A DOA estimation method based on reorganized nested arrays

Abstract

This invention discloses a direction-of-arrival (DOA) estimation method based on a reorganized nested array configuration. The method comprises the following steps: reordering two subarrays of a nested array to construct a reorganized nested array configuration; calculating the differential co-array and its maximum continuous degree of freedom of the reorganized nested array; spatially sampling the target radiator based on the reorganized nested array and vectorizing the covariance matrix of the antenna array's received signal; reconstructing the incident signal components based on a compressed sensing method; and constructing a spectral function and performing a spectral peak search to estimate the DOA of the target radiator. The invention proposes a differential co-array with a hole-free characteristic in the reorganized nested array configuration, which expands the array's degrees of freedom and effective array aperture, enabling high-precision underdetermined DOA estimation.

Description

Technical Field

[0001] The present invention belongs to the technical field of array signal processing, and in particular relates to a DOA estimation method based on a recombined nested array. Background Art

[0002] Direction of Arrival (DOA) estimation is an important research area in array signal processing, with significant applications in radar, sonar, and wireless communications. The most widely used uniform linear arrays in array signal processing are limited by their degrees of freedom and array aperture, which limits the number of resolvable signals and the accuracy of DOA estimation in direction-finding methods based on these arrays.

[0003] Currently, several sparse non-uniform linear arrays have been proposed, offering new approaches for high-precision underdetermined DOA estimation. Typical examples include the minimum redundancy array (MRA), minimum aperture array (MHA), nested array (NA), and coprime array (CPA) and its derivatives. Compared to uniform linear arrays, sparse non-uniform linear arrays have more degrees of freedom (DOF) and can estimate a greater number of signal sources. However, closed-form expressions are not available for the array configurations of MRA and MHA; the differential co-arrays of CPA and its derivatives are not continuous and have a low effective array aperture; and the differential co-arrays of nested arrays have no aperture, but their continuous DOF and effective array aperture need to be further improved. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the present invention provides a DOA estimation method based on a recombined nested array, which adopts the following technical solutions:

[0005] A DOA estimation method based on reorganized nested arrays comprises the following steps:

[0006] Step 1: reordering the two groups of subarrays of the nested array to construct a reorganized nested array;

[0007] Step 2: Calculate the differential co-matrix and maximum continuous DOF of the reorganized nested array;

[0008] Step 3: Perform spatial sampling of the target radiation source, calculate the covariance matrix of the reconstructed nested array received signal and vectorize it;

[0009] Step 4: Reconstruct the incident signal components based on the compressed sensing method using the obtained vectorized covariance matrix;

[0010] Step 5: Construct a spectrum function based on the incident signal components and perform a spectrum peak search. The spectrum function has a high-power and sharp peak at the position corresponding to the incident angle, thereby realizing the DOA estimation of the target radiation source.

[0011] Furthermore, the reorganized nested array in step 1 is composed of three sub-arrays, sub-array 1 contains N1 sensors with an array element spacing of d, sub-array 2 is an independent sensor, and sub-array 3 contains N2-1 sensors with an array element spacing of N1d, where d is the standard array element spacing and d=λ / 2, and λ is the wavelength of the incident signal; after normalizing d, the configuration expression of the reorganized nested array is:

[0012]

[0013] in, and They represent the sensor position distribution sets of sub-array 1, sub-array 2 and sub-array 3 respectively, and s1 and s2 represent the position of each sensor in sub-array 1 and sub-array 3 respectively.

[0014] Furthermore, the differential common array described in step 2 Self-differential diversity and its mirror collection Mutual Difference Diversity and its mirror collection composition:

[0015]

[0016] in,

[0017]

[0018]

[0019] d s and d c Respectively and For the elements in , the maximum continuous DOF is 2N1(N2+1)+3.

[0020] Furthermore, in step 3, the received signal obtained by spatially sampling the target radiation source is x(t)=As(t)+n(t), t=1,…,T, s(t) represents the incident signal, A is the array flow matrix, n(t) is the additive white Gaussian noise, and T is the number of snapshots;

[0021] The covariance matrix of the received signal is R ss represents the covariance matrix of the source signal, A H is the conjugate transpose of A, represents the noise power, I N represents the N×N identity matrix;

[0022] Covariance matrix R xx The vectorized result is vec(·) represents the vectorization operator, A * is the conjugate of A, ⊙ represents the Khatri-Rao product, and h represents the source vector.

[0023] Furthermore, in step 4, the compressed sensing method is used to construct the l1 norm minimization constraint equation to reconstruct the incident signal component

[0024]

[0025] Where B represents the perception matrix and κ is the penalty factor.

[0026] The recombinant nested array configuration and its degrees of freedom proposed in the present invention have simple closed-form expressions, and its differential common array has a hole-free characteristic; when the number of array elements is the same, the recombinant nested array has 4 more continuous DOFs than the nested array and 2 more continuous DOFs than the enhanced nested array; the present invention combines compressed sensing theory to transform the DOA estimation problem into a problem of solving a norm minimization constraint equation, which can achieve underdetermined and high-precision DOA estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Schematic diagram of the process of the present invention;

[0028] Figure 2 It is the intrinsic relationship diagram of the reorganized nested array, nested array and enhanced nested array based on 2D topological structure under the same conditions;

[0029] Figure 3 The curves of continuous DOF changing with the number of array elements for the reorganized nested array, nested array, and enhanced nested array under the same conditions;

[0030] Figure 4 This is a comparison chart of the DOA estimation accuracy of the recombinant nested array, nested array, and enhanced nested array under the same conditions. DETAILED DESCRIPTION

[0031] The present invention will now be described in further detail with reference to the accompanying drawings.

