A method for dynamic nonlinear error estimation and correction of TIADC system based on Volterra series

Abstract

The invention discloses a method for estimating and correcting a dynamic nonlinear error of a TIADC system based on Volterra series. After an input signal passes through the TIADC system, a digital signal y(n) is obtained. A pseudo-ideal signal is generated by extracting a characteristic value from the digital signal y(n). Then, a least square solution is obtained by using a formula of a nonlinear structure and matrix transformation to obtain an estimated value of a dynamic nonlinear error coefficient. The estimated value of the dynamic nonlinear error coefficient is approximated by the output of the system through a digital reconstruction module to obtain an estimated value of the dynamic nonlinear error, i.e., the error. Subsequently, digital correction processing is performed to obtain a signal after correcting the dynamic nonlinear error. The invention reduces the complexity of a nonlinear model while better maintaining the effect of a correction method. At the same time, the correction process does not include any complex number operations and can be implemented only by a multiplier and an adder.

Description

Technical Field

[0001] The present invention belongs to the technical field of time interleaved analog-to-digital converter (TIADC) correction, and more specifically, relates to a TIADC system dynamic nonlinear error estimation and correction method based on Volterra series. Background Art

[0002] With the rapid development of science and technology, the transmission rate of modern electronic signals has entered the field of tens of gigahertz or even hundreds of gigahertz. In order to capture and observe high-speed signals in real time, many high-performance digitizers use a time-interleaved sampling architecture, namely a time-interleaved analog-to-digital converter (TIADC), to sample and convert analog signals into digital signals. In the time-interleaved analog-to-digital converter architecture, due to the defects of the analog front-end circuit and the influence of the differential nonlinearity and integral nonlinearity of each sub-ADC, harmonic components will be introduced into the output spectrum of the sub-ADC, which will bring nonlinear errors to the ADC. The nonlinear parameters of each sub-channel are not exactly the same, resulting in nonlinear mismatch errors. For the TIADC system of the oscilloscope with large bandwidth and high sampling rate, in order to achieve good calibration results, the channel mismatch error calibration algorithm must not only consider the channel linear error, but also the channel nonlinear error.

[0003] At present, there are relatively few studies on nonlinear error estimation and correction in TIADC systems, and they are mainly focused on the study of static nonlinear errors. These studies are based on the premise that nonlinear errors will not change with the frequency of the input signal. However, for large-bandwidth TIADC systems, this premise is usually not true, and the error coefficient will change significantly with the frequency of the input signal, which we call dynamic nonlinear error. Dynamic nonlinear errors have a large impact on system indicators and are difficult to handle. Existing nonlinear models often cannot be implemented in hardware because they involve complex operations. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a TIADC system dynamic nonlinear error estimation and correction method based on Volterra series to reduce the model complexity used for nonlinear error correction in the TIADC system, and provide a dynamic nonlinear modeling based on a nonlinear model and a method based on digital post-correction to improve the signal-to-noise ratio of the TIADC system.

[0005] To achieve the above-mentioned object of the invention, the present invention provides a method for estimating and correcting dynamic nonlinear errors of a TIADC system based on Volterra series, which is characterized by comprising the following steps:

[0006] (1) Pseudo-ideal signal generation and Volterra series fitting

[0007] (1.1) For an M-channel TIADC system, the digital signal y(n) acquired by the input analog signal x(t) is extracted by eigenvalue to generate an approximate or pseudo-ideal signal Among them, the characteristic values ​​include the maximum, minimum and phase of the digital signal y(n), t is the time, and n is the sampling point number;

[0008] (1.2) The pseudo-ideal signal Discretize the input x(n) of the Volterra series fitting to get the matrix X:

[0009]

[0010] in:

[0011] x p (n) = [x(n) p-1 x(n), x(n) p-1 x(n-1), x(n) p-1 x(n-2), ..., x(n) p-1 x(nq)], p = 0, 1, ..., P, n = 1, 2, ..., N, when p is less than or equal to the set value R, q = p, when p is greater than the set value R, q = R, R < P, P represents the nonlinear order, q represents the memory effect length, and N represents the identification length used for parameter estimation;

[0012] Then, the Volterra series fitting is performed with the actual collected digital signal y(n), and the following is obtained:

[0013] Y=Xh

[0014] Among them, Y=[y(1), y(2),..., y(N)] T , T represents transposition, h is the mismatch coefficient

