Modulation broadband converter joint blind calibration method for scene with unknown sparseness

Abstract

The invention discloses a modulated broadband converter joint blind calibration method for a sparseness unknown scene, and belongs to the technical field of compressed sampling. The problems that a traditional calibration method is high in implementation process complexity and calibration cost, and the number of input signal sources needs to be predicted are solved. According to the method disclosed by the invention, the signal sparseness can be estimated by only modulating the sampling data actually output by the broadband converter during compressed sampling and combining an information theory criterion, so that synchronous solution of system joint blind calibration and signal reconstruction is realized, and meanwhile, system error calibration and accurate recovery of an original signal are completed. According to the method, a traditional active calibration method needing test excitation is not used for the calibration problem of the modulation broadband converter any more, and the system can be calibrated and the signal can be reconstructed under the condition that the sparseness is unknown, so that the implementation process is simple and convenient, and the calibration cost is greatly reduced. The method can be applied to joint blind calibration of the modulation broadband converter.

Description

Technical Field

[0001] This invention belongs to the field of compressed sampling technology, specifically relating to a joint blind calibration method for modulation broadband converters in scenarios with unknown sparsity. Background Technology

[0002] The Modulated Wideband Converter (MWC) is based on Compressed Sensing (CS), a novel sampling structure for sparse multi-frequency signals that enables compressed sampling and accurate reconstruction. It can sample signals at a sampling frequency much lower than the Nyquist frequency of the signal, and accurately recover the original signal with fewer observations.

[0003] In the hardware implementation of a modulation broadband converter system, the unknown amplitude and phase errors and mutual coupling effects of each channel affect the sampled values, making it difficult for the actual system to achieve the theoretical reconstruction effect. Furthermore, as the error increases, the original signal support set has a higher probability of reconstruction failure. Therefore, calibration of the non-ideal modulation broadband converter is necessary. Traditional calibration methods either require prior knowledge of the non-ideal parameters of the actual physical components in the system or rely on additional test excitation inputs. Moreover, calibration must be performed with prior knowledge of the number of input signal sources. Therefore, traditional calibration methods are highly complex and costly.

[0004] In summary, it is essential to propose a new calibration method to address the issues of high complexity and cost in the implementation of traditional calibration methods, as well as the need to predict the number of input signal sources. Summary of the Invention

[0005] The purpose of this invention is to address the problems of high complexity and high cost in the implementation process of traditional calibration methods, as well as the need to know the number of input signal sources in advance. Therefore, a joint blind calibration method for modulation broadband converters in sparse scenarios is proposed.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a joint blind calibration method for modulation broadband converters in scenarios with unknown sparsity, the method specifically including the following steps:

[0007] Step 1: Establish a multilinear model that considers the amplitude and phase errors and mutual coupling errors between channels, and then convert the multilinear model into a single-linear inverse problem;

[0008] Step 2: Estimate the amplitude and phase errors and mutual coupling errors based on the multilinear model and sampled value matrix Y from Step 1 to obtain the initial values ​​of the amplitude and phase errors. and initial value of mutual coupling error ;

[0009] Step 3: Based on the initial value of amplitude and phase error Initial value of mutual coupling error Information theory criteria methods are used to estimate the sparsity of signals;

[0010] Step 4: Based on the unilinear inverse problem and signal sparsity from Step 1... Obtain the reconstructed signal And the joint estimation results of amplitude and phase error and mutual coupling error.

[0011] Furthermore, the specific process of step one is as follows:

[0012] Step 11: Establish a multilinear model that considers amplitude and phase errors and mutual coupling errors between channels.

[0013] (11)

[0014] Among them, the diagonal matrix , This represents the unknown gain and phase error of the k-th channel. , , This represents the gain error of the k-th channel. Represents the phase error of the k-th channel; matrix A represents the system mutual coupling error matrix; A represents the observation matrix. It is a sampled value matrix composed of the discrete-time Fourier transform results of the sampled sequences of each channel. , This indicates the number of bandwidths, and the superscript T indicates transpose. , ;

[0015]

[0016] in, This represents the continuous-time signal input to the modulation wideband converter. It is the base of the natural logarithm. It is the imaginary unit. For time, For frequency;

[0017] Steps 1 and 2: Transform the multilinear model into a unilinear inverse problem:

[0018] (13)

[0019] in, The superscript -1 represents the inverse of the matrix.

