CN107359877B - All-digital blind compensation method for ultra-wideband signal time-interleaved sampling ADC (analog to digital converter) - Google Patents

Abstract

The invention discloses a time-interleaved sampling ADC full-digital blind compensation method of ultra-wideband signals, and relates to the field of digital-analog hybrid circuits and signal processing. The invention carries out translation and folding on the sampled output signal, produces a group of orthogonal basis functions for representing the stray signal, estimates the parameters of the error signal by utilizing the least square algorithm, carries out progressive iteration, eliminates the mismatch error and finally realizes the error compensation of the ultra-wideband signal. The compensation process of the invention is not affected by analog circuits and error parameters, and only one FIR filter is needed in the compensation process, thereby saving a large amount of filter design work and reducing the complexity of digital processing.

Description

All-digital blind compensation method for ultra-wideband signal time-interleaved sampling ADC (analog to digital converter)

Technical Field

The invention relates to the field of digital-analog hybrid circuits and signal processing, in particular to a time-interleaved sampling ADC full-digital blind compensation method for ultra-wideband signals.

Background

With the rapid development of wireless communication, instrumentation and other electronic systems, the need for high-speed sampling is increasing. High-speed Analog-to-Digital converters (ADCs) are attracting research efforts of a large number of researchers as core devices. In the existing technology level, it is difficult for a monolithic ADC to simultaneously guarantee a high sampling rate (several GS/s to several tens of GS/s) and a high precision valid bit, and the power consumption thereof is sharply increased as the sampling rate is increased. Therefore, a system architecture of a Time-Interleaved ADC (TI-ADC) is commonly adopted.

The main idea of the TI-ADC is to interleave and sample signals at different time by a plurality of parallel sub-ADCs, and then recombine the signals by a multi-path converter, so as to increase the sampling rate by multiple times or even dozens of times. The sampling mode greatly reduces the requirements on the sampling rate of the sub ADC and the circuit design, and has obvious advantages on realizing a high-speed analog-digital acquisition system with low power consumption and low cost, thereby becoming one of the most main high-speed sampling ADC frameworks. Ideally, a plurality of parallel sub-ADCs of the TI-ADC have identical channel responses, and in practical design implementation, mismatch errors exist between the respective sub-channels, which mainly include: dc Offset (Offset), Gain error (Gain), clock Skew (Timing Skew), and wideband Mismatch (Bandwidth Mismatch). The presence of mismatch errors degrades the system performance of the TI-ADC and the effective number of bits (ENOB), Spurious Free Dynamic Range (SFDR) can be severely affected. Mismatch error compensation becomes one of the core techniques of the system in order to improve the overall performance of the TI-ADC in practical applications.

The error compensation method of the TI-ADC is divided from the processing domain of the signal, and is mainly divided into two types: analog-digital hybrid compensation and all-digital domain compensation. The analog-digital hybrid compensation method generally adopts digital sampling to estimate error amount, and then feeds the error amount back to an adjustable analog circuit to eliminate system errors, however, the compensation effect of the method is affected by power supply voltage, temperature, thermal noise and the like. In comparison, the full digital domain compensation technology completes the compensation of mismatch errors in a digital domain, avoids adverse effects brought by an analog circuit, has strong portability of a full digital domain compensation algorithm, and can adapt to different TI-ADC systems after parameter change and adjustment.

Conventional full digital domain compensation techniques can be further classified into two categories: the first type is full-digital domain non-blind compensation, the technology needs known information of input signals to estimate mismatch error parameters or set filter coefficients, error parameters need to be recalculated when the system error amount changes, and particularly under the condition that the sampling rate is as high as dozens of GS/s, the process of adjusting the parameters can bring about a large amount of information loss, so that the method is difficult to meet the situation of dynamic parameter change; the second type is full digital domain blind compensation, the technology generates a new signal by performing a series of conversion on sampling output, and then performs correlation with an original actual output signal to estimate mismatch error parameters.

