A diagonal spatially smoothed coherent DOA estimation method based on non-circular signals

Abstract

The present invention discloses a diagonalized spatial smoothed coherent DOA estimation method based on non-circular signals. The method first receives non-circular signals through uniform linear array antennas to obtain received information. According to the non-circular characteristics of the signal, the received information is combined with its conjugate series to form extended received information, and its covariance matrix is ​​calculated. Then, sub-arrays are extracted from the covariance matrix along the diagonal, and enhanced spatial smoothing operations are performed on the extracted sub-arrays respectively. The results of the smoothing operation are spliced ​​to generate a new covariance matrix, and eigenvalue decomposition is performed on the new covariance matrix to obtain a noise subspace. Finally, based on the noise subspace, a dimensionality reduction MUSIC algorithm is used to estimate the DOA of the non-circular signal. The present invention generates a covariance matrix containing more information, increases the aperture through virtual expansion, reduces noise interference, can effectively restore the rank of the covariance matrix containing the non-circular phase, and improves the robustness and accuracy of DOA estimation.

Description

Technical Field

[0001] The invention belongs to the technical fields of coherent signal direction of arrival (DOA) estimation, radar, sonar positioning, etc., and particularly relates to a diagonalized spatially smoothed coherent DOA estimation method based on non-circular signals. Background Art

[0002] Direction of arrival estimation is the basis of array signal processing and has great value in acoustics, speech, radar, sonar, circuits and wireless communications. Traditional subspace-based super-resolution DOA estimation technology, however, in the actual signal transmission process, due to the reflection and refraction of the signal, multipath transmission will cause signal coherence, which is a major challenge to traditional DOA estimation. When the array sensor receives coherent signals from different directions, the rank loss in the covariance matrix obscures the key signal information, making the traditional subspace-based method ineffective.

[0003] To solve this problem, it becomes crucial to restore the rank of the covariance matrix to match the number of sources. Common techniques for decorrelation include dimensionality and non-dimensionality reduction methods, such as subspace-based methods, norm-based methods, and spatial smoothing (SS) techniques. Among them, spatial smoothing techniques are particularly prominent, which use overlapping subarrays and average their covariance matrices to restore the rank. Typical SS techniques are forward and backward spatial smoothing methods, spatial smoothing processing (SSP), enhanced spatial smoothing preprocessing, signal space-based ESS (ESS-SS), simplified spatial smoothing (SSS) methods, and enhanced spatial smoothing (ASS) methods. Although effective, these algorithms require compromising the array effective aperture, thereby reducing the number of signal estimates.

[0004] In recent years, several DOA estimation methods have improved the effective aperture through nonlinear arrays such as coprime arrays, but they performed poorly in terms of computational complexity and estimation performance. Later, some scholars introduced non-circular phase into DOA estimation. On this basis, researchers have focused their attention on coherent signal estimation based on non-circular phase. Although there are non-circular coherent signal DOA estimation methods based on forward smoothing, their computational complexity and estimation performance are not outstanding. Summary of the invention

[0005] Purpose of the invention: In order to solve the problems existing in the prior art, the present invention provides a diagonal spatially smoothed coherent DOA estimation method based on non-circular signals.

[0006] Technical solution: The present invention provides a diagonal spatial smoothed coherent DOA estimation method based on non-circular signals, comprising the following steps:

[0007] S1: Receive non-circular signals through uniform linear array antennas to obtain received information .

[0008] S2: According to the non-circular characteristics of the signal, the received information Conjugate with it Serial combination to expand the receiving information , and calculate The covariance matrix of .

[0009] S3: From Extract subarray diagonally from the center and , for the extracted sub-matrix and Perform enhanced spatial smoothing operations respectively to obtain and .

[0010] S4: Yes and Concatenate to generate a new covariance matrix , for the generated Perform eigenvalue decomposition to obtain the noise subspace .

[0011] S5: Based on noise subspace , the dimension-reduced MUSIC algorithm is used to estimate the DOA of non-circular signals.

[0012] The beneficial effects of the present invention are as follows:

[0013] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects: the present invention introduces non-circular phase and utilizes non-circular phase information. The method not only generates a covariance matrix containing more information, but also increases the aperture through virtual expansion and reduces noise interference. In addition, the inventive method seamlessly integrates ASS smoothing technology, which can effectively restore the rank of the covariance matrix containing non-circular phase, thereby improving the robustness and accuracy of DOA estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a schematic diagram of the linear array structure involved in the present invention;

[0015] Figure 2 It is a schematic diagram of the submatrix extraction process of the present invention;

[0016] Figure 3 The present invention is to provide two close non-circular coherent signals at an arrival angle of , the non-circular phase is , Schematic diagram of the reduced-dimensional MUSIC spatial spectrum when the number of snapshots is 300 and the signal-to-noise ratio is 0 dB;

[0017] Figure 4 is a schematic diagram of RMSE under different snapshot numbers using dimension reduction MUSIC in the present invention;

[0018] Figure 5 It is a schematic diagram of RMSE at different signal-to-noise ratios using dimension-reduced MUSIC in the present invention;

[0019] Figure 6 It is a schematic diagram of RMSE under different array element numbers M using dimension-reduced MUSIC in the present invention. DETAILED DESCRIPTION

[0020] 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.

