A DOA estimation method based on hybrid analog-digital structure to eliminate mutual coupling influence

Abstract

This invention relates to a DOA estimation method based on a hybrid modulus-digital architecture to eliminate mutual coupling effects, aiming to address the impact of limited RF chain numbers and antenna array mutual coupling effects on DOA estimation accuracy. The method comprises a two-stage DOA estimation framework: in the first stage, the spatial covariance matrix is ​​reconstructed by selecting an intermediate subarray and combining it with diagonal loading techniques to initially estimate the DOA and alleviate mutual coupling effects; in the second stage, the accuracy of DOA estimation is further improved using full array data and super-resolution algorithms, and high-resolution DOA estimation is achieved by compensating for mutual coupling effects. This invention also provides a corresponding system design, including a switching network, amplifiers, and phase shifters, for dynamically adjusting the array to achieve optimized signal reception and processing. Compared to traditional methods, this invention achieves high DOA estimation accuracy even with a lower RF chain configuration, demonstrating significant performance advantages and practical application value.

Description

Technical Field

[0001] This invention relates to the field of array signal DOA estimation technology, and in particular to a DOA estimation method based on eliminating mutual coupling effects under a hybrid modulus-digital structure. Background Technology

[0002] In modern wireless communication systems, angle of arrival (DOA) estimation is a key technology, widely used in numerous scenarios such as downlink beamforming at base stations, integrated sensing and communication, and interference suppression. Traditional DOA estimation methods are mostly based on a fully digital (FDS) architecture, where each antenna is connected to a dedicated radio frequency (RF) chain. However, with the development of millimeter-wave and terahertz communications, the high power consumption of large-scale arrays under FDS makes it impractical.

[0003] Hybrid Modular Structures (HADS) have gained widespread attention as an alternative due to their ability to balance low power consumption and reliable communication performance. However, because HADS significantly reduces the number of radio frequency chains and exhibits array mutual coupling (MC), traditional FDS-based angle-of-arrival (AOA) estimation methods cannot be directly applied, posing a significant challenge to achieving high-performance AOA estimation. Array mutual coupling introduces uncertainties into the array manifold, distorts signal correlation, and reduces array response, making it difficult to accurately reconstruct the full-dimensional spatial covariance matrix (SCM) required for super-resolution AOA estimation methods. This results in biased angle estimation and reduced resolution in traditional methods.

[0004] Therefore, there is an urgent need for an angle-of-arrival estimation method and system that can effectively solve the limitations of the number of radio frequency chains and the effects of array mutual coupling in HADS. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a DOA estimation method based on a hybrid modular structure to eliminate the mutual coupling effect. This method can improve the accuracy of angle of arrival estimation, reduce the computational complexity while ensuring the estimation accuracy, and improve the system's operating efficiency. It has stronger adaptability and practicality in actual communication scenarios.

[0006] The technical solution adopted in this invention is a DOA estimation method based on eliminating mutual coupling effects under a hybrid modular structure, which includes the following steps:

[0007] Step 1: Establish a signal model: Set that L far-field narrow-band signals are incident on an antenna array from different directions, wherein the antenna array adopts a hybrid analog-to-digital structure, the hybrid analog-to-digital structure includes M antennas and N radio frequency chains, wherein N<M; each of the antennas is equipped with an analog domain auxiliary unit, and the analog domain auxiliary unit includes a switch, an amplifier, and a phase shifter; among the N radio frequency chains, the first radio frequency chain is connected to all antennas, and the remaining radio frequency chains except the first radio frequency chain are sequentially connected to each antenna starting from the first antenna;

[0008] Step 2: Obtain an initial DOA estimation value: set a switch matrix S in the hybrid analog-to-digital structure w , an amplitude adjustment matrix W a and a phase adjustment matrix H p , and select M-2P antennas in the middle of the antenna array by setting the switch matrix as a block diagonal matrix, wherein M represents the total number of antennas in the antenna array, and P represents the length of an unknown mutual coupling coefficient; perform analog-to-digital conversion processing on the output signals of the M-2P antennas on the first radio frequency chain to obtain an output signal z1(k), construct an overdetermined system of equations according to the signal z1(k), construct a spatial covariance matrix by using a diagonal loading technology, and process the spatial covariance matrix by using a real-valued subspace technology to obtain an initial DOA estimation value;

[0009] Step 3: Obtain an enhanced DOA estimation value: obtain output signals z(k) of the second to the nth radio frequency chains, wherein n=1, 2, 3, ..., N; according to the output signal z(k), estimate the mutual coupling coefficient by using the initial DOA estimation value obtained in step 2, reconstruct the spatial covariance matrix according to the mutual coupling coefficient to obtain a reconstructed spatial covariance matrix, and process the reconstructed spatial covariance matrix by using the real-valued subspace technology to obtain an enhanced DOA estimation value.

