scaling and DC rotation of the signal path. This estimate may be used for at least the first execution of the set of operations.

In some embodiments, method 4500 may further include determining DC scaling and DC rotation by: providing a zero vector signal to a transmitter; providing a non-zero DC vector signal to a transmitter; a DC scaling and DC rotation is calculated based on a first DC vector response and a second DC vector response, wherein the first DC vector response is measured at the receiver in response to a zero vector signal, wherein the second DC vector response is measured at the receiver in response to a non-zero DC vector signal. For more information on the determination of DC scaling and DC rotation, see the "calculate mapping between Rx and Tx" section and the "method for calculating DC mapping and DC rotation for a single path" section.

Determining I/Q impairments of a receiver

In one set of embodiments, the method 4600 for determining the I/Q impairments of the receiver may include the operations shown in fig. 46. Method 4600 may be performed by the processing agent described above.

At 4610, the processing agent may direct the input signal to be provided to the receiver. In other words, the processing agent may issue a command to cause the input signal to be provided to (or generated by) the receiver. The input signal may include isolated tones at the displacement frequency f and null intervals (i.e., intervals containing only noise) around the displacement frequency-f. (saying that a tone is "isolated" at a given frequency means that a tone is the only source of energy other than noise at nearby frequencies of the given frequency (e.g., within a frequency interval centered at the given frequency). The receiver may be configured to demodulate the input signal to obtain a sampled complex signal, e.g., as described in various different manners above. The displacement frequencies f and-f may be displacements relative to the local oscillator frequency of the receiver.

At 4615, the processing agent may calculate an I/Q impairment for the receiver at frequency f based on the sampled complex signal.

At 4620, the processing agent may repeat the acts of directing (4610) and calculating (4615) for frequency values f spanning a prescribed frequency band (e.g., the input band or the standardized communication band of the currently selected receiver).

At 4625, the processing agent may store the receiver I/Q impairments for each value of frequency f in memory.

In some embodiments, the input signal is provided by a transmitter having a local oscillator frequency that is offset from a local oscillator frequency of the receiver by a non-zero value, e.g., as described in various different manners above.

In some embodiments, the input signal is provided by a calibrated tone synthesizer. A calibration tone synthesizer is a system configured to create quality tones for calibrating other systems. In some embodiments, the term "mass tone" implies stability in amplitude, frequency, temperature, or time. In one embodiment, the receiver includes a calibration tone synthesizer that facilitates self-calibration.

In some embodiments, the act of calculating the I/Q impairments of the receiver at frequency f comprises: calculating a discrete-time Fourier transform value C at frequency f of the I component of the sampled complex signal_I(ii) a Calculating a discrete-time Fourier transform C of the Q component of the sampled complex signal at frequency f_Q(ii) a Based on the value C_IAnd C_QCalculates the gain imbalance of the receiver at frequency f; and based on the value C_IAnd C_QCalculates the phase skew of the receiver at frequency f.

In some embodiments, method 4600 may also include a value C_IAnd C_QThe time domain window is applied to the sampled complex signal prior to the computation of (a) e.g. as described below in the section "precision measurement technique".

Measuring I/Q impairments associated with complex signals

In one set of embodiments, method 4700 may include the operations shown in FIG. 47. Method 4700 can be used to measure I/Q impairments associated with a sampled complex signal produced by a receiver. Method 4600 may be performed by a processing agent (e.g., a computer system executing under the control of program instructions).

At 4710, the processing agent may direct the device to stimulate the receiver with a stimulation signal having an isolated tone at the displacement frequency f and an inactive interval at the displacement frequency-f. The displacement frequencies f and-f may be interpreted as displacements with respect to the local oscillator frequency of the receiver. The sampled complex signal may be a baseband signal produced by the receiver in response to a stimulation action with the stimulation signal.

At 4715, the processing agent may calculate a discrete-time Fourier transform value C at frequency f for the I component of the sampled complex signal_I。

At 4720, the processing agent may calculate a discrete-time Fourier transform value C at frequency f for the Q component of the sampled complex signal_Q。

At 4725, the processing agent may be based on the value C_IAnd C_QIs calculated as a sampling at frequency fA gain imbalance g of the complex signal is obtained, wherein the gain imbalance g comprises a gain imbalance of the receiver.

At 4730, the processing agent may be based on the value C_IAnd C_QPhase calculation of (2) phase skew of the sampled complex signal at frequency f

Wherein the phase is skewed

Including the phase skew of the receiver.

In some embodiments, the processing agent may be at the value C_IAnd C_QA time domain window is applied to the sampled complex signal prior to the computation of (a).

In some embodiments, the device that provides the input signal is a calibration tone generator.

In some embodiments, the device is a transmitter whose local oscillator frequency is (deliberately) offset from the local oscillator frequency of the receiver by a non-zero amount. In one such embodiment, the sampled complex signal is frequency shifted to remove the difference between the local oscillator frequencies, in which case the gain imbalance g and the phase skew

May depend in part on the I/Q impairments of the transmitter. In particular, gain imbalance g and phase skew

The combined effect of the I/Q impairments of the transmitter, the distortion introduced by the signal path (between the I/Q modulator of the transmitter and the demodulator of the receiver), and the I/Q impairments of the receiver can be represented. In another such embodiment, the sampled complex signal is the original signal from a demodulator that has not been subjected to the frequency shift described above, and therefore, the gain imbalance g and the phase skew

It can be interpreted as including only the impairments introduced by the receiver.

In some embodiments, method 4700 can also include calculating value C_IAnd calculate the value C_QA time domain window is previously applied to the sampled complex signal, e.g., as described below.

In some embodiments, the receiver is a vector signal analyzer.

In some embodiments, one or more of operations 4715-4730 may be performed by programmable hardware elements.

In some embodiments, one or more of operations 4715-4730 may be performed in dedicated digital circuitry.

In some embodiments, one or more of operations 4715-4730 may be performed by a processor in response to execution of program instructions.

Offset LO calibration techniques

The offset Local Oscillator (LO) approach allows simultaneous measurement of I/Q impairments and carrier leakage measurements at the Receiver (RX) and Transmitter (TX). This approach uses independently tunable LOs for the transmitter and receiver, e.g., as shown in fig. 48. In some embodiments, the step size of the transmitter LO and/or the step size of the receiver LO may be fractional or integer in nature. In some embodiments, the step size of the transmitter and/or the step size of the receiver LO should be a small percentage of the total instantaneous bandwidth.

The transmitter includes an I/Q modulator 4810 and a front end 4815. The complex exponential tones at the non-zero shifted frequency f are provided to the I/Q modulator 4810. The I/Q modulator 4810 modulates a carrier signal (also referred to as a "local oscillator signal") with tones to obtain a modulated signal. The bearer signal is provided by transmitter LO 4805. The modulated signal is transmitted by transmitter front end 4815 onto a transmission medium (e.g., cable 4820).

The receiver front end 4830 receives the transmitted signal and conditions the received signal to obtain a conditioned signal. I/Q demodulator 4835 demodulates the conditioned signal using a carrier signal provided from receiver LO 4840 to obtain a demodulated signal having components denoted RX I and RX Q.

As shown in fig. 49, shifting the RX and TX carriers from each other will cause the tones, receiver images of the tones, transmitter images of the tones, carrier leakage of the transmitter, and carrier leakage of the receiver to appear at different frequencies. The illustrated spectrum is based on the demodulated signal at the receiver. The transmitter produces tones at 31 MHz. The spectrum includes two different carrier leakages, one due to the LO leakage of the transmitter and the other due to the LO leakage of the receiver. The spectrum also includes two different primary images of tones, one due to the I/Q impairments of the transmitter and the other due to the I/Q impairments of the receiver. Furthermore, the spectrum includes a receiver image of the transmitter, and a receiver image of the carrier leakage of the transmitter, both due to I/Q impairments of the receiver. In this example, the receiver carrier is set 6MHz lower than the transmitter carrier. This causes tones, transmitter images and transmitter leakage to appear at a frequency 6MHz higher at the receiver than at the transmitter. Thus, in addition to receiver Leakage, each of the three signals generated by the transmitter (tone, TX Image, and TX Leakage) has a corresponding Image after the I/Q demodulator, as a result of the impairments of the I/Q demodulator.

By knowing the frequency offset between the transmit and receive LOs and the frequency of the tone generated at the transmitter before the modulator, the exact spectral position of all impairment artifacts can be completely determined. If we order

FreqOffset-txcarrier frequency-rxcarrier frequency, (1.75) then the frequency location (as seen by the receiver) of the spectral feature in the received spectrum is:

RxTonc＝TxTonc+FrcqOffset (1.76)

TxLeakage＝FreqOffset (1.77)

TxImage＝FreqOffset-TxTone (1.78)

RxImage＝-TxTone-FreqOffset (1.79)

RxLeakage＝0Hz (1.80)

RxImageofTxImage＝TxTone-FreqOffset (1.81)

＝RxTonc-2FreqOffsct

RxImageOfTxLeakage＝-FreqOffset. (1.82)

measuring the I/Q impairments and carrier leakage of the receiver is performed in the same manner as was done in the "precision measurement technique" section. However, the impairment of the measurement transmitter is generally more involved, as there are a number of things to consider. Measuring transmitter impairments may involve removing receiver impairments. Fig. 50 shows the received spectrum after the I/Q impairments of the receiver have been removed. After that removal, the spectrum may be shifted by-FreqOffset, as shown in FIG. 51. Now, the frequency location of the "tone" in the shifted spectrum is the same as the frequency f of the tone originally produced at the transmitter. In addition, the transmitter leakage (TXLeakage) and the transmitter mirror image (TXImage) are at the correct frequency locations (f and zero, respectively) to use the algorithm found in the "precision measurement technique" section once the rotation is calculated and removed. (the rotation may be calculated using the method described in the "calculate mapping between RX and TX" section). Such an algorithm will give an estimate of the I/Q impairments of the transmitter and the LO leakage vector of the transmitter. This method for measuring the I/Q impairments of a transmitter works as long as the signal path (including the front-end of the transmitter and the front-end of the receiver) has an even magnitude response and an odd phase response. In fact, this is not the case and even small perturbations in the magnitude or phase can cause serious problems to the measurement. Iterative algorithms eliminate this problem. The iteration of the iterative algorithm involves performing a pre-correction based on the current estimate of the transmitter impairments (e.g., using a "calculate true single point vector alignment constant" approach) and removing the best available estimate of the signal path from the impairments measured at the receiver (using a "modify gain imbalance and phase skew by linear system" approach). The iterative algorithm allows the transmitter impairments to be measured even when there is error in the initial estimates of those impairments.

