DOA estimation method based on expanded co-prime nested array

Abstract

The invention discloses a DOA (direction of arrival) estimation method based on an expanded co-prime 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 aid of the expanded co-prime nested array. Meanwhile, received signals are grouped, vectorization and deduplication processing are carried out on a covariance matrix of the received signals, discrete Fourier transform is carried out on the received signals to obtain a discrete Fourier spectrum, discrete Fourier series of each group is determined through global coarse search and local fine search, and finally a DOA accurate estimation value is obtained through grouping comparison. The problem of fuzzy estimation caused by array element spacing expansion is avoided, DOA non-fuzzy estimation is achieved, and the method is more suitable for accurate target positioning.

Description

Technical Field

[0001] The invention relates to the technical field of target positioning, and in particular to a DOA estimation method based on unfolding coprime nested arrays. 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 performance of DOA estimation is mainly determined by the array aperture and the estimation algorithm. At present, the typical arrays used for DOA estimation are CLA (Coprime Linear Array), NLA (Nested Linear Array) and UCLA (Unfolded Coprime Linear Array). CLA is composed of two sparse uniform subarrays. The array element spacing of the two subarrays is an integer multiple of half the wavelength and is mutually prime. The number of array elements of the two subarrays is mutually prime. Compared with the traditional uniform linear array, CLA expands the array aperture, laying the foundation for improving the accuracy of DOA estimation. The fuzzy estimation problem caused by the expansion of the array element spacing is also suppressed by the mutual prime characteristics of the two subarrays, thus achieving DOA unambiguous estimation. However, the two subarrays of CLA overlap, and the array aperture is only determined by the larger array aperture subarray, so the array aperture of CLA cannot be fully expanded; NLA is composed of a uniform subarray and a sparse uniform subarray, and the array element spacing of the sparse uniform subarray is the array aperture of the uniform subarray. Compared with the traditional uniform linear array, the array aperture of NLA has been further expanded, which is conducive to improving the accuracy of DOA estimation, and due to the existence of uniform linear subarrays, the appearance of DOA ambiguity estimation values ​​is avoided. However, the array aperture of NLA is the sum of the apertures of the two subarrays, and the array aperture expansion of NLA is limited by the uniform subarray. Based on CLA, UCLA expands the two subarrays along the overlapping array elements, realizes the superposition of the two subarray apertures, further expands the array aperture, improves the DOA estimation performance and realizes DOA unambiguous estimation. However, the array structure of UCLA is strictly restricted by the mutual prime relationship between the two subarrays, and the array aperture expansion of UCLA is limited.

[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 unfolding coprime nested arrays, which solves the problem of limited array aperture expansion, greatly expands the array aperture and improves the DOA estimation accuracy, and at the same time realizes DOA unambiguous estimation by utilizing the coprime characteristics of subarrays.

[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 unfolding coprime nested arrays comprises the following steps:

[0008] S1. Construct an unfolded mutually prime nested array and receive target radiation signals in groups;

[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, and obtain the DOA estimation result through group comparison.

[0012] Furthermore, the coprime nested array expanded in step S1 is composed of subarray 1, subarray 2 and subarray 3, and subarray 1, subarray 2 and subarray 3 are all sparse uniform linear arrays and are collinear; wherein, the array element spacing of subarray 1 is N2λ / 2, and the number of array elements is N1, the array element spacing of subarray 2 is N1λ / 2, and the number of array elements is N2, the array element spacing of subarray 3 is N1N2λ / 2, and the number of array elements is N3, N1 and N2 are coprime and N1>N2, and λ is half a wavelength.

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

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

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

[0016] S23, performing de-duplication processing on the differential common matrix of the received group signals, and obtaining an expression of the differential common matrix of the received group signals without duplication.

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

[0018]

[0019] Among them, R i is the covariance matrix of the packet received signal, L is the number of snapshots of the received signal, For x i The conjugate transpose of (t);

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

[0021]

[0022] Among them, R i,ss is the grouped 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 packet received signal to obtain the expression of the differential covariance matrix of the packet received signal:

[0024]

[0025] in, is the signal power of the kth source, The qth bit is 1, and the rest are 0, q = 1, 2, ..., N i +N3, * is conjugated.