[0020] Furthermore, the observation matrix A is a random Bernoulli matrix, and each element in the observation matrix A has an equal probability of taking the value +1 and -1.

[0021] Furthermore, all elements off the main diagonal of the diagonal matrix D are 0, and the main diagonal elements of the diagonal matrix D are uniformly distributed around 1, that is:

[0022] (12)

[0023] in, For hyperparameters, .

[0024] Furthermore, the matrix The elements in the set satisfy: , Representation matrix The values ​​of the elements on the main diagonal. Indicates the interval with the main diagonal The values ​​of the elements on the diagonal of each element. ; The attenuation coefficient is... .

[0025] Furthermore, the specific process of step two is as follows:

[0026] make Then the sampling value matrix Y's first... The representation of a row under the 1 norm is:

[0027] (14)

[0028] in, Represents the first... OK, Represents the first of Y The 1 norm of the row;

[0029] Calculate the average of the 1-norms of all rows in matrix Y:

[0030] (15)

[0031] in, Indicates the expectation. Describes the first line on the main diagonal of matrix D. One element, Representation matrix The OK;

[0032] The initial values ​​of amplitude and phase error and mutual coupling error are obtained by combining equation (16):

[0033] (16)

[0034] in, This represents the maximum value of the 1 norm among all rows in matrix Y. This represents the minimum value of the 1 norm among all rows in matrix Y.

[0035] Furthermore, the specific process of step three is as follows:

[0036] Step 31: The framework of the information theory criterion method is as follows:

[0037] (17)

[0038] in, Representation matrix The List, and All are intermediate variables. express The corresponding information theory criterion value, ;

[0039] (18)

[0040] (19)

[0041] in, This represents the number of columns in matrix Y. This represents the eigenvalue sequence obtained by arranging the eigenvalues ​​of the covariance matrix of matrix Y in descending order. 1 eigenvalue, , Indicates the coefficient of the penalty term;

[0042] Then the sparsity of the signal for:

[0043] (20).

[0044] Furthermore, the penalty term coefficient The calculation method is as follows:

[0045] make

[0046] (twenty three)

[0047] (twenty four)

[0048] in, This represents the sequence of eigenvalues ​​of the covariance matrix of matrix Y arranged in descending order. One eigenvalue;

[0049] but Corresponding information theory criterion value Greater than Corresponding information theory criterion value probability for:

[0050] (25)

[0051] make for The root, and ,in, Indicates when the signal-to-noise ratio for hour, value traversal The minimum obtained later value; It is to satisfy The largest value;

[0052] Then the optimal penalty term coefficient for:

[0053] (26).

[0054] Furthermore, the specific process of step four is as follows:

[0055] Step 41: Define matrices S and H:

[0056] (27)

[0057] (28)

[0058] in, Indicates the Kronecker product. This represents an N×N identity matrix. This represents the first row of matrix A. This represents the second row of matrix A. Represents the first... The row, with the superscript T indicating the transpose of the matrix;

[0059] Step 42: Initialization As a vector filled with zeros, initialize For: the row vectorized vector corresponding to a diagonal matrix where only the elements on the main diagonal are 1 and all other elements are 0, with a maximum number of iterations set to . ;

[0060] Step 4.3: Initialize the number of iterations ;

[0061] Step 44: Calculation and :

[0062] (30)

[0063] (31)

[0064] in, For scaling parameters, The iteration step size, for The conjugate transpose of the matrix. for The conjugate transpose of ;

[0065] Steps four and five: Based on sparsity right Perform sparse projection to obtain the sparse projection result;

[0066] Step 46: Determine if the conditions are met. ;

[0067] If satisfied Then, the sparse projection result of the last iteration step four or five is used as the reconstruction result, and the result obtained from the last iteration step four or four is used as the reconstruction result. As a joint estimation result of amplitude and phase error and mutual coupling error;

[0068] If not satisfied Then let Then, using the sparse projection result of the current iteration step four and five, return to execute step four and four.

[0069] Furthermore, the scaling parameter iteration step size .