[0021] This embodiment provides a diagonal spatial smoothed coherent DOA estimation method based on non-circular signals based on the following principles. The specific method of this embodiment is:

[0022] Step 1: Data model of the signal under uniform linear array.

[0023] like Figure 1 As shown, considering A uniform linear array of sensors, where the array spacing is , is the signal carrier wavelength, assuming A narrowband far-field non-circularly coherent signal From the shooting angle Incident to the array, for the first sensors (with the first sensor as the reference point), at time Data received on It is expressed as:

[0024] ;

[0025] in is the direction vector, corresponding to the signal From the perspective The array response at incident light, is additive white Gaussian noise, which represents the effect of noise on the received signal.

[0026] All sensors in the array are grouped into a column vector , which can be expressed as:

[0027] ;

[0028] The signal vector , the noise vector Obeying Gaussian distribution, is the noise power, yes The identity matrix of order. yes The steering matrix is is the angle The guiding vector.

[0029] For strictly non-circular signals (such as binary phase-shift keying and amplitude modulation signals), the received signal Expressed as ,in is a diagonal matrix, It is The non-circular phase of the signal, the real signal vector .

[0030] Therefore, the array reception information of the non-circular signal is obtained:

[0031] ;

[0032] Step 2: Receive information Conjugate with it Connect in series to get the extended receiving information after the series connection ;

[0033] in represents the conjugate operation, and then The data covariance matrix is:

[0034] ;

[0035] In the formula is the covariance matrix of the array output, is the elliptic covariance matrix, represents the transpose operation, Represents the conjugate transpose operation.

[0036] The information of the array output signal covariance matrix constructed by the above formula is composed of non-circular coherent signals. The existing decorrelation algorithm cannot utilize the inherent characteristics of non-circular signals. Therefore, consider Extract by its structure and Next, we will use the decorrelation method to transform the covariance matrix of the array output and the elliptic covariance matrix Perform decorrelation processing separately.

[0037] Step 3: Obviously at this point Can be considered as The data covariance of the signal without circular phase received by the linear antenna array of the sensor is shown in the diagram of the smoothing structure before and after in order to perform the smoothing operation. Figure 2 As shown, it is assumed that The sensors are divided into overlapping subarrays (number of subarrays), each with elements, their relationship satisfies:

[0038] ;

[0039] in, is the number of overlapping subarrays, The number of sensors in each subarray, omitting the index ,but:

[0040] ;

[0041] Among them The noise vector of the sub-array is . Before the array The steering matrix corresponding to the elements is is the signal vector, is a diagonal matrix of Power, , the size is Therefore, the subarrays and The cross covariance matrix of the subarrays It can be expressed as:

[0042] ;

[0043] In the formula The dimension is The identity matrix of is the noise variance, Indicates the expected operation. represents the signal covariance matrix. Similarly, subarrays and The backward cross-covariance matrix of the subarrays Should be:

[0044] ;

[0045] in is a Antisymmetric identity matrix.

[0046] Since the received signal is fully coherent, the signal covariance matrix The rank of is 1, so all the information of the received signal is contained in the largest eigenvalue and its corresponding eigenvector. Based on this, the signal subspace matrix It can be defined as:

[0047] ;

[0048] in Representation Matrix The largest eigenvalue after eigendecomposition, and its corresponding largest eigenvector In this case, subspace-based methods such as MUSIC and ESPRIT cannot be directly applied because they operate on full-rank matrices.

[0049] make ,So , so we have:

[0050] ;

[0051] therefore, is a Let Indicates forward subarray, then , then subarrays and The forward cross-covariance matrix of the subarrays is:

[0052] ;

[0053] In the formula express of element.

[0054] Similarly, subarrays and The backward cross-covariance matrix of the subarrays can be defined as:

[0055] ;

[0056] In order to reduce the computational load, the enhanced spatial smoothing (ASS) method is used to obtain the ASS smoothing matrix

[0057] ;

[0058] Pair Matrix Perform the same operation to obtain the ASS smoothing matrix .