[0010] Preferably, in step 1, the output signal of the hybrid analog-to-digital structure at time t is expressed as: y(t) = S w W a H p x(t) = S w W a H p (CA(θ)S(t)+n(t));

[0011] wherein, x(t)=CA(θ)S(t)+n(t), x(t) represents a signal output by the antenna array itself after L far-field narrow-band signals are incident on the antenna array from different directions; S w represents a switch matrix, which is 1 when the switch corresponding to the antenna is closed, and 0 otherwise; W a represents an amplitude adjustment matrix, H pW represents the phase adjustment matrix. a =diag(ρ1,...,ρ M ), ρ M and Let s(t) represent the amplifier gain and phase shift at time t, respectively, where j is the imaginary unit; s(t) = [s1(t),...,s...] L (t)] T Let s(t) represent the set of L far-field narrowband signals incident from different angles at time t, and n(t) = [n1(t),...,n M (t)] T n(t) represents the Gaussian white noise vector; A(θ) = [a(θ1),...,a(θ)] L )], A(θ) represents the M×L antenna array manifold matrix, where, w l = -πsinθ l θ l This represents the DOA estimate to be calculated. C represents an M×M matrix with a symmetric Toeplitz structure, i.e., a mutual coupling matrix, C = Toeplitz{[c0,c1,...c...}}. p ,0 1×(M-P-1) ]}; where c i The coefficient of mutual coupling between the two antennas is represented by , and P represents the length of the unknown coefficient of mutual coupling.

[0012] As a preferred embodiment, step 2 includes the following steps:

[0013] S2.1, Setting S w S is a block diagonal matrix w =blkdiag(0 P×P ,I M-2P ,0 P×P ), where I M-2P Let W represent an identity matrix of dimension M-2P × M-2P; selecting the middle M-2P antennas, we obtain the amplitude adjustment matrix for the M-2P antennas. a =I M Among them, I M Represents an identity matrix of dimension M×M; the phase adjustment matrix for M-2P antennas is H. p =diag(1,e -jπsinθ ,...,e -j(M-1)πsinθ ), where θ represents a preset angle in the phase-shifted observation space to compensate for phase distortion caused by mutual coupling at different angles;

[0014] S2.2. Combine the output signals of the M-2P antennas on the first radio frequency chain to obtain a combined analog signal; digitally sample the combined analog signal to obtain a digital sampled signal z1(k), which is expressed as: k represents the sample time index, where each k value corresponds to a specific sampling time; q represents the candidate phase shift index, where Q represents the dimension of the phase shift observation space, and each q value corresponds to a specific candidate phase shift; H This is represented as the conjugate transpose; h q Let θ represent the phase shift of the q-th phase-shift observation space, P represent the length of the unknown mutual coupling coefficient, M represent the total number of antennas in the antenna array, and θ represent the phase shift of the q-th phase-shift observation space. q The preset angle for the q-th observation space; Let x(k) represent the M-2P elements in the middle, where x(k) represents the discrete-time representation of the original signal received by the M-2P antennas after analog processing; then calculate the average power of the digitally sampled signal z1(k). in, Let K represent the covariance matrix of the middle M-2P antennas, and K represent the number of samples relative to the candidate phase shift.

[0015] S2.3, using calculation and The definition of , where vec(.) represents the vectorized operator, The symbols represent the Kronecker product operator, where E, F, and G represent any multiplyable matrices. This represents the covariance matrix of the M-2P antennas in the middle, from which the average power can be obtained. And adjust the phase shift in the phase adjustment matrix Adjustments were made to obtain a series of average powers under different phase shifts: And the average power P under a series of different phase shifts q Construct an overdetermined system of equations: P = [P1,...,P] Q ] T =Br; where B is Where r represents the vectorized covariance matrix;

[0016] S2.4. Based on the overdetermined system of equations obtained in step S2.3, the estimated vector is obtained by solving it using the diagonal loading technique. And construct the spatial covariance matrix corresponding to the intermediate M-2P root antennas. get Wherein, unvec(.) represents the inverse vectorization process; the initial DOA estimate is obtained after processing the spatial covariance matrix using real-valued subspace techniques.

