Noncircular EBNC-PFLOM joint optimization DOA estimation method under impulse noise

Abstract

The present invention discloses a non-circular EBNC-PFLOM joint optimization DOA estimation method under impulse noise, which belongs to the technical field of array signal processing. The method first receives a received signal through an array antenna with a dual mutual proton array structure. Secondly, based on the received signal, the EBNC matrix and the PFLOM matrix are calculated respectively by different order moment parameters. Finally, based on the EBNC matrix and the PFLOM matrix, the virtual array received signals and are calculated respectively, and the covariance matrix is ​​constructed, and the DOA estimation value is obtained by dimensionality reduction MUSIC. The present invention realizes efficient DOA estimation without spatial smoothing, and solves the performance degradation problem of traditional methods under non-Gaussian noise.

Description

Technical Field

[0001] The present invention belongs to the technical field of array signal processing, and in particular relates to a non-circular signal enhanced direction of arrival (DOA) high-precision estimation method for a strong impulse noise environment. Background Art

[0002] Although the current coprime array structure can improve the degree of freedom through virtual array expansion (such as 2M+N array elements to achieve O(MN) continuous virtual aperture), its DOA estimation method mostly relies on spatial smoothing technology to solve the coherent signal problem, resulting in the algorithm complexity growing cubically with the array element scale (O(L³), L is the subarray length), which is difficult to meet real-time processing requirements.

[0003] The existing traditional DOA estimation methods based on sparse arrays all assume that the noise follows a Gaussian distribution. However, when the pulse noise accounts for more than 30% in the actual measurement environment (such as industrial electromagnetic interference and deep-sea sonar), the traditional second-order statistics fail due to divergence, resulting in increased estimation errors. In addition, non-circular signals (such as BPSK modulated signals) account for more than 70% of actual communication signals, but the traditional non-circular EBNC method only uses signal amplitude information and does not fully exploit the phase characteristics, resulting in insufficient array aperture utilization. Therefore, a new technical solution is needed to solve the above problems.

[0004] The existing non-circular EBNC and enhanced fractional lower-order moment (EFLOM) methods based on coprime arrays cannot avoid the increased computational complexity caused by spatial smoothing technology, while the method of the present invention can estimate the DOA of the signal without spatial smoothing technology. In addition, after using the segmented spatial smoothing technology, the method of the present invention has better estimation performance than the non-circular EBNC and EFLOM methods. Summary of the invention

[0005] Purpose of the invention: In view of the high computational complexity introduced by spatial smoothing in the prior art and the lack of robustness to impulse noise, the present invention proposes a non-circular EBNC-PFLOM joint optimization DOA estimation method under impulse noise. By innovatively integrating bounded nonlinear covariance matrix (EBNC) and phase fractional low-order moment (PFLOM) optimization technology, combined with the virtual aperture expansion characteristics of the dual-co-proton array, the present invention achieves efficient DOA estimation without spatial smoothing, solving the performance degradation problem of traditional methods under non-Gaussian noise.

[0006] Technical solution: The steps of the method of the present invention include:

[0007] S1, receive the received signal through the array antenna of the dual mutual proton array structure .

[0008] S2, based on the received signal , by different order moment parameters and , respectively calculate the EBNC matrix and the PFLOM matrix .

[0009] S3, based on and , the virtual array receiving signal is calculated and , and construct the covariance matrix, and obtain the DOA estimation value through dimensionality reduction MUSIC.

[0010] Beneficial effect: The present invention uses enhanced bounded nonlinear functions and phase fractional low-order moments to jointly suppress outliers in the received signal. Compared with the existing non-circular EBNC and enhanced fractional low-order moment methods based on coprime arrays, the method of the present invention has better estimation performance after using the segmented spatial smoothing technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a schematic diagram of the structure of the double mutual proton array of the present invention;

[0012] Figure 2 It is a schematic diagram of the virtual array structure of the double mutual proton array of the present invention;

[0013] Figure 3 When three sources are incident on the double-mutual proton array, , snapshot number , the generalized signal-to-noise ratio is 10 dB, and the characteristic index of the method of the present invention is Schematic diagram of the spectrum peak search in a single Monte Carlo (MC) experiment at ;

[0014] Figure 4 When 17 sources are incident on the double-mutual proton array, , snapshot number , the generalized signal-to-noise ratio is 10 dB, and the characteristic index of the method of the present invention (using the segmented spatial smoothing technique) in the impulse noise environment is Schematic diagram of the peak search in a single MC experiment;

