Blind separation sparse reconstruction coherent signal direction finding method based on uniform circular array

Abstract

The invention relates to a blind separation sparse reconstruction coherent signal direction finding method based on a uniform circular array. The method comprises the following steps: obtaining a receiving signal of the uniform circular array and preprocessing the receiving signal; utilizing a blind separation algorithm to separate out independent information sources in the pre-processed receiving signal, and obtaining guide vector estimation of each independent information source; and for each independent information source, according to the guide vector estimation of the independent information source, a sparse reconstruction algorithm is used to solve a corresponding signal arrival angle. According to the invention, the DOA estimation precision can be ensured by using the decoherence direction finding algorithm of the uniform circular array, so that the direction finding performance of the uniform circular array on coherent signals is enhanced.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and particularly to a method for direction finding of coherent signals by blind separation sparse reconstruction based on a uniform circular array. Background Technique

[0002] DOA estimation is an important technology in array signal processing and is widely used in civilian, military and other aspects. The spatial spectrum estimation technology applies the super-resolution estimation technology to DOA estimation, which can break through the constraint of the Rayleigh limit and obtain a very high angular resolution. It has extremely broad application prospects in many fields such as radar, communication, sonar, etc.

[0003] DOA estimation of coherent sources is also one of the important fields of direction finding, especially for direction finding in a multipath environment. For the scenario of coherent source signals, conventional direction finding algorithms are no longer applicable. The spatial smoothing technology is proposed to resolve coherent sources, but it can only resolve the number of coherent source signals not exceeding half of the number of physical array elements. For this reason, researchers have proposed the forward-backward spatial smoothing technology (FBSS), which can increase the number of resolvable coherent signals to two-thirds of the number of physical array elements. To solve the problem of rank deficiency of the covariance matrix under coherent sources, a covariance full-rank Toeplitz matrix is constructed, and then the spatial spectrum method is used to resolve coherence. This method compensates for the problem of array aperture loss of FBSS. The principle of the sparse reconstruction method is to perform sparse recovery on the signal, set angle grids with different intervals, and iteratively approximate the true value. It does not require estimation of the number of signal sources and can have a good estimation effect on coherent signals without resolving coherence, and the algorithm accuracy is relatively high.

[0004] A uniform circular array is a planar array in which several sensors are uniformly arranged on a circle. It has two-dimensional angle measurement ability, can measure azimuth angles of 360 degrees and has uniform direction finding without mirror ambiguity. Except that MUSIC can be directly used for direction finding, other methods need to perform certain conversions for indirect application. It is necessary to use mode space conversion to convert the array element space to the beam space. However, when converting a uniform circular array into a linear array and then using the linear array coherence resolution algorithm, it will bring relatively large array errors, resulting in a decrease in the DOA estimation accuracy and reducing the estimation performance to a certain extent. Therefore, it is urgent to develop a coherence resolution direction finding algorithm that can utilize a uniform circular array while ensuring the DOA estimation accuracy. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for direction finding of coherent signals by blind separation sparse reconstruction based on a uniform circular array, which can utilize the coherence resolution direction finding algorithm of the uniform circular array while ensuring the DOA estimation accuracy, thereby enhancing the direction finding performance of the uniform circular array for coherent signals.

[0006] The technical solution adopted by the present invention to solve its technical problems is: to provide a method for direction finding of coherent signals by blind separation sparse reconstruction based on a uniform circular array, including the following steps:

[0007] Obtain the received signals of the uniform circular array and perform preprocessing;

[0008] Use a blind separation algorithm to separate the independent signal sources in the preprocessed received signals, and obtain the steering vector estimates of each independent signal source;

[0009] For each independent signal source, according to its steering vector estimate, use a sparse reconstruction algorithm to calculate the corresponding signal arrival angle.

[0010] Further, the calculating the corresponding signal arrival angle using a sparse reconstruction algorithm according to its steering vector estimate includes:

[0011] Construct an over-complete dictionary based on the uniform circular array direction vectors corresponding to all possible directions of arrival;

[0012] Define an objective function based on the steering vector estimate of the current independent signal source and the over-complete dictionary, and transform this optimization problem into a weighted least squares problem, and iteratively solve to obtain the corresponding sparse parameter matrix;

[0013] Analyze the spectral peak of the sparse matrix to obtain the corresponding signal arrival angle.

