Radar incoming wave signal processing method based on sparse reconstruction

Abstract

The invention discloses a radar incoming wave signal processing method based on sparse reconstruction, and the method comprises the following steps: initializing system setting parameters: the number M of array elements, the number J of snapshots, an angle interval, a grid vector, and the maximum number I of iterations, and obtaining incoming wave signal parameters; setting the number of array elements of a radar array, the number of snapshots of collected signals, and a pre-divided prior grid range and number; establishing a received signal matrix by utilizing incoming wave signals and algorithm parameter setting; according to the method, the problem that the signal receiving matrix generates amplitude-phase errors due to nonlinear errors of the device can be solved.

Description

Technical Field

[0001] The present invention relates to the field of millimeter wave radar signal processing, and in particular to a method for estimating the angle of a radar incoming wave signal. Background Art

[0002] Radar, as a sensor that can detect the target's position, distance, motion status and other information at a long distance, has been widely used in many fields such as topography, navigation, aviation, meteorology, etc., including laser radar, infrared radar, millimeter wave radar, etc.

[0003] Millimeter-wave radar is widely used in fields such as autonomous driving and smart transportation due to its strong penetration ability, long detection distance, and small size. However, due to the limitations of its size and aperture, it is difficult for vehicle-mounted millimeter-wave radar to achieve high accuracy in angle measurement.

[0004] The target angle estimation algorithm is generally called the direction of arrival (DOA) estimation algorithm. The SBL algorithm constructs a priori probability distribution function of the incoming signal, and then calculates the maximum a posteriori probability of the incoming signal through the radar array receiving signal to determine the relevant parameters in the priori probability distribution function, and finally applies it to DOA estimation. Compared with other sparse reconstruction algorithms, the SBL algorithm has higher estimation accuracy and better robustness. However, the current SBL-related algorithms widely have problems with grid division and excessive computation. Summary of the invention

[0005] The present application discloses a radar incoming wave signal processing method based on sparse reconstruction, comprising the following steps:

[0006] S1: Initialize the system setting parameters: number of array elements M, number of snapshots J, angle interval, grid vector, maximum number of iterations I, and obtain the incoming signal parameters;

[0007] S2: Set the number of radar array elements, the number of snapshots to collect signals, and the range and number of pre-divided a priori grids;

[0008] S3: Using the incoming signal and algorithm parameter settings, establish a receiving signal matrix;

[0009] The received signal matrix is:

[0010] Y M×J =E M×N X N×J (t)+N M×J (t);

[0011] Where N>>M>K, N is the number of grids, M is the number of array elements, K is the number of actual signal sources, X is the signal emitted at the preset grid, and N is the noise matrix;

[0012] The process of establishing the prior probability distribution model of the signal matrix X and the noise matrix N is as follows:

[0013] Assume that the noise N has a mean of 0 and a variance of α = σ -2 The joint probability distribution density function of the noise N under J snapshots is:

[0014]

[0015] Assume that the signal X is a priori assumed to have a mean of 0 and a variance of β = [β1, β 2, …,β n ] complex Gaussian distribution;

[0016]

[0017] where Λ=diagβ

[0018] The joint probability distribution density function of the array received signal matrix Y is obtained as follows:

[0019]

[0020] S4: After obtaining the received signal matrix, recover the wave signal from the received signal matrix;

[0021] S5: Calculate the posterior probability distribution of the signal matrix to obtain the mean of the signal matrix X. The calculation process is as follows:

[0022] Combining the likelihood function and the prior distribution of the array output, the posterior distribution of Y can be obtained by the Bayesian criterion, which contains hyperparameters β and α:

[0023]

[0024] The denominator P(Y; β, α) in the above formula is the marginal distribution of the data; for given β, α, the evidence factor is a normalization factor, which is regarded as a fixed value and ignored, specifically:

[0025] p(X|Y;β,α)∝p(Y|X;α)p(X;β)

[0026] p(Y|X; α), p(X; β) are Gaussian distributions with posterior mean μ X for:

[0027]

[0028] In a more specific solution, the receiving signal matrix is ​​constructed as follows:

[0029] Assume that there are K far-field narrowband signals incident on a millimeter-wave radar array consisting of M array elements, then the kth incident signal can be set as:

[0030] s k (t) = w k (t)e jwt ;

[0031] Then all incident signals at a certain moment can be expressed as:

