A Design Method and System for Channel Equalizer with Flexibly Controllable Frequency Response Error

Abstract

The present invention discloses a design method and system for a channel equalizer with flexible controllability of frequency response error, belonging to the technical field of digital array channel equalizer design, and solving the problem that the prior art cannot flexibly control the fitting errors of the channel amplitude-frequency and phase-frequency responses; by constructing convex constraint conditions for the amplitude-frequency and phase-frequency response fitting errors, the channel equalizer design problem is transformed into a second-order cone programming optimization problem that can obtain a global optimal solution, and the design method has strong robustness and is convenient for practical engineering applications; at the same time, compared with the frequency-domain least squares design method, the channel equalizer design method provided by the present invention can independently and flexibly control the fitting errors of the channel amplitude-frequency response and phase-frequency response. When the engineering implementation resources are limited, appropriately relaxing the fitting error of the amplitude-frequency (or phase-frequency) response can obtain a higher-precision fitting error of the phase-frequency (or amplitude-frequency) response, and the control is flexible.

Description

Technical Field

[0001] The present invention belongs to the technical field of digital array channel equalizer design, and relates to a channel equalizer design method and system with flexible and controllable frequency response error. Background Art

[0002] With the continuous development of high-speed acquisition and digital signal processing technologies, wideband digital arrays have been widely used in the fields of radar, measurement and control communication, information confrontation, etc. due to their characteristics of wide airspace, wide frequency band coverage, and flexible beam design. In engineering applications, the receiving or transmitting channels of actual wideband digital arrays are inevitably affected by analog devices and A / D converters, resulting in frequency response inconsistency errors between channels. Such mismatch errors will seriously affect the performance of subsequent digital array processing.

[0003] In order to compensate for the frequency response inconsistency errors between channels and improve the performance of digital array processing, many literatures have studied the design of channel equalizers. For example, "Two Modified Adaptive Channel Equalization Methods" published in the Journal of Electronics & Information Technology in 2006; "Multi-Channel Equalization Calibration Technology Based on Wideband Digital Beamforming" published by Beijing Institute of Telemetry Technology in 2018; "Broadband Array Channel Calibration Based on Frequency Domain Equalization" published by Sun Hongliang in 2015; "Research on Engineering Implementation Methods of Wideband Array Channel Equalization" published by Nanjing Research Institute of Electronics Technology in 2019. These literatures all discuss a channel equalizer design method based on frequency domain least squares that is currently widely used in actual engineering. This method controls the diagonal weighting matrix to minimize the fitting error between the frequency responses of each channel after equalization and the frequency response of the reference channel within the system passband range. The fitting accuracy of the amplitude-frequency response of the equalizer is better than that of the phase-frequency response, but it cannot separately control the fitting errors of the amplitude-frequency and phase-frequency responses of the channels. From the sorted literatures, there are few literatures discussing channel equalizer design methods that can flexibly control the fitting accuracy of the amplitude-frequency and phase-frequency responses of channels. Summary of the Invention

[0004] The technical problem to be solved by the present invention is that the prior art cannot flexibly control the fitting errors of the amplitude-frequency and phase-frequency responses of channels.

[0005] The present invention solves the above technical problem through the following technical solutions:

[0006] A channel equalizer design method with flexible and controllable frequency response error, comprising the following steps:

[0007] Step 1: Divide the radio frequency working range of the digital array into P equally spaced discrete radio frequencies, measure the frequency responses at each discrete radio frequency, and calculate the inter-channel frequency responses at P discrete radio frequencies with the rth receiving or transmitting channel as the reference channel;

[0008] Step 2: Divide the sampling frequency range of the digital array into L equally spaced discrete frequencies, linearly interpolate the inter-channel frequency responses at P discrete radio frequencies, and calculate the frequency response values of all receive or transmit channels relative to the reference channel at the L discrete frequencies;

[0009] Step 3: According to the frequency response values of all receive or transmit channels relative to the reference channel at the L discrete frequencies, and the L discrete frequencies within the sampling frequency range, construct a real-valued Fourier transform matrix corresponding to the normalized discrete frequency set, and the reference frequency response vector of each receive or transmit channel equalizer; According to the given amplitude-frequency response of the low-pass filter, construct a real-valued fitting diagonal weighting matrix; According to the complex coefficient FIR-type channel equalizer coefficients corresponding to each receive or transmit channel, construct the channel equalizer coefficient vector of each receive or transmit channel;

[0010] Step 4: Given the constraint factor of the amplitude-frequency response fitting error and the constraint factor of the phase-frequency response fitting error, use the frequency response values of all receive or transmit channels relative to the reference channel within the system operating bandwidth, and the channel equalizer coefficient vectors of each receive or transmit channel, to construct constraint inequalities for constraining the amplitude-frequency response fitting error and the phase-frequency response fitting error;

[0011] Step 5: According to the vectors, matrices or inequalities obtained in Step 3 and Step 4, transform the channel equalizer design into a second-order cone programming optimization problem to obtain the global optimal solution, and by solving this second-order cone programming optimization problem, obtain the channel equalizer coefficient vectors of each receive or transmit channel.

[0012] By constructing convex constraint conditions for the amplitude-frequency and phase-frequency response fitting errors, the present invention transforms the channel equalizer design problem into a second-order cone programming optimization problem that can obtain the global optimal solution. The design method has strong robustness and is convenient for practical engineering applications; at the same time, compared with the frequency-domain least squares design method, the channel equalizer design method provided by the present invention can independently and flexibly control the amplitude-frequency response and phase-frequency response fitting errors of the channels. When the engineering implementation resources are limited, appropriately relaxing the amplitude-frequency (or phase-frequency) response fitting error can obtain a higher-precision phase-frequency (or amplitude-frequency) response fitting error, with flexible control.

[0013] Preferably, the Step 1 further includes:

[0014] Step 1-1: The radio frequency operating frequency range of the digital array is where is the minimum radio frequency operating frequency of the array, is the maximum radio frequency operating frequency of the array, then the operating bandwidth of the digital array is The frequency range of the array operating bandwidth The corresponding discrete frequency set Meet For any discrete frequency The digital array measures the frequency response of each receiving or transmitting channel at discrete frequencies At the frequency response Is the frequency response value of the m-th receiving or transmitting channel at discrete frequencies At the frequency response value;

[0015] Step 1-2: Taking the r-th (1 ≤ r ≤ M) receiving or transmitting channel as the reference channel, its frequency response is Use a complex coefficient FIR channel equalizer of order N-1 to fit the frequency response of each channel. The frequency response value of the m-th receiving or transmitting channel relative to the reference channel at discrete frequencies At the frequency response value Can be expressed as

[0016]

[0017] Among them, Is the normalized digital frequency, F s Is the sampling frequency of the digital array, And Are respectively Amplitude-frequency and phase-frequency responses.

