CN109257311B - Method and system for determining error vector magnitude - Google Patents
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Abstract
The invention provides a method for determining error vector magnitude, which comprises receiving a signal from a signal transmitter to obtain a baseband signal; estimating IQ-related error parameters of the baseband signals based on a pseudo-inverse matrix; correcting the baseband signal by using the IQ related error parameter to obtain a corrected baseband signal; determining an error vector magnitude for the signal transmitter based on the baseband signal and the modified baseband signal. According to the method, IQ related error parameters obtained based on the pseudo-inverse matrix are considered in the calculation process of the EVM so as to correct the received baseband signals, and therefore a more accurate EVM value is obtained.
Description
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a method and a system for determining error vector magnitude based on a pseudo-inverse matrix.
Background
Error Vector Magnitude (EVM) refers to the difference between an ideal Error-free reference signal (or reference signal) and an actual measured signal over time, and can be characterized as a complex number that includes both Magnitude and phase components. In a wireless communication system, a basic process of band transmission of digital signals is that a baseband signal at a transmitting end is orthogonally modulated and then transmitted to a receiving end through a wireless communication channel, and then the original baseband signal is recovered after the receiving end performs corresponding demodulation. In the transmission process, due to factors such as modulation errors generated by the modulator, the quality of radio frequency devices, phase-locked loop noise, thermal noise, design deviation of the modulator and the like, errors are generated in the modulation signals. This error can be measured using EVM. Accurate measurement of the EVM of a signal transmitter is important for communication system design and transmitter metrics. In order to improve the measurement accuracy of the EVM, it is necessary to compensate for an error generated in the transmission process of the estimated signal after receiving the signal, so as to obtain a relatively accurate reference signal.
For a quadrature modulation communication system, for example, 3G, LTE, a signal is divided into two paths of IQ, and the two paths of signals are respectively quadrature-modulated and then superposed to generate a radio frequency signal. However, the method for determining the transmitter EVM in the prior art has a main problem that only the frequency offset and/or the phase offset are corrected, and other parameters related to IQ, such as IQ two-path gain, IQ two-path dc offset, IQ phase imbalance, etc., are not considered sufficiently, so that various offsets generated during the signal transmission process cannot be calibrated comprehensively.
Accordingly, there is a need for improvements in the art to address the above-mentioned problems.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for efficiently estimating IQ related parameters by a pseudo-inverse matrix solution so as to obtain accurate EVM.
According to an aspect of the invention, a method of determining an error vector magnitude is provided. The method comprises the following steps:
step 1: receiving a signal from a signal transmitter to obtain a baseband signal;
step 2: estimating IQ-related error parameters of the baseband signals based on a pseudo-inverse matrix;
and step 3: correcting the baseband signal by using the IQ related error parameter to obtain a corrected baseband signal;
and 4, step 4: determining an error vector magnitude for the signal transmitter based on the baseband signal and the modified baseband signal.
In the method of the present invention, the IQ related error parameters include one or more of IQ two-path gain, IQ two-path dc offset, and IQ phase imbalance parameters.
In the method of the present invention, step 2 comprises:
step 21: representing the baseband signal as a system of equations:
wherein, IiRepresenting the real part, Q, of the ith symbol of the pilot sequence at the transmitting endiDenotes the imaginary part of the ith symbol of the pilot sequence at the transmitting end, N denotes the pilot length, I'iAnd Q'iRespectively the real and imaginary parts, A, of the pilot band of the baseband signal1Is the gain applied to the I path during transmission, A2Is the gain added on the Q path in the transmitting process, a and b are respectively the DC offset of IQ path introduced in the transmitting process, alpha and beta are the angle on IQ path carrier in the modulation,
step 22: the system of equations is further represented using a pseudo-inverse matrix as:
wherein, it is made
U+Is the pseudo-inverse of U;
step 23: calculating to obtain the IQ related error parameter:
α＝arctan[C2(1)/C1(1)]
β＝-arctan[C1(2)/C2(2)]
A1＝C1(1)/cosα
A2＝-C1(2)/sinβ
a＝C1(3)/(A1ejα)
b＝C2(3)/(A2ejβ)
wherein, C1(1)＝A1cosα，C1(2)＝-A2sinβ，
C2(1)＝A1sinα，C2(2)＝A2cosβ，
In the method of the present invention, before step 2, timing synchronization of the baseband signal is further included.