[0015] Figure 5 When three sources are incident on the double-mutual proton array, , run 1000 MC experiments using the proposed method and other algorithms in Schematic diagram of RMSE performance under different generalized signal-to-noise ratio conditions;

[0016] Figure 6 When three sources are incident on the double-mutual proton array, , run 1000 MC experiments using the proposed method and other algorithms Schematic diagram of RMSE performance under different snapshot numbers. DETAILED DESCRIPTION

[0017] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0018] 1. Noise Model

[0019] The traditional DOA method uses the Gaussian noise assumption, but the actual situation shows that in scenarios such as radar electronic countermeasures and underwater acoustic detection, impulse noise accounts for a large proportion. The present invention uses a symmetric α-stable distribution to accurately model impulse noise, and its characteristic function is defined as Defined as:

[0020]

[0021] in, is the variable of the characteristic function, is the characteristic index, is an imaginary unit, is the dispersion parameter, and its meaning is consistent with the variance of the Gaussian distribution.

[0022] 2. Angle Estimation Method

[0023] This embodiment provides a non-circular EBNC-PFLOM joint optimization DOA estimation method under impulse noise, including the following steps:

[0024] S1. A received signal is received by an array antenna with a dual mutual proton array structure. The schematic diagram of the dual mutual proton array structure of the present invention is shown in FIG. Figure 1 shown.

[0025] S2, based on the received signal, by different order moment parameters and , respectively calculate the EBNC matrix and the PFLOM matrix .

[0026] S3, based on and , the virtual array receiving signal is calculated and , and construct the covariance matrix, and obtain the DOA estimation value through dimensionality reduction MUSIC.

[0027] The specific steps are as follows:

[0028] Step S1: The dual-reciprocal proton array antenna receives the signal and obtains the received signal information .

[0029] like Figure 1 As shown, the present invention adopts a double mutual proton array: subarray A: number of array elements , the array element spacing is ,in is half wavelength; Subarray B: the number of array elements is , the array element spacing is ,in and are mutually prime numbers, and The two sub-arrays have only one element overlapped at the origin. In the present invention, the element position set for:

[0030]

[0031] make , ,according to Figure 1 The positions of the array elements are arranged from left to right. It is a sorting operation from small to large. Assume that there are K DOAs, respectively Narrowband signal Incidence on Figure 1 On the dual mutual proton array shown, the array receiving signal can be expressed as:

[0032]

[0033] is the direction matrix,

[0034] is the direction vector of the kth signal, is an imaginary unit; is a noncircular phase matrix, represents the non-circular phase of the kth signal, is an impulse noise that follows a symmetric α-stable distribution, is a real signal vector.

[0035] Step S2: Construct extended signal information , preset different order moment parameters and , calculate their EBNC matrices respectively and the PFLOM matrix .

[0036] Using the non-circular characteristics of the signal, the extended array receives the signal:

[0037]

[0038] in is the expansion direction matrix, is the extended impulse noise term; is the conjugate operation;

[0039] According to the set moment parameters , calculate the EBNC matrix :

[0040]

[0041]

[0042]

[0043] in, is the Cauchy kernel function, and is an adjustable parameter used to adjust the linear region of the signal. , , and They represent the real part operation, imaginary part operation, expectation operation and conjugate transpose respectively. Then according to the moment parameter , calculate the PFLOM matrix :

[0044]

[0045] in Both mean OK; Representation vector No. OK, Representation vector No. row, T represents the total number of time-domain snapshots, In the present invention, respectively , with a step size of 0.05, .

[0046] The specific implementation process of step S3 is as follows:

[0047] S3.1. and Perform vectorization and rearrangement processing respectively to calculate the virtual array receiving signal and , Figure 2 It is a schematic diagram of the virtual array structure of the double mutual proton array of the present invention;

[0048] The covariance matrix Through sparse array processing, the virtual array receiving signal is obtained :

[0049]

[0050] The covariance matrix Through sparse array processing, the virtual array receiving signal is obtained :

[0051]

[0052] in Represents vectorized operation, is the expansion direction matrix, and represents the signal energy, and represents the impulse noise vector, represents KR product; is a row exchange matrix.

[0053] S3.2, respectively and Remove redundancy and smooth the segmented space, and then splice to obtain virtual array information and , and construct the combined covariance matrix , and then use the reduced-dimensional MUSIC to get the estimated value of DOA.