[0032] S=[s1(t),s2(t),...,s k (t)] T ;

[0033] The signal received by M array elements at a certain moment can be expressed as:

[0034] Y=[y1(t),y2(t),…,y m (t)];

[0035] The array model is set to a uniform linear array. According to the uniform linear array model, the value of the kth signal received at the mth array element can be expressed as:

[0036]

[0037] Where c is the speed of sound, d is the array element spacing, which is set to λ / 2 here, and φ is the angle between the incident signal and the array axis. It represents the time delay required for the kth signal to reach the mth array. The data received in a single snapshot of the array can be expressed in matrix form as:

[0038]

[0039] γ m (t) represents the noise at the mth array element. Assuming the number of snapshots is J, the array receiving signal vector form under J snapshots can be expressed as:

[0040] Y M×J =E M×K S K×J (t)+N M×J (t).

[0041] In a more specific solution, the method to recover the wave signal is as follows:

[0042] Assume the number of discrete grids is N, and get a power vector with dimension N. Find the point in the discrete grid where the power exceeds the threshold, which is the direction of the incoming signal.

[0043] The divided angle set has a total of N grid points, which are evenly divided between [-π / 2,π / 2]. According to the signal model, the array receiving signal can be obtained as:

[0044] Y M×J =EM×N X N×J (t)+N M×J (t)

[0045] Among them, N>>M>K, N is the number of grids, M is the number of array elements, K is the number of actual signal sources, X is the signal emitted at the preset grid, and N is the noise matrix.

[0046] In a more specific solution, the method to restore the signal matrix is ​​as follows:

[0047] The process of establishing the prior probability distribution model of the signal matrix X and the noise matrix N is as follows:

[0048] Assume that the noise N has a mean of 0 and a variance of α = σ -2 The joint probability distribution density function of the noise N under J snapshots is:

[0049]

[0050] Similarly, we make a priori assumption about the signal X, assuming that its mean is 0 and its variance is β=[β1,β 2, …,β n ] is a complex Gaussian distribution.

[0051]

[0052] where Λ=diagβ

[0053] From the above, we can conclude that the joint probability distribution density function of the array received signal matrix Y is:

[0054]

[0055] In a more specific solution, the method further includes updating the incident angle set Φ, updating the parameter dictionary matrix E, and updating the signal matrix X.

[0056] In a more specific solution, the method further includes: calculating probability distribution hyperparameters α, β.

[0057] In a more specific solution, the method for calculating the probability distribution hyperparameters α and β is as follows:

[0058] Integrate the product of the likelihood function and the prior with respect to X to obtain the evidence factor P(Y; β, α):

[0059]

[0060] Then its log-likelihood function is:

[0061]

[0062] The estimated values of the hyperparameters can be obtained by maximizing the above formula. According to the fast evidence factor maximization method, the hyperparameters are updated alternately. The fast evidence factor maximization method is as follows:

[0063]

[0064]

[0065] where F y = YY H / J, B M is composed of the columns of the η maximum values in the matrix β.

[0066] If the number of signal sources K is known, then η = K; otherwise, a value of η < M is selected; different values of η only affect the convergence of the algorithm, and η can be selected as any number from 0 to M.

[0067] Compared with the traditional sparse Bayesian compressive sensing algorithm, the code running efficiency of this method is higher. Compared with the traditional sparse Bayesian compressive sensing algorithm, this method has higher angle estimation accuracy. This method can overcome the problem that the amplitude-phase error of the signal reception matrix is caused by the nonlinear error of the device. Brief Description of the Drawings

[0068] Figure 1 is a schematic diagram of the search strategy. Detailed Embodiments

[0069] The following will describe the present invention in detail with reference to the accompanying drawings.

[0070] Use simulation software to set the parameters of the incoming wave signal, including the number of signals, the arrival angle of the signal source, the signal-to-noise ratio, etc., for the subsequent processing of the signal estimation algorithm. The incoming wave signal in this part has the following premises and assumptions:

[0071] (1) The array elements of the receiving array are all omnidirectional passive array elements with equal gain, and the mutual coupling is ignored;

[0072] (2) The propagation medium of the spatial signal is uniform and isotropic, that is, the signal propagates in a straight line in space;

[0073] (3) The receiving array is in the far field of the spatial signal radiation, that is, the signal is regarded as a plane wave when it arrives at the array;

[0074] (4) The source signal is a narrowband signal and satisfies the ergodicity;

[0075] (5) Noise will be generated when the array receives the signal, and the noise between each array element and the noise and the signal are all statistically independent.