[0070] The beneficial effects of this invention are:

[0071] This invention's method only requires the actual sampled data output by the modulated broadband converter during compressed sampling. Combined with information theory criteria, the signal sparsity can be estimated, enabling simultaneous solution of joint blind calibration and signal reconstruction, while simultaneously completing system error calibration and accurate recovery of the original signal. This invention eliminates the need for traditional active calibration methods requiring test stimuli in the calibration of modulated broadband converters. That is, it requires no prior knowledge of hardware parameters and no additional test stimuli; it can simultaneously complete system error calibration and accurate recovery of the original signal using only actual sampled data under conditions of unknown signal sparsity. Compared with other methods, this invention can simultaneously calibrate the system and reconstruct the signal even with unknown sparsity, requires no test stimuli, and is simple and convenient to implement, significantly reducing calibration costs.

[0072] Experiments show that when the number of channels is greater than or equal to 50, and the amplitude-phase error is less than or equal to 0.3 and the mutual coupling error is less than or equal to 0.35, the support set reconstruction power of the method of this invention exceeds 95%. The mean of the sparsity estimation is 11.98 and the variance is 0.02, therefore, the sparsity estimation error is close to 0. Compared with existing methods, the method of this invention improves the reconstruction power under the same error conditions by more than 40%, especially in scenarios where the mutual coupling error is greater than 0.3. The method of this invention can achieve real-time calibration without test excitation in any environment, significantly reducing the system's operation and maintenance costs. Attached Figure Description

[0073] Figure 1 This is a schematic diagram of the structure of a modulation broadband converter;

[0074] Figure 2 This is the amplitude-frequency response diagram of an ideal low-pass filter;

[0075] Figure 3 A schematic diagram of the mathematical model of a non-ideal modulation broadband converter;

[0076] Figure 4 This is a comparison chart of the mean and variance of sparsity estimates for each method under different amplitude and phase errors;

[0077] In the figure, Gain-phase error represents amplitude and phase error, and Estimated Sparsity represents sparsity estimation;

[0078] Figure 5 This is a comparison chart of the mean and variance of sparsity estimates for each method under different mutual coupling errors;

[0079] In the diagram, mutual coupling error represents the mutual coupling error;

[0080] Figure 6 This is a comparison chart of the support aggregation power of each method when the joint error coefficient is 0.2;

[0081] In the diagram, Channel number represents the number of channels, and Success rate represents the power of the supporting aggregate structure.

[0082] Figure 7 This is a comparison chart of the support aggregation power of each method when the joint error coefficient is 0.3;

[0083] Figure 8 This is a comparison chart of the support aggregation power of each method when the joint error coefficient is 0.4;

[0084] Figure 9 This is a comparison chart of the power composition of the support weights of different methods under different amplitude and phase errors;

[0085] Figure 10 This is a comparison chart of the power of the support aggregate structure under different mutual coupling error conditions. Detailed Implementation

[0086] Specific Implementation Method 1: Modulation-Broadband Converter System, such as... Figure 1 As shown, continuous time signal Fourier transform It can be represented as:

[0087] (1)

[0088] In the mixing stage, a random ±1 sequence is used to mix with the original signal. The mixing function expression is as follows:

[0089] (2)

[0090] Because the mixing function is Since it is periodic, its Fourier series expansion can be written as:

[0091] (3)

[0092] in, The Fourier coefficients can be obtained using the following formula:

[0093] (4)

[0094] Therefore, after mixing, the mixer output signal The Fourier transform can be written in the following form:

[0095] (5)

[0096] in, is the repetition frequency of the waveform.

[0097] Hypothetical Filter The cutoff frequency is An ideal low-pass filter has a frequency response that is a rectangular function, such as... Figure 2 As shown. The passband range of this ideal LPF is defined as follows. Then the sampling sequence of the i-th channel The Discrete-Time Fourier Transform (DTFT) can be expressed as:

[0098] (6)

[0099] Equation (6) can be expressed in matrix form:

[0100] (7)

[0101] in, for Row matrix, matrix The Behavior ; for A matrix of rows, , of which A row can be represented as:

[0102] (8)

[0103] matrix for A matrix of dimension , whose ? Line number The column elements are:

[0104] (9)

[0105] Among them, Fourier coefficients It can be represented as:

[0106] (10)

[0107] in, , .