[0014] Further, the objective function is expressed as

[0015]

[0016] where, is the steering vector estimate, D is the over-complete dictionary, κ is the sparse parameter matrix, λ spe is the sparse factor.

[0017] Further, the transforming this optimization problem into a weighted least squares problem and iteratively solving to obtain the corresponding sparse parameter matrix includes;

[0018] Set the initial iteration value κ0 of the sparse parameter matrix,

[0019]

[0020] Iteratively update the weight matrix W according to the following formula,

[0021]

[0022]

[0023] where, λ reg is the regularization factor, λ spe is the sparse factor, I is the identity matrix;

[0024] When the number of iterations exceeds the maximum given number or the error is less than the error limit, end the iteration and output the value κ of this round of iteration. k is the sparse parameter matrix of the current independent information source.

[0025] Furthermore, constructing the over-complete dictionary according to the uniform circular array direction vectors corresponding to all possible directions of arrival includes:

[0026] Discretize the azimuth space into multiple grid points with a spacing of 1° and containing 360° of angular information;

[0027] Calculate the uniform circular array direction vector of each grid point to obtain the over-complete dictionary.

[0028] Furthermore, the over-complete dictionary is expressed as

[0029] D = [d(α1), d(α2),..., d(α Q )]

[0030] d(α q ) = [exp(-j×2πr / λ×cos(α q -(i - 1)×2π / M))] T i = 1,..., M

[0031] where α q is the uniform circular array direction vector corresponding to the possible direction of arrival, D is the over-complete dictionary, d(α q ) is the column vector of the over-complete dictionary, Q is the number of grid points, and M is the number of array elements.

[0032] Furthermore, separating the independent information sources in the preprocessed received signal by using the blind separation algorithm includes:

[0033] Iteratively update the weight vector w according to the following formula, and normalize the updated weight vector w n+1 for processing

[0034]

[0035] y = w H x white

[0036] g(y) = G￠(y)

[0037] g(y) = G(y)

[0038] where y is the output result, and g(y) and g'(y) are the first derivative and the second derivative of the output result y respectively;

[0039] When the number of iterations reaches the set number, a demixing coefficient matrix composed of weight vectors w is obtained, and then the estimation of the number of independent sources and the estimation of the steering vector of each independent source are calculated.

[0040] Further, the preprocessing includes wavelet denoising, decentralization, and whitening processing performed in sequence.

[0041] Beneficial effects

[0042] Due to the adoption of the above technical solution, compared with the prior art, the present invention has the following advantages and positive effects: The present invention separates multiple independent sources by using a blind separation algorithm, and then for the coherent signals of a single source, uses a sparse reconstruction algorithm to achieve direction finding. It can use the coherent signal direction finding algorithm of a uniform circular array to achieve the direction finding function of multiple coherent signals with the same frequency and multiple sources while ensuring the DOA estimation accuracy, thereby enhancing the direction finding performance of the uniform circular array for coherent signals. Description of the drawings

[0043] Figure 1 is a flowchart of an embodiment of the present invention;

[0044] Figure 2 is a schematic diagram of the signals received by the uniform circular array in an embodiment of the present invention;

[0045] Figure 3 is a schematic diagram of the simulation result of the direction finding performance of the coherent signal in an embodiment of the present invention. Specific embodiments

[0046] The following further elaborates the present invention in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by the appended claims of this application.

[0047] The embodiment of the present invention relates to a blind separation and sparse reconstruction coherent signal direction finding algorithm based on a uniform circular array, as Figure 1 shown, including the following steps:

[0048] S1: The uniform circular array receives coherent signals with the same frequency

[0049] As Figure 2 shown, when considering a uniform circular array with M array elements, the radius of the circular array is R, and the coordinates of the m-th array element are p m = [Rcos(2πm / M) Rcos(2πm / M) 0]. Taking the center of the circular array as the origin reference point, the unit vector of the signal incident direction is where θ is the azimuth angle, is the pitch angle. Assume that the time delay of the incident signal received by element m is

[0050]

[0051] The corresponding phase difference is

[0052]

[0053] The corresponding steering vector of the circular array is expressed as

[0054]

[0055] Then when K far-field narrowband signals are incident from directions θ1, θ2,..., θ K the received signal x(n) of the uniform circular array can be expressed as

[0056]

[0057] The expansion is

[0058]

[0059] where A is the array manifold matrix, s(n) is the incident signal, and v(n) is the noise signal, m = 0, 1, L, M - 1, k = 1, 2, L, K.