By doing everything in the above method except for the receiver impairments, the impairments of the measuring transmitter can be further optimized. Shown in fig. 52 is the frequency shifted spectrum without first removing the receiver impairments. By leaving these impairments in the spectrum, the measured impairments at frequency f (i.e., 31MHz in this example) are not exactly equal to the I/Q impairments of the transmitter, since the receiver impairments distort the measurements. However, the same iterative algorithm used to remove distortion of the RF front end can also remove distortion due to receiver impairments. While ideally it is better to remove the impairments of the receiver, in practice this takes extra time during calibration.

Constraining

While this approach is highly desirable because multiple measurements can be made in parallel, it does come with constraints. The main constraint is that it cannot be used to measure amplitude because it measures a combination of receiver amplitude and transmitter amplitude without any way of separating the two without other measurements. However, if either the receiver amplitude or the transmitter amplitude is known, the two may be separated. In most cases, the amplitude ratio I/Q impairments vary slowly with respect to frequency. Thus, a separate measurement process can be used to measure either the receiver amplitude or the transmitter amplitude with a coarser frequency step than the step used to determine the I/Q impairments over the instantaneous bandwidth. Therefore, the total measurement time, including the amplitude, is still much faster than the alternative (alternative).

Another small problem with the offset LO approach is that it places constraints on the calibration frequency plan. Depending on the value of LO offset Δ LO, it is possible to get a corrupt measurement at each measurement offset. As shown in fig. 49, there are seven locations in the frequency spectrum where energy appears in response to the transmission of a tone. In order to correctly measure the total impairments to the transmitter and receiver, all of the seven signals must remain orthogonal, i.e., no two signals may occur at the same frequency location. For example, if the receiver's LO is set to 2.400GHz and the transmitter's LO is set to 2.39GHz, measurement corruption will occur when the transmitted baseband tone is 4MHz, as this will place the tone exactly at RX Leakage (RX Leakage); this occurs at-4 MHz, since this will place the TX mirror at RX leakage; or at 8MHz, since this will place the RX Image (RX Image) at TX leakage. To avoid these problems, the transmitted tone (TxTone) cannot be located at the following frequencies:

{N*FreqOffset：N＝-3，-2，-1，0，1，2，3}.

＊ in ＊ addition ＊, ＊ there ＊ is ＊ a ＊ bandwidth ＊ limitation ＊, ＊ the ＊ total ＊ measurable ＊ bandwidth ＊ is ＊ (＊ TotalBW ＊ - ＊ LO ＊ _ ＊ StepSize ＊) ＊, ＊ and ＊ the ＊ total ＊ symmetric ＊ measurable ＊ bandwidth ＊ is ＊ (＊ TotalBW ＊ - ＊ 2 ＊, ＊ LO ＊ _ ＊ StepSize ＊) ＊, ＊ which ＊ is ＊ why ＊ the ＊ LO ＊ step ＊ must ＊ be ＊ a ＊ fraction ＊ (＊ preferably ＊ a ＊ small ＊ fraction ＊) ＊ of ＊ the ＊ total ＊ instantaneous ＊ bandwidth ＊. ＊

Computing true single point vector calibration constants

Considering that with knowledge of the I/Q impairments of f and-f, this section shows how to calculate a constant for a true single-point calibration that would ideally be pre-corrected at a single location (i.e., ideally pre-compensate for the I/Q impairments of a single frequency f), as indicated in fig. 53A and 53B. The single point vector calibration correction 5310 precedes the two point vector destruction model 5320. Thus, the complex exponential tones at frequency f, provided as input to the single point vector alignment correction, are predistorted to produce a complex signal cos (2 π ft) + j Γ sin (2 π ft + θ)

The pre-distorted signal is further distorted by the destruction model 5320 resulting in a corrected output signal equal to the original complex exponential pitch.

From the "corrupt I/Q impairments" part, we know how to derive a 2x2 frequency response matrix H representing the I/Q impairments of the system. In this section, we find A (f), E_B(f) C (f) and D (f) are determined by the "two-point I/Q impairments" (i.e., by the I/Q impairments at f and the I/Q impairments at-f). Further, according to the "Add constraint" part (i.e., case 6, where A and C are constants, and E is_BAnd E_Dis zero) the structure of the single point correction is known using this information the true single point calibration coefficients α and β can be determined.

Given A (f), E_B(f) C (f) and E_D(f) Thesevalues for determining the values α and β given the two-point I/Q impairments, i.e. the gain imbalance value g₁(f) G (f) and g₂(f) G (-f) and phase skew value

And is

A(f)、E_B(f) C (f) and E_D(f) the values of α and β can be determined from Γ and θ as shown in the following expressions:

α＝Γsin(θ) (1.75)

β＝Γcos(θ). (1.76)

using the vector diagram of fig. 54, the summation along the x-axis yields equation (1.77), and the summation along the y-axis yields equation (1.78):

CΓsin(θ)-E_DΓcos(θ)＝-A (1.77)

CΓcos(θ)+E_DΓsin(θ)＝1-E_B(1.78)

we rely on the fact that:

HT{sin(t)}＝-cos(t)，

HT{cos(t)}＝sin(t)，

where HT denotes the Hilbert transform. Equations (1.77) and (1.78) imply:

solving for Γ and θ will tell us that the new gain and phase of the waveform need to exactly eliminate the effects of I/Q corruptions when α and β do not need to be solved for.

it should be noted that the correction coefficients α and β given by (1.81) and (1.82) are generally different from α and β in conventional single-point compensation as used in the "perform conventional impairment compensation at a single frequency" section (thus, conventional single-point compensation values will generally give less than ideal compensation when used as pre-compensation, i.e., when used in fig. 53A and 53B.) however, there are certain situations where the two coefficient pairs conflict.

E_B(f)＝0

E_D(f)＝0.

Thus, equations (1.81) and (1.82) will be specific to:

this is the same value as used for conventional single point compensation.

Iterative technique for measuring TX impairment

Referring now to fig. 55A, the problem of measuring the amplitude response of receive filter 5525 and the I/Q impairments of the receiver is simplified (relative to the corresponding problem of the transmitter), since the I/Q impairments originating from I/Q demodulator 5530 occur after the distortion effects of receive filter 5525. For example, if a pure tone is the input signal to the receive path, the distortion of the receive filter will only alter the magnitude and phase of a single tone. This modified pure tone will then be distorted by the I/Q demodulator, resulting in I/Q impairments. When calibrating the receiver, we can first remove the I/Q impairments of the receiver, leaving only the amplitude and phase response effects of the filter, and then, if desired, correct the amplitude and phase distortions of the filter in additional steps.

However, this is not the case for the transmitter. Shown in fig. 55B is a signal path for a transmitter and receiver combination. The transmitter includes an I/Q modulator 5510 and a transmission filter 5515. In some embodiments, the transmit and receive LOs are shared. When the transmitter creates a single tone, the I/Q modulator 5510 introduces transmit I/Q impairments. These impairments then traverse through the transmit signal path, the cable, and the receive signal path before finally reaching the I/Q demodulator. This path between the I/Q modulator output and the I/Q demodulator input corrupts the transmitted I/Q impairment measurements taken at the receiver. In addition, the I/Q impairments of the demodulator further corrupt the transmitter I/Q impairment measurements taken at the receiver. In an alternative embodiment, the receiver may be based on an alternative RF architecture (i.e., different from the direct conversion architecture) such that the I/Q impairments of the receiver are very small, i.e., small enough to be negligible.

Shown in fig. 55C is an example of how the non-flat amplitude response in the signal path corrupts the I/Q impairments seen at the receiver. What the I/Q modulator produces is the actual I/Q impairments. The transmit signal path then corrupts them, followed by a phase rotation due to the electrical delay of the cable, followed by another corruption by the receive signal path. In addition to amplitude, the phase response (not shown in fig. 55C) also causes different but related problems.

For initial observation, it would appear to be an ideal solution to first characterize the magnitude and phase of the signal path between the I/Q modulator and the I/Q demodulator. Then, by using the calculations in the "alter gain imbalance and phase skew by filter" section, the effect of the signal path can be removed from the I/Q impairments measured by the receiver. However, this is not a reasonable task given the performance requirements for impairment suppression. To achieve better image rejection than-80 dB, the phase skew needs to be less than 0.01 degrees. Even at lower RF frequencies, this means that the absolute phase must be stable and measurable, better than picosecond accuracy. Furthermore, the I/Q impairments alter the magnitude and phase of the signal from the modulator, as described in the "magnitude and phase corruption from I/Q impairments" section and expressed in equation (4.9) of fig. 58A. Thus, to determine the magnitude and phase response of the signal path, the I/Q impairments of the transmitter would need to be known, and the I/Q impairments of the transmitter we are trying to measure.

A better way to determine the exact I/Q impairments through the signal path is to iterate the solution. Given a rough estimate of the amplitude and phase of the signal path and an estimate of the I/Q impairments, the exact I/Q impairments can be determined with sufficient iterations. (iterations may be performed using a shared LO or an offset LO as described below. The total number of iterations will depend to a large extent on the initial estimate and the performance criterion. Listed below is a procedure for determining transmitter impairments for the shared LO and the offset LO. This process measures all of the calibration frequency locations within the instantaneous bandwidth and only iterates on these measurements once all have been completed for a given instantaneous bandwidth. Given in the section on optimization is a modified procedure that achieves the same result but generally requires fewer iterations.

Iterative method steps (overview):

1. RX and TX LO are tuned.

2. The RX impairment is measured.

3. The mapping between RX and TX is measured.

4. The estimated impairment correction is applied at TX.

5. Tones are generated at TX and measured at RX.

6. RX impairments were removed from # 5.

7. The signal path estimate is removed (e.g., the mapping from #3 is applied).

8. The results from all iterations of #7 are combined to produce an updated impairment estimate.

9. If the performance metric is acceptable, go to # 10; otherwise go to #4 for iteration.

10. Steps #1 to #9 are repeated for each LO frequency.

Iterative method step (description)

1. The transmit and receive LOs are tuned to a first desired LO frequency. If a shared LO is used (either with the same LO or with two separate LOs locked together), the LO will be at the same frequency. In the case of offsetting LOs, the LOs are offset from each other by some known exact amount. In either case, it is ensured that all LOs are phase locked. For more information on selecting the working offset, see the "constraints" subsection of the "offset LO method calibration method" section. The window used in the measurement is also remembered. If no window is used, as is done in the "rectangular window optimization" section, it is ensured that the offset LO values are limited to the given frequency in that section.