[0015] (2) Dynamic nonlinear error coefficient estimation

[0016] Find the least squares solution for Y = Xh and get the solution of the dynamic nonlinear error coefficient h, that is, the estimated value of h is The superscript H indicates the conjugate transpose operation of the matrix, and the superscript -1 indicates the inverse operation of the matrix;

[0017] (3) Dynamic nonlinear error correction

[0018] (3.1) Reconstruct the error

[0019] The TIADC system output y(n) is used to approximate the actual input x(n), and the dynamic nonlinear error coefficient is estimated. Generate error

[0020]

[0021] Among them, f p (k 1 , …, k p+1 ) is the estimated value of the dynamic nonlinear error coefficient The result of "minus 1" on the first parameter of the first-order term, k 1 , …, k p+1 is the estimated value of the dynamic nonlinear error coefficient That is, the number of terms index of the Volterra kernel function;

[0022] (3.2) Error correction

[0023] Subtract the error from the output digital signal y(n) of the TIADC system The corrected signal can be obtained

[0024] The object of the invention of the present invention is achieved in this way:

[0025] In the dynamic nonlinear error estimation and correction method of the TIADC system based on Volterra series of the present invention, the input signal is passed through the TIADC system to obtain a digital signal y(n), and the pseudo ideal signal is generated by extracting the eigenvalue from the digital signal y(n). Then, the least squares solution is obtained through the formula of the nonlinear structure and matrix transformation to obtain the dynamic nonlinear error coefficient estimate Estimated dynamic nonlinear error coefficient The estimated value of the dynamic nonlinear error, i.e., the error, is obtained by approximating the output of the system through the digital reconstruction module. Then the digital correction process is performed by the adder to obtain the signal after correcting the dynamic nonlinear error.

[0026] At the same time, the TIADC system dynamic nonlinear error estimation and correction method based on Volterra series of the present invention also has the following beneficial effects:

[0027] (1) Based on the characteristics of the nonlinear error of the TIADC system, a method is proposed to regard the mismatch of multiple channels as part of the nonlinear error of the system. This method reduces the complexity of the nonlinear model while maintaining the effect of the correction method.

[0028] (2) According to the characteristics of the single-tone sinusoidal signal, the error of the dynamic nonlinearity of the system is estimated. During the correction process, only the error coefficient estimated in the foreground and the output of the system are needed. It is not necessary to wait for the error estimation process every time the system is started.

[0029] (3) In the correction method of the present invention, the correction process does not include any complex number operations, and can be implemented only with multipliers and adders. In practical applications, most TIADC digital post-correction algorithms are implemented in FPGAs, but FPGAs cannot process complex numbers. This method provides a good reference. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flow chart of a specific implementation method of the TIADC system dynamic nonlinear error estimation and correction method based on Volterra series of the present invention;

[0031] Figure 2 It is a signal processing schematic diagram of a specific implementation method of a TIADC system dynamic nonlinear error estimation and correction method based on Volterra series of the present invention;

[0032] Figure 3 It is a schematic diagram of generating a pseudo ideal signal from a digital signal collected by a TIADC system;

[0033] Figure 4 is a flowchart of a digital post-correction method based on error reconstruction;

[0034] Figure 5 It is the spectrum diagram of the test signal before correction;

[0035] Figure 6 It is a spectrum diagram of the test signal after being corrected by the method of the present invention. DETAILED DESCRIPTION

[0036] The specific implementation of the present invention is described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

[0037] Figure 1 , 2 They are respectively a flow chart and a principle schematic diagram of a specific implementation of the method for dynamic nonlinear error estimation and correction of a TIADC system based on Volterra series of the present invention.

[0038] In this embodiment, if Figure 1As shown, the method for estimating and correcting the dynamic nonlinear error of the TIADC system based on the Volterra series of the present invention comprises the following steps:

[0039] Step S1: Pseudo-ideal signal generation and Volterra series fitting

[0040] Step S1.1: Generate a pseudo-ideal signal

[0041] like Figure 2 As shown, for an M-channel TIADC system, the digital signal y(n) is collected from the input analog signal x(t), and then the pseudo-ideal signal generation module generates an approximate pseudo-ideal signal through eigenvalue extraction. Among them, Figure 3 As shown in , the characteristic values ​​include the maximum, minimum and phase of the digital signal y(n), t is the time, and n is the sampling point number. Figure 3 As shown, the characteristic values, namely the maximum, minimum and phase (not shown in the phase diagram), are extracted from the digital signal y(n), and then a pseudo ideal signal is generated based on the maximum, minimum and phase.