[0018] Preferably, the step 2 further includes:

[0019] Step 2-1: The frequency response value of the m-th receiving or transmitting channel relative to the reference channel at discrete frequencies F l At the frequency response value A r,m (F l ) and Are respectively the amplitude-frequency and phase-frequency responses of G r,m (F l ). According to the amplitude-frequency responses of each receiving or transmitting channel at the discrete frequency set At the amplitude-frequency response Use linear interpolation to calculate the amplitude-frequency response value of each receiving or transmitting channel at the radio frequency operating frequency F l At the amplitude-frequency response value That is

[0020]

[0021] Step 2-2: According to the phase-frequency response errors of each receiving or transmitting channel at the discrete frequency set At the phase-frequency response error Use linear interpolation to calculate the phase-frequency response value of each receiving or transmitting channel at discrete frequencies F l At the phase-frequency response value That is

[0022]

[0023] Preferably, step 3 further includes:

[0024] Step 3-1: Normalize the discrete digital frequency set The corresponding real-valued Fourier transform matrix A L is a 2L×2N-dimensional matrix, and this matrix is expressed as

[0025]

[0026] Step 3-2: Given a low-pass filter with a normalized bandwidth of its frequency response value at the normalized discrete digital frequency set is Then the real-valued fitting diagonal weighted matrix W is a 2L×2L-dimensional matrix, and this matrix is expressed as

[0027]

[0028] where W(f l ) = W I (f l ) + j·W Q (f l ), l = 0, …, L - 1, W I (f l ) and W Q (f l ) are the real part and the imaginary part of W(f l ) respectively;

[0029] Step 3-3: According to the complex coefficient FIR-type channel equalizer coefficients corresponding to each receiving or transmitting channel Then the equalizer coefficient vectors of each receiving or transmitting channel are all 2N×1-dimensional vectors and can be expressed as

[0030] g m = [g I,m (0) g Q,m (0) g I,m (1) g Q,m (1) … g I,m (N - 1) g Q,m (N - 1)] T

[0031] where g m (n) = g I,m (n) + j·g Q,m (n), n = 0, …, N - 1, gI,m (n) and g Q,m (n) are respectively g m (n)'s real part and imaginary part, the superscript T is the matrix transpose operation;

[0032] Step 3-4: According to the frequency response values of all receiving or transmitting channels relative to the reference channel at the discrete frequency set the normalized discrete digital frequency set can be obtained and the reference frequency response values of the equalizers of each receiving or transmitting channel Therefore, the reference frequency response vector of the equalizer of each receiving or transmitting channel is a 2L×1 dimensional vector and can be expressed as

[0033]

[0034] wherein, and are respectively the real part and imaginary part of G r,m (f l ), the superscript T is the matrix transpose operation.

[0035] Preferably, step 4 further includes:

[0036] Step 4-1: The real-valued Fourier transform matrix A corresponding to the amplitude-frequency response of the m-th receiving or transmitting channel E,m can be expressed as

[0037]

[0038] wherein, is the phase-frequency response value of the m-th receiving or transmitting channel at the normalized digital discrete frequency f l ;

[0039] Step 4-2: The fitted amplitude-frequency response vector b of the m-th receiving or transmitting channel m can be expressed as

[0040]

[0041] wherein, δ u and δ l (l = 0, …, K-1) are both positive real numbers, and their calculation formulas are as follows

[0042] δ u = δ

[0043] δ l = δcos(ε) + |G r,m (fl )|(1 - cos(ε))l = 0, …, K - 1;

[0044] Step 4 - 3: The real - valued Fourier transform matrix A corresponding to the phase - frequency response of the m - th receiving (or transmitting) channel P,m can be expressed as

[0045] A P,m = [a PU (f0) a PL (f0) a PU (f1) a PL (f1) … a PU (f K-1 ) a PL (f K-1 )] T

[0046] where, for l = 0, …, K - 1, the 2N×1 - dimensional vector a PU (f l ) satisfies: when holds, there is

[0047]

[0048] When holds, there is

[0049]

[0050] When holds, there is

[0051]

[0052] For l = 0, …, K - 1, the 2N×1 - dimensional vector a PL (f l ) satisfies: when holds, there is

[0053]

[0054] When holds, there is

[0055]

[0056] When holds, there is

[0057]

[0058] where, sign{·} is the sign function, tan{·} is the tangent function, the superscript T represents the matrix transpose operation, a I (f l) and a Q (f l ),respectively, are

[0059] a I (fl) = [cos(2πf l ·0) sin(2πf l ·0) … cos(2πf l ·(N - 1)) sin(2πf l ·(N - 1))] T

[0060] a Q (f l ) = [-sin(2πf l ·0) cos(2πf l ·0) … -sin(2πf l ·(N - 1)) cos(2πf l ·(N - 1))]T.

[0061] A channel equalizer system with flexible and controllable frequency response error, comprising the following modules:

[0062] Frequency division module: Divide the radio frequency operating range of the digital array into P equally spaced discrete radio frequencies, measure the frequency responses at each discrete radio frequency, and calculate the inter-channel frequency responses at P discrete radio frequencies with the r-th receiving or transmitting channel as the reference channel;

[0063] Linear interpolation module: Divide the sampling frequency range of the digital array into L equally spaced discrete frequencies, linearly interpolate the inter-channel frequency responses at P discrete radio frequencies, and calculate the frequency response values of all receiving or transmitting channels relative to the reference channel at L discrete frequencies;

[0064] Data construction module: Construct a real-valued Fourier transform matrix corresponding to the normalized discrete frequency set, the reference frequency response vector of each receiving or transmitting channel equalizer, according to the frequency response values of all receiving or transmitting channels relative to the reference channel at L discrete frequencies and the L discrete frequencies within the sampling frequency range; Construct a real-valued fitting diagonal weighting matrix according to the given amplitude-frequency response of the low-pass filter; Construct the equalizer coefficient vector of each receiving or transmitting channel according to the complex coefficient FIR-type channel equalizer coefficients corresponding to each receiving or transmitting channel;

[0065] Inequality construction module: Given the constraint factors of the amplitude-frequency response fitting error and the phase-frequency response fitting error, use the frequency response values of all receiving or transmitting channels relative to the reference channel within the system operating bandwidth and the equalizer coefficient vectors of each receiving or transmitting channel to construct constraint inequalities for constraining the amplitude-frequency response fitting error and the phase-frequency response fitting error;

[0066] Second-order cone programming optimization module: Obtain each vector, matrix or inequality according to the data construction module and the inequality construction module, transform the channel equalizer design into a second-order cone programming optimization problem for obtaining the global optimal solution, and obtain the channel equalizer coefficient vectors of each receiving or transmitting channel by solving this second-order cone programming optimization problem.

[0067] Preferably, the frequency division module further includes: The radio frequency operating frequency range of the digital array is wherein, is the minimum radio frequency operating frequency of the array, is the maximum radio frequency operating frequency of the array, then the operating bandwidth of the digital array is The frequency range of the array operating bandwidth The corresponding discrete frequency set satisfies For any discrete frequency The digital array measures the frequency response of each receiving or transmitting channel at the discrete frequency at is the frequency response value of the m-th receiving or transmitting channel at the discrete frequency at;

[0068] Taking the r-th (1 ≤ r ≤ M) receiving or transmitting channel as the reference channel, its frequency response is Use a complex coefficient FIR-type channel equalizer of order N - 1 to fit the frequency responses of each channel. The frequency response value of the m-th receiving or transmitting channel relative to the reference channel at the discrete frequency can be expressed as

[0069]

[0070] wherein, is the normalized digital frequency, F s is the sampling frequency of the digital array, and are respectively the amplitude-frequency and phase-frequency responses of.

[0071] Preferably, the linear interpolation module further includes: The frequency response value l of the m-th receiving or transmitting channel relative to the reference channel at the discrete frequency F A r,m (F l ) and are respectively the amplitude-frequency and phase-frequency responses of G r,m (F l ). According to each receiving or transmitting channel in the discrete frequency set Amplitude-frequency response at Using linear interpolation, calculate the amplitude-frequency response value of each receiving or transmitting channel at the radio frequency operating frequency F l That is

[0072]

[0073] According to the phase-frequency response error of each receiving or transmitting channel in the discrete frequency set Using linear interpolation, calculate the phase-frequency response value of each receiving or transmitting channel at the discrete frequency F l That is

[0074]

[0075] Preferably, the data construction module further includes: a normalized discrete digital frequency set The corresponding real-valued Fourier transform matrix A L Is a 2L×2N-dimensional matrix, and this matrix is expressed as

[0076]

[0077] Given a low-pass filter with a normalized bandwidth of Its frequency response value at the normalized discrete digital frequency set Is Then the real-valued fitting diagonal weighted matrix W is a 2L×2L-dimensional matrix, and this matrix is expressed as

[0078]