(optional when using the offset LO method) for each in-band offset frequency of the transmitter to be measured, the gain imbalance and phase skew of the receiver are measured. This can be achieved by using the measurement methods specified in the section "precision measurement techniques". Since the use of an offset LO makes the image appear to be at different frequencies for reception and transmission, removing the reception impairments is not as critical as in the case of a shared LO. In all known datasets, this iterative approach converges when the LO is shifted, without knowing the receive impairments. However, the receive impairments do cause some disruption to the transmit impairments. Therefore, if they are too severe, they cause this iterative method to diverge, rather than converge, even when an offset LO is used.

3. The transmitter output is connected to the receiver input.

(for the offset LO method only) frequency shifting the receiver's spectrum by an amount equal to the LO offset. For example, if the transmitter's LO is at 2.400GHz and the receiver's LO is at 2.404GHz, the spectrum is shifted by positive 4 MHz. The frequency shift must be phase locked to the LO or the rotation estimate made in step 5 will not remain fixed.

5. The rotational and scaling mapping between reception and transmission is determined by using the algorithm in the "calculate mapping between RX and TX" part. Since leakage is sensitive to in-band power, tones are applied somewhere in the instantaneous bandwidth for better results. This mapping will be constant and may be repeated once the LO is set. Thus, in at least some embodiments, the LO needs to be phase-locked. When the offset LO method is used, the exact LO offset is known.

6. If this is the first iteration of #6, no correction is applied at the transmitter (pass-through) and the process proceeds to # 7. Otherwise, a correction filter is applied at the transmitter based on the measurement in # 10.

7. For each desired in-band measurement position, a complex exponential tone is applied at the transmitter and the original gain imbalance and phase skew are determined at each frequency offset by using the calculation method in the "precision measurement technique" section.

(optional when using the offset LO method) for each measured value in #7, the gain imbalance and phase skew of the receiver are mathematically removed. This can be done by the calculations described in the section "remove receiver impairments from measured output impairments". This places the transmitter's measurements before the demodulator. Instead of step #8, another approach is to apply a correction filter at the receiver (according to the "wideband I/Q impairment equalization" part) and pass the captured waveform through the correction before step # 7. This method is inaccurate because, due to the limited filter valves, the correction filter may not be as accurate as the measurement.

9. For each calculated value in #8, the approximately known rotation, scaling, magnitude and phase are removed by using the transformation described in "altering gain imbalance and phase skew by linear system". The rotation and scaling are determined in step # 5. After the first iteration, an estimate of the magnitude may also be determined. This approximately sets the measurement at the output of the modulator. We will not need this iterative method if the measurement is exactly at the output of the modulator. This iterative approach is needed because we do not know the rotation, scaling, magnitude and phase of the path between the output of the modulator and the input of the demodulator within the required accuracy.

10. The results from all iterations of #9 are combined by finding the product of all gain imbalances (when using linear scaling) and the sum of all phase skews based on each frequency offset and LO combination. For example, if measurements are performed at-15 MHz, -5MHz, and 15MHz, only measurements taken at-15 MHz are combined from other iterations. When moving to another LO in #13, this combination restarts so that measurements at-15 MHz and LO-2.4 GHz are not combined with measurements at-15 MHz and LO-2.6 GHz.

11. The image rejection is calculated from the gain imbalance and phase skew for each in-band frequency location measured in #9 and calculated by equation 4.15. The image rejection of the whole band in the worse case is determined by finding the minimum of all image rejection calculations.

12. If the image rejection from #11 meets the required performance metrics, the final gain imbalance and phase skew measurements are those calculated in step #10 and no more iterations are required for this LO frequency, otherwise the solution is iterated by going to # 6.

13. Steps #1 to #11 are repeated for each LO frequency.

In one set of embodiments, the I/Q impairments of the transmitter can be estimated according to the method given in appendix a.

Results

Fig. 56A and 56B illustrate the improvement (i.e., convergence rate) per iteration according to one embodiment of an iterative method. In at least some embodiments, the iterative method has a convergence interval of [ -3dB, 3dB ] for magnitude and [ -30 degrees, 30 degrees ] for phase. In these embodiments, the measurement sequence will diverge if the magnitude or phase has an error outside of these intervals. Fig. 56A and 56B show convergence for each iteration of magnitude and phase errors.

Optimization

This section describes how the iterative process described above can be optimized to use less total acquisition and therefore less calibration time. The problems with the above iterative process are: in addition to computing new filters between iterations, it also makes multiple acquisitions of a single wideband measurement within the instantaneous bandwidth. However, by using single point vector calibration to iterate through the individual points to determine their actual impairment values, the total number of acquisitions can be greatly reduced. Then, by stepping through the belt, the previous measurement location of the impairment becomes an estimate of the next measurement location. This works well when the impairment does not change very fast across the band, thus providing a good estimate of the actual values in the vicinity.

By adding such optimizations, it is advisable to create a frequency plan as follows:

[Δf/2，-Δf/2，2*Δf/2，-2*Δf/2，3*Δf/2，-3*Δf/2，...，N*Δf/2，-N*Δf/2]

for integer N, where Δ f is the spacing of the frequency measurement locations in the instantaneous bandwidth. This yields the maximum benefit of the optimization since it produces the best estimate of the new point to measure by using its neighbors. Since this method uses a true single point calibration of the transmitter, it requires information about the impairments at the tone location and its mirror image. This is the reason for alternating between positive and negative frequencies. This alternate frequency plan is also assumed for the process numbered below.

Iterative method step of optimization (descriptive):

1. the transmit and receive LOs are tuned to a first desired LO frequency. If a shared LO is used (either with the same LO or with two separate LOs locked together), the LO will be at the same frequency. In the case of offsetting LOs, the LOs are offset from each other by some known exact amount. In either case, it is ensured that all LOs are phase locked. For more information on choosing the working offset, see the "constraints" subsection of the "offset LO method calibration method" section. The window used in the measurement is also remembered. If no window is used, as is done in the "rectangular window optimization" section, it is ensured that the offset LO value is limited to a given frequency in that section.

(optional when using the offset LO method) for each in-band offset frequency of the transmitter to be measured, the gain imbalance and phase skew of the receiver are measured. This can be achieved by using the measurement methods specified in the section "precision measurement techniques". Since the use of an offset LO makes the image appear to be at different frequencies for reception and transmission, removing the reception impairments is not as critical as in the case of a shared LO. In all known datasets, when the LO is an offset, this iterative approach converges without knowing the receive impairments. However, the receive impairments do cause some disruption to the transmit impairments. Therefore, if they are too severe, they cause this iterative method to diverge, rather than converge, even when an offset LO is used.

3. The transmitter output is connected to the receiver input.

Frequency shifting the spectrum of the receiver by an amount equal to the LO offset (for the offset LO method only). For example, if the transmitter's LO is at 2.400GHz and the receiver's LO is at 2.404GHz, the spectrum is shifted by positive 4 MHz. The frequency shift is phase locked to the LO. (otherwise the rotation estimate made in step 5 would not remain fixed.)

5. The rotational and scaling mapping between reception and transmission is determined by using the algorithm in "calculate mapping between RX and TX". Since leakage is sensitive to in-band power, tones are applied somewhere in the instantaneous bandwidth for better results. This mapping should remain constant and may be repeated once the LO is set. Thus, in at least some embodiments, the LO is phase-locked. When the offset LO method is used, the exact LO offset is known.

6. If this is the first iteration of #6 for this particular LO frequency, no correction is applied at the transmitter (pass only) and the process proceeds to # 7. Alternatively, if this is the first iteration of #6 for this particular LO frequency, then in step # 5a tone around 0Hz is applied and an initial estimate of impairment is generated for both tone and image using gain imbalance and phase skew information obtained simultaneously with the leakage (0Hz) information used in the algorithm. Otherwise, a single point correction is applied at the transmitter based on the following measurements (assuming the frequency plan provided above) with the calculations found in "calculate true single point vector calibration constants".

a. If this is the first iteration of #6, starting with #13, then the best pitch estimate is found in the variable $ Previous _ approximations 2. Otherwise, the current value of #10 is the best estimate.

b. The best image estimate is found in the variable $ Previous _ images 1.

7. For the current measurement position, the complex exponential tone is applied at the transmitter and the original gain imbalance and phase skew are determined for this particular in-band frequency offset by using the calculation method in the "precision measurement technique" section.

(optional when using the offset LO method) for each measured value in #7, the gain imbalance and phase skew of the receiver are mathematically removed. This can be done by the calculations described in the section "remove receiver impairments from measured output impairments". This sets the transmitter's measurements before the demodulator. Instead of step #8, another approach is to apply a correction filter at the receiver before step #7 by calculating the required correction (from the "wideband I/Q impairment equalization" part) and pass the captured waveform through the correction. This method is inaccurate because, due to the limited filter valves, the correction filter may not be as accurate as the measurement.

9. The approximately known rotation, scaling, magnitude and phase are removed from #8 by using the transformation described in "altering gain imbalance and phase skew by linear system". The rotation and scaling are determined in step # 5. A good estimate of the magnitude can be found by using its neighbor magnitudes in the same way as the good estimate of the impairment is found in step # 6. This approximately sets the measurement at the output of the modulator. If the measurement is exactly at the output of the modulator we will not need this iterative method. This iterative approach is needed because we do not know the rotation, scaling, magnitude and phase of the path between the output of the modulator and the input of the demodulator within the required accuracy.

10. The result from all iterations of #9 is combined with the variable $ Previous _ offsets 2 by finding the product of all gain imbalances (when using linear scaling) and the sum of all phase skews based on each frequency offset and LO combination. For example, if measurements are performed at-15 MHz, -5MHz, and 15MHz, only measurements taken at-15 MHz are combined from other iterations. When moving to another LO in #13, this combination restarts so that measurements at-15 MHz and LO 2.4GHz are not combined with measurements at-15 MHz and LO 2.6 GHz.

11. Image rejection is calculated by using the gain imbalance and phase skew information from #9 and equation 4.15.

12. If the image rejection from #11 meets the required performance metric, the final gain imbalance and phase skew measurements for the current measurement position are those calculated in step #10 and no more iterations are required for this LO frequency. Therefore, proceed to #13 and save the value in the variable $ Previous _ interferences 1 to $ Previous _ interferences 2 and store the current measurement in the variable $ Previous _ interferences 1. Otherwise, the solution is iterated by going to # 6.

13. Steps #6 to #12 are repeated for each in-band frequency measurement location.

14. Steps #1 to #13 are repeated for each LO frequency and all variables are cleared.

In some embodiments, the I/Q impairments of the transmitter may be estimated using an offset LO as described in appendix B.