[0076] Set the number of radar array elements, the number of snapshots to collect signals, the range and number of pre-divided priori grids, and other parameters. This part is the setting of algorithm-related parameters.

[0077] The number of array elements in this part is the number of radars that can receive signals.

[0078] The number of snapshots indicates how many cycles of incoming signals the algorithm has to process.

[0079] Priori grid division: In order to construct a sparse signal by utilizing the spatial sparsity of the input signal, and taking into account the finiteness of the incident signal in the spatial domain, the spatial continuous angle set is divided into a finite discrete angle set by using the grid while allowing a certain quantization error. An overcomplete discrete angle set can be obtained by exhaustive method. , where N is the number of grid points. Consider a linear array (the spatial incident angle range is θ∈[-90°,90°], and without loss of generality, the spatial domain range [-90°,90°] is uniformly gridded using a grid interval r=1°, and a supercomplete discrete angle set θ∈{-90°,-89°,…,0,…,89°,90°} can be obtained.

[0080] Using the incoming signal and algorithm parameter settings, the receiving signal matrix is ​​established. This matrix is ​​the signal matrix received on the radar array. The matrix construction method is as follows:

[0081] Assuming that there are K far-field narrowband signals incident on a millimeter-wave radar array consisting of M array elements, the kth incident signal can be set to

[0082] s k (t) = w k (t)e jwt

[0083] Then all incident signals at a certain moment can be expressed as

[0084] S=[s1(t),s2(t),...,s k (t)] T

[0085] The signal received by M array elements at a certain moment can be expressed as

[0086] Y=[y1(t),y2(t),…,y m (t)]

[0087] Assuming that the array model is a uniform linear array, according to the uniform linear array model, it can be concluded that the value of the kth signal received at the mth array element can be expressed as

[0088]

[0089] Where c is the speed of sound, d is the array element spacing, which is set to λ / 2 here, and φ represents the angle between the incident signal and the array axis. c (m-1)dcosφ represents the time delay required for the kth signal to reach the mth array. The data received in a single snapshot of the array can be expressed in matrix form as follows:

[0090]

[0091] γ m (t) represents the noise at the mth array element. Assuming the number of snapshots is J, the array receiving signal vector form under J snapshots can be expressed as:

[0092] Y M×J =E M×K S K×J (t)+N M×J (t)

[0093] After obtaining the received signal matrix, the wave signal must be recovered from the received signal matrix. Here, the spatial sparse model is applied. Assuming that the incoming wave signal is concentrated from a discrete angle, the number of discrete grids is set to N. The purpose of the algorithm is to obtain a power vector with a dimension of N, and find the point in the discrete grid where the power exceeds the threshold, which is the direction of the incoming wave signal.

[0094] The divided angle set has a total of N grid points, which are evenly divided between [-π / 2,π / 2]. According to the signal model, the array receiving signal can be obtained as

[0095] Y M×J =E M×N X N×J (t)+N M×J (t)

[0096] Among them, N>>M>K, N is the number of grids, M is the number of array elements, K is the number of actual signal sources, X is the signal emitted at the preset grid, and N is the noise matrix.

[0097] On the premise that the received signal matrix has been obtained, the current task is to restore the signal matrix X. Here, according to the sparse Bayesian method, the prior probability distribution model of the signal matrix X and the noise matrix N is established. The establishment process is as follows:

[0098] Assume that the noise N has a mean of 0 and a variance of α = σ -2 The joint probability distribution density function of the noise N under J snapshots is:

[0099]

[0100] Similarly, we make a priori assumption about the signal X, assuming that its mean is 0 and its variance is β=[β1,β2, …,β n ] is a complex Gaussian distribution.