[0079] Where, W(f l ) = W I (f l ) + j·W Q (f l ), l = 0, …, L - 1, W I (f l ) and W Q (f l ) are respectively the real part and the imaginary part of W(f l );

[0080] According to the complex coefficient FIR type channel equalizer coefficients corresponding to each receiving or transmitting channel Then the equalizer coefficient vector of each receiving or transmitting channel Is a 2N×1-dimensional vector and can be expressed as

[0081] g m = [g​​​I,m (0) g Q,m (0) g I,m (1) g Q,m (1) … g I,m (N - 1) g Q,m (N - 1)] T

[0082] where g m (n) = g I,m (n) + j·g Q,m (n), n = 0, …, N - 1, g I,m (n) and g Q,m (n) are the real and imaginary parts of g m (n) respectively, and the superscript T represents the matrix transpose operation;

[0083] According to the frequency response values of all receiving or transmitting channels relative to the reference channel at the discrete frequency set the normalized discrete digital frequency set can be obtained, and the reference frequency response values of the equalizers for the corresponding receiving or transmitting channels Therefore, the reference frequency response vectors of the equalizers for the receiving or transmitting channels are all 2L×1 - dimensional vectors and can be expressed as

[0084]

[0085] where and are the real and imaginary parts of G r,m (f l ) respectively, and the superscript T represents the matrix transpose operation.

[0086] Preferably, the inequality construction module further includes: the real - valued Fourier transform matrix A corresponding to the amplitude - frequency response of the m - th receiving or transmitting channel E,m which can be expressed as

[0087]

[0088] where is the phase - frequency response value of the m - th receiving or transmitting channel at the normalized digital discrete frequency f l ;

[0089] The fitting amplitude - frequency response vector b of the m - th receiving or transmitting channel m can be expressed as

[0090] ​

[0091] wherein, δ u and δ l (l = 0, …, K - 1) are all positive real numbers, and their calculation formulas are as follows

[0092] δ u = δ

[0093] δ l = δcos(ε) + |G r,m (f l )|(1 - cos(ε)) for l = 0, …, K - 1;

[0094] The real - valued Fourier transform matrix A corresponding to the phase - frequency response of the m - th receiving (or transmitting) channel P,m can be expressed as

[0095] A P,m = [a PU (f0) a PL (f0) a PU (f1) a PL (f1) … a PU (f K-1 ) a PL (f K-1 )] T

[0096] wherein, for l = 0, …, K - 1, the 2N×1 - dimensional vector a PU (f l ) satisfies: when , there is

[0097]

[0098] When , there is

[0099]

[0100] When , there is

[0101]

[0102] For l = 0, …, K - 1, the 2N×1 - dimensional vector a PL (f l ) satisfies: when , there is

[0103]

[0104] When , there is

[0105]

[0106] When it is the case that there are

[0107]

[0108] where sign{·} is the sign function, tan{·} is the tangent function, the superscript T is the matrix transpose operation, a I (f l ) and a Q (f l ) are respectively

[0109] a I (f l ) = [cos(2πf l ·0) sin(2πf l ·0) … cos(2πf l ·(N - 1)) sin(2πf l ·(N - 1))] T

[0110] a Q (f l ) = [-sin(2πf l ·0) cos(2πf l ·0) … -sin(2πf l ·(N - 1)) cos(2πf l ·(N - 1))] T .

[0111] The advantages of the present invention are as follows:

[0112] By constructing convex constraint conditions for the fitting errors of the amplitude-frequency and phase-frequency responses, the present invention transforms the channel equalizer design problem into a second-order cone programming optimization problem that can obtain a globally optimal solution. The design method has strong robustness and is convenient for practical engineering applications. At the same time, compared with the frequency-domain least squares design method, the channel equalizer design method provided by the present invention can independently and flexibly control the fitting errors of the channel amplitude-frequency response and phase-frequency response. When the engineering implementation resources are limited, by appropriately relaxing the fitting error of the amplitude-frequency (or phase-frequency) response, a higher-precision fitting error of the phase-frequency (or amplitude-frequency) response can be obtained, and the control is flexible.

[0113] The channel equalizer design method provided by the present invention is independent of the geometry of the digital array and is applicable to both conformal digital arrays and planar digital arrays.

[0114] The design method provided by the present invention can not only be used to design channel equalizers, but also be equally applicable to other scenarios based on the fitting of the reference (or known) frequency response of FIR filters. Description of the Drawings

[0115] Figure 1 is the structural diagram of a method for designing a channel equalizer with flexible and controllable frequency response error according to the first embodiment of the present invention;

[0116] Figure 2 is the simulation diagram of the measured amplitude-frequency response of three channels in the simulation experiment of a method for designing a channel equalizer with flexible and controllable frequency response error according to the first embodiment of the present invention;

[0117] Figure 3 is the simulation diagram of the measured group delay of three channels in the simulation experiment of a method for designing a channel equalizer with flexible and controllable frequency response error according to the first embodiment of the present invention;

[0118] Figure 4 is the simulation diagram of the amplitude-frequency response error after equalization of different channels by the least squares design method in the frequency domain in the simulation experiment of a method for designing a channel equalizer with flexible and controllable frequency response error according to the first embodiment of the present invention;

[0119] Figure 5 is the simulation diagram of the phase-frequency response error after equalization of different channels by the least squares design method in the frequency domain in the simulation experiment of a method for designing a channel equalizer with flexible and controllable frequency response error according to the first embodiment of the present invention;

[0120] Figure 6 is the simulation diagram of the amplitude-frequency response error after equalization of different channels by the second-order cone programming design method when the constraint condition 1 is satisfied in the simulation experiment of a method for designing a channel equalizer with flexible and controllable frequency response error according to the first embodiment of the present invention;

[0121] Figure 7 is the simulation diagram of the phase-frequency response error after equalization of different channels by the second-order cone programming design method when the constraint condition 1 is satisfied in the simulation experiment of a method for designing a channel equalizer with flexible and controllable frequency response error according to the first embodiment of the present invention;

[0122] Figure 8 is the simulation diagram of the amplitude-frequency response error after equalization of different channels by the second-order cone programming design method when the constraint condition 2 is satisfied in the simulation experiment of a method for designing a channel equalizer with flexible and controllable frequency response error according to the first embodiment of the present invention;

[0123] Figure 9 is the simulation diagram of the phase-frequency response error after equalization of different channels by the second-order cone programming design method when the constraint condition 2 is satisfied in the simulation experiment of a method for designing a channel equalizer with flexible and controllable frequency response error according to the first embodiment of the present invention;

[0124] Figure 10It is the simulation diagram of the remaining amplitude mismatch error after channel equalization in the simulation experiment of a channel equalizer design method with flexible and controllable frequency response error according to Embodiment 1 of the present invention;

[0125] Figure 11 It is the simulation diagram of the remaining phase mismatch error after channel equalization in the simulation experiment of a channel equalizer design method with flexible and controllable frequency response error according to Embodiment 1 of the present invention;

[0126] Figure 12 It is the amplitude-frequency response simulation diagram of the fractional delay filter in the simulation experiment of a channel equalizer design method with flexible and controllable frequency response error according to Embodiment 1 of the present invention;

[0127] Figure 13 It is the group delay simulation diagram of the fractional delay filter in the simulation experiment of a channel equalizer design method with flexible and controllable frequency response error according to Embodiment 1 of the present invention. Detailed implementation manners

[0128] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0129] The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings of the specification and specific embodiments:

[0130] Embodiment 1

[0131] See Figure 1 The structural diagram of a channel equalizer design method with flexible and controllable frequency response error according to Embodiment 1. A channel equalizer design method with flexible and controllable frequency response error of the present invention includes the following steps:

[0132] Step 1: The radio frequency operating frequency range of the digital array is wherein, is the minimum radio frequency operating frequency of the array, is the maximum radio frequency operating frequency of the array, then the operating bandwidth of the digital array is The frequency range of the operating bandwidth is divided into P equally spaced discrete frequency sets Taking the rth (1≤r≤M) receiving (or transmitting) channel as the reference channel, calculate the inter-channel frequency response at each frequency point of the discrete frequency set ​is the frequency response value of the m-th receiving (or transmitting) channel relative to the reference channel at the radio frequency operating frequency The calculation of the frequency response of each receiving (or transmitting) channel relative to the reference channel includes:

[0133] Step 1-1: The frequency range of the array operating bandwidth The corresponding discrete frequency set Satisfy For any discrete frequency The digital array measures the frequency response of each receiving (or transmitting) channel at the discrete frequency The frequency response at this point is the frequency response value of the m-th receiving (or transmitting) channel at the discrete frequency ;

[0134] Step 1-2: Taking the r-th (1≤r≤M) receiving (or transmitting) channel as the reference channel, its frequency response is If a complex coefficient FIR-type channel equalizer of order N-1 is used to fit the frequency response of each channel, then the frequency response value of the m-th receiving (or transmitting) channel relative to the reference channel at the discrete frequency can be expressed as where

[0135]

[0136] Among them, is the normalized digital frequency, F s is the sampling frequency of the digital array. and are respectively the amplitude-frequency and phase-frequency responses of.

[0137] Step 2: The sampling frequency of the digital array is F s , divide the frequency range [-F s / 2, F s / 2] into a set of L (L>P) equally spaced discrete frequencies Using linear interpolation, calculate the frequency response values of all receiving (or transmitting) channels relative to the reference channel at the discrete frequency set Specifically include: Step 2-1: The frequency response value of the m-th receiving (or transmitting) channel relative to the reference channel at the discrete frequency F

[0138] The frequency response value of the m-th receiving (or transmitting) channel relative to the reference channel at the discrete frequency F l is A r,m (F l ) and are respectively G r,m (Fl ) amplitude-frequency and phase-frequency responses; based on the amplitude-frequency responses of each receiving (or transmitting) channel at the discrete frequency set at Using linear interpolation, calculate the amplitude-frequency response value of each receiving or transmitting channel at the radio frequency operating frequency F l at That is

[0139]

[0140] Step 2-2: Based on the phase-frequency response errors of each receiving (or transmitting) channel at the discrete frequency set at Using linear interpolation, calculate the phase-frequency response value of each receiving (or transmitting) channel at the discrete frequency F l at That is

[0141]

[0142] Step 3: The normalized discrete digital frequency set corresponding to the discrete frequency set is Construct the normalized discrete digital frequency set corresponding real-valued Fourier transform matrix A L , real-valued fitting diagonal weighting matrix W, reference frequency response vector of each receiving (or transmitting) channel equalizer The complex coefficient FIR-type channel equalizer coefficients of order N-1 corresponding to each receiving (or transmitting) channel are Construct the equalizer coefficient vector of each receiving (or transmitting) channel Specifically including:

[0143] Step 3-1: The real-valued Fourier transform matrix A corresponding to the normalized discrete digital frequency set L is a 2L×2N-dimensional matrix, and this matrix is expressed as

[0144]

[0145] Step 3-2: Given a low-pass filter with a normalized bandwidth of , its frequency response value at the normalized discrete digital frequency set is Then the real-valued fitting diagonal weighting matrix W is a 2L×2L-dimensional matrix, and this matrix is expressed as

[0146]

[0147] where W(f l ) = W I (f l)+j·W Q (f l ),l=0,…,L-1. W I (f l ) and W Q (f l ) are W(f l )’s real and imaginary parts;

[0148] Step 3-3: According to the complex coefficient FIR type channel equalizer coefficient corresponding to each receiving (or transmitting) channel Then the equalizer coefficient vector of each receiving (or transmitting) channel is are all 2N×1 dimensional vectors, which can be expressed as

[0149] g m =[g I,m (0) g Q,m (0) g I,m (1) g Q,m (1) … g I,m (N-1) g Q,m (N-1)] T

[0150] Among them, g m (n) = g I,m (n)+j·g Q,m (n),n=0,…,N-1, g I,m (n) and g Q,m (n) are g m The real and imaginary parts of (n), the superscript T represents the matrix (or vector) transpose operation;

[0151] Step 3-4: According to all receiving (or transmitting) channels in the discrete frequency set The frequency response value relative to the reference channel The normalized discrete digital frequency set can be obtained The corresponding reference frequency response value of each receiving (or transmitting) channel equalizer Therefore, the reference frequency response vector of each receiving (or transmitting) channel equalizer is are all 2L×1 dimensional vectors and can be expressed as

[0152]

[0153] in, and G r,m (f l) The real and imaginary parts, where the superscript T represents the matrix (or vector) transpose operation.

[0154] Step 4: Given the constraint factor δ for the amplitude-frequency response fitting error and the constraint factor ε for the phase-frequency response fitting error, construct the amplitude-frequency response fitting error constraint inequalities corresponding to each receiving (or transmitting) channel

[0155] A E,m ·g m ≤b m

[0156] where the 2K×2N-dimensional matrix A E,m is the real Fourier transform matrix corresponding to the amplitude-frequency response of the m-th receiving (or transmitting) channel, the 2N×1-dimensional vector g m is the equalizer coefficient vector of the m-th receiving (or transmitting) channel, and the 2K×1-dimensional vector b m is the fitted amplitude-frequency response vector of the m-th receiving (or transmitting) channel. The phase-frequency response fitting error constraint inequality

[0157] A P,m ·g m ≤0 2K×1

[0158] where the 2K×2N-dimensional matrix A P,m is the real Fourier transform matrix corresponding to the phase-frequency response of the m-th receiving (or transmitting) channel, 0 2K×1 is a column vector of all zeros with the number of elements equal to 2K, K is the number of normalized digital discrete frequencies within the system operating bandwidth. The amplitude-frequency and phase-frequency response fitting error constraint inequalities specifically include:

[0159] Step 4-1: The real Fourier transform matrix A corresponding to the amplitude-frequency response of the m-th receiving (or transmitting) channel E,m can be expressed as

[0160]

[0161] where is the phase-frequency response value of the m-th receiving (or transmitting) channel at the normalized digital discrete frequency f l ;

[0162] Step 4-2: The fitted amplitude-frequency response vector b of the m-th receiving (or transmitting) channel m can be expressed as

[0163]

[0164] where δ u and δ l(l = 0, …, K - 1) are all positive real numbers, and their calculation formulas are as follows

[0165] δ u = δ

[0166] δ l = δcos(ε) + |G r,m (f l )|(1 - cos(ε)) l = 0, …, K - 1

[0167] Step 4 - 3: The real - valued Fourier transform matrix A corresponding to the phase - frequency response of the m - th receiving (or transmitting) channel P,m can be expressed as

[0168] A P,m = [a PU (f0) a PL (f0) a PU (f1) a PL (f1) … a PU (f K-1 ) a PL (f K-1 )] T

[0169] where, for l = 0, …, K - 1, the 2N×1 - dimensional vector a PU (f l ) satisfies: when then, there is

[0170]

[0171] When then, there is

[0172]

[0173] When then, there is

[0174]

[0175] For l = 0, …, K - 1, the 2N×1 - dimensional vector a PL (f l ) satisfies: when then, there is

[0176]

[0177] When then, there is

[0178]

[0179] When then, there is

[0180]

[0181] where sign{·} is the sign function and tan{·} is the tangent function. The superscript T represents the transpose operation of a matrix (or vector), and a I (f l ) and a Q (f l ) are, respectively

[0182] a I (f l ) = [cos(2πf l ·0) sin(2πf l ·0) … cos(2πf l ·(N - 1)) sin(2πf l ·(N - 1))] T

[0183] a Q (f l ) = [-sin(2πf l ·0) cos(2πf l ·0) … -sin(2πf l ·(N - 1)) cos(2πf l ·(N - 1))] T .