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

[0027]

[0028] in, The (N1+1)(N3+1)th bit of is 1, and the rest of the bits are 0. The (N2+1)N3th bit is 1, and the rest are 0. N 13 =2(N1+1)(N3+1)-1, N 23 =2(N2+1)N3-1, when i is 1, β is N2, when i is 2, β is N1.

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

[0030]

[0031] Perform discrete Fourier transform on the group received signal without repeated difference common array, and get the group 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 grouped discrete Fourier spectrum to obtain K spectrum peaks, and the initial discrete Fourier series corresponding to the position of the kth spectrum peak is

[0036] F in the grouped discrete Fourier spectrum i b i,s (θ k ) is:

[0037]

[0038] When N i3 As it approaches infinity,

[0039]

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

[0041]

[0042] Among them, η i,k is the correction coefficient and satisfies -π / N i3 <η i,k <π / N i3 ;

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

[0044]

[0045] When N i3 As it approaches infinity,

[0046]

[0047] F i b i,s (θ k ) The elements are constructed as:

[0048]

[0049] in, F i No. OK,

[0050] Reconstruct the grouped discrete Fourier spectrum as:

[0051]

[0052] In the initial discrete Fourier series Surrounding pairs |F i z i ' ,s |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, for different groups, according to K correction coefficients Obtain the DOA estimation value set of each source in different groups:

[0056]

[0057] The DOA estimation value of each source is obtained by the following formula:

[0058]

[0059] in, is the DOA estimate of the kth source, and are the kth pair of closest DOA estimates selected from S1 and S2 respectively.

[0060] The beneficial effects of the present invention are:

[0061] (1) Expanding the array aperture by expanding the coprime nested arrays can lead to better DOA estimation performance;

[0062] (2) Obtain accurate DOA estimates by performing a global coarse search and a local fine search on the discrete Fourier spectrum;

[0063] (3) The coprime characteristics of the subarrays are used to suppress the DOA ambiguity estimation value and achieve DOA unambiguous estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 A flowchart of a DOA estimation method based on unfolding coprime nested arrays provided in an embodiment of the present invention;

[0065] Figure 2A schematic diagram of a mutually prime nested array is shown for an embodiment of the present invention:

[0066] Figure 3 It is a scatter diagram of DOA estimation results according to an embodiment of the present invention;

[0067] Figure 4 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;

[0068] Figure 5 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

[0069] 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.

[0070] like Figure 1 As shown, in one embodiment of the present invention, a DOA estimation method based on unfolding coprime nested arrays includes the following steps:

[0071] S1. Construct an unfolded coprime nested array and receive target radiation signals in groups.

[0072] like Figure 2 As shown, the expanded coprime nested array is composed of subarray 1, subarray 2 and subarray 3, and subarray 1, subarray 2 and subarray 3 are all sparse uniform linear arrays and collinear; wherein, the array element spacing of subarray 1 is N2λ / 2, and the number of array elements is N1, the array element spacing of subarray 2 is N1λ / 2, and the number of array elements is N2, the array element spacing of subarray 3 is N1N2λ / 2, and the number of array elements is N3, N1 and N2 are coprime and N1>N2, and λ is a half wavelength;

[0073] 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 group receiving signal x i (t) is:

[0074] x i (t) = A i s i (t)+n i (t),i=1,2

[0075] Among them, A i =[(a i (θ1); a3(θ1)), (a i(θ2); a3(θ2)),...,(a i (θ K ); a3(θ K ))], i=1,2 is the direction vector, s i (t) = [s i,1 (t),s i,2 (t),...,s i,K (t)] T , i=1,2 is the signal vector, n i (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, is the direction vector of sub-matrix 3.

[0076] S2. Construct the covariance matrix of the received signal and perform vectorization and de-duplication processing.

[0077] Step S2 includes the following sub-steps:

[0078] S21. Calculate the packet received signal covariance matrix using the following formula:

[0079]

[0080] Among them, R i is the covariance matrix of the packet received signal, L is the number of snapshots of the received signal, For x i The conjugate transpose of (t);

[0081] The packet received signal covariance matrix is ​​constructed as:

[0082]

[0083] Among them, R i,ss is the grouped amplitude covariance matrix, is the noise power, and I is the unit matrix.