Disclosure of Invention

In order to overcome the defects and shortcomings in the prior art, the invention provides a full-digital blind compensation method for the time-interleaved sampling ADC of the ultra-wideband signal. The compensation process of the invention is not affected by analog circuits and error parameters, and only one FIR filter is needed in the compensation process, thereby saving a large amount of filter design work and reducing the complexity of digital processing.

In order to solve the problems in the prior art, the invention is realized by the following technical scheme:

the time interleaving sampling ADC full-digital blind compensation method of the ultra-wideband signal is characterized in that: and translating and folding the sampled output signal to produce a group of orthogonal basis functions for representing the stray signal, estimating parameters of the error signal by using a least square algorithm, performing progressive iteration, eliminating mismatch errors and finally realizing error compensation of the ultra-wideband signal.

Comprising acquisition of a sampled output signal: establishing a TI-ADC error model, wherein the error model comprises M sub-channels, each channel has different direct current offset, gain and sampling clock, and the frequency response of the mth channel is expressed as:

wherein, △_gmAnd △_tmRespectively representing the gain error and the clock skew error of the mth channel, wherein omega represents the normalized angular frequency, and the value range of omega is-pi is not less than omega is not more than pi;

recombining sampling output of each channel to obtain a frequency domain expression of TI-ADC sampling output y (n):

wherein

First item X (j)ω) is a frequency domain representation of the ideal sampled input signal x (n); the second term represents the spurious signals caused by gain error and clock skew, shifted in frequency by ω (j ω) for the ideal signal X (j ω)_s,iThen modulating; the third term represents the spurious signal caused by DC offset, and is a set of frequencies at ω_o,iThe single tone signal of (a).

The translating and folding of the sampling output signal specifically means: production of corresponding basis functions x by means of frequency translation and folding_B,i(n) spurious signals caused by DC offset, directly using the single-tone signal as the basis function o_B,i(n)；

Preprocessing signals by Hilbert transform, converting real signals into complex signals for processing, and setting y_B(n) and x_B(n) are the signals after Hilbert transform of y (n) and x (n), respectively, i.e.

Wherein HT {. denotes a Hilbert transform;

by means of frequency translation and folding, can obtain

Re {. is a real part operation, and thus y is obtained_BThe expression of (n) is as follows:

for the ultra-wideband signal, the mixing phenomenon exists between the spurious signal and the ideal signal caused by the gain and the clock skew, and in order to reduce the influence of the mixing, the mixing phenomenon exists

Wherein

Im {. is } to represent an imaginary part operation;

in formulae (5) and (8) using y_B(n) substitution of x_B(n) to obtain y_Bi(n) and

two sets of basis functions; writing the equations (6) and (7) into a matrix form to obtain a blind estimation method of error parameters:

wherein { }^TAnd { }⁺Respectively representing transpose and pseudo-inverse operations, y_BRepresenting a sampled output vector, having a length of N; u and

representing a matrix of basis functions of size N × (2M-1), w and

an error parameter vector of length (2M-1);

obtained from the above formulas (4) to (9):

thus, the signal after compensation is:

wherein mu represents the compensation step size and takes a value between 0 and 1.

Compared with the prior art, the beneficial technical effects brought by the invention are as follows:

1. compared with the traditional analog-digital mixed compensation method, the method disclosed by the invention directly processes the sampling signal in a digital domain, does not need to design a redundant analog circuit adjusting module, and can be suitable for TI-ADC systems with different channel numbers. Compared with the traditional full digital domain non-blind compensation method, the method does not need prior information of signals, and is suitable for the situation of dynamic change of system parameters.

2. Compared with the traditional full digital domain blind compensation method, the method has the advantages that the error parameters are directly calculated, complex filter design and correlation solving processes are not needed, extraction and interpolation processing are not needed, the storage space is saved, and the complexity is lower.

3. Compared with the traditional ultra-wideband signal compensation method, the method adopts the frequency translation and folding method to estimate the error signal, does not need a system to meet the oversampling condition, and does not need an additional filter to separate the error signal, so that the method has stronger universality on the input signal.