[0184] Step 5: According to Steps 3 and 4, a second-order cone programming optimization method for solving the equalizer coefficients of each receiving (or transmitting) channel can be constructed. For the m-th receiving (or transmitting) channel, its second-order cone programming optimization method for the equalizer coefficients is

[0185]

[0186] where ||·||2 represents the L2 norm of a vector (or matrix), and the symbol s.t. represents the constraint condition. By solving the aforementioned second-order cone programming optimization problem, the channel equalizer coefficient vector of each receiving (or transmitting) channel can be obtained

[0187] The present invention verifies the correctness of the channel equalizer design method with flexible and controllable frequency response error through three scenarios of simulation experiments. In the first two scenarios, the number of channels to be equalized is 3, and the measured amplitude-frequency response and group delay of each channel are as Figure 2 and Figure 3As shown, the working bandwidth of the channel in the measured data is 200 MHz, and the sampling frequency is 240 MHz. When designing the equalizer, the number of discrete frequency points is taken as 2048, and the frequency response W(f) of the low-pass filter used for constructing the diagonal weighting matrix is the ideal frequency response, that is, it is set to 1 within the passband of the channel equalizer and 0 otherwise. Define the amplitude-frequency response fitting error fluctuation factor γ, and its relationship with the amplitude-frequency response fitting error constraint factor δ is

[0188]

[0189] Scenario 1: Flexible and controllable frequency response error

[0190] The order of the channel equalizer is 32, and the frequency-domain least squares design method is adopted. After channel equalization, the relative amplitude-frequency response and phase-frequency response errors between channels are as Figure 4 and Figure 5 shown. The maximum amplitude fitting error of the 3 equalized channels in the figure within the passband is 0.11153 dB, and the maximum phase fitting error is 0.302 degrees. From Figure 4 and Figure 5 it can be seen that the channel equalizer design method based on frequency-domain least squares has a relatively high fitting accuracy for the amplitude-frequency response, but a relatively poor fitting accuracy for the phase-frequency response. After the sampling frequency, working bandwidth, equalizer order, and weighting coefficient are given, the amplitude-frequency and phase-frequency response fitting errors are fixed and cannot be flexibly set for the fitting errors.

[0191] Constraint condition 1: The order of the channel equalizer is 32, the phase-frequency response fitting error constraint factor ε = 0.06 degrees, the amplitude-frequency response fitting error fluctuation factor γ = 0.7 dB. Adopt the channel equalizer design algorithm of second-order cone programming. After channel equalization, the relative amplitude-frequency response and phase-frequency response errors between channels are as Figure 6 and Figure 7 shown; the maximum amplitude fitting error of the 3 equalized channels in the figure within the passband is 0.18604 dB, and the maximum phase fitting error is 0.0599 degrees.

[0192] Constraint condition 2: The order of the channel equalizer is 32, the phase-frequency response fitting error constraint factor ε = 0.08 degrees, the amplitude-frequency response fitting error fluctuation factor γ = 0.5 dB. Adopt the channel equalizer design algorithm of second-order cone programming. After channel equalization, the relative amplitude-frequency response and phase-frequency response errors between channels are as Figure 8 and Figure 9 shown. The maximum amplitude fitting error of the 3 equalized channels in the figure within the passband is 0.11044 dB, and the maximum phase fitting error is 0.07996 degrees.

[0193] From Figures 6 to 9It can be seen that the channel equalizer design method based on second-order cone programming obtains an amplitude-frequency response fitting error that meets the constraint requirements, and the fitting accuracy of the phase-frequency response is significantly improved. Compared with the frequency-domain least squares design method, the proposed algorithm can flexibly set the fitting errors of the amplitude-frequency response and the phase-frequency response. By appropriately relaxing the fitting error of the amplitude-frequency response, a higher-precision fitting error of the phase-frequency response can be obtained.

[0194] Scenario 2: Equalization performance under different equalizer orders

[0195] The order of the channel equalizer takes values between 12 and 32, the fluctuation factor γ of the amplitude-frequency response fitting error is 0.5 dB, and the constraint factor ε of the phase-frequency response fitting error takes values between 1.6 degrees and 0.06 degrees. Under different equalizer orders, the frequency-domain least squares method and the second-order cone programming method are respectively adopted. After channel equalization, the remaining amplitude and phase mismatch errors are respectively as Figure 10 and 11 shown.

[0196] It can be seen from Figure 10 and Figure 11 that when the order of the channel equalizer is fixed, by appropriately relaxing the constraint of the amplitude-frequency response fitting error, the channel equalizer design algorithm based on second-order cone programming can obtain a more accurate fitting accuracy of the phase-frequency response.

[0197] Scenario 3: Other scenarios based on fitting the reference (or known) frequency response of FIR filters

[0198] In this scenario, the proposed design method is used to fit three FIR-type fractional delay filters. The bandwidth of the filter is 200 MHz, the sampling frequency is 240 MHz, and the fractional delay values in the passband are 0.2, 0.4, and 0.6 sampling periods respectively. The filter order is taken as 24, the fluctuation factor γ of the amplitude-frequency response fitting error is 0.3 dB, the constraint factor ε of the phase-frequency response fitting error is 0.0005 degrees, and the construction method of the diagonal weighting matrix is the same as that in Scenarios 1 and 2.

[0199] Figure 12 and Figure 13 respectively give the amplitude-frequency response and group delay of the three designed fractional delay filters. The maximum amplitude fluctuation error of the three fractional delay filters in the passband is 0.299 dB, and the maximum group delay fluctuation error is 0.0013 sampling periods. It can be seen from the figure that the design method proposed in the present invention can also be used to design fractional delay filters.

[0200] The present invention discloses a method and system for designing a channel equalizer with flexible and controllable frequency response error. According to the frequency responses measured by M channels, the frequency responses of all channels relative to the reference channel at the measured frequencies are calculated. The sampling frequency range of the digital array is discretized at equal intervals. The relative amplitude-frequency and phase-frequency responses between channels at the measured frequencies are linearly interpolated respectively, and the relative amplitude-frequency and phase-frequency responses between channels corresponding to each normalized digital discrete frequency within the sampling frequency range can be obtained. Using the interpolated amplitude-frequency and phase-frequency responses and the set of normalized digital discrete frequencies, a real Fourier transform matrix, a real fitting diagonal weighting matrix, a reference frequency response vector of each channel equalizer, and a channel equalizer coefficient vector are constructed. Given the constraint factors of the amplitude-frequency and phase-frequency response fitting errors, an amplitude-frequency and phase-frequency response fitting error constraint inequality is constructed, and the channel equalizer design is transformed into an optimization problem based on second-order cone programming. Solving this optimization problem can obtain the channel equalizer coefficient vectors of each channel. The advantages of the present invention are as follows: it can independently and flexibly control the amplitude-frequency response and phase-frequency response fitting errors of the channels. When the engineering implementation resources are limited, by appropriately relaxing the amplitude-frequency (or phase-frequency) response fitting error, a higher-precision phase-frequency (or amplitude-frequency) response fitting error can be obtained. It can be used not only for designing channel equalizers but also for other scenarios based on FIR filter fitting of reference (or known) frequency responses.