[0042] In this embodiment, according to the amplitude and phase characteristics of the sinusoidal signal, the digital output signal after the analog input signal is collected by the TIADC system is feature extracted to obtain the amplitude, offset and phase of the analog pseudo-ideal signal, and the discrete pseudo-ideal signal is obtained by discretizing the analog pseudo-ideal signal in subsequent calculations. It is particularly noted that in the foreground estimation process of this embodiment, it is assumed that the frequency of the training signal used for estimation is known, and the signal can be the actual sampling result obtained by the signal generator after passing through the TIADC system.

[0043] Step S1.2: Volterra series fitting to obtain matrix

[0044] In this embodiment, if Figure 2 As shown, the Volterra series fitting module converts the pseudo-ideal signal Discretize the input x(n) of the Volterra series fitting to get the matrix X:

[0045]

[0046] in:

[0047] x p (n) = [x(n) p-1 x(n), x(n) p-1 x(n-1), x(n) p-1 x(n-2), ..., x(n) p-1x(nq)], p=0, 1, ..., P, n=1, 2, ..., N, when p is less than or equal to the set value R, q=p, when p is greater than the set value R, q=R, R<P, P represents the nonlinear order, q represents the memory effect length, and N represents the identification length used for parameter estimation.

[0048] Specifically, when p = 0, q = 0, then x 0 (n) = x(n) 0-1 x(n)=1, that is, x 0 (n) has only one element, namely 1. When p = 1, q = 1, then x 1 (n) = [x(n) 1-1 x(n), x(n) 1-1 x(n-1)]=(n,x(n-1)], there are two elements, namely 1, and so on. When p is greater than the set value R, x p The number of elements in (n) is maintained at R+1.

[0049] In this embodiment, the nonlinear order P=3, and the set value R=2.

[0050] Then, the Volterra series fitting is performed with the actual collected digital signal y(n), and the following is obtained:

[0051] Y=Xh

[0052] Among them, Y=[y(1), y(2),..., y(N)] T , T represents transpose, and h is the mismatch coefficient.

[0053] Step S2: Dynamic nonlinear error coefficient estimation

[0054] like Figure 2 As shown, the Volterra series fitting module finds the least squares solution for Y = Xh and obtains the solution of the dynamic nonlinear error coefficient h, that is, the estimated value of h is The superscript H indicates the conjugate transpose operation of the matrix, and the superscript -1 indicates the inverse operation of the matrix.

[0055] Finding the least squares solution for Y=Xh is a common mathematical method, and the specific process will not be repeated here.

[0056] In this embodiment, the error coefficient of each channel in the TIADC system is represented by a unified system overall error coefficient, and there is no need to perform a 2π / M phase operation on the data, thereby greatly reducing the complexity of the matrix calculation process. At this time, the overall nonlinear error coefficient of the system represents the common error of each channel, which covers most of the nonlinear error components. It should be noted that if the high-order harmonics of the signal frequency have exceeded the bandwidth range of the TIADC system, the model can be reduced in order to unify the vector length of the error coefficient, and the high-order coefficients can be taken as zero.

[0057] In this embodiment, the estimation process needs to be able to cover most of the system bandwidth. Frequency points can be taken at certain intervals as training signals, and the error coefficient of the frequency between two frequency points is obtained by curve fitting.

[0058] Step S3: Dynamic nonlinear error correction

[0059] Step S3.1: Reconstruct the error

[0060] In this embodiment, if Figure 2 As shown, the TIADC system output y(n) is used to approximate the actual input x(n), and the dynamic nonlinear error coefficient is estimated. Generate error

[0061]

[0062] Among them, f p (k 1 , …, k p+1 ) is the estimated value of the dynamic nonlinear error coefficient The result of "minus 1" on the first parameter of the first-order term, k 1 , …, k p+1 is the estimated value of the dynamic nonlinear error coefficient That is, the number of terms in the Volterra kernel function. If p = 1, f 1 (k 1 ) points to the first-order kernel function f 1 The first parameter, f 1 (k 2 ) points to the first-order kernel function f 1 The second parameter of the Volterra series expression belongs to the prior art and will not be described in detail in the present invention.