[0101]

[0102] where Λ=diagβ

[0103] From the above, we can conclude that the joint probability distribution density function of the array received signal matrix Y is:

[0104] Step 6: In step 5, the prior probability distribution has been assumed. Here, the posterior probability distribution of the signal matrix needs to be calculated to obtain the mean of the signal matrix X. The calculation process is as follows:

[0105] Combining the likelihood function and prior distribution of the array output, the posterior distribution of Y can be obtained by the Bayesian criterion, which contains hyperparameters β and α

[0106]

[0107] The denominator P(Y; β, α) in the above formula is the evidence factor, that is, the marginal distribution of the data. For a given β, α, the evidence factor is a normalization factor, so we first treat it as a fixed value and ignore it, and we have:

[0108] p(X|Y;β,α)∝p(Y|X;α)p(X;β)

[0109] Here we know that p(Y|X; α), p(X; β) are Gaussian distributed, so their product also follows Gaussian distribution, and their posterior mean μ X for

[0110]

[0111] α, β

[0112] After obtaining the signal matrix mean calculation formula in the previous step, it is necessary to calculate the probability distribution hyperparameters to finally obtain the normalized power vector of the signal matrix. The hyperparameter calculation method is as follows:

[0113] Integrate the product of the likelihood function and the prior with respect to X to obtain the evidence factor P(Y; β, α):

[0114]

[0115] Then its log-likelihood function is

[0116]

[0117] The estimated values of the hyperparameters can be obtained by maximizing the above formula. According to the fast evidence factor maximization method, the hyperparameters are updated alternately. This fast factor maximization method converges faster than the expectation maximization method, and its local convergence has been confirmed. The fast evidence factor maximization method gives:

[0118]

[0119]

[0120] where F y = YY H / J, B M is composed of the columns of the η maximum values in the matrix β.

[0121] If the number of signal sources K is known, then η = K; otherwise, a value of η < M is selected. Different values of η only affect the convergence of the algorithm, and when η takes any number from 0 to M, the estimation effect is better than the expectation maximization method.

[0122] Due to the problem of finite partitioning of the prior grid, the estimation accuracy of the incoming wave signal will decrease. Therefore, in order to improve the estimation accuracy, this patent adopts a method of adaptively updating the prior grid points. This method is to iteratively update the grid partitioning parameters synchronously during the iteration of the prior distribution hyperparameters until convergence, and obtain new adaptive grid parameters in each iteration to make it closer to the true incoming wave direction.

[0123] The grid update process is divided into a coarse estimation process and a fine estimation process, which are used for optimizing the grid in a large range and searching the grid in a small range respectively. The search strategy is as Figure 1 shown.

[0124] The coarse estimation method is as follows:

[0125] First, according to the normalized power formula judge the active grid points φ i , and then use the active grid points and the front and back grid points as boundaries, that is, (φ i-1 , φ i ), (φ i , φ i+1 ) for dichotomy grid fission, and repeat the fission until the preset grid accuracy is reached.

[0126] During the process of iterating the grid points by grid fission, the preset angle set Φ, the parameter dictionary matrix E, and the signal matrix X will each increase a column in each iteration. The newly added elements of these three matrices will be discussed below.

[0127] (1) Update the incident angle set Φ

[0128] First, traverse the elements in the normalized power vector P and find all P(i)>P min Points, where P min is the power threshold of the preset active grid point, and records the location information of all adjacent active grid points, denoted as

[0129] I=(i1,i1+1,,…,i n ,i n +1)n∈(1,N)

[0130] Then calculate i n The grid angle corresponding to the position is:

[0131]

[0132] The resulting updated angle set is:

[0133]

[0134] (2) Update the parameter dictionary matrix E

[0135] When a new grid point is added, a corresponding column will be added to the parameter dictionary matrix. The column vector can be calculated as follows:

[0136]

[0137] (3) Update the signal matrix X

[0138] The mean and variance of the signal matrix are actually determined by α and β. α is determined by the noise variance. During the grid update process, the noise variance can be approximated to be unchanged, so only β needs to be updated here. The newly added β is set to 1 here, and it can converge after multiple iterations.

[0139] When the coarse estimation method reaches the preset number of iterations, the fine estimation method is used, which is just the root-finding algorithm to continue the grid iteration. The calculation method is to focus on the update of θ during the iteration process, ignore irrelevant terms and maximize the following formula

[0140]

[0141] In order to refine θ at each sampling position i , i = 1, 2, ..., N, and its exponential form, we take its derivative and then assume it is equal to 0

[0142] After some algebraic manipulation, we can get the following polynomial form

[0143]

[0144] as well as:

[0145]

[0146]

[0147] in, e i represents the i-th column of E, μ it Represents μ x The (i, t)th element of ij Represents ∑ x The (i, j)th element of y t-i =y(t)-Σ j≠i μ tj e j .