[0059] Step 4: Based on the previous and The extraction method will and Splice along the diagonal angle to get , at this time It is the covariance matrix after ASS smoothing:

[0060] ;

[0061] Next, Perform eigenvalue decomposition:

[0062] ;

[0063] Among them The eigenvectors corresponding to the eigenvalues ​​form the signal subspace , It is from the previous The remaining eigenvectors form the noise subspace , is a diagonal matrix consisting of the remaining eigenvalues.

[0064] Step 5: The noise subspace obtained after eigenvalue decomposition is after array expansion. At this time, the MUSIC algorithm is used to perform a two-bit search to obtain The elevation angle and non-circular phase of a signal are calculated. Due to the introduction of two-dimensional search, the computational complexity of two-dimensional MUSIC is very high. Therefore, the dimension-reduced MUSIC algorithm is considered to estimate the DOA of non-circular signals. This method only requires one-dimensional search, which greatly reduces the computational complexity. Then the corresponding steering vector also needs to be expanded according to the characteristics of the array after expansion. The original steering vector is , the expanded steering vector should be:

[0065] ;

[0066] The noise subspace finally obtained from step 4 above is and the corresponding steering vector , the dimension-reduced MUSIC is used to accurately estimate the DOA, and the dimension-reduced MUSIC spectrum peak search function is:

[0067] ;

[0068] in , find the location of the spectrum peak in the above formula, which is the estimated value of DOA.

[0069] 3. Performance Analysis and Experimental Analysis

[0070] 1. Complexity analysis

[0071] The complexity of the method of the present invention mainly includes: calculating the sample covariance matrix The required computational complexity , where SNAP represents the number of snapshots, and the complexity of the ASS algorithm is ,right Perform EVD to find the noise subspace The computational complexity is , the computational complexity required for spectral function search is ,in represents the number of searches. Combining all these components, the overall computational complexity of the proposed algorithm is:

[0072] ;

[0073] 2. Experimental analysis

[0074] In order to verify the effect of the above method, multiple simulation experiments were conducted in this embodiment, and the experimental performance was analyzed, as follows:

[0075] (1) Experimental performance evaluation indicators:

[0076] The main metric used to quantify performance is the root mean square error (RMSE), defined as follows:

[0077] ;

[0078] in, For the The accurate estimate of the DOA of the kth source in the Monte Carlo process is: represents the number of information sources, MC represents the number of Monte Carlo tests, No. The true DOA of the source.

[0079] In the following simulation, the signal carrier frequency , the speed of light , the arrival angle of the fully coherent signal is , the circular phase is .

[0080] 3. Experimental effect diagram

[0081] Figure 3 The invention is that the arrival angle of two close coherent signals is The circular phase is , Snapshots , MUSIC spatial spectrum under the condition of SNR=0dB. In this experiment, two incident angles are calculated The circular phase is It can be clearly seen that the proposed method can accurately identify the spectrum peaks of the two signals, and the effect is better than other methods.

[0082] Figure 4 The invention is that the arrival angle of two close coherent signals is The circular phase is Root mean square error (RMSE) images of DOA angle estimation using reduced-dimensional MUSIC with different snapshot numbers, SNR=0dB, number of antennas M=10, and Monte Carlo MC=1000 runs. The number of snapshots varies from 200 to 1000. It is clear that the proposed algorithm shows significant performance improvement as the number of snapshots increases, and consistently outperforms other algorithms.

[0083] Figure 5 The invention is that the arrival angle of two close coherent signals is The circular phase is , SNAP=300, M=10, and 1000 MC runs, the RMS error images of DOA angle estimation using reduced-dimensional MUSIC at different SNRs. The SNR varies from -2dB to 6dB. It is clear that the proposed algorithm shows significant performance improvement and consistently outperforms other algorithms.

[0084] Figure 6 The SNR-RMS error image of the present invention under different antenna numbers is shown in Figure 2. Taking SNR as the independent variable, the images of M = 9, M = 10, and M = 11 are plotted respectively. The other simulation parameters are the same as Figure 5 From the comparison of the figures, it can be seen that under the same signal-to-noise ratio, the performance under different numbers of antennas is stable and better than other algorithms, which shows that the algorithm of the present invention has a high utilization rate of the number of array antennas, which is also consistent with the conclusion in theory that the array aperture is increased by virtual expansion.

[0085] In summary, from the analysis of the simulation effect diagram, it can be seen that the diagonalized spatial smoothing coherent DOA estimation algorithm based on non-circular signals proposed in the present invention realizes the accurate DOA estimation of non-circular phase coherent signals. This method not only generates a covariance matrix containing more information, but also effectively solves the DOA estimation problem of coherent signals by smoothing, and improves the array aperture by virtual expansion. Compared with conventional smoothing algorithms, the proposed method has a higher aperture utilization rate, and the estimation performance is better than the DOA method of estimating coherent signals using traditional smoothing technology.