In other embodiments, the I/Q impairments of the transmitter may be estimated using the shared LO as described in appendix C.

Magnitude and phase disruption from I/Q impairments

This section derives various equations useful for understanding how the I/Q impairments corrupt the magnitude and phase of the signal. We will see the form as

fig. 57 provides a notation for the amplitude of the tones and images fig. 58A and 58B include a derivation of equations (4.8) through (4.21) equation (4.11) specifies that the amplitude of the tones | α | is the result of an I/Q impairment note that if the gain imbalance is equal to one and the phase skew is equal to zero, the amplitude of the tones does not change, again, once the impairment is known, the image rejection can be calculated directly by using equation (4.15).

Precision measurement technique

This section describes methods for accurately and quickly measuring magnitude, phase, leakage, gain imbalance, and phase skew. In addition to measuring mass and speed, the method also facilitates FPGA implementations for even greater computational acceleration.

This method is a stimulus/response method where a known signal is injected at the input and then measured at the output. In particular, the stimulus is a pure complex exponential, the frequency of which is equal to the frequency location for the desired measurement. In some embodiments, such a complex exponent is generated by a calibration synthesizer or by a transmitter that cycles back to the receiver. For each frequency of the complex exponential, the response is digitized and processed to determine a corresponding measurement. The remainder of this section discusses how the digitized response data is processed to give the measurement of interest.

When this process is considered to be in the time domain, the basic idea is to mix each signal to DC and then use an averaging method to get accurate results. In the frequency domain, this can be seen as the computation of a few single point windowed discrete-time fourier transforms. This interpretation and derivation will assume that a rectangular window (whose width is equal to the acquisition length) is used before calculating the DTFT. Windowing and its effects are discussed in more detail in the next section "rectangular window optimization".

Equation 6.1 describes the expected form of the simulated response. This form assumes that the stimulus is complex exponential at a known frequency f. Equation 6.3 defines a DTFT with infinite support and is therefore not realizable for practical calculations. Equation 6.4 gives a DTFT with limited support by using a rectangular window. The value w represents the normalized digitization frequency with respect to the interval [ pi, pi ]. The conversion from f to w is given by w-2 pi f/sample rate.

The leakage of the measurement signal does not need to be shifted and only an averaging is needed, since its spectral content is already at 0 Hz. To measure the magnitude and phase of a given tone, complex tones down to 0Hz are first mixed by multiplying the complex exponential by a frequency equal and opposite to the tone frequency. The results are then averaged over the length of the acquisition. The same is equivalent for taking a single point DTFT on a complex input signal at the frequency of interest.

s[n]＝ADC_Sampling(s(t，f)) (6.2)

A_I＝Re(Avg{s[n]exp(-jwn)}) (6.6B)

A_Q＝Im(Avg{s[n]exp(-jwn)}) (6.6C)

Alternatively, the phase of { s [ n ] } can be calculated according to the following expression:

calculating gain imbalance and phase skew involves finding the magnitude and phase of the I and Q signals independently. For example, in fig. 59, the "Q real" signal is a 26MHz signal with 0.6 gain imbalance and 20 degrees phase skew compared to the in-phase signal (i.e., the "I reference" signal). However, the "Q desired" trace gives the ideal quadrature signal, which is offset by 90 degrees from the in-phase signal. By measuring the magnitude and phase of the in-phase component ("I reference"), the ideal quadrature signal can be determined by its orthogonality with respect to the in-phase component. Then, by knowing the actual magnitude and phase of the quadrature signal ("Qreal"), the difference between the ideal quadrature signal and the actual quadrature signal can be determined.

Shown in fig. 60 and 61 are magnitudes for the in-phase and quadrature-phase signal components (i.e., for the "I reference" signal and the "Q actual signal" in fig. 59). Since each component of the complex signal s (t) is a real-valued signal, it is expected to have a symmetric magnitude response. To find the gain imbalance g (f), the gain of each signal component at the frequency location of the tone is determined, and then the Q gain is removed with the I gain, as given in equation 6.12.

Equations 6.8 through 6.11 show how the magnitude and phase of each component is calculated. Following the convention of assuming that the in-phase signal is ideal and the quadrature-phase signal contains all impairments calculated with respect to the in-phase signal reference. (other conventions are also possible, as described in various different ways above. Thus, the magnitude and phase are calculated for each of the I and Q signals by finding a single point DTFT. These magnitudes and phases are then combined together by equations 6.12 and 6.13 to determine the gain imbalance and phase skew of the quadrature signal components.

In the following equations, I (n, w) is a sampled version of I (t, w) and Q (n, w) is a sampled version of Q (t, w).

||I(w)||＝|Avg{I(n，w)exp(-jwn)}| (6.8)

||Q(w)||＝|Avg{Q(n，w)exp(-jwn)}| (6.10)

In alternative embodiments, | I (w) |, Phase { I (w) }, | | Q (w) | and Phase { Q (w) } may be calculated as follows:

||I(w)||＝|Sum{I(n，w)exp(-jwn)}|/N. (6.8)

||Q(w)||＝|Sum{Q(n，w)exp(-jwn)}|/N (6.10)

where N is the acquisition size.

Fig. 62 illustrates a software embodiment (written in LabVIEW graphical programming language) for calculating LO leakage, amplitude, gain imbalance, image rejection, and phase skew.

In some embodiments, the calculations to follow are performed by programmable hardware elements (e.g., the FPGA of the receiver).

Sum{Re(Q(n，w)exp(-jwn))}

Sum{Im(Q(n，w)exp(-jwn))}

Sum{Re(s[n])}

Sum{Im(s[n])}

Fig. 63 shows a LabVIEW graph program (VI) that receives the summed values calculated by the FPGA and calculates LO leakage, amplitude, gain imbalance and phase skew based on those summed values and the acquisition length. (any of the various computer systems described herein can include software infrastructure for executing a software program, including a computer program such as a LabVIEW graphics program).

Rectangular window optimization

In some embodiments, a non-rectangular window may be applied to the complex digital signal s (n). Any of a variety of standard window types may be used. In other embodiments, no window is explicitly applied to the complex digital signal. However, by performing the calculations only for a limited acquisition interval, a rectangular window is implicitly applied. If we place frequency planning constraints on the pitch settings in the spectrum or judge the calculated measurement error to be acceptable, no window needs to be explicitly applied to the complex digital signal. (thus, we can avoid the memory required to store the window value, thereby minimizing hardware utilization). Otherwise, the window should be used to make the measurement. This section will discuss: derivation of frequency plan constraints, and measurement errors that would result if the constrained frequency plan were not used when the window was not used.

The following is a derivation of a rectangular window (i.e., no explicit window). For reference only, equation 5.9 is an equation for standard DTFT and equation 5.12 gives a closed form solution for a finite geometry series. A rectangular window is defined as one over a finite interval and zero elsewhere. Thus, its DTFT is given by 5.11. Using the geometric identity of equation 5.12, the DTFT of the window can be reduced to equation 5.13. Finally, since the first term of the last expression of 5.13 has a unit magnitude, the logarithmic amplitude is given by equation 5.14.

It should be noted that for pure tones, null values (null) in the windowed tones will occur at Ftone +/-N × SampleRate/AcqLength, Ftone being the tone frequency, AcqLength being the number of samples in the acquisition of the complex digital signal, and SampleRate being the rate at which samples of the complex digital signal are acquired. Note also that for image rejection calculations, if we make sure that all the generated tones exist only in multiples of SampleRate/AcqLength, there will not be any spectral leakage in the measurement.

Fig. 64-65 show two corresponding plots of the amplitude spectrum | RECT (w) | with a common sampling rate of 120MHz and different acquisition lengths. The first plot (fig. 64) corresponds to the acquisition length 20. The second plot (fig. 65) corresponds to the acquisition length 128.

Generalized derivation

Given the system model of FIG. 66, we can reduce the g from the input I/Q_in(ω) and

and output I/Q impairments g_out(ω) and

the functional form is derived for the frequency responses U (ω) and V (ω). Furthermore, we can derive the output impairments from the frequency responses U (ω) and V (ω) and the input I/Q impairments. Both of these derivations rely on the following preliminary steps. The system model implies that:

where U (t) and V (t) are impulse responses corresponding to U (ω) and V (ω), respectively.

Using the standard identity for cosine and sine functions, we obtain:

collecting the coefficients of the terms in exp (j ω t) and separately in exp (-j ω t) gives the following two equations:

however, equation (7.8a) applies to all ω. Thus, we can replace ω with- ω and obtain:

equations (7.7) and (7.8b) define the unknown vector [ 2 ]]U(ω)，V(ω)]^TThe 2x2 matrix equation in (a), the solution of which is given by equations (7.9) and (7.10) in fig. 67.

Now, given the input impairments and the frequency responses of the filters U (ω) and V (ω), we derive the output impairments. According to equation (7.7)And (7.8a) it can be seen that computing the output impairment is not possible because the problem is overdetermined. However, since both U (ω) and V (ω) are real-valued filters, there is a direct relationship between their positive and negative frequency responses, i.e., U (-f) ═ U^＊(f) And V (-f) ═ V^＊(f) In that respect Therefore, the temperature of the molten metal is controlled,

removing receiver impairments from measured output impairments

In this section, the output penalty g is given_out(f) And

and system intrinsic impairments g_sys(f) And

we derive the input impairment g for the computing system_in(f) And

the method of (1). This method may be used to remove receiver-intrinsic impairments from impairments measured at the output of the receiver (e.g., the output of an I/Q demodulator) to determine impairments at the input of the receiver (e.g., the input of an I/Q demodulator). Given the frequency responses U (f) and V (f) and the output impairments g for the system model of FIG. 66_out(f) And

we can calculate the input impairment g starting from equation (7.7)_in(f) And

here we copy with f instead of ω with respect to frequency:

if we define

Equation (7.14) can be more succinctly expressed as:

Z_in(f)＝{-jU(f)+Z_out(f)}/V(f). (7.17)

we can use g_in(f) Is constantly equal to one,

Is equal to zero, g_out(f) Equal to the gain imbalance g of the system_sys(f) And is

Equal to the phase skew of the system

Is determined from equations (7.9) and (7.10) of fig. 67. Under these specific assumptions, equations (7.9) and (7.10) are specific to:

if we define

Equations (7.15) and (7.16) can be expressed as:

U(f)＝(j/2){Z_sys(-f)^*-Z_sys(f)} (7.21)

V(f)＝(1/2){Z_sys(f)+Z_sys(-f)^*}. (7.22)

by substituting these expressions into equation (7.17), we obtain:

this calculation method specified by equations (7.23) to (7.25) can be used to measure the impairments g from the output at the receiver (e.g., the output of an I/Q demodulator)_M(f) And

removing receiver intrinsic impairments g_RX(f) And

in order to obtain the impairment g at the input of the receiver (e.g. the input of an I/Q demodulator) as follows_in(f) And

additional embodiments are disclosed in the following numbered paragraphs.