[0108] To address the issues of amplitude and phase errors and mutual coupling effects in practical applications of modulation broadband converters, this embodiment proposes a joint blind calibration method for modulation broadband converters in scenarios with unknown sparsity. The method specifically includes the following steps:

[0109] Step 1: Let matrix Y represent Matrix X represents ,like Figure 3 As shown, a multilinear model considering inter-channel amplitude and phase errors and mutual coupling errors is established, and then the multilinear model is converted into a single-linear inverse problem.

[0110] The specific process of step one is as follows:

[0111] Step 11: Establish a multilinear model that considers amplitude and phase errors and mutual coupling errors between channels.

[0112] (11)

[0113] Among them, the diagonal matrix , This represents the unknown gain and phase error of the k-th channel. , , This represents the gain error of the k-th channel. This represents the phase error of the k-th channel. It is the variable that determines the magnitude of the phase error of the k-th channel; matrix Let represent the system mutual coupling error matrix with the Toeplitz matrix property, and , Denotes the real number field; A denotes the observation matrix; It is a sampled value matrix composed of the discrete-time Fourier transform results of the sampled sequences of each channel. , Indicates the number of frequency bands. The superscript T indicates transpose. , ;

[0114]

[0115] in, This represents the continuous-time signal input to the modulation wideband converter. It is the base of the natural logarithm. It is the imaginary unit. For time, For frequency;

[0116] The following three assumptions are made:

[0117] Assumption 1. The observation matrix A is a random Bernoulli matrix, and each element in the observation matrix A has an equal probability of taking the value +1 and -1;

[0118] Assumption 2. The elements off-diagonal of the diagonal matrix D are all 0, and the elements on the main diagonal of the diagonal matrix D are uniformly distributed around 1:

[0119] (12)

[0120] in, For hyperparameters, ;

[0121] Assumption 3. Matrix There is a certain attenuation coefficient among the elements. This invention assumes that... , Representation matrix The element values ​​on the main diagonal (by default, all element values ​​on the main diagonal are 1). Indicates the interval with the main diagonal The element values ​​on the diagonal of each element (it should be noted that this refers to the interval between the two diagonals along the row direction). ; The attenuation coefficient is... ;

[0122] The specific explanation of Assumption 3 is as follows: using a matrix Taking the first line as an example, the first element of the first line is... The second element in the first row The third element in the first row is And so on, until all elements of the first row are obtained. For the matrix... In any other row, the element on the main diagonal of that row is Starting from the main diagonal element of this row, the elements to the right of the main diagonal element are as follows: The elements to the left of the main diagonal element are also arranged in order. ,Right now The element values ​​on both sides are .

[0123] Steps 1 and 2: Transform the multilinear model into a unilinear inverse problem:

[0124] (13)

[0125] in, The superscript -1 represents the inverse of the matrix.

[0126] Step 2: Estimate the amplitude and phase errors and mutual coupling errors based on the multilinear model and sampled value matrix Y from Step 1 to obtain the initial values ​​of the amplitude and phase errors. and initial value of mutual coupling error The specific process of step two is as follows:

[0127] According to hypothesis 1, in the absence of error, the 1-norm of each row of Y is equal. Let Then the sampling value matrix Y's first... The representation of a row under the 1 norm is:

[0128] (14)

[0129] in, Represents the first... OK, Represents the first of Y The 1 norm of the row;

[0130] Since each element in matrix A has the same probability of being +1 and -1, therefore Each element in the matrix has an equal probability of being positive or negative. Furthermore, since the gain phase error in Assumption 2 is uniformly distributed around 1, calculating the average of the 1-norm of all rows in matrix Y yields a result without any error. :

[0131] (15)

[0132] in, Indicates the expectation. Describes the first line on the main diagonal of matrix D. One element, Representation matrix The OK;

[0133] The initial values ​​of amplitude and phase error and mutual coupling error are obtained by combining equation (16):

[0134] (16)

[0135] in, This represents the maximum value of the 1 norm among all rows in matrix Y. This represents the minimum value of the 1 norm among all rows in matrix Y;

[0136] Step 3: Based on the initial value of amplitude and phase error Initial value of mutual coupling error The sparsity of the signal is estimated using the Information Theory Criterion (ITC) method; the specific process of step three is as follows:

[0137] Step 31: The framework of the information theory criterion method is as follows:

[0138] (17)

[0139] in, Representation matrix The List, and All are intermediate variables. express The corresponding information theory criterion value, ;

