DOA estimation method based on expanded augmented nested array

Abstract

The invention discloses a DOA estimation method based on an expanded and augmented nested array, relates to the technical field of target positioning, and lays a foundation for improving DOA estimation performance by expanding an array aperture with the help of the expanded and augmented nested array. Meanwhile, vectorization and deduplication processing are performed on a covariance matrix of a received signal, discrete Fourier transform is performed on the received signal to obtain a discrete Fourier spectrum, a discrete Fourier series is determined through global coarse search and local fine search, a DOA accurate estimation value is finally obtained, the problem of fuzzy estimation caused by array element spacing extension is avoided, and the accuracy of DOA estimation is improved. The method is more suitable for target positioning.

Description

Technical Field

[0001] The present invention relates to the technical field of target positioning, and in particular to a DOA estimation method based on an expanded augmented nested array. Background Art

[0002] Direction of Arrival (DOA) estimation refers to the use of the path difference of signals received by different array elements to estimate the direction of the signal source. It is an important research direction in the field of array signal processing and has broad application prospects in civil and military fields such as wireless communications, mobile communications and navigation.

[0003] The DOA estimation performance is mainly determined by the array aperture and the estimation algorithm. At present, the typical arrays used for DOA estimation are ULA (Uniform Linear Array), CLA (Coprime Linear Array) and NLA (Nested Linear Array). The array element spacing of ULA is half a wavelength, and the array aperture is proportional to the array element spacing and the number of array elements. The expansion of the array aperture can only be achieved by adding array elements, which is not conducive to system cost control and seriously limits the improvement of DOA estimation performance; CLA is composed of two sub-arrays, the array element spacing of the two sub-arrays is an integer multiple of half a wavelength and is coprime, the number of array elements of the two sub-arrays is coprime, and the array aperture is determined by the larger array aperture sub-array. Compared with ULA, the array aperture of CLA has been greatly improved, laying the foundation for the improvement of DOA estimation accuracy, and the fuzzy estimation problem caused by the expansion of the array element spacing is also suppressed by the coprime characteristics of the two sub-arrays, thus achieving DOA unambiguous estimation. However, the expansion of the CLA array aperture can only be achieved by increasing the number of array elements, and the array aperture expansion space is limited; NLA consists of a uniform subarray and a sparse subarray, and the array element spacing of the sparse subarray is the array aperture of the uniform subarray. The array aperture of NLA is the sum of the two subarray apertures. Compared with ULA, the array aperture of NLA has been further expanded, which is conducive to the improvement of DOA estimation accuracy, and due to the existence of the uniform line subarray, the appearance of DOA ambiguity estimation value is avoided. However, the array aperture of NLA is determined by the number of array elements, and the expansion of the array aperture is limited by the ratio of the number of array elements of the two subarrays.

[0004] Therefore, it is necessary to propose a new array and DOA estimation method to solve the above problems. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a DOA estimation method based on an expanded augmented nested array, which suppresses the DOA ambiguity estimation value while expanding the array aperture and improving the DOA estimation accuracy, thereby solving the contradiction between array aperture expansion and unambiguous estimation.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0007] A DOA estimation method based on an expanded augmented nested array comprises the following steps:

[0008] S1. Construct an expanded and nested array and receive target radiation signals;

[0009] S2, construct the covariance matrix of the received signal, and perform vectorization and de-duplication processing;

[0010] S3, constructing a discrete Fourier transform normalization matrix and performing discrete Fourier transform on the received signal;

[0011] S4. Perform a global coarse search and a local fine search on the discrete Fourier spectrum to obtain the DOA estimation result.

[0012] Furthermore, the expanded nested array in step S1 is composed of sub-array 1 and sub-array 2, and both sub-array 1 and sub-array 2 are linear arrays and collinear; wherein, the array element spacing of sub-array 1 is βλ / 2, and the number of array elements is N1, the array element spacing of sub-array 2 is (N1+1)βλ / 2, and the number of array elements is N2, and the spacing between sub-array 1 and sub-array 2 is N1βλ / 2, β is the augmentation coefficient, and λ is the half wavelength.