[0201] Embodiment 2

[0202] A channel equalizer system with flexible and controllable frequency response error according to the present invention includes the following modules:

[0203] Digital array radio frequency operating frequency module: The radio frequency operating frequency range of the digital array is Among them, is the minimum radio frequency operating frequency of the array, is the maximum radio frequency operating frequency of the array, Then the operating bandwidth of the digital array is The frequency range of the operating bandwidth is divided into P equally spaced discrete frequency sets Taking the rth receiving (or transmitting) channel as the reference channel, calculate the inter-channel frequency responses at the discrete frequency set at each frequency point is the frequency response value of the mth receiving (or transmitting) channel relative to the reference channel at the radio frequency operating frequency ; The calculation of the frequency responses of each receiving (or transmitting) channel relative to the reference channel includes:

[0204] The frequency range of the array operating bandwidth The corresponding discrete frequency set satisfies For any discrete frequency The digital array measures the frequency responses of each receiving (or transmitting) channel at discrete frequencies at is the frequency response value of the m-th receiving (or transmitting) channel at the discrete frequency at

[0205] Taking the r-th (1 ≤ r ≤ M) receiving (or transmitting) channel as the reference channel, its frequency response is If a complex coefficient FIR-type channel equalizer of order N - 1 is used to fit the frequency responses of each channel, then the frequency response value of the m-th receiving (or transmitting) channel relative to the reference channel at the discrete frequency at can be expressed as

[0206]

[0207] where is the normalized digital frequency, and F s is the sampling frequency of the digital array and are respectively the amplitude-frequency and phase-frequency responses of

[0208] Sampling frequency module of the digital array: The sampling frequency of the digital array is F s , and the frequency range [-F s / 2, F s / 2] is divided into a set of L (L > P) equally spaced discrete frequencies Using linear interpolation, calculate the frequency response values of all receiving (or transmitting) channels relative to the reference channel at the discrete frequency set at Specifically, it includes

[0209] The frequency response value of the m-th receiving (or transmitting) channel relative to the reference channel at the discrete frequency F l at A r,m (F l ) and are respectively the amplitude-frequency and phase-frequency responses of G r,m (F l ); According to the amplitude-frequency responses of each receiving (or transmitting) channel at the discrete frequency set at Using linear interpolation, calculate the amplitude-frequency response value of each receiving or transmitting channel at the RF operating frequency F l at That is

[0210]

[0211] According to the phase-frequency response errors of each receiving (or transmitting) channel at the discrete frequency set and using linear interpolation, calculate the phase-frequency response values of each receiving (or transmitting) channel at the discrete frequency F That is l at which

[0212]

[0213] Data construction module: The discrete frequency set The corresponding normalized discrete digital frequency set is Construct the normalized discrete digital frequency set The corresponding real Fourier transform matrix A L , the real fitting diagonal weighted matrix W, and the reference frequency response vector of each receiving (or transmitting) channel equalizer The complex coefficient FIR type channel equalizer coefficients of order N - 1 corresponding to each receiving (or transmitting) channel are Construct the channel equalizer coefficient vector of each receiving (or transmitting) channel Specifically including:

[0214] The normalized discrete digital frequency set The corresponding real Fourier transform matrix A L is a 2L×2N dimensional matrix, and this matrix is expressed as

[0215]

[0216] Given a low-pass filter with a normalized bandwidth of , its frequency response value at the normalized discrete digital frequency set is Then the real fitting diagonal weighted matrix W is a 2L×2L dimensional matrix, and this matrix is expressed as

[0217]

[0218] where W(f l ) = W I (f l ) + j·W Q (f l ), l = 0, …, L - 1. W I (f l ) and W Q (f l ) are the real part and the imaginary part of W(f l ) respectively;

[0219] According to the complex coefficient FIR type channel equalizer coefficients corresponding to each receiving (or transmitting) channel Then the equalizer coefficient vector of each receiving (or transmitting) channel is are all 2N×1 dimensional vectors, which can be expressed as

[0220] g m =[g I,m (0) g Q,m (0) g I,m (1) g Q,m (1) … g I,m (N-1) g Q,m (N-1)] T

[0221] Among them, g m (n) = g I,m (n)+j·g Q,m (n),n=0,…,N-1, g I,m (n) and g Q,m (n) are g m The real and imaginary parts of (n), the superscript T represents the matrix (or vector) transpose operation;

[0222] According to all receiving (or transmitting) channels in the discrete frequency set The frequency response value relative to the reference channel The normalized discrete digital frequency set can be obtained The corresponding reference frequency response value of each receiving (or transmitting) channel equalizer Therefore, the reference frequency response vector of each receiving (or transmitting) channel equalizer is are all 2L×1 dimensional vectors and can be expressed as

[0223]

[0224] in, and G r,m (f l ), and the superscript T represents the matrix (or vector) transpose operation.

[0225] Amplitude-frequency response fitting error construction module: Given the constraint factor δ of the amplitude-frequency response fitting error and the constraint factor ε of the phase-frequency response fitting error, construct the amplitude-frequency response fitting error constraint inequality corresponding to each receiving (or transmitting) channel

[0226] A E,m ·g m ≤ b m

[0227] Among them, the 2K×2N dimensional matrix AE,m is the real Fourier transform matrix corresponding to the amplitude-frequency response of the m-th receiving (or transmitting) channel, and the 2N×1 vector g m is the equalizer coefficient vector of the m-th receiving (or transmitting) channel, and the 2K×1 vector b m is the fitted amplitude-frequency response vector of the m-th receiving (or transmitting) channel. Phase-frequency response fitting error constraint inequality

[0228] A P,m ·g m ≤0 2K×1

[0229] wherein, the 2K×2N matrix A P,m is the real Fourier transform matrix corresponding to the phase-frequency response of the m-th receiving (or transmitting) channel, and 0 2K×1 is a column vector of all zeros with the number of elements equal to 2K. K is the number of normalized digital discrete frequencies within the system operating bandwidth. The amplitude-frequency and phase-frequency response fitting error constraint inequalities specifically include:

[0230] The real Fourier transform matrix A corresponding to the amplitude-frequency response of the m-th receiving (or transmitting) channel E,m can be expressed as

[0231]

[0232] wherein, is the phase-frequency response value of the m-th receiving (or transmitting) channel at the normalized digital discrete frequency f l ;

[0233] The fitted amplitude-frequency response vector b of the m-th receiving (or transmitting) channel m can be expressed as

[0234]

[0235] wherein, δ u and δ l (l = 0, …, K - 1) are both positive real numbers, and their calculation formulas are as follows

[0236] δ u = δ

[0237] δ l = δcos(ε) + |G r,m (f l )|(1 - cos(ε)) l = 0, …, K - 1

[0238] The real Fourier transform matrix A corresponding to the phase-frequency response of the m-th receiving (or transmitting) channel P,m can be expressed as

[0239] A P,m = [a PU (f0) a PL (f0) a PU (f1) a PL (f1) … a PU (f K-1 ) a PL (f K-1 )] T

[0240] where, for l = 0, …, K - 1, the 2N×1 dimensional vector a PU (f l ) satisfies: when , there is

[0241]

[0242] When , there is

[0243]

[0244] When , there is

[0245]

[0246] For l = 0, …, K - 1, the 2N×1 dimensional vector a PL (f l ) satisfies: when , there is

[0247]

[0248] When , there is

[0249]

[0250] When , there is

[0251]

[0252] where sign{·} is the sign function and tan{·} is the tangent function. The superscript T represents the transpose operation of a matrix (or vector), a I (f l ) and a Q (f l ), are respectively

[0253] a I (f l ) = [cos(2πf l·0) sin(2πf l ·0) … cos(2πf l ·(N - 1)) sin(2πf l ·(N - 1))] T

[0254] a Q (f l ) = [-sin(2πf l ·0) cos(2πf l ·0) … -sin(2πf l ·(N - 1)) cos(2πf l ·(N - 1))] T 。

[0255] Second - order cone programming optimization module: According to steps 3 and 4, a second - order cone programming optimization method for solving the equalizer coefficients of each receiving (or transmitting) channel can be constructed. For the m - th receiving (or transmitting) channel, the second - order cone programming optimization method for its equalizer coefficients is

[0256]

[0257] where, ||·||2 represents calculating the L2 - norm of a vector (or matrix), and the symbol s.t. represents the constraint condition. By solving the aforementioned second - order cone programming optimization problem, the equalizer coefficient vectors of each receiving (or transmitting) channel can be obtained