[0140] (18)

[0141] (19)

[0142] in, This represents the number of columns in matrix Y. This represents the eigenvalue sequence obtained by arranging the eigenvalues ​​of the covariance matrix of matrix Y in descending order. 1 eigenvalue, , Indicates the coefficient of the penalty term;

[0143] Then the sparsity of the signal for:

[0144] (20)

[0145] The penalty term coefficient The calculation method is as follows:

[0146] (twenty one)

[0147] Formula (21) represents the calculation of making The value of satisfies The largest Value, determine After determining the value, then confirm the destination. The value of satisfies Minimum penalty term coefficient . Denotes the coefficient of the optimal penalty term. Indicates when the signal-to-noise ratio for At that time, traverse The minimum value obtained by taking the value of value;

[0148] (twenty two)

[0149] in, express The probability of;

[0150] Considering the worst-case scenario, where the maximum value of the noise characteristic is subject to the greatest perturbation, let...

[0151] (twenty three)

[0152] (twenty four)

[0153] in, This represents the sequence of eigenvalues ​​of the covariance matrix of matrix Y arranged in descending order. One eigenvalue;

[0154] but Corresponding information theory criterion value Greater than Corresponding information theory criterion value probability for:

[0155] (25)

[0156] Obviously, It has only one root, and the left-hand side of the inequality is monotonically decreasing with respect to k. Let for The root, and ,in, Indicates when the signal-to-noise ratio for hour, value traversal The minimum obtained later value; It is to satisfy The largest value;

[0157] Then the optimal penalty term coefficient for:

[0158] (26)

[0159] Step 4: Based on the unilinear inverse problem and signal sparsity from Step 1... Obtain the reconstructed signal And the joint estimation results of amplitude and phase error and mutual coupling error; the specific process of step four is as follows:

[0160] Step 41: Define matrices S and H:

[0161] (27)

[0162] (28)

[0163] in, Indicates the Kronecker product. This represents an N×N identity matrix. This represents the first row of matrix A. This represents the second row of matrix A. Represents the first... OK, The superscript T indicates the column number of matrix A, and the superscript T indicates the transpose of the matrix.

[0164] Column vectorization of matrix X yields x, and column vectorization of matrix J yields... According to the unilinear inverse problem of formula (13), formulas (27) and (28) are transformed into the form of formula (29). Then the solution to the problem of this invention is the eigenvector corresponding to the largest eigenvalue in the matrix form represented by formula (29).

[0165] (29)

[0166] Step 42: Initialization As a vector filled with zeros, initialize For: the row vectorized vector corresponding to a diagonal matrix where only the diagonal elements are 1 and all other elements are 0 (i.e., the initialized vector for a diagonal matrix where only the diagonal elements are 1 and all other elements are 0). This is the row vectorized form of a diagonal matrix (note that the dimension of the diagonal matrix here is the same as the dimension of matrix J). The maximum number of iterations is set to... ;

[0167] Step 4.3: Initialize the number of iterations ;

[0168] Step 44: Calculation and :

[0169] (30)

[0170] (31)

[0171] in, For scaling parameters, The iteration step size, for The conjugate transpose of the matrix. for The conjugate transpose of ;

[0172] Steps four and five: Based on sparsity right Perform sparse projection to obtain the sparse projection result;

[0173] The specific method of sparse projection is as follows: Transform it into a matrix with the same dimensions as matrix X, then calculate the 1-norm of each row of the transformed matrix, and then... The elements of the rows corresponding to the large 1 norm values ​​are retained, the elements of the other rows in the matrix are set to 0, and the processed matrix is ​​then vectorized into rows. The vectorized result is used as the sparse projection result. That is, in the sparse projection result, the elements in the vector are the first row element, the second row element, ..., the last row element of the processed matrix in sequence.

[0174] Step 46: Determine if the conditions are met. ;

[0175] If satisfied Then, the sparse projection result of the last iteration step four or five is used as the reconstruction result, and the result obtained from the last iteration step four or four is used as the reconstruction result. As a joint estimation result of amplitude and phase error and mutual coupling error;

[0176] If not satisfied Then let Then, using the sparse projection result of the current iteration step four and five, return to execute step four and four.