[0054] Receive signals to virtual array , intercept the virtual array information of the continuous array element part, and obtain the virtual uniform linear array receiving signal with an array element spacing of half a wavelength :

[0055]

[0056] in is the noise vector, represents the direction matrix of the virtual uniform linear array, Represents the signal energy. Corresponding to the continuous uniform linear array information of the differential common array, Continuous uniform line array information corresponding to the negative sum array and the positive sum array respectively;

[0057] Difference Matrix And two arrays The continuous array elements of the array are spatially smoothed to obtain a smooth sub-array , and , the specific calculation is as follows:

[0058] ;

[0059] ;

[0060] ;

[0061] in is the number of matrix smoothing times, is the number of smoothing times of the difference matrix, Operation means taking vector Middle To elements; combine all smooth sub-arrays to construct virtual array information ;

[0062] right The virtual array receives the signal and The same operation process is used to obtain virtual array information. For each moment parameter and ,get and Then, construct the covariance matrix :

[0063]

[0064] in and Denote the moment parameters and The above formula can be regarded as a The covariance matrix of a uniform linear array with elements can be directly estimated using the reduced-dimensional MUSIC estimation algorithm, and Compared with the traditional circular signal DOA estimation algorithm, the degree of freedom and estimation accuracy are improved to a certain extent.

[0065] Get the covariance matrix After that, the noise subspace is obtained by eigenvalue decomposition , the signal DOA estimation can be obtained by using the dimension-reduced MUSIC spectrum peak search function:

[0066]

[0067] in , The search grid value for the peak is the search direction vector:

[0068]

[0069] in , .

[0070] 3. Experimental simulation analysis and performance analysis

[0071] 1. Computational complexity analysis

[0072] Taking the number of complex multiplications as the criterion for computational complexity, the complexity of the method of the present invention mainly includes: the complexity of the EBNC matrix is , the complexity of piecewise spatial smoothing is: ,in ; Similarly, the complexity of the PFLOM matrix is , the complexity of piecewise spatial smoothing is: ; Covariance matrix The complexity of the eigendecomposition is , the complexity required for the dimension reduction MUSIC method is , n is the number of searches, so the total complexity of the method of the present invention is:

[0073] .

[0074] 2. Experimental configuration and evaluation indicators

[0075] Noise environment: The symmetric α-stable distribution is used to simulate impulse noise. In the impulse noise environment, the generalized signal-to-noise ratio is defined as:

[0076]

[0077] Performance metric: The joint root mean square error (RMSE) is defined as:

[0078]

[0079] in For the The accurate estimate of the DOA of the kth source in the MC trial, represents the number of information sources, and MC represents the number of Monte Carlo trials.

[0080] 3. Key experimental results

[0081] The method of the present invention (EBNC-PFLOM) is compared with existing methods, including enhanced bounded nonlinear covariance method and enhanced fractional low-order moment method, both of which are based on non-circular signals and doubly mutual proton array background.

[0082] Figure 3 When three sources are incident on the dual-reciprocal proton array, the DOA is , using the spectrum peak search diagram obtained by the method of the present invention, only one MC experiment was run. At this time, the number of sub-array elements of the double mutual proton array is , snapshot number , . Impulse Noise Characteristic Index It can be seen that the method of the present invention can obtain accurate DOA estimation without spatial smoothing.

[0083] Figure 4 When 17 sources are incident on the dual-reciprocal proton array, the DOA is , with 5° intervals, using the spectrum peak search diagram obtained by the present invention, only one MC experiment was run. At this time, the number of subarray elements of the double mutual proton array is , snapshot number , . Impulse Noise Characteristic Index It can be seen that the present invention can estimate more signals than the number of array elements.

[0084] Figure 5 is , Snap In the case of , the algorithm performance is compared under different GSNRs. 1000 MC experiments are run. The azimuth angles of the three signal sources are It can be seen that under the same generalized signal-to-noise ratio condition, the present invention has better DOA estimation performance.

[0085] Figure 6 is , In the case of , the algorithm performance is compared under different snapshot numbers. 1000 MC experiments are run. The azimuth angles of the three sources are It can be seen that the performance of the present invention improves with the increase of the number of snapshots. Under the same snapshot conditions, the estimation performance of the present invention is better than other methods.

[0086] In summary, from the analysis of the simulation effect diagram, it can be seen that the non-circular EBNC-PFLOM joint optimization DOA estimation method under impulse noise proposed in the present invention realizes accurate DOA estimation under the impulse noise environment of dual coprime arrays. The degree of freedom is improved, and compared with the existing non-circular EBNC based on coprime arrays and enhanced fractional low-order moments, the estimation performance of the method of the present invention is better after the segmented spatial smoothing technology.