1. A method for operating a receiver, the method comprising:

receiving an analog input signal from a communication medium;

performing I/Q demodulation on the analog input signal to generate an analog in-phase signal and an analog quadrature signal;

digitizing the analog in-phase signal and the analog quadrature signal to produce a digital in-phase signal I (n) and a digital quadrature signal Q (n), respectively;

transforming the digital in-phase signal I (n) and the digital quadrature signal Q (n) according to the following expression to produce a resulting digital in-phase signal I_R(n) and the resulting digital quadrature signal Q_R(n)

I_R(n)＝I(n)，

Q_R(n)＝a*I(n)+HT{b*I(n)}+c*Q(n)+HT{d*Q(n)}，

Where HT denotes the Hilbert transform, wherein coefficients a, b, c and d are calculated to achieve at least partial compensation of the receiver's I/Q impairments at frequencies f and-f, wherein each coefficient is calculated based on the measured I/Q impairments of the receiver at frequency f and the measured I/Q impairments of the receiver at frequency-f.

The method of paragraph 1, wherein, as an alternative to the expression given above, the result is a digital in-phase signal I_R(n) and the resulting digital quadrature signal Q_R(n) transforming according to the following expression:

I_R(n)＝a*I(n)+HT{b*I(n)}+c*Q(n)+HT{d*Q(n)}，

Q_R(n)＝Q(n).

2. the method of paragraph 1, wherein the analog input signal is a pure tone.

3. The method of paragraph 1, wherein the analog input signal is a communication signal carrying a stream of binary information.

4. A receiver, comprising:

an I/Q demodulator configured to receive an analog input signal and perform I/Q demodulation on the analog input signal to generate an analog in-phase signal and an analog quadrature signal;

a digitizing unit configured to digitize the analog in-phase signal and the analog quadrature signal to generate a digital in-phase signal I (n) and a digital quadrature signal Q (n), respectively;

a digital circuit configured to transform the digital in-phase signal I (n) and the digital quadrature signal Q (n) according to the following expression to produce a resulting digital in-phase signal I_R(n) and the resulting digital quadrature signal Q_R(n)：

I_R(n)＝I(n)，

Q_R(n)＝a*I(n)+HT{b*I(n)}+c*Q(n)+HT{d*Q(n)}，

Where HT denotes the Hilbert transform, wherein coefficients a, b, c and d are calculated to at least partially compensate for the I/Q impairments of the receiver at frequencies f and-f, wherein each coefficient is calculated based on the measured I/Q impairments of the receiver at frequency f and the measured I/Q impairments of the receiver at frequency-f.

Receiver of paragraph 4, wherein, as an alternative to the expression given above, the result is a digital in-phase signal I_R(n) and the resulting digital quadrature signal Q_R(n) transforming according to the following expression:

I_R(n)＝a*I(n)+HT{b*I(n)}+c*Q(n)+HT{d*Q(n)}，

Q_R(n)＝Q(n).

5. the receiver of paragraph 4, wherein the analog input signal is a pure tone.

6. The receiver of paragraph 4 wherein the analog input signal is a communication signal carrying a stream of binary information.

7. A method for operating a transmitter, the method comprising:

receiving a digital in-phase signal I (n) and a digital quadrature signal Q (n);

transforming the digital in-phase signal I (n) and the digital quadrature signal Q (n) according to the following expression to obtain a resulting digital in-phase signal I_R(n) and the resulting digital quadrature signal Q_R(n)：

I_R(n)＝I(n)，

Q_R(n)＝a*l(n)+HT{b*I(n)}+c*Q(n)+HT{d*Q(n)}，

Wherein HT represents a Hilbert transform, wherein coefficients a, b, c, and d are calculated to at least partially pre-compensate for the I/Q impairments of the transmitter at frequencies f and-f, wherein each coefficient is calculated based on an estimate of the I/Q impairments of the transmitter at frequency f and an estimate of the I/Q impairments of the transmitter at frequency-f;

the resulting digital in-phase signal I_R(n) and the resulting digital quadrature signal Q_R(n) converting to analog form to obtain an analog I signal and an analog Q signal, respectively;

I/Q modulation is performed on the analog I signal and the analog Q signal to produce a modulated analog signal.

The method of paragraph 7, wherein, as an alternative to the expression given above, the result is a digital in-phase signal I_R(n) and the resulting digital quadrature signal Q_R(n) transforming according to the following expression:

I_R(n)＝a*I(n)+HT{b*I(n)}+c*Q(n)+HT{d*Q(n)}，

Q_R(n)＝Q(n).

8. the method of paragraph 7, wherein the digital in-phase signal and the digital quadrature signal represent complex exponential tones at a frequency f.

9. The method of paragraph 7, wherein the digital in-phase signal and the digital quadrature signal carry corresponding streams of binary information.

10. A transmitter, comprising:

a digital circuit configured to receive a digital in-phase signal I (n) and a digital quadrature signal Q (n) and to transform the digital in-phase signal I (n) and the digital quadrature signal Q (n) according to the following expression to obtain a resulting digital in-phase signal I_R(n) and the resulting digital quadrature signal Q_R(n)：

I_R(n)＝I(n)，

Q_R(n)＝a*I(n)+HT{b*I(n)}+c*Q(n)+HT{d*Q(n)}，

a digital-to-analog conversion (DAC) unit configured to convert the resulting digital in-phase signal and the resulting digital quadrature signal into analog form to obtain an analog I signal and an analog Q signal, respectively;

an I/Q modulator configured to perform I/Q modulation on the analog I signal and the analog Q signal to generate a modulated analog signal.

The transmitter of paragraph 10, wherein, as an alternative to the expression given above, the result is a digital in-phase signal I_R(n) and the resulting digital quadrature signal Q_R(n) transforming according to the following expression:

I_R(n)＝a*I(n)+HT{b*I(n)}+c*Q(n)+HT{d*Q(n)}，

Q_R(n)＝Q(n).

11. the transmitter of paragraph 10 wherein the digital in-phase signal and the digital quadrature signal represent complex exponential tones at a frequency f.

12. The transmitter of paragraph 10 wherein the digital in-phase signal and the digital quadrature signal carry corresponding streams of binary information.

Still additional embodiments are disclosed in the following numbered paragraphs.

1. A method for correcting I/Q impairments in a received transmission signal, the method comprising: receiving a transmission signal via a transmission medium; performing I/Q demodulation on the received transmission signal to generate analog I (in-phase) and Q (quadrature) signals; performing analog-to-digital conversion on each of the analog I signal and the analog Q signal to generate digital I and Q signals; and performing wideband I/Q impairment correction on the digital I and Q signals, wherein the wideband I/Q impairment correction compensates for frequency-dependent variations in gain imbalance and phase imbalance in the digital I and Q signals.

2. The method of paragraph 1, wherein the wideband I/Q impairment correction compensates for frequency-dependent variations in gain imbalance and phase imbalance in the digital I and Q signals due to one or more of I/Q demodulation or analog-to-digital conversion of the analog I signal and the analog Q signal.

3. The method of paragraph 1, wherein the method is implemented by a receiving device, wherein the wideband I/Q impairment correction compensates for frequency-dependent variations of gain imbalance and phase imbalance in the digital I and Q signals at a plurality of frequency offsets across an instantaneous bandwidth of the receiving device.

4. The method of paragraph 1, wherein performing wideband I/Q impairment correction on the digital I and Q signals comprises filtering one or more of the digital I signals or the digital Q signals.

5. The method of paragraph 4, wherein performing wideband I/Q impairment correction on the digital I and Q signals comprises filtering the digital Q signal and leaving the digital I signal unchanged.

6. The method of paragraph 4, wherein performing wideband I/Q impairment correction on the digital I and Q signals comprises filtering the digital I signal and leaving the digital Q signal unchanged.

7. The method of paragraph 4, wherein performing wideband I/Q impairment correction on the digital I and Q signals comprises filtering both the digital Q signal and the digital I signal.

8. The method of paragraph 1, wherein the method is implemented by a receiving device, wherein the method further comprises determining correction information by providing a plurality of known test signals to the receiving device and measuring I/Q impairments introduced by the receiving device in response to the known test signals, wherein the wideband I/Q impairment correction utilizes the correction information to compensate for frequency-dependent variations in gain imbalance and phase imbalance in the digital I and Q signals.

9. The method of paragraph 8, wherein providing the plurality of known test signals to the receiving device includes providing one or more of: a plurality of sinusoids at different frequencies; or a plurality of cosine waves at different frequencies.

10. The method of paragraph 1, wherein receiving the transmission signal via the communication medium includes receiving the transmission signal via one or more of: a wireless communication medium; or a cable.

11. The method of paragraph 1, wherein the received transmission signal is a Radio Frequency (RF) signal.

12. A receiving device configured to: receiving a transmission signal via a transmission medium; performing I/Q demodulation on the received transmission signal to generate analog I (in-phase) and Q (quadrature) signals; performing analog-to-digital conversion on each of the analog I signal and the analog Q signal to generate digital I and Q signals; and performing wideband I/Q impairment correction on the digital I and Q signals, wherein the wideband I/Q impairment correction compensates for frequency-dependent variations in gain imbalance and phase imbalance in the digital I and Q signals.

13. The receiving apparatus of paragraph 12, wherein the receiving apparatus comprises: one or more input ports for receiving a transmission signal; one or more output ports for outputting one or more of the corrected digital I signal or the corrected digital Q signal; and a programmable hardware element configured to perform wideband I/Q impairment correction.

14. The receiving device of paragraph 13, wherein the programmable hardware element comprises an FPGA (field programmable gate array).

19. A method for correcting I/Q impairments, the method comprising: receiving digital I (in-phase) and Q (quadrature) signals to be transmitted; performing wideband I/Q impairment pre-correction on the digital I and Q signals, wherein performing wideband I/Q impairment pre-correction comprises filtering one or more of the digital I and Q signals to produce one or more pre-corrected digital signals to pre-compensate for frequency-dependent variations of gain imbalance and phase imbalance that will subsequently be introduced during synthesis of the transmission signal; and synthesizing the transmission signal using the one or more pre-corrected digital signals.