In the method of the present invention, before step 2, the method further comprises correcting the baseband signal by using the estimated frequency offset and phase offset.
According to a second aspect of the invention, a system for determining an error vector magnitude is provided. The system comprises:
a unit for receiving a signal from a signal transmitter to obtain a baseband signal;
means for estimating IQ-related error parameters of the baseband signal based on a pseudo-inverse matrix;
means for modifying the baseband signal using the IQ related error parameter to obtain a modified baseband signal;
means for determining an error vector magnitude of the signal transmitter based on the baseband signal and the modified baseband signal.
In the system of the present invention, the IQ related error parameters include one or more of IQ two-path gain, IQ two-path dc offset, and IQ phase imbalance parameters.
According to a third aspect of the invention, there is provided a receiver comprising the system for determining the magnitude of an error vector as provided by the invention.
Compared with the prior art, the method has the advantages that the estimated values of a plurality of IQ related error parameters can be obtained based on a pseudo-inverse matrix method so as to correct the received baseband signals, thereby obtaining more accurate EVM values.
Drawings
Embodiments of the invention are further described below with reference to the accompanying drawings, in which:
fig. 1 shows a flow diagram of a method of determining an EVM according to one embodiment of the invention.
Fig. 2 shows a functional unit diagram of a system for determining an EVM according to one embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions, design methods, and advantages of the present invention more apparent, the present invention will be further described in detail by specific embodiments with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Fig. 1 shows a schematic flow diagram of a method of determining an EVM according to one embodiment of the invention. As shown in fig. 1, the method according to the invention comprises the following steps:
1) step S110, obtaining baseband signals
In this step, a signal from a signal transmitter is received, resulting in a baseband signal.
For example, when testing the EVM of a signal transmitter with a test instrument (receiver), the signal transmitter to be tested is directly connected to the test instrument via a radio frequency cable, and the test instrument receives the signal at radio frequency and converts it into baseband IQ chip data, resulting in a baseband signal. For example, for TD-LTE system, after filtering by RRC layer, the resulting baseband signal can be expressed as (taking the ith group of signals as an example):
wherein n is the length of the synchronization window, A1Is the gain applied to the I path during transmission, A2Is the gain applied to the Q path during transmission, i.e. A1And A2Gains are respectively added on IQ two paths in the sending process; a and b are respectively introduced in the transmission processThe IQ two-path direct current bias, alpha and beta are angles on IQ two-path carrier waves during modulation, delta fi is frequency deviation error,
is the phase offset error, N (i) is the noise, Ts is the sampling period, ejα＝cos(α)+jsin(α)，ejβ＝cos(β)+jsin(β)。
According to an embodiment of the present invention, in order to obtain a more accurate baseband signal, after receiving a signal, a receiving end may first perform preprocessing on the signal, for example, smoothing, filtering, equalizing, and the like on the signal, so as to weaken the influence of noise interference introduced during transmission of the signal, intersymbol interference caused by signal sampling, and the like.
2) Step S120, timing synchronization
In order to correct the frequency and time offset of the signal caused by multipath fading, doppler shift, etc., symbol synchronization, or coarse synchronization, is required.
Assuming a coarse synchronization window of n, the signal is coded i<n, the length of which is the burst length plus the redundancy length, from
And obtaining each group of signal data, firstly carrying out symbol positioning on the data, then carrying out sampling point positioning, and finding out synchronous sampling points.
For symbol synchronization, the pilot sequence is arranged according to
Performing front and back symbol conjugation to construct a new local sequence, and taking out each symbol in the coarse synchronization window sequence to construct a new sequence; and (3) multiplying the new local sequence and the new sequence by the alignment, summing and modulo to obtain a correlation module value, calculating the correlation module value until the cycle of the coarse synchronization window is finished to obtain a correlation peak, wherein the peak point is a coarse synchronization point Sych _ P, and calculating the coarse frequency offset according to the following formula (2).
Wherein,
representing the coarse frequency offset, the angle function is used to find the complex signal angle,
representing that n groups of received signals are conjugate complex multiplied with ideal pilot frequency sequence to obtain a plurality of U2Value from
Get the maximum value of the conjugate complex multiplication (i.e., U at the coarse synchronization point Sych _ P)2Value), M is the interpolation multiple of the sample, TsIs the sample period.