[0084] S22, vectorize the covariance matrix of the packet received signal to obtain the expression of the differential covariance matrix of the packet received signal:

[0085]

[0086] in, is the signal power of the kth source, The qth bit is 1, and the rest are 0, q = 1, 2, ..., N i +N3, * is conjugated.

[0087] S23, perform de-duplication processing on the differential common matrix of the received group signal, and obtain the expression of the differential common matrix of the received group signal without duplication:

[0088]

[0089] in, The (N1+1)(N3+1)th bit of is 1, and the rest of the bits are 0. The (N2+1)N3th bit is 1, and the rest are 0. N 13 =2(N1+1)(N3+1)-1, N 23 =2(N2+1)N3-1, when i is 1, β is N2, when i is 2, β is N1.

[0090] S3. Construct a discrete Fourier transform normalization matrix and perform discrete Fourier transform on the received signal.

[0091] The normalized discrete Fourier transform matrix is ​​constructed as F i The (n,m)th element of is:

[0092]

[0093] Perform discrete Fourier transform on the group received signal without repeated difference common array, and get the group discrete Fourier spectrum expression:

[0094]

[0095] Among them, |·| is the absolute value.

[0096] S4. Perform a global coarse search and a local fine search on the discrete Fourier spectrum, and obtain the DOA estimation result through group comparison.

[0097] Step S4 includes the following sub-steps:

[0098] S41, perform a global rough search on the grouped discrete Fourier spectrum to obtain K spectrum peaks, and the initial discrete Fourier series corresponding to the position of the kth spectrum peak is

[0099] F in the grouped discrete Fourier spectrum i b i,s (θ k ) is:

[0100]

[0101] When N i3 As it approaches infinity,

[0102]

[0103] S42, the initial discrete Fourier series Corrected to:

[0104]

[0105] Among them, η i,k is the correction coefficient and satisfies -π / N i3 <η i,k <π / N i3 ;

[0106] Substituting the modified discrete Fourier series into the grouped discrete Fourier spectrum, we get F i b i,s (θ k ) Elements:

[0107]

[0108] When N i3 As it approaches infinity,

[0109]

[0110] F i b i,s (θ k ) The elements are constructed as:

[0111]

[0112] in, F i No. OK,

[0113] Reconstruct the grouped discrete Fourier spectrum as:

[0114]

[0115] In the initial discrete Fourier series Surrounding pairs |F i z i ' ,s |Perform a local fine search to obtain the correction coefficient:

[0116]

[0117] Among them, arc[·] is the inverse function, ||·|| F is the Frobenius norm.

[0118] S43, for different groups, according to K correction coefficients Obtain the DOA estimation value set of each source in different groups:

[0119]

[0120] The DOA estimation value of each source is obtained by the following formula:

[0121]

[0122] in, is the DOA estimate of the kth source, and are the kth pair of closest DOA estimates selected from S1 and S2 respectively.

[0123] The present invention is further described below in conjunction with the MALTAB simulation experiment results:

[0124] To evaluate the present invention, consider an unfolded coprime nested array, where the array element spacing of subarray 1 is N2λ / 2, the number of array elements is N1, the array element spacing of subarray 2 is N1λ / 2, the number of array elements is N2, the array element spacing of subarray 3 is N1N2λ / 2, the number of array elements is N3, N1 and N2 are coprime and N1>N2, and the discrete Fourier spectrum local fine search step is d i,s =π / 50N i3 In order to evaluate the performance of different arrays, the root mean square error (RMSE) is introduced, that is,

[0125]

[0126] 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.

[0127] Figure 3 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=4,N3=4,L=500,SNR=5dB,p=300. Observation Figure 3 It can be seen that the present invention can accurately obtain the DOA estimation values ​​of all targets in each simulation experiment, which is mainly due to the large array aperture and sub-array coprime characteristics of the unfolded coprime nested array. Figure 3 The results verify the reliability of the present invention in DOA estimation.

[0128] Figure 4 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=7, N2=6, N3=4, L=200, and p=400. Figure 5 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 = 7, N2 = 6, N3 = 4, SNR = 5dB, p = 400. Observation Figure 4 and Figure 5 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. In addition, the DOA estimation accuracy of the unfolded coprime nested array is better than that of NLA, Super NLA, Augmented NLA and MISC, which is mainly due to the fact that the unfolded coprime nested array greatly expands the array aperture. Figure 4 and Figure 5 The results verify the superiority of the present invention in DOA estimation.