20. The method of paragraph 19, wherein the wideband I/Q impairment pre-correction filtering the digital Q signal is performed to produce a pre-corrected digital Q signal and leaving the digital I signal unchanged; wherein the transmission signal is synthesized from a pre-corrected digital Q signal and an invariant digital I signal.

21. The method of paragraph 19, wherein the wideband I/Q impairment pre-correction filtering the digital I signal is performed to produce a pre-corrected digital I signal and leaving the digital Q signal unchanged; wherein the transmission signal is synthesized from a pre-corrected digital I signal and an invariant digital Q signal.

22. The method of paragraph 19, wherein the wideband I/Q impairment pre-correction filtering the digital I signal to produce a pre-corrected digital I signal and the filtering the digital Q signal to produce a pre-corrected digital Q signal are performed; wherein the transmission signal is synthesized from the pre-corrected digital I signal and the pre-corrected digital Q signal.

23. The method of paragraph 19, wherein synthesizing the transmission signal comprises: performing digital-to-analog conversion of the one or more pre-corrected digital signals to produce one or more of an analog I signal or an analog Q signal; and performing I/Q modulation with one or more of the analog I signal or the analog Q signal to generate a transmission signal; wherein the one or more pre-corrected digital signals pre-compensate for frequency-dependent variations in gain imbalance and phase imbalance caused by one or more of digital-to-analog conversion or I/Q modulation.

24. The method of paragraph 23, wherein performing one or more digital to analog conversions of the precorrected digital signal produces an analog Q signal; wherein the method further comprises performing a digital-to-analog conversion of the digital I signal to produce an analog I signal; wherein the performing of the I/Q modulation to generate the transmission signal uses the analog Q signal and the analog I signal.

25. The method of paragraph 19, wherein the method is implemented by a sending device; wherein the wideband I/Q impairment pre-correction pre-compensates for gain imbalance and phase imbalance at a plurality of frequency offsets across an instantaneous bandwidth of a transmitting device.

26. The method of paragraph 19, wherein the method is implemented by a sending device; wherein the method further comprises determining correction information by providing a plurality of known test signals to the transmitting device and measuring I/Q impairments introduced by the transmitting device in response to the known test signals; wherein the wideband I/Q impairment pre-correction utilizes the correction information to generate one or more pre-corrected digital signals.

27. The method of paragraph 26, wherein providing the plurality of known test signals to the transmitting device includes providing one or more of: a plurality of sinusoids at different frequencies; or a plurality of cosine waves at different frequencies.

28. The method of paragraph 19, further comprising sending the transmission signal via one or more of: a wireless communication medium; or a cable.

29. The method of paragraph 19, wherein the transmission signal is a Radio Frequency (RF) signal.

30. A transmitting device configured to: receiving digital I (in-phase) and Q (quadrature) signals to be transmitted; performing wideband I/Q impairment pre-correction on the digital I signal and the digital Q signal, wherein the wideband I/Q impairment pre-correction is performed filtering one or more of the digital I signal and the digital Q signal to produce one or more pre-corrected digital signals to pre-compensate for frequency-dependent variations of gain imbalance and phase imbalance that will be subsequently introduced during synthesis of the transmission signal; and synthesizing the transmission signal using the one or more pre-corrected digital signals.

31. The transmitting apparatus of paragraph 30, wherein the transmitting apparatus comprises: one or more input ports for receiving a digital I signal and a digital Q signal; one or more output ports for outputting a transmission signal; and a programmable hardware element configured to perform wideband I/Q impairment pre-correction on the digital I signal and the digital Q signal.

32. The transmitting device of paragraph 31 wherein the programmable hardware element comprises an FPGA (field programmable gate array).

34. A measurement system, comprising: a receiving device; and a device under test; wherein the receiving device is configured to: receiving a transmission signal including measurement data acquired from a device under test; performing I/Q demodulation on the received transmission signal to generate analog I (in-phase) and Q (quadrature) signals; performing analog-to-digital conversion of each of the analog I signal and the analog Q signal to generate a digital I signal and a digital Q signal, wherein the wideband I/Q impairment correction compensates for frequency-dependent variations in gain imbalance and phase imbalance in the digital I signal and the digital Q signal.

35. The measurement system of paragraph 34, further comprising: a transmitting device, wherein the transmitting device is configured to: receiving a digital I signal and a digital Q signal to be transmitted, wherein the digital I signal and the digital Q signal specify information to be transmitted to a device under test; performing wideband I/Q impairment pre-correction on the digital I signal and the digital Q signal, wherein the wideband I/Q impairment pre-correction is performed filtering one or more of the digital I signal and the digital Q signal to produce one or more pre-corrected digital signals to pre-compensate for frequency-dependent variations of gain imbalance and phase imbalance that will be subsequently introduced during synthesis of the transmission signal; synthesizing a transmission signal using one or more pre-corrected digital signals; and transmits the transmission signal to the device under test.

36. The measurement system of paragraph 35, wherein the transmission signal includes a control signal for controlling the device under test.

37. The measurement system of paragraph 34, further comprising: a chassis; wherein the receiving device is implemented as a first module mounted in the chassis; wherein the sending device is implemented as a second module mounted in the chassis.

38. The measurement system of paragraph 37 wherein the chassis is a PXI (PCI expansion for instrumentation) chassis.

FIG. 68 illustrates one embodiment of a computer system 6800 that may be used to perform any of the method embodiments described herein or any combination or subset of any of the method embodiments described herein.

The computer system 6800 can include a processing unit 6810, a system memory 6812, a set of one or more memory devices 6815, a communication bus 6820, a set of input devices 6825, and a display system 6830.

The system memory 6812 may include a set of semiconductor devices such as a RAM device (and possibly a set of ROM devices as well).

The storage 6815 can include any of a variety of storage devices, such as one or more memory media and/or memory access devices. For example, storage 6815 may include devices such as CD/DVD-ROM drives, hard disks, disk drives, tape drives, and the like.

Processing unit 6810 is configured to read and execute program instructions, such as those stored within system memory 6812 and/or on one or more storage devices 6815. Processing unit 6810 may be coupled to system memory 6812 via a communication bus 6820 (or via a system of interconnected buses, or via a network). The program instructions configure the computer system 6800 to implement a method, e.g., any of the method embodiments described herein, or any combination of the method embodiments described herein, or any subset of any of the method embodiments described herein, or any combination of such subsets.

The processing unit 6810 may include one or more processors (e.g., microprocessors).

One or more users may provide input to the computer system 6800 through input device(s) 6825. Input devices 6825 may include devices such as a keyboard, mouse, touch-sensitive pad, touch-sensitive screen, drawing pad, trackball, light pen, data glove, eye-orientation and/or head-orientation sensors, microphone (or collection of microphones), or any combination thereof.

Display system 6830 can include any of a variety of display devices that represent any of a variety of display technologies. For example, the display system may be a computer monitor, a head mounted display, a projector system, a stereoscopic display, or a combination thereof. In some embodiments, a display system may include multiple display devices. In one embodiment, the display system may include a printer and/or a plotter.

In some embodiments, the computer system 6800 can include other devices, such as, for example, devices like one or more graphics accelerators, one or more speakers, sound cards, video and video cards, data acquisition systems.

In some embodiments, the computer system 6800 can include one or more communication devices 6835, such as a network interface card for interfacing with a computer network. As another example, the communication device 6835 can include a proprietary interface for communicating via any of a number of established communication standards or protocols (e.g., USB, Firewire, PCI Express, PXI).

The computer system may utilize one or more graphics APIs (such as

Direct3D、Java 3D^TM) Is configured with the software infrastructure. In some embodiments, the software infrastructureMay include LabVIEW from National Instruments of the United states^TMSoftware, and/or LabVIEW^TMFPGA。

In some embodiments, the computer system 6800 can be configured to interface with the transmitter 6840. The transmitter may be configured to transmit signals (onto the communication channel) as described in various different manners herein. The transmitter may operate under the control of software executing on the processor 6810 and/or software executing on the transmitter itself.

In some embodiments, computer system 6800 can be configured to communicate with receiver 6850. The receiver may be configured to receive signals (from a communication channel) as described in various different ways herein. The receiver may operate under the control of software executing on the processor 6810 and/or software executing on the receiver itself.

In some embodiments, the transmitter and/or receiver may include one or more programmable hardware elements and/or one or more microprocessors for performing digital processing on digital data (e.g., on digital baseband signals or digital IF signals), as described in various different manners herein.

Although embodiments have been described above in considerable detail, numerous variations and modifications will become apparent to those skilled in the art once the above disclosure is fully appreciated. It is intended that the following claims be interpreted to embrace all such variations and modifications.

Appendix A

Iterative method for estimating transmitter I/Q impairments with shared LO

1. For gain imbalance gT and phase skew of transmitter to be measured at

Measuring the gain imbalance gR and phase skew of the receiver

(in some embodiments, the set of frequency offsets is symmetric about zero, i.e., for each of the setsA frequency offset f, also in the set). For each f, the tone transmitter is directed to generate a signal at a frequency v ═ f_LOTone at + f, where f_LOIs the LO frequency, the tone is applied to the input of the receiver, and the complex baseband sequence z (n) is captured at the output of the I/Q demodulator of the receiver. Gain imbalance gR and phase skew

Is calculated based on the complex baseband sequence z (n), as described in the section "precision measurement technique".

2. Configuring the receiver and transmitter such that they use the same LO frequency f_LO. If the receiver and transmitter use two different LO circuits, the transmitter is tuned such that its LO is phase locked to the same reference. Thus, the frequency of the transmitter and the frequency of the receiver are both f_LO。

3. The output of the transmitter is connected to the input of the receiver, e.g. via a cable or a wireless connection.

4. The DC scaling m (0) and the DC rotation θ (0) of the signal path between the I/Q modulator of the transmitter and the I/Q demodulator of the receiver are estimated by using the algorithm in the section "calculate mapping between RX and TX". For best results, tone K is applied to the I/Q modulator of the transmitter in addition to the DC test vector. Tone K is applied because leakage is sensitive to in-band power. Tone K is applied at a frequency within the instantaneous bandwidth that is different from DC. (As part of the estimation of DC scaling and DC rotation, the methods of the "precision measurement technique" section apply to the sampled complex data if the sampled complex data is not windowed, then a constraint is placed on the frequency of the tone K.)