The coarse synchronization signal is obtained through the coarse synchronization point Sych _ P and the signal structure. And taking out each group of coarse synchronization signals in the coarse synchronization window, and solving the amplitude variance of each group of signals, wherein the corresponding point of the minimum value of the variance is the position of the optimal synchronization point. Through the symbol timing synchronization process, a coarse synchronization signal and a coarse estimation of the frequency deviation can be obtained preliminarily. Coarse frequency deviation obtained in the step
Substituting Δ fi in equation (1) to correct S2,nTo obtain S3,n。
For communication signals under different standards, the timing synchronization method may be different due to different signal structures of the physical layer. For example, for LTE systems, depending on the inherent structure of the OFDM symbols, various algorithms may be employed for symbol synchronization, such as maximum likelihood estimation, blind estimation, etc. The basic procedure of timing synchronization belongs to the prior art, and is not described herein again.
3) Step S130, estimating frequency offset and phase deviation
For further estimation of frequency offset (or fine frequency offset estimation), a special synchronous data block is generated at the transmitting end, where the data block may be a symbol or a plurality of symbols, and the data block may be composed of 2 or more identical parts (i.e. redundant data). At the receiving end, the redundant data still have great correlation, and the carrier frequency offset of the system can be estimated by observing the phase angle offset of the corresponding received data.
For example, the characteristic that each burst of the communication system contains at least two pilot frequencies with the same length is utilized, from S3,nTaking out the two pilot sequences as xp(i) And xq(i) And calculating conjugate complex multiplication summation. Calculating the fine frequency offset Δ f according to equation (3):
wherein f issFor the sampling frequency, M is the interpolated multiple of the samples,sumthe sum, obtained for conjugate complex multiplication of the pilot sequence, of the angle function used to determine the complex signal angle, LdpIs the length of the pilot sequence, LdataIs the number of data symbols in the two pilot sequences,
indicating a coarse frequency offset. The frequency deviation estimation range of the fine frequency deviation algorithm can reach +/-5 KHz, and the estimation precision is within 1 Hz.
To pair
After removing the frequency deviation, obtaining
Reuse of
Calculating the coarse phase remaining in the phase part
Will be provided with
Segmenting the medium data and the pilot frequency band, and calculating the phase of each segment and the average value of the phases of the segments, wherein the phases are allThe value is the fine phase deviation
The total phase shift is
4) S140, correcting frequency offset and phase deviation
Using the estimated total phase offset correction S3,nIn (1)
Value of S is obtained4,n。
5) S150, estimating IQ parameters based on the pseudo-inverse matrix
The process of estimating the I/Q parameters is actually the process of solving a finite-dimension linear equation set by analyzing the formula (1), and the equation set cannot be directly solved by an inverse matrix because the coefficient matrix of the equation set is a rectangular matrix, so that the equation set is solved by introducing a pseudo-inverse matrix method. The pseudo-inverse matrix is a generalized inverse matrix that extends the method of solving a system of equations with an inverse matrix to the case of non-square matrix coefficients. The pseudo-inverse matrix may be obtained by QR (orthogonal trigonometric) decomposition.
Specifically, for the form of equation (1) in step S110, it can be simplified as:
wherein, I and Q are respectively the real part and the imaginary part of the signal guide band at the transmitting end, and I 'and Q' are respectively S4,nThe real and imaginary parts of the pilot band.
The two equations about I 'and Q' in formula (4) are respectively obtained by performing matrix operation:
wherein, IiRepresenting the real part of the ith symbol of the local (transmitting) pilot sequence, QiDenotes the imaginary part of the ith symbol of the local pilot sequence, N denotes the pilot length, I'iAnd Q'iRespectively the real and imaginary parts of the baseband signal pilot band.
Order:
the pseudo-inverse matrix of U is represented as U+From equations (5) and (6), we can obtain:
i.e. the column vector C can be calculated based on the pseudo-inverse matrix1And C2The value of each element in the vector is calculated according to the value of the obtained column vector to obtain IQ related error parameters including two paths of gain parameters A1And A2IQ two-path direct current offset, parameters a and b, IQ phase unbalance parameters alpha and beta, namely:
α＝arctan[C2(1)/C1(1)] (10)
β＝-arctan[C1(2)/C2(2)] (11)
A1＝C1(1)/cosα (12)
A2＝-C1(2)/sinβ (13)
a＝C1(3)/(A1ejα) (14)
b＝C2(3)/(A2ejβ) (15)
wherein, C2(1) Represents a column vector C2The value corresponding to the first element in (a), and so on,namely, there is the following correspondence relationship, C1(1)＝A1cosα，C1(2)＝-A2sinβ，
C2(1)＝A1sinα，C2(2)＝A2cosβ，
Therefore, the method introduces the pseudo-inverse matrix into the estimation of the I/Q related error parameters, solves the problem of solving the inverse matrix of the rectangular matrix, and improves the efficiency and the accuracy of IQ parameter estimation.