[0258] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A channel equalizer design method with flexible and controllable frequency response error, characterized by: The following steps are involved: Step 1: Divide the RF working range of the digital array into P equally spaced discrete RF frequencies, measure the frequency response at each discrete RF frequency, and use the rth receiving or transmitting channel as the reference channel to calculate the inter-channel frequency response at the P discrete RF frequencies; Step 2: The sampling frequency range of the digital array is divided into L equally spaced discrete frequencies, the inter-channel frequency responses at P discrete RF frequencies are linearly interpolated, and the frequency response values ​​of all receiving or transmitting channels at the L discrete frequencies relative to the reference channel are calculated; Step 3: According to the frequency response values ​​of all receiving or transmitting channels at L discrete frequencies relative to the reference channel and the L discrete frequencies within the sampling frequency range, construct a real Fourier transform matrix corresponding to the normalized discrete frequency set and a reference frequency response vector of each receiving or transmitting channel equalizer; according to the given low-pass filter amplitude-frequency response, construct a real fitting diagonal weighting matrix; according to the complex coefficient FIR type channel equalizer coefficient corresponding to each receiving or transmitting channel, construct the equalizer coefficient vector of each receiving or transmitting channel; Step 4: Given the constraint factor of the amplitude-frequency response fitting error and the constraint factor of the phase-frequency response fitting error, use the frequency response values ​​of all receiving or transmitting channels within the system working bandwidth relative to the reference channel, as well as the equalizer coefficient vector of each receiving or transmitting channel to construct the amplitude-frequency response fitting error constraint inequality corresponding to each receiving or transmitting channel. A E,m ·g m ≤b m Among them, A E,m is the real-number Fourier transform matrix corresponding to the amplitude-frequency response of the mth receiving or transmitting channel, A E,m is a 2K×2N dimensional matrix; g m is the mth receiving or transmitting channel equalizer coefficient vector, g m is a 2N×1 dimensional vector; b m is the fitted amplitude-frequency response vector of the mth receiving or transmitting channel, b m is a 2K×1 dimensional vector; K is the number of normalized digital discrete frequencies within the system operating bandwidth; Construct the phase-frequency response fitting error constraint inequality corresponding to each receiving or transmitting channel A P,m ·g m ≤0 2K×1 Among them, A P,m is the real-number Fourier transform matrix corresponding to the phase-frequency response of the mth receiving or transmitting channel, A P,m is a 2K×2N dimensional matrix; 2K×1 is an all-zero column vector with 2K elements; The step 4 also includes: Step 4-1: The real Fourier transform matrix A corresponding to the amplitude-frequency response of the mth receiving or transmitting channel E,m Specifically in, The mth receiving or transmitting channel at the normalized digital discrete frequency f l Phase-frequency response value at ; Step 4-2: Fitting frequency response vector b of the mth receiving or transmitting channel m Specifically Among them, δ u and δ l are all positive real numbers, l=0,…,K-1, and the calculation formula is as follows d u =d δ l =δcos(ε)+|G r,m (f l )|(1-cos(ε))l=0,…,K-1; where ε is the constraint factor of the phase-frequency response fitting error; Step 4-3: The real Fourier transform matrix A corresponding to the phase-frequency response of the mth receiving or transmitting channel P,m Specifically A P,m =[a PU (f0)a PL (f0)a PU (f1)a PL (f1)…a PU (f K-1 )a PL (f K-1 )] T Among them, for l = 0, ..., K-1, the 2N × 1-dimensional vector a PU (f l ) satisfies: when Sometimes, there is when Sometimes, there is when Sometimes, there is For l = 0, ..., K-1, the 2N × 1-dimensional vector a PL (f l ) satisfies: when Sometimes, there is when Sometimes, there is when Sometimes, there is Among them, sign{·} is the sign function, tan{·} is the tangent function, the superscript T is the matrix transpose operation, and a I (f l ) and a Q (f l ), respectively a I (f l )=[cos(2πf l `0)sin(2πf l ·0)…cos(2πf l ·(N-1))sin(2πf l ·(N-1))] T a Q (f l )=[-sin(2πf l ·0)cos(2πf l ·0)…-sin(2πf l `(N-1))cos(2πf l `(N-1))] T ; Step 5: According to steps 3 and 4, the vectors, matrices or inequalities are obtained, and the channel equalizer design is converted into a second-order cone programming optimization problem to obtain a global optimal solution. By solving this second-order cone programming optimization problem, the channel equalizer coefficient vector of each receiving or transmitting channel is obtained.

2. The method for designing a channel equalizer with a flexibly controllable frequency response error according to claim 1, characterized in that: The step 1 also includes: Step 1-1: The RF operating frequency range of the digital array is in, is the array minimum RF operating frequency, is the maximum RF operating frequency of the array, Then the working bandwidth of the digital array is Frequency range of array operating bandwidth The corresponding discrete frequency set satisfy For any discrete frequency Digital array measurement of each receive or transmit channel at discrete frequencies Frequency response at For the mth receiving or transmitting channel at discrete frequency Frequency response value at ; Step 1-2: Take the rth receiving or transmitting channel as the reference channel, and its frequency response is The frequency response of each channel is fitted using a complex coefficient FIR channel equalizer with an order of N-1. The mth receiving or transmitting channel is The frequency response value relative to the reference channel for in, is the normalized digital frequency, F s is the sampling frequency of the digital array, and They are The amplitude-frequency and phase-frequency responses.

3. The method for designing a channel equalizer with a flexibly controllable frequency response error according to claim 2, characterized in that: The step 2 also includes: Step 2-1: The mth receiving or transmitting channel is at a discrete frequency F l The frequency response value relative to the reference channel A r,m (F l )and G r,m (F l )'s amplitude-frequency and phase-frequency responses, according to the discrete frequency set of each receiving or transmitting channel The amplitude-frequency response at Use linear interpolation to calculate the value of each receiving or transmitting channel at the RF operating frequency F l The amplitude-frequency response value at Right now Step 2-2: According to each receiving or transmitting channel in the discrete frequency set Phase frequency response error at Use linear interpolation to calculate the discrete frequency F of each receiving or transmitting channel l Phase frequency response value at Right now 4. The method for designing a channel equalizer with a flexibly controllable frequency response error according to claim 3, characterized in that: The step 3 also includes: Step 3-1: Normalize the discrete digital frequency set The corresponding real-number Fourier transform matrix A L is a 2L×2N dimensional matrix, which is expressed as Step 3-2: Given a normalized bandwidth of A low-pass filter that normalizes the discrete digital frequency set The frequency response value at is F s is the sampling frequency of the digital array, then the real number fitting diagonal weighting matrix W is a 2L×2L dimensional matrix, which is expressed as Among them, W(f l )=W I (f l )+j·W Q (f l ),l=0,…,L-1, W I (f l ) and W Q (f l ) are W(f l )’s real and imaginary parts; Step 3-3: According to the complex coefficient FIR type channel equalizer coefficient corresponding to each receiving or transmitting channel Then the equalizer coefficient vector of each receiving or transmitting channel is are all 2N×1 dimensional vectors, specifically g m =[g I,m (0)g Q,m (0)g I,m (1)g Q,m (1)…g I,m (N-1)g Q,m (N-1)] T Among them, g m (n) = g I,m (n)+j·g Q,m (n),n=0,…,N-1, g I,m (n) and g Q,m (n) are g m The real and imaginary parts of (n), the superscript T indicates the matrix transpose operation; Step 3-4: According to all receiving or transmitting channels in the discrete frequency set The frequency response value relative to the reference channel The normalized discrete digital frequency set can be obtained Corresponding reference frequency response value of each receiving or transmitting channel equalizer Therefore, the reference frequency response vector of each receiving or transmitting channel equalizer is are all 2L×1 dimensional vectors, specifically in, and G r,m (f l ), and the superscript T indicates the matrix transpose operation.