[0063] Step S3.2: Error correction

[0064] In this embodiment, if Figure 2As shown, the error correction module subtracts the error from the output digital signal y(n) of the TIADC system. The corrected signal can be obtained In this embodiment, if Figure 4 As shown, the error correction module is an adder, the error Take the negative value and add it to the output digital signal y(n) to get the corrected signal

[0065] Example Simulation

[0066] In this embodiment, a four-channel TIADC system is simulated. The system consists of two ADC12DJ5200RF interleaved chips, each of which has two 5.2GSPS ADC cores. The sampling rate of the TIADC system is set to 20GSPS, and the total bandwidth of the analog input signal is 5GHz. Sine single-tone signals with frequencies of 1.251GHz, 1.351GHz, 1.451GHz and 1.551GHz are selected as test signals, and the amplitude range of the signal is -0.4 to 0.4V. Figure 5 As shown, the second harmonic and third harmonic of the single-tone test signal are both in-band, at twice the signal input frequency and three times the signal frequency, respectively. The second harmonic amplitudes of the test signal are -41.9479dB, -53.4766dB, -44.7922dB, and -44.53dB, respectively; the third harmonic amplitudes of the test signal are -40.117dB, -41.1539dB, -38.3111dB, and -39.4305dB, respectively. Figure 5 It can be clearly seen that the magnitude of the nonlinear error of the system is related to the frequency and is a dynamic nonlinear error. Figure 6 This is the spectrum after the dynamic nonlinear correction of the present invention. According to the comparison, it can be seen that the present invention can correct the dynamic nonlinear error of the TIADC system with an effect of about 6 to 17 dB. Finally, the signal-to-noise ratio of the system is improved. Compared with the method of correcting a single ADC separately, the method of the present invention is simpler and has a good correction effect.

[0067] Although the above describes the illustrative specific embodiments of the present invention to facilitate those skilled in the art to understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.

Claims

1. A method for estimating and correcting dynamic nonlinear errors of a TIADC system based on Volterra series, characterized in that: The following steps are involved: (1) Pseudo-ideal signal generation and Volterra series fitting (1.1) For an M-channel TIADC system, the digital signal y(n) acquired by the input analog signal x(t) is extracted by eigenvalue to generate an approximate or pseudo-ideal signal Among them, the characteristic values ​​include the maximum, minimum and phase of the digital signal y(n), t is the time, and n is the sampling point number; (1.2) The pseudo-ideal signal Discretize the input x(n) of the Volterra series fitting to get the matrix X: in: x p (n) = [x(n) p-1 x(n), x(n) p-1 x(n - 1), x(n) p-1 x(n - 2), …, x(n) p-1 x(n - q)], p = 0, 1, …, P, n = 1, 2, …, N. When p is less than or equal to the set value R, q = p; when p is greater than the set value R, q = R, where R < P, P represents the non - linear order, q represents the memory effect length, and N represents the identification length for parameter estimation; Then, the Volterra series fitting is performed with the actual collected digital signal y(n), and the following is obtained: Y=Xh Among them, Y=[y(1),y(2),…,y(N)] T , T represents transposition, h is the mismatch coefficient (2) Dynamic nonlinear error coefficient estimation Find the least squares solution for Y = Xh and get the solution of the dynamic nonlinear error coefficient h, that is, the estimated value of h is The superscript H indicates the conjugate transpose operation of the matrix, and the superscript -1 indicates the inverse operation of the matrix; (3) Dynamic nonlinear error correction (3.1) Reconstruct the error The TIADC system output y(n) is used to approximate the actual input x(n), and the dynamic nonlinear error coefficient is estimated. Generate error Among them, f p (k1,…,k p+1 ) is the estimated value of the dynamic nonlinear error coefficient The result of "minus 1" on the first parameter of the first-order term, k1,…,k p+1 is the estimated value of the dynamic nonlinear error coefficient That is, the number of terms index of the Volterra kernel function; (3.2) Error correction Subtract the error from the output digital signal y(n) of the TIADC system The corrected signal can be obtained 2. The method for dynamic nonlinear error estimation and correction of TIADC system based on Volterra series according to claim 1, characterized in that: The nonlinear order P=3, and the set value R=2.

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