6) S160, correcting IQ related parameters
Correcting S according to the IQ-related parameters obtained in step S1504,nTo further improve the accuracy of the received signal.
7) S170, obtaining a reference signal
In this step, the baseband signal modified in step S160 is demodulated and then modulated to obtain a reference signal. For example, the modified baseband signal is demodulated and remodulated in the same modulation scheme as the transmitter to obtain modulated symbols, i.e., reference signals. In the TD-LTE system, modulation schemes such as BPSK, QPSK, 16QAM, 64QAM, and the like can be supported. The specific processes for modulation and demodulation belong to the prior art and are not described in detail herein.
8) S180, calculating Error Vector Magnitude (EVM)
The EVM is calculated according to the following equation (16):
in the above equation, EVM is the ratio of the root mean square value of the error vector to the root mean square value of the reference signal, and is expressed in percentage. Wherein S (n) represents the vector form of the received signal on the I-Q plane, corresponding to the baseband signal modified in step S120 and step S140, i.e. S4,nAnd r (n) represents a vector form of the reference signal, corresponding to the reference signal obtained in step S170.
It should be noted that, although the steps are described in a specific order, the steps are not necessarily performed in the specific order, as long as the required functions can be achieved. Some of these steps may be performed concurrently or may be optional. For example, for step S120, step S130 or step S140, although in practical applications, the estimation process of symbol synchronization and frequency offset is usually included to improve the calculation accuracy of EVM, these steps are not necessary, and it should be understood that S (n) in the calculation formula of EVM may correspond to S (n) in the case that these steps are optional2,nOr S3,nThe same applies to the process of solving the IQ related error parameters by using the pseudo-inverse matrix.
9) Determining whether it is a minimum EVM
In this step, the EVM values of the multiple sets of signals are searched, and the smallest EVM is selected for output or reporting.
In summary, the present invention can estimate a plurality of IQ error parameters simultaneously by using the pseudo-inverse matrix method to calibrate the received baseband signal, thereby obtaining a more accurate reference signal and calculating the EVM accurately reflecting the performance of the signal transmitter.
Fig. 2 shows a functional unit diagram of a system for determining an EVM according to one embodiment of the present invention.
Corresponding to the method shown in fig. 1, the system shown in fig. 2 comprises a signal receiving unit 210, a timing synchronization unit 220, a frequency offset and phase offset estimation unit 230, a frequency offset and phase offset correction unit 240, an IQ related error parameter estimation unit 250, an IQ related error parameter correction unit 260, a reference signal calculation unit 270 and an error vector magnitude determination unit 280.
The signal receiving unit 210 is configured to receive a signal from a signal transmitter to obtain a baseband signal.
A timing synchronization unit 220, configured to calculate a coarse frequency offset to correct the received baseband signal.
And a frequency offset phase offset estimation unit 230, configured to calculate a fine frequency offset and a fine phase offset.
And a frequency offset and phase offset correction unit 240, configured to further correct the received baseband signal according to the obtained fine frequency offset and fine phase offset.
An IQ-related error parameter estimation unit 250, configured to estimate an IQ-related error parameter based on a pseudo-inverse matrix method.
An IQ dependent error parameter modification unit 260 for modifying the baseband signal with the IQ dependent error parameter.
And a reference signal calculating unit 270, configured to demodulate and remodulate the modified baseband signal to obtain a reference signal.
An error vector magnitude determining unit 280 for determining an error vector magnitude of the signal transmitter based on the obtained reference signal and the modified baseband signal.
According to the embodiment of the invention, the method and the system for determining the EVM can be used in test technologies or test equipment under various communication standards, for example, EVM measurement of WLAN, LTE or 3G terminals.
The method and system according to the invention can be applied to measure the EVM index of a receiver, for example in a test instrument to determine the EVM of a base station or a terminal, or in a base station to determine the EVM of a terminal from a signal received from the terminal.