[0177] Experimental comparison

[0178] The first set of experiments compares the method of this invention (denoted as JBC) with classic source number estimation methods, including AIC, BIC, MDL, MSEE, RAE, and SORTE. The second set of experiments compares the method of this invention with classic signal reconstruction methods, including OMP, BGPC, and MGSM.

[0179] The goal of the first set of experiments is to verify the effectiveness of the sparsity estimation method proposed in this invention; the goal of the second set of experiments is to verify the effectiveness of the blind calibration method proposed in this invention.

[0180] Step 1: Generate a signal

[0181] Signal The form is shown in formula (32):

[0182] (32)

[0183] in, The signal energy is represented by B, which is randomly distributed within the range [10, 30]. B represents the maximum bandwidth of the signal, and the delay... The carrier frequency f is a random value, randomly distributed in the range of 0-5 GHz, and n represents Gaussian white noise.

[0184] Step 2: Signal Sampling

[0185] pass Figure 1 The modulation broadband converter system shown is sampled, and the other key parameters are shown in Table 1:

[0186] Table 1 Key Parameter Settings for Signal Sampling

[0187]

[0188] Step 3: Signal sparsity estimation

[0189] Based on the sampled value Y, the sparsity estimated by each method is obtained. ;

[0190] Experiment 1: Comparison of the mean and variance of sparsity estimation by different methods under different amplitude and phase errors. Figure 4 As shown.

[0191] exist Figure 4 In the middle, the mutual coupling error is set to 0. The vertical axis is in Figure 4 The 'm' represents the average value of the estimated sparsity, which is the average value of 1000 probabilistic experiments. The horizontal axis represents the gain phase error. The curve corresponding to each method will have an upper and lower bound, representing the variance. That is, the closer the average value is to the true sparsity (equal to 12) and the closer the variance is to 0, the higher the effectiveness and stability of the method.

[0192] The AIC, BIC, and MDL methods perform poorly and have large variances because these information theory criteria methods deal with different signal models than compressed sampled signals, and their actual degrees of freedom differ from those of the joint error model. As the gain and phase error increase, the distribution range of the sum of eigenvalues ​​corresponding to the noise subspace fluctuates more, resulting in increased mean and variance in the sparsity estimate. The MSEE and SORTE methods deal with different signal models than the MWC signal generation model; therefore, although these two methods are sufficiently stable, they fail to estimate the true sparsity. The performance of the RAE method is significantly affected by the signal-to-noise ratio, thus its sparsity estimate is inaccurate. The mean and variance curves of the method presented in this invention are significantly better than all other methods. Experiment 1 verifies the accuracy and stability of the sparsity estimation presented in this invention under different amplitude and phase errors.

[0193] Experiment 2: Comparison of mean and variance of sparsity estimation by different methods under different mutual coupling errors. Figure 5 As shown.

[0194] exist Figure 5 In this case, the gain phase error is set to 0. It can be seen that the performance of all methods is similar to... Figure 4 Similar to other methods, AIC, BIC, and MDL are more affected by mutual coupling errors than amplitude-phase errors because mutual coupling errors introduce larger perturbations into the eigenvalues ​​with the same coefficients. The MSEE method is based on an estimate of the noise variance, therefore its performance is almost identical to other methods. The RAE and SORTE methods, however, are less correlated with the magnitude of the overall eigenvalues, and therefore their performance is also similar to other methods. Figure 4 The results are almost identical. The mean and variance curves of the method of this invention are significantly better than all other methods. Experiment 2 verifies the accuracy and stability of the sparsity estimation of the method of this invention under different mutual coupling errors.

[0195] Step 4: Signal Reconstruction and Calibration

[0196] Step 3 yields the signal sparsity required for joint blind calibration and classical signal reconstruction. Therefore, assuming the sparsity estimation is correct, the effectiveness of the method of this invention for signal reconstruction and system blind calibration is verified in Experiments 3 and 4 below.

[0197] Experiment 3: Comparison of support aggregation power of different methods under different channel numbers and joint errors. Figure 6 , Figure 7 and Figure 8 As shown.