[0013] Furthermore, the step S2 includes the following sub-steps:

[0014] S21, calculate and obtain the covariance matrix of the received signal;

[0015] S22, performing vector processing on the covariance matrix of the received signal to obtain an expression of the differential covariance matrix of the received signal;

[0016] S23, performing de-duplication processing on the differential common matrix of the received signal to obtain an expression of the differential common matrix without duplication of the received signal.

[0017] Furthermore, the step S21 calculates the received signal covariance matrix by the following formula:

[0018]

[0019] Where R is the covariance matrix of the received signal, L is the number of snapshots of the received signal, and x H (t) is the conjugate transpose of x(t);

[0020] The received signal covariance matrix is ​​constructed as:

[0021]

[0022] Among them, R SS is the amplitude covariance matrix, is the noise power, and I is the unit matrix.

[0023] Furthermore, the step S22 performs vectorization processing on the covariance matrix of the received signal to obtain the expression of the differential covariance matrix of the received signal:

[0024]

[0025] in, is the signal power of the kth source, The i-th bit is 1, and the rest are 0, B = A * ⊙A=[b(θ1),b(θ2),...,b(θ K )], * is conjugated.

[0026] Furthermore, the step S23 performs de-duplication processing on the differential common matrix of the received signal to obtain an expression of the differential common matrix of the received signal without duplication:

[0027]

[0028] in, The (N2+1)(N1+1)th bit is 1, and the rest are 0. s =[b s (θ1),b s (θ2),...,b s (θ K )], N=2(N2+1)(N1+1)-1.

[0029] Furthermore, in step S3, the normalized discrete Fourier transform matrix is ​​constructed as The (n,m)th element of F is:

[0030]

[0031] Perform discrete Fourier transform on the received signal without repeated difference common array, and get the discrete Fourier spectrum expression:

[0032]

[0033] Among them, |·| is the absolute value.

[0034] Furthermore, the step S4 includes the following sub-steps:

[0035] S41. Perform a global rough search on the discrete Fourier spectrum to obtain K spectrum peaks. The initial discrete Fourier series corresponding to the position of the kth spectrum peak is:

[0036] Discrete Fourier spectroscopy Fb s (θ k ) is:

[0037]

[0038] As N approaches infinity,

[0039]

[0040] S42, the initial discrete Fourier series Corrected to:

[0041]

[0042] Wherein, η is the correction coefficient and satisfies -π / N<η<π / N;

[0043] Substituting the modified discrete Fourier series into the discrete Fourier spectrum, we get Fb s (θ k ) Elements:

[0044]

[0045] As N approaches infinity,

[0046]

[0047] Fb s (θ k ) The elements are reconstructed into:

[0048]

[0049] in, For F OK, Φ=diag(1,e -jη ,e -j2η ,...,e -j(M-1)η );

[0050] Reconstruct the discrete Fourier spectrum as:

[0051]

[0052] In the initial discrete Fourier series Around Perform a local fine search and obtain the correction coefficient:

[0053]

[0054] Among them, arc[·] is the inverse function, ||·|| F is the Frobenius norm;

[0055] S43, based on K correction coefficients η1, η2, ..., η k , the DOA estimation value of each source is obtained by the following formula:

[0056]

[0057] in, is the estimated DOA of the kth source, and arcsin[·] is the inverse sine function.

[0058] The beneficial effects of the present invention are:

[0059] (1) Expanding the array aperture by expanding the augmented nested array can bring better DOA estimation performance;

[0060] (2) Obtain accurate DOA estimates by performing a global coarse search and a local fine search on the discrete Fourier spectrum;

[0061] (3) It avoids the fuzzy estimation problem caused by the expansion of array element spacing and realizes DOA unambiguous estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 A flowchart of a DOA estimation method based on an expanded augmented nested array provided by an embodiment of the present invention;

[0063] Figure 2 The schematic diagram of the augmented nested array is shown in the following figure for an embodiment of the present invention:

[0064] Figure 3 The discrete Fourier spectrum of the embodiment of the present invention;

[0065] Figure 4 It is a scatter diagram of DOA estimation results according to an embodiment of the present invention;

[0066] Figure 5 A comparison diagram of the DOA root mean square error of the embodiment of the present invention and other arrays as the signal-to-noise ratio changes;

[0067] Figure 6 The figure is a comparison chart of the DOA root mean square error of the embodiment of the present invention and other arrays as the number of snapshots changes. DETAILED DESCRIPTION

[0068] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0069] like Figure 1 As shown, in one embodiment of the present invention, a DOA estimation method based on an expanded augmented nested array includes the following steps:

[0070] S1. Construct an expanded augmented nested array and receive the target radiation signal.