Drawings

FIG. 1 is a schematic diagram of an error model of a time interleaved sampling ADC (TI-ADC);

FIG. 2 is a graph of the spectrum of the 4-channel TI-ADC sample output;

FIG. 3 is a flow chart of an implementation of the ultra-wideband all-digital blind compensation method of the present invention;

fig. 4 is a comparison graph of compensation effects under an ultra wideband signal.

Detailed Description

Example 1

Referring to fig. 1 and 3 of the specification, this embodiment discloses:

the full-digital blind compensation method of the time-interleaved sampling ADC of the ultra-wideband signal is characterized in that a sampling output signal is translated and folded to produce a group of orthogonal basis functions for representing stray signals, parameters of error signals are estimated by using a least square algorithm, progressive iteration is carried out, mismatch errors are eliminated, and finally error compensation of the ultra-wideband signal is achieved. Compared with the traditional analog-digital mixed compensation method, the method disclosed by the invention directly processes the sampling signal in a digital domain, does not need to design a redundant analog circuit adjusting module, and can be suitable for TI-ADC systems with different channel numbers. Compared with the traditional full digital domain non-blind compensation method, the method does not need prior information of signals, and is suitable for the situation of dynamic change of system parameters. Compared with the traditional full digital domain blind compensation method, the method has the advantages that the error parameters are directly calculated, complex filter design and correlation solving processes are not needed, extraction and interpolation processing are not needed, the storage space is saved, and the complexity is lower. Compared with the traditional ultra-wideband signal compensation method, the method adopts the frequency translation and folding method to estimate the error signal, does not need a system to meet the oversampling condition, and does not need an additional filter to separate the error signal, so that the method has stronger universality on the input signal.

Example 2

Referring to fig. 1-4 of the specification, this embodiment discloses as another preferred embodiment of the present invention:

the full-digital blind compensation method of the time interleaving sampling ADC of the ultra-wideband signal comprises the steps of firstly carrying out frequency translation and folding on a sampling output signal to generate a group of orthogonal basis functions for representing a stray signal, then estimating error parameters by using a least square (L eastSquare, L S) algorithm, and carrying out successive iteration to eliminate mismatch errors, thereby finally realizing the error compensation of the ultra-wideband signal.

The error model for the TI-ADC is shown in fig. 1, and the system contains M sub-channels, each with different dc offset, gain, and sampling clock. The frequency response of the mth channel (without dc offset) can be expressed as:

wherein, △_gmAnd △_tmThe gain error and the clock skew error of the mth channel are respectively expressed, and are both 0 under the ideal condition, and omega represents the normalized angular frequency, and the value range of the normalized angular frequency is-pi is less than or equal to omega is less than or equal to pi. By recombining the sampling outputs of the channels, a frequency domain expression of the sampling output y (n) of the TI-ADC can be obtained:

wherein

The first term X (j ω) is a frequency domain representation of the ideal sampled input signal X (n); the second term represents the spurious signals caused by gain error and clock skew, and can be considered as the ideal signal X (j ω) shifted in frequency by ω_s,iThen modulating; the third term represents the spurious signal caused by DC offset, and is a set of frequencies at ω_o,iThe single tone signal of (a). Fig. 2 shows a spectrum diagram of a 4-channel TI-ADC sampling output signal, which only needs to be compensated for the signal in the first nyquist frequency domain because the output signal has symmetry in the spectrum. Preprocessing of signals is achieved herein using the Hilbert Transform (HT), let y be_B(n) and x_B(n) are the signals after Hilbert transform of y (n) and x (n), respectively, i.e.

Wherein HT {. is } represents a Hilbert transform. In the first Nyquist frequency domain, the spurious signals caused by gain and clock skew contain image components, and the corresponding basis functions x need to be generated by a frequency translation and folding method_B,i(n) of (a). The spurious signal caused by DC offset can be directly used as the base function o_B,i(n) of (a). The two realization ideas are as follows:

re {. is a real part operation, and thus y is obtained_BThe expression of (n) is as follows:

for an ultra-wideband signal, a mixing phenomenon exists between a spurious signal and an ideal signal caused by gain and clock skew of the ultra-wideband signal, and in order to reduce the influence of the mixing, another set of expressions is given on the basis of (6):