[0198] Figure 6 , Figure 7 and Figure 8 In the diagram, the vertical axis represents the support set reconstructing power, i.e., whether the support set of the reconstructed signal is completely consistent with the real support set. Experiment 3 also repeated this experiment 1000 times. The horizontal axis represents the number of channels in the MWC system. Here, the joint error coefficients represent that the amplitude and phase error coefficients and the mutual coupling error coefficients are the same value; that is, in Experiment 3, the amplitude and phase error coefficients and the mutual coupling error coefficients are set to the same value.

[0199] It is evident that all four methods are highly dependent on the number of channels, especially when the joint error coefficient is large. The method of this invention exhibits overwhelming superiority under any joint error coefficient. MWC (actually an OMP method with pre-CTF operation), BGPC, and MGSM methods demonstrate some robustness at a joint coefficient of 0.2. However, at higher joint error coefficients, the mutual coupling between channels severely affects the sampled data. The sampled value of a single channel is influenced by neighboring channels, reducing the independence between channels. Experiment 3 verifies the effectiveness of the reconstructed signal and calibration system of this invention under different channel numbers and joint errors.

[0200] Experiment 4: Under different amplitude and phase errors and mutual coupling errors, the power of the support aggregation structure constructed by different methods is compared as follows: Figure 9 and Figure 10 As shown.

[0201] Figure 9 In the figure, the vertical axis represents the power of the supporting concentrated weight structure, the horizontal axis represents the amplitude and phase error of the MWC system, and the mutual coupling error is set to 0.3. Figure 10 In the diagram, the vertical axis represents the power of the supporting concentrated weight structure, and the horizontal axis represents the mutual coupling error of the MWC system, with the amplitude and phase error set to 0.3. Furthermore, Figure 9 and Figure 10 The number of channels in the configuration is set to 50.

[0202] It can be seen that the magnitude of the mutual coupling error has a greater impact on the performance of the MWC, BGPC, and MGSM methods than the gain error. The method of this invention has stronger robustness to amplitude and phase errors. Since the goal of the BGPC method is to calibrate unknown gain and phase errors, it exhibits robustness under different amplitude and phase errors. The performance of the MWC and MGSM methods is similar, and their success rate decreases with increasing amplitude and phase errors. When the mutual coupling error is less than 0.35, the method of this invention can maintain stable performance, and its success rate is mainly affected by the number of channels. When the mutual coupling error is greater than or equal to 0.35, the reconstruction power begins to decrease, and increasing the number of channels can suppress the decrease in success rate. With the increase of mutual coupling error, the success rates of the other three methods all show a downward trend. When the mutual coupling error exceeds 0.35, reconstruction is almost impossible because mutual coupling significantly reduces the independence of the sampled values. Experiment 4 verifies the effectiveness of the reconstructed signal and calibration system of this invention under different amplitude and phase errors and mutual coupling errors.

[0203] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A joint blind calibration method for modulation-wideband converters in scenarios with unknown sparsity, characterized in that, The method specifically includes the following steps: Step 1: Establish a multilinear model that considers the amplitude and phase errors and mutual coupling errors between channels, and then convert the multilinear model into a single-linear inverse problem; Step 2: Estimate the amplitude and phase errors and mutual coupling errors based on the multilinear model and sampled value matrix Y from Step 1 to obtain the initial values ​​of the amplitude and phase errors. and initial value of mutual coupling error ; Step 3: Based on the initial value of amplitude and phase error Initial value of mutual coupling error Information theory criteria methods are used to estimate the sparsity of signals; Step 4: Based on the unilinear inverse problem and signal sparsity from Step 1... Obtain the reconstructed signal And the joint estimation results of amplitude and phase error and mutual coupling error.

2. The joint blind calibration method for modulation broadband converters in sparse unknown scenarios according to claim 1, characterized in that, The specific process of step one is as follows: Step 11: Establish a multilinear model that considers amplitude and phase errors and mutual coupling errors between channels. (11) Among them, the diagonal matrix , This represents the unknown gain and phase error of the k-th channel. , , This represents the gain error of the k-th channel. Represents the phase error of the k-th channel; matrix A represents the system mutual coupling error matrix; A represents the observation matrix. It is a sampled value matrix composed of the discrete-time Fourier transform results of the sampled sequences of each channel. , This indicates the number of bandwidths, and the superscript T indicates transpose. , ; in, This represents the continuous-time signal input to the modulation wideband converter. It is the base of the natural logarithm. It is the imaginary unit. For time, For frequency; Steps 1 and 2: Transform the multilinear model into a unilinear inverse problem: (13) in, The superscript -1 represents the inverse of the matrix.