[0071] like Figure 2 As shown, the expanded augmented nested array is composed of sub-array 1 and sub-array 2, and both sub-array 1 and sub-array 2 are linear arrays and collinear; wherein, the array element spacing of sub-array 1 is βλ / 2, and the number of array elements is N1; the array element spacing of sub-array 2 is (N1+1)βλ / 2, and the number of array elements is N2; the spacing between sub-array 1 and sub-array 2 is N1βλ / 2, β is the augmentation coefficient, and λ is the half wavelength;

[0072] Assume that there are K narrowband uncorrelated signal sources θ in the far field k , k=1,2,...,K radiates to the array, then the array receives the signal x(t):

[0073] x(t)=As(t)+n(t)

[0074] Among them, A=[(a1(θ1); a2(θ1)), (a1(θ2); a2(θ2)),...,(a1(θ K );a2(θ K ))] is the direction vector, s(t)=[s1(t),s2(t),...,s K (t)] T is the signal vector, n(t) has a mean of 0 and a variance of σ 2 The additive white Gaussian noise vector of is the direction vector of submatrix 1, is the direction vector of sub-matrix 2.

[0075] S2. Construct the covariance matrix of the received signal and perform vectorization and de-duplication processing.

[0076] Step S2 includes the following sub-steps:

[0077] S21. The received signal covariance matrix is ​​calculated by the following formula:

[0078]

[0079] Where R is the covariance matrix of the received signal, L is the number of snapshots of the received signal, and x H (t) is the conjugate transpose of x(t);

[0080] The received signal covariance matrix is ​​constructed as:

[0081]

[0082] Among them, R SS is the amplitude covariance matrix, is the noise power, and I is the unit matrix.

[0083] S22, vectorize the covariance matrix of the received signal to obtain the expression of the differential covariance matrix of the received signal:

[0084]

[0085] in, is the signal power of the kth source, The i-th bit is 1, and the rest are 0, B = A * ⊙A=[b(θ1),b(θ2),...,b(θ K )], * is conjugated.

[0086] S23, perform de-duplication processing on the differential common array of the received signal, and obtain the expression of the differential common array without duplication of the received signal:

[0087]

[0088] in, The (N2+1)(N1+1)th bit is 1, and the rest are 0. s =[b s (θ1),b s (θ2),...,b s (θ K )], N=2(N2+1)(N1+1)-1.

[0089] S3. Construct a discrete Fourier transform normalization matrix and perform discrete Fourier transform on the received signal.

[0090] The normalized discrete Fourier transform matrix is ​​constructed as The (n,m)th element of F is:

[0091]

[0092] Perform discrete Fourier transform on the received signal without repeated difference common array, and get the discrete Fourier spectrum expression:

[0093]

[0094] Among them, |·| is the absolute value.

[0095] S4. Perform a global coarse search and a local fine search on the discrete Fourier spectrum to obtain the DOA estimation result.

[0096] Step S4 includes the following sub-steps:

[0097] S41. Perform a global rough search on the discrete Fourier spectrum to obtain K spectrum peaks. The initial discrete Fourier series corresponding to the position of the kth spectrum peak is:

[0098] Discrete Fourier spectroscopy Fb s (θ k ) is:

[0099]

[0100] As N approaches infinity,

[0101]

[0102] S42, the initial discrete Fourier series Corrected to:

[0103]

[0104] Wherein, η is the correction coefficient and satisfies -π / N<η<π / N;

[0105] Substituting the modified discrete Fourier series into the discrete Fourier spectrum, we get Fb s (θ k ) Elements:

[0106]

[0107] As N approaches infinity,

[0108]

[0109] Fb s (θ k ) The elements are reconstructed into:

[0110]

[0111] in, For F OK, Φ=diag(1,e -jη ,e -j2η ,...,e -j(M-1)η ); reconstruct the discrete Fourier spectrum as:

[0112]

[0113] In the initial discrete Fourier series Around Perform a local fine search and obtain the correction coefficient:

[0114]

[0115] Among them, arc[·] is the inverse function, ||·|| F is the Frobenius norm.