[0060] S2: Perform denoising preprocessing on the received signal

[0061] First, perform wavelet denoising on the coherent signals received by the circular array. Wavelet denoising mainly uses the threshold method. Perform blind separation on the received data preprocessed by wavelet denoising. Before performing blind separation iteration, it is still necessary to perform decentration and whitening processing. Perform decentration processing on the denoised received signal. Through decentration, data with zero mean can be obtained, reducing calculation errors. The eigenvector U obtained by singular value decomposition is M×M, and the singular value matrix Σ is also M×M. Then the whitening matrix C white and the whitened received signal x white can be expressed by the formula

[0062]

[0063] x white = C white x

[0064] S3: Perform independent source blind separation

[0065] Extract independent sources, separate the independent signals and noise signals in the mixed signal, and use the blind separation algorithm to separate all signals for the preprocessed data, and there is

[0066]

[0067] The output result after processing is y = w H x white . Among them, y represents the output result after the signal is multiplied by the conjugate transpose of the algorithm iteration weight. g(y) = G'(y), g(y) = G(y), G'(y) and G(y) respectively represent the first derivative and the second derivative of the non-linear function. w represents the algorithm iteration weight, and * represents taking the conjugate.

[0068] After m times of iterative calculation, the M×M-dimensional demixing coefficient W = W(WW H ) -1 / 2 matrix is obtained, and incident source estimation is performed. There is

[0069]

[0070] Among them, F represents the separation matrix, represents the estimation of the number of source signals.

[0071] The demixed signal and noise exist independently. Just judge according to the characteristics of the noise and the signal, and the signal can be found. After blind separation, h independent components are obtained, and the noise determination is used to judge the independent components to obtain the mixing matrix formula of the independent source

[0072]

[0073] Estimation of the steering vector The calculation method is as follows

[0074]

[0075] S4: Establish a spatial domain sparse complete dictionary

[0076] Assume is the nth column of, that is, the steering vector of the nth source signal. The goal of the algorithm is to obtain the arrival angle θ of the incoherent source through the estimated steering vector n or the arrival angles θ1, θ2,..., θ of the coherent group signals lk , θ lk represents the kth signal azimuth of the lth coherent source.

[0077] Regarding the steering vector a n as a sparse representation problem, an over-complete dictionary D including all possible DOAs of incident signals is introduced. Assume the sampling network is the following formula

[0078] Ψ = [α1,..., α Q ​

[0079] In the formula, α i There is a 1° interval between them, that is, Ψ contains 360° of angle information. The columns in the matrix Ψ represent the uniform circular array direction vectors corresponding to the potential incident signal DOAs. Construct an overcomplete dictionary D = [d(α1), d(α2),..., d(α Q i)], D is known and independent of the actual positions of the signal sources, where d(α q i) is expressed by the formula:

[0080] d(α q i) = [exp(-j×2πr / λ×cos(α q i - (i - 1)×2π / M))] T i = 1,..., M

[0081] Therefore, The spatial overcomplete representation of is as shown in formula

[0082]

[0083] In the above formula, is the noise part, κ q is regarded as a single sampling of the incident signal. The sparse parameter matrix κ = [κ1, κ2,..., κ Q i]. If α q i = θ lk i, then κ q i = μ lk i, μ lk i represents the incident signal data of a single snapshot; otherwise κ q i = 0.

[0084] The direction finding problem is transformed into an estimation problem of the sparse spectrum of κ, and the peaks at the incident angles of the incident signals are included in κ.

[0085] Define the objective function as

[0086]

[0087] Step 5: The above problem is non-convex. By iteratively updating the weight matrix, the non-convex problem is converted into a weighted least squares problem to achieve the solution of the sparse solution. Determine the initial iteration value κ0,

[0088]

[0089] Iteration process:

[0090]

[0091]

[0092] Among them, λreg is the regularization factor. If it is too large, the solution will tend to 0; if it is too small, the result will diverge; λ spe is the sparsity factor, and its effect is equivalent to the norm constraint of the sparse solution. When the number of iterations exceeds the maximum given number or the error is less than the error limit λ err (that is ), the iteration ends.