3. The joint blind calibration method for modulation broadband converters in sparse unknown scenarios according to claim 2, characterized in that, The observation matrix A is a random Bernoulli matrix, and each element in the observation matrix A has an equal probability of taking the value +1 and -1.

4. The joint blind calibration method for modulation broadband converters in sparse unknown scenarios according to claim 3, characterized in that, The elements off-diagonal of the diagonal matrix D are all 0, and the elements on the main diagonal of the diagonal matrix D are uniformly distributed around 1, that is: (12) in, For hyperparameters, .

5. The joint blind calibration method for modulation broadband converters in sparse unknown scenarios according to claim 4, characterized in that, The matrix The elements in the set satisfy: , Representation matrix The values ​​of the elements on the main diagonal. Indicates the interval with the main diagonal The values ​​of the elements on the diagonal of each element. ; The attenuation coefficient is... .

6. The joint blind calibration method for modulation broadband converters in sparse unknown scenarios according to claim 5, characterized in that, The specific process of step two is as follows: make Then the sampling value matrix Y's first... The representation of a row under the 1 norm is: (14) in, Represents the first... OK, Represents the first of Y The 1 norm of the row; Calculate the average of the 1-norms of all rows in matrix Y: (15) in, Indicates the expectation. Describes the first line on the main diagonal of matrix D. One element, Representation matrix The OK; The initial values ​​of amplitude and phase error and mutual coupling error are obtained by combining equation (16): (16) in, This represents the maximum value of the 1 norm among all rows in matrix Y. This represents the minimum value of the 1 norm among all rows in matrix Y.

7. The joint blind calibration method for modulation broadband converters in sparse unknown scenarios according to claim 6, characterized in that, The specific process of step three is as follows: Step 31: The framework of the information theory criterion method is as follows: (17) in, Representation matrix The List, and All are intermediate variables. express The corresponding information theory criterion value, ; (18) (19) in, This represents the number of columns in matrix Y. This represents the eigenvalue sequence obtained by arranging the eigenvalues ​​of the covariance matrix of matrix Y in descending order. 1 eigenvalue, , Indicates the coefficient of the penalty term; Then the sparsity of the signal for: (20)。 8. The joint blind calibration method for modulation broadband converters in sparse unknown scenarios according to claim 7, characterized in that, The penalty term coefficient The calculation method is as follows: make (23) (24) in, This represents the sequence of eigenvalues ​​of the covariance matrix of matrix Y arranged in descending order. One eigenvalue; but Corresponding information theory criterion value Greater than Corresponding information theory criterion value probability for: (25) make for The root, and ,in, Indicates when the signal-to-noise ratio for hour, value traversal The minimum obtained later value; It is to satisfy The largest value; Then the optimal penalty term coefficient for: (26)。 9. The joint blind calibration method for modulation broadband converters in sparse unknown scenarios according to claim 8, characterized in that, The specific process of step four is as follows: Step 41: Define matrices S and H: (27) (28) in, Indicates the Kronecker product. This represents an N×N identity matrix. This represents the first row of matrix A. This represents the second row of matrix A. Represents the first... The row, with the superscript T indicating the transpose of the matrix; Step 42: Initialization As a vector filled with zeros, initialize For: the row vectorized vector corresponding to a diagonal matrix where only the elements on the main diagonal are 1 and all other elements are 0, with a maximum number of iterations set to . ; Step 4.3: Initialize the number of iterations ; Step 44: Calculation and : (30) (31) in, For scaling parameters, The iteration step size, for The conjugate transpose of the matrix. for The conjugate transpose of ; Steps four and five: Based on sparsity right Perform sparse projection to obtain the sparse projection result; Step 46: Determine if the conditions are met. ; If satisfied Then, the sparse projection result of the last iteration step four or five is used as the reconstruction result, and the result obtained from the last iteration step four or four is used as the reconstruction result. As a joint estimation result of amplitude and phase error and mutual coupling error; If not satisfied Then let Then, using the sparse projection result of the current iteration step four and five, return to execute step four and four.

10. The joint blind calibration method for modulation broadband converters in sparse unknown scenarios according to claim 9, characterized in that, The scaling parameters iteration step size .

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