5. Iteration index k ← 0

Do while (quality measurement Q less than threshold)

For each frequency offset f:

set gT (f, 0) ← 0 and

6A.If k＝0：

no pre-correction is applied at the transmitter, i.e. the pre-correction circuitry configuring the transmitter uses the values α -0 and β -1

Else(k＞0)

Pre-correction coefficients α and β are calculated for the frequency offset f based on the current transmitter gain imbalance estimate gT (f, k) and the current transmitter phase skew estimate

Current transmitter gain imbalance estimate gT (-f, k); current transmitter phase skew estimation

(if the set of frequency offsets is asymmetric about zero, then the pairs gT (-f, k) and

the frequency closest to under-f) is selected. Alternatively, a transmitter pre-correction filter may be created.

Endif

the pre-correction circuitry is configured to use the calculated values α and β (or pre-correction filters).

The input to the pre-correction circuitry is applied a complex exponential signal u (n) ═ exp (j2 pi fn).

Measuring the complex baseband signal z (n) at the output of the I/Q demodulator of the receiver.

Determining raw gain imbalance gz (f) and raw phase skew based on complex baseband signal z (n) using a calculation method in "precision measurement technique

8. From the original gain imbalance gz (f) and the original phase skew

Removing gain imbalance gR (f) and phase skew of receiver

To obtain pre-demodulation gain imbalance gPD (f) and pre-demodulation phase skew

(for performing this removal, there are at least two methods: a direct conversion method and a filtering method. the direct conversion method would have a higher quality than the filtering method. the direct conversion method is discussed in the section entitled "removing receiver impairments from measured output impairments". The filtering method involves applying a 2x2 matrix of digital filters to the complex baseband signal z (n) ═ (I (n), Q (n)) to obtain a partially corrected signal PCS (n). the 2x2 matrix of digital filters may be calculated as described above in connection with FIGS. 2A, 2B, and 3 and in the partial "wideband I/Q impairment equalization")

9. The best current estimate of the signal path between the I/Q modulator of the transmitter and the I/Q demodulator of the receiver is removed. m (0) and θ (0) will provide the basic estimates. Better estimation will increase the convergence rate. For example, step 9 may be implemented as follows.

If k＝0

From gain imbalance gPD and phase skew using the transformation described in "altering gain imbalance and phase skew by linear system

Removing the estimated DC scaling m (0) and DC rotation θ (0) to obtain a post-modulation gain imbalance gPM and a post-modulation phase skew

H (f) and H (-f) are set equal to H (0) ═ exp (-j θ (0))/m (0).

Else(k＞0)

The scaling m (f) at the frequency offset f is calculated based on the complex baseband signal z (n). The scaling m (f) can be determined by calculating the magnitude of the frequency component at frequency f in the complex signal z (n) at f, as explained in the section "precision measurement technique", especially in equation 6.6.

By using "pass linearityThe transformation described in System Change gain imbalance and phase skew "from gain imbalance gPD (f) and phase skew

Removing the estimated linear signal path to obtain a post-modulated gain imbalance gPM (f) and a post-modulated phase skew

Wherein H (f) ═ exp (-j θ (0))/m (f) and H (-f) ═ exp (-j θ (0))/m (-f).

Note that: if-f has not been seen by the frequency offset loop, then m (-f) in the calculation in the previous iteration of mass k-1 is used.

10. Transmitter gain imbalance gT and transmitter phase skew according to

And (3) generating an update:

gT (f, k + l) ← gT (f, k) × gPM (f) and

11. gain imbalance from post-modulation gPM (f) and phase skew of post-modulation based on equation (4.15)

Computing image rejection I_R(f)。

Endfor

k←k+1

Calculating a quality measurement Q-I for all values of f_R(f) Is measured. (I)_R(f) More negative values correspond to higher quality. Thus, I_R(f) Corresponds to the mass at frequency f. Q is the maximum value of the quality over the frequency band. )

End While

Appendix B

Iterative estimation-optimization of transmitter impairments with offset LO

1. Configuring a receiverAnd a transmitter for enabling a local oscillator frequency LO of the receiver_RXAnd local oscillator frequency LO of the transmitter_TXThe difference is equal to the selected value Δ LO:

LO_RX-LO_TX＝ΔLO。

the selected value is a non-zero portion (e.g., a fraction) of the instantaneous bandwidth of the transmitter. The two local oscillators are phase locked.

2. The output of the transmitter is connected to the input of the receiver.

3. The DC scaling m (0) and the DC rotation θ (0) of the signal path between the I/Q modulator of the transmitter and the I/Q demodulator of the receiver are estimated using the algorithm in the section "calculate mapping between RX and TX". This estimation involves the following steps.

3a. apply the zero stimulus signal as an input to the I/Q modulator of the transmitter.

Capturing the response signal z at the output of the I/Q demodulator of the receiver_A(n)。

3C frequency shift response signal z_A(n) an amount DeltaLO to obtain a frequency shifted signal FSz_A(n)。

Apply the DC test vector as input to the I/Q demodulator.

Capture of response signal z at output of I/Q demodulator_C(n)。

Frequency shift response signal z_B(n) an amount Δ LO to obtain a frequency shifted signal FSz_B(n)。

Based on frequency shifted signal FSz_A(n) frequency-shifted signal FSz_B(n) and DC test vector calculate DC scaling m (0) and DC rotation θ (0), as described in the section "calculate mapping between RX and TX".

For best results, tone K is applied to the I/Q modulator of the transmitter in addition to the DC test vector. Tone K is applied because leakage is sensitive to in-band power. Tone K is applied at a frequency within the instantaneous bandwidth that is different from DC.

Note that: the frequency shifting operation may be performed with a signal FS (n) whose phase is continuous in time and travels at a rate Δ LO. For example, FS (n) may have the form:

FS(n)＝exp{j2π(ΔLO/ADC_SampleRate)n}.

the frequency shifting operation may be implemented according to the following relationship:

FSz(n)＝z(n)FS(n)，

where z (n) is the signal to be frequency shifted.

In one embodiment, the frequency shifting operation may be implemented in the FPGA of the receiver. The frequency shifting operation may be performed at the sampling rate of the ADC of the receiver, i.e. a new output value FSz (n) may be generated for each new ADC data vector z (n). Thus, the ADC sampling clock may be provided as an input to the FPGA. The phase continuity of the signal FS will then be guaranteed by the phase continuity of the ADC sampling clock. The ADC sampling clock is phase locked to the local oscillator.

In an alternative embodiment, the frequency shifting operation may be performed in software. The iterative approach presented involves repeated acquisition of the signal z (n) from the I/Q demodulator. Thus, to achieve phase continuity of the signal FS, the software is provided with information about the time difference between the start of the present acquisition and the start of the first acquisition (or the start of the previous acquisition). For example, the software may be provided with the time of the first sample z (0) taken this time relative to the time of the first sample z (0) taken the first time. Let m be defined as the sample count for a continuous run and n be the sample count for this acquisition. Thus, for the first acquisition of z (n), m-0 corresponds to n-0. Then, the phase-continuous frequency shift signal FSz (m) can be expressed as:

FS(m)＝exp{j2π(ΔLO/ADC_SampleRate)m}.

let k be defined by the sampling distance between the current acquisition and the first acquisition for the first sample z (0). Thus, the

FS(m)＝FS(k+n)＝exp{j2π(ΔLO/ADC_SampleRate)(k+n)}.

Now, FSz (n) can be calculated from the following expression

FSz(n)＝FS(k+n)z(n)＝FS(n)z(n)FSOffset，

Wherein

FS(n)＝exp{j2π(ΔLO/ADC_SampleRate)n}

FSOffset＝FS(k)＝exp{j2π(ΔLO/ADC_SampleRate)k}.

Note that k will only change from one acquisition to the next.

For each of the normal tone frequency offsets f to N Δ f (stepped by Δ f), the constraint described in the "constraint" section is accepted.

k←0

S element in For {1, -1}

Do while (for tone frequency offset v ═ S ×, — Image _ reject less than threshold):

4. based on at least the best available estimate for transmitter impairments at frequency v, the α and β coefficients for the pre-correction circuitry are calculated as follows:

5. configuring pre-correction circuitry to use the calculated values α and β

6. Applying a complex exponential signal u (n) ═ exp (j2 pi vn) to the input of the pre-correction circuitry

Measuring complex baseband signal z (n) at the output of I/Q demodulator of receiver

This step is optional.

The I/Q impairments of the receiver are removed from the complex baseband signal z (n) to obtain a modified complex signal. For example, such removal may involve filtering the complex baseband signal with a 2x2 matrix of digital filters, or multiplying the complex baseband signal with a 2x2 constant matrix, as described above in part "transmitter I/Q impairment determination with offset LO".

A phase-continuous frequency offset equal to Δ LO is applied to the signal z (n) (as described above) to obtain the frequency shifted signal FSz (n). If step 7B has been performed, a frequency shift is applied to the modified complex signal.

8. Using the calculation methods described in the section "precision measurement techniquesDetermining a raw gain imbalance gFSz (v) and a raw phase skew based on a complex baseband signal FSz (n)

9. From the original gain imbalance gFSz (v) and the original phase skew

Removing the best current estimate of the signal path (between the I/Q modulator of the transmitter and the I/Q demodulator of the receiver) to obtain an estimated post-modulation gain imbalance gPM (v) and post-modulation phase skew

m (0) and θ (0) will provide the basic estimates of the signal path. Better estimation will increase the convergence rate. For example, step 9 may be implemented as follows.

If f＝Δf

Conversion from raw gain imbalance gFSz (v) and raw phase skew using the transformation described in "altering gain imbalance and phase skew by linear system

Removing the estimated DC scaling m (0) and DC rotation θ (0) to obtain an estimated post-modulation gain imbalance gPM (v) and post-modulation phase skew

So that H (v) ═ exp (-j θ (0))/m (0) and H (-v) ═ exp (-j θ (0))/m (0).

Else f＞Δf

The scale m (v) at the pitch v is calculated based on the signal FSz (n) of step 7C. The scaling m (v) may be determined by calculating the magnitude of the frequency components in the complex signal FSz (n) at the frequency v, as explained in the "precision measurement technique", in particular in equation 6.6.

(Note: in an alternative embodiment, the measurement of z (n) is synchronized with the generation of the tone t (n), e.g., by using a trigger signal shared between the transmitter and receiver, e.g., a trigger generated by a controller

From the original gain imbalance gFSz (v) and the original phase skew by using the transformation described in "modifying gain imbalance and phase skew by linear system

Removing the estimated linear signal to obtain an estimated post-modulation gain imbalance gPM (v) and post-modulation phase skew

Such that H (v) ═ exp (-j theta (0))/m (v) and H (-v) ═ exp (-j theta (0))/m_BAE(-v), wherein m_BAE(-v) is the best available estimate for scaling m (-v).