[0087] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. Non-circular EBNC-PFLOM joint optimization DOA estimation method under impulse noise, characterized by: The following steps are involved: S1. Receive a received signal x(t) through an array antenna with a dual mutual proton array structure; S2, based on the received signal x(t), by different order moment parameters p i and b i , respectively calculate the EBNC matrix and the PFLOM matrix S3, based on and Calculate the virtual array receiving signal and And construct the covariance matrix, and obtain the DOA estimation value through dimensionality reduction MUSIC. The specific implementation process is as follows: S3.

1. and Perform vectorization and rearrangement processing respectively to calculate the virtual array receiving signal and S3.2, respectively and Remove redundancy and smooth the segmented space, and then splice to obtain virtual array information and And construct the combined covariance matrix R Y , and then use the reduced-dimensional MUSIC to get the estimated value of DOA.

2. The non-circular EBNC-PFLOM joint optimization DOA estimation method under impulse noise according to claim 1, characterized in that: The specific implementation process of step S2 is: Using the non-circular characteristics of the signal, the extended array receives the signal: in is the expansion direction matrix, is the extended impulse noise term; * is the conjugation operation; According to the set moment parameter p i , calculate the EBNC matrix g(y′(t))=score(real(y′(t)))+j·score(imag(y′(t))); Where score(x) is the Cauchy kernel function, λ1 and λ2 are adjustable parameters used to adjust the linear region of the signal, real(·), imag(·), and[] H They represent the real part operation, imaginary part operation, expectation operation and conjugate transpose respectively, 0<p i <2; According to the moment parameter b i , calculate the PFLOM matrix Where i and s both represent rows; y s (t) represents the sth row of the vector y(t), y i (t) represents the i-th row of the vector y(t), T represents the total number of time domain snapshots, and P = 2M + N-1.

3. The non-circular EBNC-PFLOM joint optimization DOA estimation method under impulse noise according to claim 2, characterized in that: The calculation obtains the virtual array receiving signal and The process is as follows: The covariance matrix Through sparse array processing, the virtual array receiving signal is obtained The covariance matrix Through sparse array processing, the virtual array receiving signal is obtained Where vec(·) represents the vectorized operation, B is the expansion direction matrix, and represents the signal energy, and represents the impulse noise vector, ⊙ represents the KR product; J is the row exchange matrix.

4. The non-circular EBNC-PFLOM joint optimization DOA estimation method under impulse noise according to claim 3, characterized in that: The virtual array information is obtained and The specific process is as follows: Receive signals to virtual array The virtual array information of the continuous array element part is intercepted to obtain the virtual uniform linear array receiving signal with the array element spacing of half wavelength. in is the noise vector, represents the direction matrix of the virtual uniform linear array, represents the signal energy; Corresponding to the continuous uniform linear array information of the differential common array, Continuous uniform line array information corresponding to the negative sum array and the positive sum array respectively; Difference Matrix And two arrays The continuous array elements of the array are spatially smoothed to obtain a smooth sub-array and The specific calculation is as follows: Among them, Q=M+N-1 is the number of times the sum matrix is ​​smoothed, and R1=MN+M-1 is the number of times the difference matrix is ​​smoothed. Operation means taking vector The i-th to j-th elements in the array; combine all smooth sub-arrays to construct virtual array information right The virtual array receives the signal and The same operation process is used to obtain virtual array information.

5. The non-circular EBNC-PFLOM joint optimization DOA estimation method under impulse noise according to claim 4, characterized in that: The constructed combined covariance matrix R Y , and then use the dimension reduction MUSIC to get the estimated value of DOA. The specific implementation process is as follows: For each moment parameter p i and b i ,get and Then, construct the covariance matrix R: where length(p i ) and length(b i ) represent the order moment parameters p i and b i The above formula is a covariance matrix of a uniform linear array consisting of R1+1 elements. The dimensionality reduction MUSIC estimation algorithm is directly used, and MN+3M+2N signal sources can be estimated; After obtaining the covariance matrix R, the noise subspace U is obtained by eigenvalue decomposition N , and the signal DOA estimation value is obtained by reducing the dimension of the MUSIC spectrum peak search function: where e = [0 1 0] T , θ is the peak search grid value, and the search direction vector is: Among them, R2=(M-1)(N-1), R3=2MN+M-1.

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