[0086] 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. A diagonal spatially smoothed coherent DOA estimation method based on non-circular signals, characterized in that: The steps include: S1: Receive non-circular signals through uniform linear array antennas to obtain received information ; S2: According to the non-circular characteristics of the signal, the received information Conjugate with it Serial combination to expand the receiving information , and calculate The covariance matrix of ; S3: From Extract subarray diagonally from the center and , for the extracted sub-matrix and Perform enhanced spatial smoothing operations respectively to obtain and ; S4: Yes and Concatenate to generate a new covariance matrix , for the generated Perform eigenvalue decomposition to obtain the noise subspace ; S5: Based on noise subspace , the dimension-reduced MUSIC algorithm is used to estimate the DOA of non-circular signals.

2. The diagonalized spatially smoothed coherent DOA estimation method based on non-circular signals according to claim 1, characterized in that: The received information obtained in step S1 The specific process is as follows: Depend on A uniform linear array of sensors, where the array spacing is , is the signal carrier wavelength, assuming A narrowband far-field non-circularly coherent signal From the shooting angle Incident to the array, for the first sensors, at time Data received on It is expressed as: ； in is the direction vector, corresponding to the signal From the perspective The array response at incident light, is additive white Gaussian noise; All sensors in the array are grouped into a column vector , expressed as , the signal vector , the noise vector Obeying Gaussian distribution, is the noise power, yes The identity matrix of order; yes The steering matrix is is the angle The steering vector of For strictly non-circular signals, the received signal Expressed as ,in is a diagonal matrix, It is The non-circular phase of the signal, the real signal vector , get the array receiving information of non-circular signal: 。 3. The diagonalized spatially smoothed coherent DOA estimation method based on non-circular signals according to claim 2, characterized in that: The specific implementation process of step S2 is as follows: Will receive information Conjugate with it Connect in series to get the extended receiving information after connecting in series , ； in represents the conjugate operation, and then The data covariance matrix is: ； In the formula is the covariance matrix of the array output, is the elliptic covariance matrix, represents the transpose operation, Represents the conjugate transpose operation.

4. The diagonalized spatially smoothed coherent DOA estimation method based on non-circular signals according to claim 3, characterized in that: The specific implementation process of step S3 is as follows: Assumptions The sensors are divided into overlapping subarrays, each with elements, satisfying ,in is the number of overlapping subarrays, The number of sensors in each subarray, omitting the index ,but , among which The noise vector of the sub-array is ; Before the array The steering matrix corresponding to the elements is is the signal vector, is a diagonal matrix of Power, , the size is ;No. subarrays and The cross covariance matrix of the subarrays It is expressed as: ； In the formula The dimension is The identity matrix of is the noise variance, Indicates the expected operation. represents the signal covariance matrix; similarly, subarrays and The backward cross-covariance matrix of the subarrays Should be: ,in is a Antisymmetric identity matrix; Signal subspace matrix Defined as , Representation Matrix The largest eigenvalue after eigendecomposition, and its corresponding largest eigenvector ;make ,So , so we have: ； therefore, is a vector; let Indicates forward subarray, then , then subarrays and The forward cross-covariance matrix of the subarrays is: ； In the formula express of element; Similarly, subarrays and The backward cross-covariance matrix of the subarrays is defined as: ； Using the enhanced spatial smoothing ASS method, we get the ASS smoothing matrix : ； Pair Matrix Perform the same operation to obtain the ASS smoothing matrix .

5. The diagonalized spatially smoothed coherent DOA estimation method based on non-circular signals according to claim 4, characterized in that: The noise subspace obtained in step S4 is The specific process is as follows: According to and The extraction method will and Splice along the diagonal , at this time It is the covariance matrix after ASS smoothing: ; Next, Perform eigenvalue decomposition: ； Among them The eigenvectors corresponding to the eigenvalues ​​form the signal subspace , It is from the previous The remaining eigenvectors form the noise subspace. , is a diagonal matrix consisting of the remaining eigenvalues.

6. The diagonalized spatially smoothed coherent DOA estimation method based on non-circular signals according to claim 5, characterized in that: The specific implementation process of step S5 is as follows: The original steering vector is , the expanded steering vector should be: ； From the noise subspace and the corresponding steering vector , the dimension-reduced MUSIC is used to accurately estimate the DOA, and the dimension-reduced MUSIC spectrum peak search function is: ； in , the location of the spectrum peak of the spectrum peak search function is the estimated value of DOA.

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