5. A channel equalizer system with flexible and controllable frequency response error, characterized in that: Includes the following modules: Frequency division module: divides the RF working range of the digital array into P equally spaced discrete RF frequencies, measures the frequency response at each discrete RF frequency, and uses the rth receiving or transmitting channel as the reference channel to calculate the inter-channel frequency response at the P discrete RF frequencies; Linear interpolation module: The sampling frequency range of the digital array is divided into L equally spaced discrete frequencies, and the inter-channel frequency responses at P discrete RF frequencies are linearly interpolated to calculate the frequency response values ​​of all receiving or transmitting channels at L discrete frequencies relative to the reference channel; Data construction module: Based on the frequency response values ​​of all receiving or transmitting channels at L discrete frequencies relative to the reference channel and the L discrete frequencies within the sampling frequency range, construct the real Fourier transform matrix corresponding to the normalized discrete frequency set and the reference frequency response vector of each receiving or transmitting channel equalizer; based on the given low-pass filter amplitude-frequency response, construct the real fitting diagonal weighting matrix; based on the complex coefficient FIR type channel equalizer coefficient corresponding to each receiving or transmitting channel, construct the equalizer coefficient vector of each receiving or transmitting channel; Inequality construction module: Given the constraint factors of the amplitude-frequency response fitting error and the phase-frequency response fitting error, the frequency response values ​​of all receiving or transmitting channels within the system working bandwidth relative to the reference channel, as well as the equalizer coefficient vectors of each receiving or transmitting channel, are used to construct the amplitude-frequency response fitting error constraint inequality corresponding to each receiving or transmitting channel. A E,m ·g m ≤b m Among them, A E,m is the real-number Fourier transform matrix corresponding to the amplitude-frequency response of the mth receiving or transmitting channel, A E,m is a 2K×2N dimensional matrix; g m is the mth receiving or transmitting channel equalizer coefficient vector, g m is a 2N×1 dimensional vector; b m is the fitted amplitude-frequency response vector of the mth receiving or transmitting channel, b m is a 2K×1 dimensional vector; K is the number of normalized digital discrete frequencies within the system operating bandwidth; Construct the phase-frequency response fitting error constraint inequality corresponding to each receiving or transmitting channel A P,m ·g m ≤0 2K×1 Among them, A P,m is the real-number Fourier transform matrix corresponding to the phase-frequency response of the mth receiving or transmitting channel, A P,m is a 2K×2N dimensional matrix; 2K×1 is an all-zero column vector with 2K elements; The inequality construction module also includes: a real-number Fourier transform matrix A corresponding to the amplitude-frequency response of the mth receiving or transmitting channel E,m Specifically in, The mth receiving or transmitting channel at the normalized digital discrete frequency f l Phase-frequency response value at ; The fitted amplitude-frequency response vector b of the mth receiving or transmitting channel m Specifically Among them, δ u and δ l are all positive real numbers, l=0,…,K-1, and the calculation formula is as follows d u =d δ l =δcos(ε)+|G r,m (f l )|(1-cos(ε))l=0,…,K-1; where ε is the constraint factor of the phase-frequency response fitting error; The real-number Fourier transform matrix A corresponding to the phase-frequency response of the mth receiving (or transmitting) channel P,m Specifically A P,m =[a PU (f0) a PL (f0) a PU (f1) a PL (f1) … a PU (f K-1 ) a PL (f K-1 )] T Among them, for l = 0, ..., K-1, the 2N × 1-dimensional vector a PU (f l ) satisfies: when Sometimes, there is when Sometimes, there is when Sometimes, there is For l = 0, ..., K-1, the 2N × 1-dimensional vector a PL (f l ) satisfies: when Sometimes, there is when Sometimes, there is when Sometimes, there is Among them, sign{·} is the sign function, tan{·} is the tangent function, the superscript T is the matrix transpose operation, and a I (f l ) and a Q (f l ), respectively a I (f l )=[cos(2πf l ·0) sin(2πf l ·0) … cos(2πf l ·(N-1)) sin(2πf l ·(N-1))] T a Q (f l )=[-sin(2πf l ·0) cos(2πf l ·0) … -sin(2πf l ·(N-1)) cos(2πf l ·(N-1))] T ; Second-order cone programming optimization module: According to the data construction module and the inequality construction module, each vector, matrix or inequality is obtained, and the channel equalizer design is converted into a second-order cone programming optimization problem to obtain a global optimal solution. By solving this second-order cone programming optimization problem, the channel equalizer coefficient vector of each receiving or transmitting channel is obtained.

6. A channel equalizer system with flexibly controllable frequency response error according to claim 5, characterized in that: The frequency division module also includes: the radio frequency operating frequency range of the digital array is in, is the array minimum RF operating frequency, is the maximum RF operating frequency of the array, Then the working bandwidth of the digital array is Frequency range of array operating bandwidth The corresponding discrete frequency set satisfy For any discrete frequency Digital array measurement of each receive or transmit channel at discrete frequencies Frequency response at For the mth receiving or transmitting channel at discrete frequency Frequency response value at ; Taking the rth receiving or transmitting channel as the reference channel, its frequency response is The frequency response of each channel is fitted using a complex coefficient FIR channel equalizer with an order of N-1. The mth receiving or transmitting channel is The frequency response value relative to the reference channel for in, is the normalized digital frequency, F s is the sampling frequency of the digital array, and They are The amplitude-frequency and phase-frequency responses.

7. A channel equalizer system with flexibly controllable frequency response error according to claim 6, characterized in that: The linear interpolation module also includes: the mth receiving or transmitting channel at a discrete frequency F l The frequency response value relative to the reference channel A r,m (F l )and G r,m (F l )'s amplitude-frequency and phase-frequency responses, according to the discrete frequency set of each receiving or transmitting channel The amplitude-frequency response at Use linear interpolation to calculate the value of each receiving or transmitting channel at the RF operating frequency F l The amplitude-frequency response value at Right now According to the discrete frequency set of each receiving or transmitting channel Phase frequency response error at Use linear interpolation to calculate the discrete frequency F of each receiving or transmitting channel l Phase frequency response value at Right now 8. A channel equalizer system with flexibly controllable frequency response error according to claim 7, characterized in that: The data construction module also includes: normalizing the discrete digital frequency set The corresponding real-number Fourier transform matrix A L is a 2L×2N dimensional matrix, which is expressed as Given a normalized bandwidth of A low-pass filter that normalizes the discrete digital frequency set The frequency response value at is F s is the sampling frequency of the digital array, then the real number fitting diagonal weighting matrix W is a 2L×2L dimensional matrix, which is expressed as Among them, W(f l )=W I (f l )+j·W Q (f l ),l=0,…,L-1, W I (f l ) and W Q (f l ) are W(f l )’s real and imaginary parts; According to the complex coefficient FIR type channel equalizer coefficient corresponding to each receiving or transmitting channel Then the equalizer coefficient vector of each receiving or transmitting channel is are all 2N×1 dimensional vectors, specifically g m =[g I,m (0) g Q,m (0) g I,m (1) g Q,m (1) … g I,m (N-1) g Q,m (N-1)] T Among them, g m (n) = g I,m (n)+j·g Q,m (n),n=0,…,N-1, g I,m (n) and g Q,m (n) are g m The real and imaginary parts of (n), the superscript T indicates the matrix transpose operation; Based on all receive or transmit channels in discrete frequency sets The frequency response value relative to the reference channel The normalized discrete digital frequency set can be obtained Corresponding reference frequency response value of each receiving or transmitting channel equalizer Therefore, the reference frequency response vector of each receiving or transmitting channel equalizer is are all 2L×1 dimensional vectors, specifically in, and G r,m (f l ), and the superscript T indicates the matrix transpose operation.

Images