Although some specific embodiments of the present invention have been described in detail by way of examples, it should be understood by those skilled in the art that the above examples are for illustrative purposes only and are not intended to limit the scope of the present invention. It will be appreciated by those skilled in the art that modifications may be made to the above embodiments without departing from the scope and spirit of the invention. The scope of the invention is defined by the appended claims.
Claims (9)
1. A method of determining the magnitude of an error vector comprising the steps of:
step 1: receiving a signal from a signal transmitter to obtain a baseband signal;
step 2: estimating IQ-related error parameters of the baseband signal based on a pseudo-inverse matrix, comprising:
step 21: representing the baseband signal as a system of equations:
wherein, IiRepresenting the real part, Q, of the ith symbol of the pilot sequence at the transmitting endiDenotes the imaginary part of the ith symbol of the pilot sequence at the transmitting end, N denotes the pilot length, I'iAnd Q'iRespectively the real and imaginary parts, A, of the pilot band of the baseband signal1Is the gain applied to the I path during transmission, A2Is the gain added on the Q path in the transmitting process, a and b are respectively the DC offset of IQ path introduced in the transmitting process, alpha and beta are the angle on IQ path carrier in the modulation,
step 22: the system of equations is further represented using a pseudo-inverse matrix as:
wherein, it is made
U+Is the pseudo-inverse of U;
step 23: calculating to obtain the IQ related error parameter:
α＝arctan[C2(1)/C1(1)]
β＝-arctan[C1(2)/C2(2)]
A1＝C1(1)/cosα
A2＝-C1(2)/sinβ
a＝C1(3)/(A1ejα)
b＝C2(3)/(A2ejβ)
wherein, C1(1)＝A1cosα，C1(2)＝-A2sinβ，
C2(1)＝A1sinα，C2(2)＝A2cosβ，
And step 3: correcting the baseband signal by using the IQ related error parameter to obtain a corrected baseband signal;
and 4, step 4: determining an error vector magnitude for the signal transmitter based on the baseband signal and the modified baseband signal.
2. The method of claim 1, wherein the IQ-related error parameters comprise one or more of IQ-two-path gain, IQ-two-path dc-bias, IQ-phase imbalance parameters.
3. The method of claim 1, wherein prior to step 2, further comprising timing synchronizing the baseband signal.
4. The method of claim 1, wherein prior to step 2, further comprising correcting the baseband signal using the estimated frequency offset and phase offset.
5. A system for determining an error vector magnitude, comprising:
a unit for receiving a signal from a signal transmitter to obtain a baseband signal;
means for estimating IQ-related error parameters of the baseband signal based on a pseudo-inverse matrix, comprising:
representing the baseband signal as a system of equations:
wherein, IiRepresenting the real part, Q, of the ith symbol of the pilot sequence at the transmitting endiDenotes the imaginary part of the ith symbol of the pilot sequence at the transmitting end, N denotes the pilot length, I'iAnd Q'iRespectively the real and imaginary parts, A, of the pilot band of the baseband signal1Is the gain applied to the I path during transmission, A2Is the gain added on the Q path in the transmitting process, a and b are respectively the DC offset of IQ path introduced in the transmitting process, alpha and beta are the angle on IQ path carrier in the modulation,
the system of equations is further represented using a pseudo-inverse matrix as:
wherein, it is made
U+Is the pseudo-inverse of U;
calculating to obtain the IQ related error parameter:
α＝arctan[C2(1)/C1(1)]
β＝-arctan[C1(2)/C2(2)]
A1＝C1(1)/cosα
A2＝-C1(2)/sinβ
a＝C1(3)/(A1ejα)
b＝C2(3)/(A2ejβ)
wherein, C1(1)＝A1cosα，C1(2)＝-A2sinβ，
C2(1)＝A1sinα，C2(2)＝A2cosβ，
Means for modifying the baseband signal using the IQ related error parameter to obtain a modified baseband signal;
means for determining an error vector magnitude of the signal transmitter based on the baseband signal and the modified baseband signal.
6. The system of claim 5, wherein the IQ-related error parameters include one or more of IQ two-way gain, IQ two-way DC bias, and IQ phase imbalance parameters.
7. A receiver comprising a system according to any of claims 5-6 for determining an error vector magnitude of a signal transmitter.
8. A computer-readable storage medium, in which a computer program is stored which, when being executed, is adapted to carry out the method of any one of claims 1-4.
9. A computing device comprising a processor and a memory, the memory having stored therein a computer program for implementing the method of any one of claims 1-4 when executed by the processor.
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