[0116] S43, based on K correction coefficients η1, η2, ..., η k , the DOA estimation value of each source is obtained by the following formula:

[0117]

[0118] in, is the estimated DOA of the kth source, and arcsin[·] is the inverse sine function.

[0119] The present invention is further described below in conjunction with the MALTAB simulation experiment results:

[0120] To evaluate the present invention, consider an expanded augmented nested array, where the element spacing of subarray 1 is βλ / 2, the number of elements is N1, the element spacing of subarray 2 is (N1+1)βλ / 2, the number of elements is N2, the spacing between subarray 1 and subarray 2 is N1βλ / 2, and the discrete Fourier spectrum local fine search step is d s =π / 50N. In order to evaluate the performance of different algorithms, the root mean square error (RMSE) is introduced, that is,

[0121]

[0122] Among them, K is the number of sources, P is the number of Monte Carlo simulations, is the estimated DOA value of the p-th simulation experiment of the k-th information source, and is the true DOA value of the k-th information source.

[0123] Figure 3This is the discrete Fourier spectrum of the present invention, where θ1=10°, θ2=30°, K=2, N1=6, N2=6, L=300, SNR=10dB, β=3. Figure 3 It can be seen that two obvious spectral peaks appear at the discrete Fourier spectral series of m1=25 and m2=73, corresponding to the two targets at θ1=10° and θ2=30° respectively. Apart from this, there are no ambiguous DOA estimation values, which is mainly due to the unambiguous estimation characteristics of the present invention. Figure 3 The results verify the effectiveness of the present invention in DOA estimation.

[0124] Figure 4 The DOA estimation result scatter diagram of the present invention, where the DOA value of K=8 targets is θ k =10°,20°,...,80°,k=1,2,...,8,N1=5,N2=5,L=500,SNR=10dB,β=2,p=200. Observation Figure 4 It can be seen that in each simulation experiment, the present invention can accurately obtain the DOA estimation values ​​of all targets. Figure 4 The results verify the reliability of the present invention in DOA estimation.

[0125] Figure 5 This is a comparison diagram of the DOA root mean square error of the present invention and other arrays as the signal-to-noise ratio changes, where θ1=10°, θ2=20°, K=2, N1=6, N2=6, L=200, and p=400. Figure 6 This is a comparison of the root mean square error of DOA of the present invention and other arrays with the change of the number of snapshots. Among them, θ1 = 10°, θ2 = 20°, K = 2, N1 = 6, N2 = 6, SNR = 5dB, p = 400. Observation Figure 5 and Figure 6 It can be seen that the DOA root mean square error curves of different arrays gradually decrease with the increase of signal-to-noise ratio and snapshot number, and the present invention is also applicable to traditional nested arrays. In addition, the DOA estimation accuracy of expanded augmented nested arrays with different augmentation degrees is better than that of traditional nested arrays and MISC arrays, and with the increase of augmentation degree, the DOA estimation accuracy increases accordingly, which is mainly due to the fact that the expanded augmented nested array greatly expands the array aperture. Figure 5 and Figure 6 The results verify the superiority of the present invention in DOA estimation.

[0126] In summary, the present invention expands the array aperture by unfolding the augmented nested array, laying the foundation for improving the DOA estimation performance; at the same time, the covariance matrix of the received signal is vectorized and de-duplicated, and the discrete Fourier transform is performed on the received signal to obtain a discrete Fourier spectrum. The discrete Fourier series is determined by global coarse search and local fine search, and finally an accurate DOA estimation value is obtained, which avoids the fuzzy estimation problem caused by the expansion of the array element spacing and is more suitable for target positioning.