[0148] For this root-finding equation, φi We can get M-1 complex roots. Here we take the root vector with the modulus closest to 1 to perform grid point φ i Update of φ i The update formula is as follows:

[0149]

[0150] After the hyperparameter iteration converges, the hyperparameters are substituted into the posterior probability calculation formula in step 6 to calculate the mean of the signal matrix. Finally, the normalized power vector of the signal is calculated to obtain the grid point where the incoming signal power exceeds the threshold, which is the direction of the incoming signal. The normalized power calculation formula is:

[0151]

[0152] As the working environment and the physical characteristics of the radar signal receiving array element itself change, the received signal matrix will also have a fixed error in amplitude and phase. If this error cannot be eliminated, there will always be some gap between all the measured values ​​of the incoming wave direction and the true value, resulting in a decrease in the accuracy of DOA estimation. This patent refers to the amplitude-phase error model, adds an amplitude-phase error matrix, regards the amplitude-phase error as a variable parameter, and uses an alternating update strategy to update the amplitude-phase error parameters and prior distribution hyperparameters, thereby obtaining the amplitude-phase error matrix. The amplitude-phase error parameter matrix is ​​eliminated on the basis of the original receiving matrix, and then the above steps are repeated to obtain the normalized power of the incoming wave signal, which can further improve the estimation accuracy. The amplitude-phase error matrix calculation method is as follows:

[0153] When there is an amplitude and phase error in the array, as shown, assuming that the number of array elements is M, the number of observation angles is N, and the number of snapshots is L, the mathematical model of the array receiving data is:

[0154] Y=EAX+N(4.1)

[0155] Where Y represents the data received by the radar array, E represents the amplitude and phase error matrix of each channel of the array, X represents the sampled signal data, A represents the array flow matrix, and N represents the noise at the radar array element position. The noise received by the array is Gaussian distributed and independent of each other at each snapshot.

[0156]

[0157] Then the likelihood probability distribution of the radar array receiving data is:

[0158]

[0159] Among them, the prior distribution of the sparse signal X is:

[0160]

[0161] In summary, the joint distribution of the variables is:

[0162] P(Y,X,β,α)=P(Y|X,α)P(X|β)P(β)P(α)(4.5)

[0163] By using the variational method, let the posterior probability P(X,α,β|Y)≈Q(X,α,β)=Q(X)Q(α)Q(β), then the amplitude and phase errors of the array can be estimated by the variational EM algorithm.

[0164]

[0165] Variational EM algorithm E step:

[0166]

[0167] The amplitude and phase error can be expressed as the sum of the real and imaginary parts. Then the amplitude and phase error matrix E can be expressed as

[0168] E=diag(a1+jb1,…,a M +jb M )(4.8)

[0169]

[0170]

[0171] Variation M step: By taking partial derivatives of a and b at both ends of the above equation and setting the partial derivative equal to 0, we can get: Real part of amplitude and phase error:

[0172]

[0173] Imaginary part of amplitude and phase error:

[0174]

Claims

1. A radar incoming signal processing method based on sparse reconstruction, characterized in that: The steps include: S1: Initialize the system setting parameters: number of array elements M, number of snapshots J, angle interval, grid vector, maximum number of iterations I, and obtain the incoming signal parameters; S2: Set the number of radar array elements, the number of snapshots to collect signals, and the range and number of pre-divided a priori grids; S3: Using the incoming signal and algorithm parameter settings, establish a receiving signal matrix; The received signal matrix is: Y M×J =E M×N X N×J (t)+N M×J (t); Where N>>M>K, N is the number of grids, M is the number of array elements, K is the number of actual signal sources, X is the signal emitted at the preset grid, and N is the noise matrix; The process of establishing the prior probability distribution model of the signal matrix X and the noise matrix N is as follows: Assume that the noise N has a mean of 0 and a variance of α = σ -2 The joint probability distribution density function of the noise N under J snapshots is: Assume that the signal X is a priori assumed to have a mean of 0 and a variance of β = [β1, β 2, …,β n ] complex Gaussian distribution; where Λ=diagβ The joint probability distribution density function of the array received signal matrix Y is obtained as follows: S4: After obtaining the received signal matrix, recover the wave signal from the received signal matrix; S5: Calculate the posterior probability distribution of the signal matrix to obtain the mean of the signal matrix X. The calculation process is as follows: Combining the likelihood function and the prior distribution of the array output, the posterior distribution of Y can be obtained by the Bayesian criterion, which contains hyperparameters β and α: The denominator P(Y; β, α) in the above formula is the marginal distribution of the data; for given β, α, the evidence factor is a normalization factor, which is regarded as a fixed value and ignored, specifically: p(X|Y;β,α)∝p(Y|X;α)p(X;β) p(Y|X; α), p(X; β) are Gaussian distributions with posterior mean μ X for:

2. The radar incoming wave signal processing method based on sparse reconstruction according to claim 1 is characterized in that: The receiving signal matrix is ​​constructed as follows: Assume that there are K far-field narrowband signals incident on a millimeter-wave radar array consisting of M array elements, then the kth incident signal can be set as: s k (t)=w k (t)e jwt ; Then all incident signals at a certain moment can be expressed as: S=[s1(t),s2(t),...,s k (t)] T ; The signal received by M array elements at a certain moment can be expressed as: Y=[y1(t),y2(t),…,y m (t)]; The array model is set to a uniform linear array. According to the uniform linear array model, the value of the kth signal received at the mth array element can be expressed as: Where c is the speed of sound, d is the array element spacing, which is set to λ / 2 here, and φ is the angle between the incident signal and the array axis. It represents the time delay required for the kth signal to reach the mth array. The data received in a single snapshot of the array can be expressed in matrix form as: γ m (t) represents the noise at the mth array element. Assuming the number of snapshots is J, the array receiving signal vector form under J snapshots can be expressed as: Y M×J =E M×K S K×J (t)+N M×J (t)。 3. The radar incoming wave signal processing method based on sparse reconstruction according to claim 2 is characterized in that: The method to recover the outgoing wave signal is as follows: Assume the number of discrete grids is N, and get a power vector with dimension N. Find the point in the discrete grid where the power exceeds the threshold, which is the direction of the incoming signal. The divided angle set has a total of N grid points, which are evenly divided between [-π / 2,π / 2]. According to the signal model, the array receiving signal can be obtained as: Y M×J =E M×N X N×J (t)+N M×J (t) Among them, N>>M>K, N is the number of grids, M is the number of array elements, K is the number of actual signal sources, X is the signal emitted at the preset grid, and N is the noise matrix.

4. The radar incoming signal processing method based on sparse reconstruction according to claim 3 is characterized in that: The method to restore the signal matrix is ​​as follows: The process of establishing the prior probability distribution model of the signal matrix X and the noise matrix N is as follows: Assume that the noise N has a mean of 0 and a variance of α = σ -2 The joint probability distribution density function of the noise N under J snapshots is: Similarly, we make a priori assumption about the signal X, assuming that its mean is 0 and its variance is β=[β1,β 2, …,β n ] is a complex Gaussian distribution. where Λ=diagβ From the above, we can conclude that the joint probability distribution density function of the array received signal matrix Y is:

5. The radar incoming wave signal processing method based on sparse reconstruction according to claim 4 is characterized in that: The posterior probability distribution of the signal matrix is ​​calculated to obtain the mean of the signal matrix X.

6. The radar incoming wave signal processing method based on sparse reconstruction according to claim 5 is characterized in that: The method further includes updating the incident angle set Φ, updating the parameter dictionary matrix E, and updating the signal matrix X.

7. The radar incoming wave signal processing method based on sparse reconstruction according to claim 6 is characterized in that: The method also includes: calculating probability distribution hyperparameters α, β.

8. The radar incoming wave signal processing method based on sparse reconstruction according to claim 7 is characterized in that: The method to calculate the probability distribution hyperparameters α and β is as follows: Integrate the product of the likelihood function and the prior with respect to X to obtain the evidence factor P(Y; β, α): Then its log-likelihood function is: The estimated values of the hyperparameters can be obtained by maximizing the above formula. According to the fast evidence factor maximization method, the hyperparameters are updated alternately. The fast evidence factor maximization method is as follows: Among them, F y =YY H / J,B M It consists of the columns of the n largest values ​​in the matrix β. If the number of signal sources K is known, then η = K; otherwise, a value that satisfies η < M is selected. Different values of η only affect the convergence of the algorithm, and η can be any number from 0 to M.

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