wherein

Im {. is } represents taking the imaginary part operation. Note that in both (6) and (7), an ideal signal x is assumed_B(n) is known, whereas in practical blind compensation methods the ideal signal is unknown. Since the spurious signal in the sampled output is much smaller than the ideal signal, y is available in (5) and (8)_B(n) substitution of x_B(n) to obtain y_Bi(n) and

two sets of basis functions. Writing the equations (6) and (7) in a matrix form, thereby obtaining a blind estimation method of error parameters:

wherein { }^TAnd { }⁺Respectively representing transposing and pseudo-inverting operations. y is_BRepresenting a sampled output vector, having a length of N; u and

representing a matrix of basis functions of size N × (2M-1), w and

and the error parameter vector is (2M-1) in length. The specific production method is as follows:

thus, the compensated signal can be obtained as:

in the actual compensation process, the error amount in sampling output is reduced every time iteration is performed, so that the optimal compensation effect can be achieved through a loop iteration method, the method can be used for processing the sampling data in a segmented mode, under the scene with high real-time requirement, only a least Square algorithm needs to be rewritten into a minimum root Mean Square (L east Mean Square, L MS) algorithm, and the purpose of point-by-point processing can be achieved.

Claims (2)

1. The time interleaving sampling ADC full-digital blind compensation method of the ultra-wideband signal is characterized in that: translating and folding the sampling output signal to generate a group of orthogonal basis functions for representing the stray signals, estimating parameters of error signals by using a least square algorithm, carrying out progressive iteration, eliminating mismatch errors and finally realizing error compensation of the ultra-wideband signals;

comprising acquisition of a sampled output signal: establishing a TI-ADC error model, wherein the error model comprises M sub-channels, each channel has different direct current offset, gain and sampling clock, and the frequency response of the mth channel is expressed as:

wherein, △_gmAnd △_tmRespectively, the gain error and the clock skew error of the mth channel, and ω is the normalized angular frequency, whichThe value range is-pi is less than or equal to omega and less than or equal to pi;

recombining sampling output of each channel to obtain a frequency domain expression of TI-ADC sampling output y (n):

wherein

The first term X (j ω) is a frequency domain representation of the ideal sampled input signal X (n); the second term represents the spurious signals caused by gain error and clock skew, shifted in frequency by ω (j ω) for the ideal signal X (j ω)_s,iThen modulating; the third term represents the spurious signal caused by DC offset, and is a set of frequencies at ω_o,iThe single tone signal of (a).

2. The method for time-interleaved sampled ADC all-digital blind compensation of ultra-wideband signals as claimed in claim 1, wherein: the translating and folding of the sampling output signal specifically means: production of corresponding basis functions x by means of frequency translation and folding_B,i(n) spurious signals caused by DC offset, directly using the single-tone signal as the basis function o_B,i(n)；

Preprocessing signals by Hilbert transform, converting real signals into complex signals for processing, and setting y_B(n) and x_B(n) are the signals after Hilbert transform of y (n) and x (n), respectively, i.e.

Wherein HT { i } represents a Hilbert transform;

by means of frequency translation and folding, can obtain

Re { i } represents the operation of the real part, thus obtaining y_BThe expression of (n) is as follows:

for the ultra-wideband signal, the mixing phenomenon exists between the spurious signal and the ideal signal caused by the gain and the clock skew, and in order to reduce the influence of the mixing, the mixing phenomenon exists

Wherein

Im {. is } to represent an imaginary part operation;

in formulae (5) and (8) using y_B(n) substitution of x_B(n) to obtain y_Bi(n) and

two sets of basis functions; writing the equations (6) and (7) into a matrix form to obtain a blind estimation method of error parameters:

wherein { }^TAnd { }⁺Respectively representing transpose and pseudo-inverse operations, y_BRepresenting a sampled output vector, having a length of N; u and

representing a matrix of basis functions of size N × (2M-1), w and

the vector of error parameters is then used to determine,the length is (2M-1);

obtained from the above formulas (4) to (9):

thus, the signal after compensation is:

wherein mu represents the compensation step size and takes a value between 0 and 1.

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