Claims

1. A DOA estimation method based on expanded augmented nested array, characterized in that: The following steps are involved: S1. Construct an expanded and nested array and receive target radiation signals; S2, construct the covariance matrix of the received signal, and perform vectorization and de-duplication processing; S3, constructing a discrete Fourier transform normalization matrix and performing discrete Fourier transform on the received signal; S4. Perform a global coarse search and a local fine search on the discrete Fourier spectrum to obtain the DOA estimation result.

2. The DOA estimation method based on expanded augmented nested matrix according to claim 1, characterized in that: The expanded nested augmented array in step S1 is composed of sub-array 1 and sub-array 2, both of which are linear arrays and collinear; wherein the array element spacing of sub-array 1 is βλ / 2, the number of array elements is N1, the array element spacing of sub-array 2 is (N1+1)βλ / 2, the number of array elements is N2, the spacing between sub-array 1 and sub-array 2 is N1βλ / 2, β is the augmentation coefficient, and λ is the half wavelength.

3. A DOA estimation method based on expanded augmented nested matrix according to claim 2, characterized in that: The step S2 comprises the following sub-steps: S21, calculate and obtain the covariance matrix of the received signal; S22, performing vector processing on the covariance matrix of the received signal to obtain an expression of the differential covariance matrix of the received signal; S23, performing de-duplication processing on the differential common matrix of the received signal to obtain an expression of the differential common matrix without duplication of the received signal.

4. The DOA estimation method based on expanded augmented nested matrix according to claim 3, characterized in that: The step S21 calculates the received signal covariance matrix by the following formula: Where R is the covariance matrix of the received signal, L is the number of snapshots of the received signal, and x H (t) is the conjugate transpose of x(t); The received signal covariance matrix is ​​constructed as: Among them, R ss is the amplitude covariance matrix, is the noise power, and I is the unit matrix.

5. The DOA estimation method based on expanded augmented nested matrix according to claim 4, characterized in that: The step S22 performs vector processing on the covariance matrix of the received signal to obtain the expression of the differential covariance matrix of the received signal: in, is the signal power of the kth source, The i-th bit is 1, and the rest are 0, B = A * ⊙A=[b(θ1),b(θ2),...,b(θ K )], * is conjugated.

6. A DOA estimation method based on expanded augmented nested matrix according to claim 5, characterized in that: The step S23 performs de-duplication processing on the differential common matrix of the received signal to obtain the expression of the differential common matrix without duplication of the received signal: in, The (N2+1)(N1+1)th bit is 1, and the rest are 0. s =[b s (θ1),b s (θ2),...,b s (θ K )], 7. The DOA estimation method based on expanded augmented nested matrix according to claim 6, characterized in that: In step S3, the normalized discrete Fourier transform matrix is ​​constructed as The (n,m)th element of F is: Perform discrete Fourier transform on the received signal without repeated difference common array, and get the discrete Fourier spectrum expression: Among them, |·| is the absolute value.

8. The DOA estimation method based on expanded augmented nested matrix according to claim 7, characterized in that: The step S4 comprises the following sub-steps: S41. Perform a global rough search on the discrete Fourier spectrum to obtain K spectrum peaks. The initial discrete Fourier series corresponding to the position of the kth spectrum peak is: Discrete Fourier spectroscopy Fb s (θ k ) is: As N approaches infinity, S42, the initial discrete Fourier series Corrected to: Wherein, η is the correction coefficient and satisfies -π / N<η<π / N; Substituting the modified discrete Fourier series into the discrete Fourier spectrum, we get Fb s (θ k ) Elements: As N approaches infinity, Fb s (θ k ) The elements are reconstructed as: in, For F OK, Reconstruct the discrete Fourier spectrum as: In the initial discrete Fourier series Around Perform a local fine search and obtain the correction coefficient: Among them, arc[·] is the inverse function, ||·|| F is the Frobenius norm; S43, based on K correction coefficients η1, η2, ..., η k , the DOA estimation value of each source is obtained by the following formula: in, is the estimated DOA of the kth source, and arcsin[·] is the inverse sine function.

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