[0129] In summary, the present invention expands the array aperture by unfolding coprime nested arrays, laying the foundation for improving the DOA estimation performance; at the same time, the received signals are grouped and the covariance matrix of the received signals is vectorized and de-duplicated, and the received signals are discrete Fourier transformed to obtain a discrete Fourier spectrum, and the discrete Fourier series of each group is determined by global coarse search and local fine search, and finally an accurate DOA estimation value is obtained by group comparison, avoiding the fuzzy estimation problem caused by the expansion of array element spacing, realizing DOA fuzzy-free estimation, and being more suitable for precise target positioning.

Claims

1. A DOA estimation method based on unfolding coprime nested arrays, characterized in that: The following steps are involved: S1. Construct an unfolded mutually prime nested array and receive target radiation signals in groups; 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, and obtain the DOA estimation result through group comparison.

2. A DOA estimation method based on unfolding coprime nested arrays according to claim 1, characterized in that: The coprime nested array expanded in step S1 is composed of subarray 1, subarray 2 and subarray 3, and subarray 1, subarray 2 and subarray 3 are all sparse uniform linear arrays and are collinear; wherein, the array element spacing of subarray 1 is N2λ / 2, and the number of array elements is N1, the array element spacing of subarray 2 is N1λ / 2, and the number of array elements is N2, the array element spacing of subarray 3 is N1N2λ / 2, and the number of array elements is N3, N1 and N2 are coprime and N1>N2, and λ is half wavelength.

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

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

5. A DOA estimation method based on unfolding coprime nested arrays according to claim 4, characterized in that: The step S22 performs vector processing on the covariance matrix of the packet received signal to obtain the expression of the differential covariance matrix of the packet received signal: in, is the signal power of the kth source, The qth bit is 1, and the rest are 0, q = 1, 2, ..., N i +N3, * is conjugated.

6. A DOA estimation method based on unfolding coprime nested arrays according to claim 5, characterized in that: The step S23 performs de-duplication processing on the differential common matrix of the received group signals to obtain the expression of the differential common matrix of the received group signals without duplication: Among them, B i,s =[b i,s (θ1),b i,s (θ2),...,b i,s (θ K )], The (N1+1)(N3+1)th bit of is 1, and the rest of the bits are 0. The (N2+1)N3th bit is 1, and the rest are 0. N 13 =2(N1+1)(N3+1)-1, N 23 =2(N2+1)N3-1, when i is 1, β is N2, when i is 2, β is N1.

7. A DOA estimation method based on unfolding coprime nested arrays according to claim 6, characterized in that: In step S3, the normalized discrete Fourier transform matrix is ​​constructed as F i The (n,m)th element of is: Perform discrete Fourier transform on the group received signal without repeated difference common array, and get the group discrete Fourier spectrum expression: Among them, |·| is the absolute value.

8. A DOA estimation method based on unfolding coprime nested arrays according to claim 7, characterized in that: The step S4 comprises the following sub-steps: S41, perform a global rough search on the grouped discrete Fourier spectrum to obtain K spectrum peaks, and the initial discrete Fourier series corresponding to the position of the kth spectrum peak is F in the grouped discrete Fourier spectrum i b i,s (θ k ) is: When N i3 As it approaches infinity, S42, the initial discrete Fourier series Corrected to: Among them, η i,k is the correction coefficient and satisfies -π / N i3 <η i,k <π / N i3 ; Substituting the modified discrete Fourier series into the grouped discrete Fourier spectrum, we get F i b i,s (θ k ) Elements: When N i3 As it approaches infinity, F i b i,s (θ k ) The elements are constructed as: in, F i No. OK, Reconstruct the grouped discrete Fourier spectrum as: In the initial discrete Fourier series Surrounding pairs |F i z i ' ,s |Perform a local fine search to obtain the correction coefficient: Among them, arc[·] is the inverse function, ||·|| F is the Frobenius norm; S43, for different groups, according to K correction coefficients Obtain the DOA estimation value set of each source in different groups: The DOA estimation value of each source is obtained by the following formula: in, is the DOA estimate of the kth source, and are the kth pair of closest DOA estimates selected from S1 and S2 respectively.

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