[0093] Find according to the spectral peak of κ the incident angles of the incoherent or coherent signals included in

[0094] The following further illustrates this embodiment through specific simulation results.

[0095] Simulation parameters:

[0096] A 5-element circular array with a diameter of 180 mm is adopted; it is assumed that there are at most 3 coherent signals of the same frequency incident on the array, the signal frequency is 2500 MHz, the signal-to-noise ratio of each signal is 20 dB, the number of signal snapshots is 1024, the signal arrival phase error is 10°, and the signal directions are -30°, 40°, and 90° respectively.

[0097] Simulation analysis:

[0098] As Figure 3 shown, it can be seen from the simulation results that it is difficult for the traditional MUSIC direction-finding algorithm to effectively distinguish and direction-find multiple coherent signals, while the proposed sparse reconstruction algorithm can effectively direction-find multiple coherent signals of the same frequency and indicate the correct signal directions. In addition, the peak of the sparse reconstruction algorithm is narrower, while the traditional MUSIC algorithm may produce side lobes in other directions, which may affect the direction-finding results.

Claims

1. A method for direction finding of coherent signals by blind separation and sparse reconstruction based on uniform circular array, characterized in that: The following steps are involved: Obtain the received signal of the uniform circular array and perform preprocessing; Separating independent signal sources from the preprocessed received signal using a blind separation algorithm to obtain steering vector estimates for each independent signal source; For each of the independent signal sources, the corresponding signal arrival angle is calculated using a sparse reconstruction algorithm based on the steering vector estimate.

2. The method according to claim 1, characterized in that The method of estimating the steering vector and calculating the corresponding signal arrival angle using a sparse reconstruction algorithm includes: An overcomplete dictionary is constructed based on the uniform circular array direction vectors corresponding to all possible directions of arrival; An objective function is defined based on the steering vector estimate of the current independent information source and the overcomplete dictionary, and the optimization problem is converted into a weighted least squares problem, and the corresponding sparse parameter matrix is obtained by iterative solution; According to the spectrum peak of the sparse matrix, the corresponding signal arrival angle is analyzed and obtained.

3. The method according to claim 2, characterized in that The objective function is expressed as in, is the guidance vector estimation, D is the overcomplete dictionary, κ is the sparse parameter matrix, λ spe is the sparse factor.

4. The method according to claim 2, characterized in that The optimization problem is converted into a weighted least squares problem, and the corresponding sparse parameter matrix is obtained by iterative solution, including: Set the initial value of the iteration of the sparse parameter matrix κ0, The weight matrix W is iteratively updated according to the following formula: Among them, λ reg is the regularization factor, λ spe is the sparse factor, I is the identity matrix; When the number of iterations exceeds the maximum given number or the error is less than the error limit, the iteration ends and the iteration value κ of this round is output. k is the sparse parameter matrix of the current independent information source.

5. The method according to claim 2, characterized in that The overcomplete dictionary is constructed based on the uniform circular array direction vectors corresponding to all possible directions of arrival, including: The azimuth angle space is discretized into multiple grid points with a spacing of 1° and containing 360° angle information; The uniform circular array direction vector of each grid point is calculated to obtain the overcomplete dictionary.

6. The method according to claim 5, characterized in that The overcomplete dictionary is represented as D=[d(α1),d(α2),...,d(α Q )] d(α q )=[ezp(-j×2πr / λ×cos(α q -i-1l)×2π / M))] T i=1,…,M Among them, α q is the uniform circular array direction vector corresponding to the possible wave arrival direction, D is an overcomplete dictionary, d(α q ) is the column vector of the overcomplete dictionary, Q is the number of grid points, and M is the number of array elements.

7. The method according to claim 1, characterized in that The method of separating the independent signal sources from the pre-processed received signal by using a blind separation algorithm includes: Iteratively update the weight vector w according to the following formula, and update the weight vector w n+1 Perform normalization y=w H x white g(y)=G￠(y) g(y)=G(y) Where y is the output result, g(y) and g'(y) are the first-order derivative and second-order derivative of the output result y respectively; When the number of iterations reaches the set number, an unmixing coefficient matrix consisting of the weight vector w is obtained, and then an estimate of the number of independent information sources and an estimate of the steering vector of each of the independent information sources are calculated.

8. The method according to claim 1, characterized in that The preprocessing includes wavelet denoising, decentralization and whitening processing performed in sequence.

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