If S＝1：m_BAE(-v)＝m(-v+Δf，∞)

If S＝-1：m_BAE(-v)＝m(-v，∞).

Generally, notation m (x, ∞) denotes the scaling m (x) in the computation in the last k iterations of the previously visited frequency x.

10. Transmitter gain imbalance gT and transmitter phase skew according to

And (3) generating an update:

gT(v，k+1)←gT(v，k)*gPM(v)and

11. post modulation gain imbalance gPM (v) and post modulation phase skew based on equation 4.15

Image rejection IR (v) is calculated.

k←k+1

EndDo

S element in EndFor {1, -1}

Appendix C

Iterative estimation-optimization of transmitter impairments with shared LO

1. In order to measure the gain imbalance gT and phase skew of the transmitter at it

Each in-band offset frequency measurement receiver's gain imbalance gR and phase skew

For each f, the tone generator generates a tone at a frequency v ═ f_LOTone at + f, where f_LOIs the LO frequency, the tone is applied to the input of the receiver, and the complex baseband sequence z (n) is captured at the output of the I/Q demodulator of the receiver. Gain imbalance gR and phase skew

Calculated as described in the "precision measurement techniques" section.

3. The output of the transmitter is connected to the input of the receiver.

4. The DC scaling m (0) and the DC rotation θ (0) of the signal path between the I/Q modulator of the transmitter and the I/Q demodulator of the receiver are estimated by using the algorithm in the section "calculate mapping between RX and TX". For best results, tone K is applied to the I/Q modulator of the transmitter in addition to the DC test vector.

calculating alpha and β coefficients for the pre-correction circuitry based at least on the best available estimate for transmitter impairment at frequency v.

configuring pre-correction circuitry to use the calculated values α and β.

6. The complex exponential signal u (n) ═ exp (j2 pi vn) is applied to the input of the pre-correction circuitry.

Determining raw gain imbalance gz (v) and raw phase skew based on complex baseband signal z (n) using a computational method in part of the "precision measurement technique

8. From the original gain imbalance gz (v) and the original phase skew

Removing gain imbalance gR (v) and phase skew of receiver

To obtain a pre-demodulated gain imbalance gPD (v) and a pre-demodulated phase skew

There are a variety of ways to achieve this removal, including mathematical transformation methods and filtering methods, as described above for the continuous method 4400. The mathematical transformation method is described in part in "removing receiver impairments from the measured output impairments".

9. The best but expensive estimate of the signal path between the I/Q modulator of the transmitter and the I/Q demodulator of the receiver is removed. m (0) and θ (0) will provide the best estimates. Better estimates will increase the rate of convergence. For example, step 9 may be implemented as follows.

If f＝Δf：

Conversion from gain imbalance gPD (v) and phase skew using the description in "altering gain imbalance and phase skew by linear system

Wherein H (v) and H (-v) are set equal to exp (-j theta (0))/m (0).

Else f＞Δf

A scaling m (v) at the pitch frequency v is calculated based on the complex baseband signal z (n) of step 7A. The scaling m (v) may be determined by calculating the magnitude of the frequency components in the complex signal z (n) at the frequency v, as explained in the "precision measurement technique", in particular in equation 6.6.

Deriving gain imbalance gPD (v) and phase skew from gain imbalance gPD (v) and phase skew by using the transformation described in "altering gain imbalance and phase skew by linear system

Removing the estimated linear signal path to obtain an estimated post-modulation gain imbalance gPM (v) and post-modulation phase skew

Wherein H (v) ═ exp (-j theta (0))/m (v) and H (-v) ═ exp (-j theta (0))/m_BAE(-v), wherein m_BAE(-v) is the best available estimate for scaling m (-v).

If S＝I：m_BAE(-v)＝m(-v+Δf，∞)

If S＝-1：m_BAE(-v)＝m(-v，∞).

10. Transmitter gain imbalance gT and transmitter phase skew according to

And (3) generating an update:

gT (v, k +1) ← gT (v, k) × gPM (v) and

Image rejection IR (v) is calculated.

Claims

1. A method for determining I/Q impairments of a transmitter, the method comprising:

configuring a Local Oscillator (LO) of the transmitter and a Local Oscillator (LO) of the receiver to be phase-locked to a common reference and such that a frequency of the LO of the receiver minus a frequency of the LO of the transmitter is equal to an amount alo;

performing a set of operations, wherein the set of operations comprises:

(a) directing complex exponential tones at a frequency f to be provided to a transmitter;

(b) a pre-compensation circuit that provides a pre-compensation transform to the transmitter, wherein the pre-compensation circuit is configured to apply the pre-compensation transform to the complex exponential tones to obtain an adjusted complex signal, wherein the pre-compensation transform is configured to pre-compensate a current estimate of I/Q impairments of the transmitter, wherein the transmitter is configured to transmit the transmitted signal based on the adjusted complex signal, wherein the receiver is configured to receive the transmitted signal and capture a sampled complex signal representative of the received transmitted signal;

(c) frequency shifting the sampled complex signal by an amount Δ LO to obtain a frequency shifted signal;

(d) calculating an original I/Q impairment at a frequency f based on the frequency shifted signal;

(e) removing a current estimate of a signal path from the original I/Q impairments at the frequency f to obtain path-compensated I/Q impairments at the frequency f, wherein the signal path comprises a path from an I/Q modulator of the transmitter to a demodulator of the receiver; and

(f) the current estimate of the transmitter's I/Q impairments at frequency f is updated based on the path compensated I/Q impairments at frequency f.

2. The method of claim 1, further comprising:

repeating the set of operations to determine a converged estimate of the I/Q impairment of the transmitter at the frequency f, wherein the set of operations are repeated until the path-compensated I/Q impairment-based quality measurement is greater than a threshold, wherein the converged estimate can be used to at least partially compensate the I/Q impairment of the transmitter at the frequency f, wherein the frequency shifting is performed using a frequency shifted signal that is phase continuous between successive repetitions of the set of operations.

3. The method of claim 2, further comprising:

this iterative action is performed a plurality of times to determine the convergence estimate at a plurality of different values for the frequency f.

4. The method of claim 1, wherein the set of operations further comprises:

the measured I/Q impairments of the receiver at the frequency f- Δ LO are removed from the sampled complex signal prior to the frequency shifting.

5. The method of claim 1, wherein the set of operations comprises measuring I/Q impairments of the receiver at the frequency f- Δ LO by:

calculating a discrete-time Fourier transform C of the I component of the sampled complex signal at a frequency f- Δ LO_I；

Calculating a discrete-time Fourier transform C of the Q component of the sampled complex signal at a frequency f- Δ LO_Q；

Based on the value C_IAnd C_QCalculates the receiver gain imbalance at frequency f- Δ LO;

based on the value C_IAnd C_QCalculates the receiver phase skew at the frequency f- Δ LO.

6. The method of claim 5, further comprising:

at the calculated value C_IAnd C_QA time domain window was previously applied to the sampled complex signal.

7. The method of claim 1, wherein the pre-compensation transform has the form of a 2x2 matrix, wherein a first diagonal element of the matrix is computed based on a current estimate of the I/Q impairments of the transmitter at frequencies f and-f, wherein a first off-diagonal element of the matrix is computed based on a current estimate of the I/Q impairments of the transmitter at frequencies f and-f.

8. The method of claim 1, wherein the current estimate of the signal path comprises a measured amplitude of the frequency shifted signal at frequency f.

9. The method of claim 8, wherein the current estimate of the signal path further comprises a measured rotation of the frequency shifted signal at frequency f.

10. The method of claim 1, wherein at least in a first execution of the set of operations, the current estimate of the signal path is based on a DC scaling and a DC rotation of the signal path.

11. The method of claim 10, further comprising determining DC scaling and DC rotation by:

providing a zero vector signal to a transmitter;

providing a non-zero DC vector signal to a transmitter;

the DC scaling and DC rotation are calculated based on a first DC vector response and a second DC vector response, where the first DC vector response is measured at the receiver in response to a zero vector signal and the second DC vector response is measured at the receiver in response to a non-zero DC vector signal.

12. The method of claim 1, wherein the transmitter adheres to a direct conversion architecture, wherein the demodulator is an I/Q demodulator.

13. A computer system for determining I/Q impairments of a transmitter, the computer system comprising:

a processor; and

a memory storing program instructions, wherein the program instructions, when executed by the processor, cause the processor to:

configuring a Local Oscillator (LO) of the transmitter and a Local Oscillator (LO) of the receiver to be phase-locked to a common reference and such that a frequency of the LO of the receiver minus a frequency of the LO of the transmitter is equal to an amount alo; and is

Performing a set of operations, wherein the set of operations comprises:

14. The computer system of claim 13, wherein the program instructions, when executed by the processor, further cause the processor to:

15. The computer system of claim 14, wherein the program instructions, when executed by the processor, further cause the processor to:

16. The computer system of claim 13, wherein the set of operations further comprises:

17. The computer system of claim 13, wherein the program instructions, when executed by the processor, further cause the processor to measure I/Q impairments of the receiver at the frequency f- Δ LO by:

calculate sampledDiscrete-time Fourier transform value C at frequency f-DeltaLO of I component of complex signal_I；

18. The computer system of claim 17, wherein the program instructions, when executed by the processor, further cause the processor to:

19. The computer system of claim 13, wherein the pre-compensation transform has the form of a 2x2 matrix, wherein a first diagonal element of the matrix is computed based on a current estimate of the I/Q impairments of the transmitters at frequencies f and-f, wherein a first off-diagonal element of the matrix is computed based on a current estimate of the I/Q impairments of the transmitters at frequencies f and-f.

20. The computer system of claim 13, wherein the current estimate of the signal path comprises a measured amplitude of the frequency shifted signal at the frequency f.

21. The computer system of claim 20, wherein the current estimate of the signal path further comprises a measured rotation of the frequency shifted signal at frequency f.

22. The computer system of claim 13, wherein at least in a first execution of the set of operations, the current estimate of the signal path is based on a DC scaling and a DC rotation of the signal path.

23. The computer system of claim 22, wherein the program instructions, when executed by the processor, further cause the processor to determine the DC scaling and the DC rotation by:

providing a zero vector signal to a transmitter;

providing a non-zero DC vector signal to a transmitter;

the DC scaling and DC rotation are calculated based on a first DC vector response and a second DC vector response, wherein the first DC vector response is measured at the receiver in response to a zero vector signal, wherein the second DC vector response is measured at the receiver in response to a non-zero DC vector signal.