[0032] like Figure 1 As shown, the method of the present invention mainly comprises the following steps:

[0033] Step 1: Reorder the two subarrays of the nested array to construct a reorganized nested array configuration. The reorganized nested array consists of three subarrays: Subarray 1 contains N1 sensors with an element spacing of d, Subarray 2 is an independent sensor, and Subarray 3 contains N2-1 sensors with an element spacing of N1d, where d = λ / 2 represents the standard element spacing, λ represents the wavelength of the incident signal, and the total number of elements is N = N1 + N2. After normalizing d, the reorganized nested array configuration expression is:

[0034]

[0035] Step 2: Calculate the differential co-matrix and maximum continuous DOF of the reorganized nested array, including:

[0036] Step 2.1: Calculate the differential co-matrix: The differential co-matrix of the reconstructed nested array is obtained by the self-difference set Mutual Difference Diversity and its mirror collection Composition, namely:

[0037]

[0038] in,

[0039]

[0040]

[0041] Step 2.2: Calculate the maximum continuous DOF:

[0042] For a recombined nested array configuration with the number of array elements being N=N1+N2, the maximum continuous DOF is: 2N1(N2+1)+3.

[0043] Step 3: Perform spatial sampling of the target radiation source and vectorize the covariance matrix of the antenna array received signal, including:

[0044] Step 3.1: Perform spatial sampling on the target radiation source and obtain the antenna array received signal vector:

[0045] x(t)=As(t)+n(t),t=1,…,T;

[0046] Where s(t) represents the incident signal, A is the array flow matrix, n(t) is the additive white Gaussian noise, and T is the number of snapshots;

[0047] Step 3.2: Calculate the covariance matrix of the antenna array received signal:

[0048] For the multi-snapshot case, the covariance matrix of the signal received by the antenna array is: Among them, R ss represents the covariance matrix of the source signal, represents the noise power, I N represents the N×N unit matrix;

[0049] Step 3.3: R xx Perform vectorized processing

[0050]

[0051] Where vec(·) represents the vectorization operator, ⊙ represents the Khatri-Rao product, and h represents the source vector.

[0052] Step 4: Based on the compressed sensing method, reconstruct the incident signal components, construct the l1 norm minimization constraint equation, and reconstruct the incident signal components:

[0053]

[0054] Where B represents the perception matrix and κ is the penalty factor.

[0055] Step 5: Construct a spectrum function and perform spectrum peak search to achieve DOA estimation of the target radiation source. There is a high-power and sharp spectrum peak at the position corresponding to the incident angle, thereby achieving DOA estimation of the target radiation source.

[0056] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions based on the principles of the present invention are within the scope of protection of the present invention. It should be noted that for those skilled in the art, various improvements and modifications that do not depart from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A DOA estimation method based on recombined nested arrays, characterized in that: The following steps are involved: Step 1: Reorder the two subarrays of the nested array to construct a recombined nested array; the recombined nested array consists of three subarrays, subarray 1 contains N1 sensors with an array element spacing of d, subarray 2 is an independent sensor, and subarray 3 contains N2-1 sensors with an array element spacing of N1d, where d is the standard array element spacing and d = λ / 2, and λ is the wavelength of the incident signal; after normalizing d, the configuration expression of the recombined nested array is: in, and They represent the sensor position distribution sets of sub-array 1, sub-array 2 and sub-array 3 respectively, s1 and s2 represent the position of each sensor in sub-array 1 and sub-array 3 respectively; Step 2: Calculate the differential co-matrix of the reorganized nested array and its maximum continuous DOF; including: Step 2.1: Calculate the differential co-matrix: The differential co-matrix of the reconstructed nested array is obtained by the self-difference set Mutual Difference Diversity and its mirror collection composition: in, Step 2.2: Calculate the maximum continuous DOF: For the recombined nested array configuration with the number of array elements N=N1+N2, the maximum continuous DOF is: 2N1(N2+1)+3; Step 3: Perform spatial sampling of the target radiation source, calculate the covariance matrix of the reconstructed nested array received signal and vectorize it; Step 4: Reconstruct the incident signal components based on the compressed sensing method using the obtained vectorized covariance matrix; Step 5: Construct a spectrum function based on the incident signal components and perform a spectrum peak search. The spectrum function has a high-power and sharp peak at the position corresponding to the incident angle, thereby realizing the DOA estimation of the target radiation source.

2. A DOA estimation method based on reorganized nested arrays as claimed in claim 1, characterized in that: In step 3, the received signal obtained by spatial sampling the target radiation source is x(t)=As(t)+n(t), t=1,…,T, A is the array flow matrix, s(t) represents the incident signal, n(t) is the additive white Gaussian noise, and T is the number of snapshots; The covariance matrix of the received signal is R ss represents the covariance matrix of the source signal, A H is the conjugate transpose of A, represents the noise power, I N represents the N×N identity matrix; Covariance matrix R xx The vectorized result is vec(·) represents the vectorization operator, A * is the conjugate of A, ⊙ represents the Khatri-Rao product, and h represents the source vector.

3. A DOA estimation method based on reorganized nested arrays as claimed in claim 1, characterized in that: In step 4, the compressed sensing method is used to construct the l1 norm minimization constraint equation to reconstruct the incident signal component Where B represents the perception matrix and κ is the penalty factor.

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