[0017] Preferably, in step S2.4, the specific process of processing the spatial covariance matrix using the real-valued subspace technique is as follows:

[0018] S2.41, the aforementioned spatial covariance matrix Convert to a real-valued matrix, and define the Hermitian supersymmetric matrix as follows: in, Represents the reversed matrix. (.) * Indicates conjugate. The covariance matrix is ​​represented by the signal received using a portion of the antennas; then the unitary transformation matrix is ​​defined. The unitary transformation matrix is ​​based on Parity has different definitions, when When it is even, when When it is an odd number,

[0019] S2.42, through the unitary transformation matrix For Hermitian supersymmetric matrices Perform transformations to construct the real-valued space covariance matrix right Perform eigenvalue decomposition to obtain the noise subspace matrix E n Through search function The L peaks are used to obtain the initial DOA estimate. Where l = 1,...,L, This is the guiding vector matrix.

[0020] As a preferred embodiment, step 3 includes the following steps:

[0021] S3.1, Reset S w =W a =H P =I M The output signals from the second RF chain to the nth RF chain are obtained as follows: in, Corresponding to the mutual coupling effect between the first N-1 antennas, it has a symmetric Toeplitz structure similar to the overall mutual coupling matrix C; Let c = [1, c1, c2, ..., c] represent a matrix transformation. p ] T A vector representing the mutual coupling parameters;

[0022] S3.2 Using the initial DOA estimate obtained in step 2 Construct another overdetermined system of equations Ξ T c = 0 L(N-1-L)×1 ,in, Denotes the noise subspace matrix, and solving this overdetermined system of equations yields the estimated values ​​of the mutual coupling coefficients. And thereby reconstruct the mutual coupling matrix

[0023] S3.3, Reconfigure S w =I M , The average power of the digital sampled signal z1(k) is calculated again, and the spatial covariance matrix corresponding to the middle M-2P antennas is reconstructed again using the diagonal loading technique. Finally, the real-valued subspace technique is used to reconstruct the spatial covariance matrix. Processed, and through a search function The L peaks are used to obtain an enhanced DOA estimate.

[0024] The beneficial effects of this invention are as follows: Through a two-stage design, the first stage effectively mitigates the impact of array mutual coupling by rationally setting the matrix and employing diagonal loading technology, obtaining a more accurate initial DOA estimate. The second stage utilizes the initial DOA estimate to further estimate and compensate for the mutual coupling coefficients, fully utilizing the data from the entire array to achieve enhanced DOA estimation and significantly improve the accuracy of the angle of arrival (DOA) estimation. The method proposed in this invention can effectively utilize the limited RF chain resources in a hybrid modular digital structure, exhibiting stronger adaptability and practicality in real-world communication scenarios, and providing strong support for applications such as efficient downlink beamforming. By introducing real-valued subspace technology, computational complexity is reduced while ensuring estimation accuracy, thus improving system operating efficiency. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the hybrid modular structure of the present invention;

[0026] Figure 2 This is a flowchart of a DOA estimation method based on a hybrid modular structure to eliminate mutual coupling effects according to the present invention;

[0027] Figure 3 This is a schematic diagram showing the relationship between the mean square error and the signal-to-noise ratio of the method proposed in this invention;

[0028] Figure 4 This is a schematic diagram showing the relationship between the mean square error of the method proposed in this invention and the number of samples.

[0029] Figure 5 This is a schematic diagram showing the relationship between the mean square error of the method proposed in this invention and the number of antennas;

[0030] Figure 6 This is a schematic diagram illustrating the relationship between the estimation success rate and the signal-to-noise ratio of the method proposed in this invention;

[0031] Figure 7 is a schematic diagram of the relationship between the estimation success rate and the number of samples of the method proposed by the present invention;

[0032] Figure 8 is a schematic diagram of the relationship between the estimation success rate and the number of antennas of the method proposed by the present invention. Detailed Description of the Embodiments

[0033] The present invention is further described below with reference to the accompanying drawings and in combination with specific embodiments, so that those skilled in the art can implement the invention with reference to the description of the specification, and the protection scope of the present invention is not limited to the specific embodiments.

[0034] Hybrid analog-digital structure (HADS) has become an effective solution for reducing transmission loss and lowering system overhead in multiple-input multiple-output (MIMO) systems. However, the limited number of radio frequency (RF) chains and the existence of array mutual coupling (MC) pose significant challenges to achieving high-performance direction of arrival (DOA) estimation, thereby hindering effective downlink beamforming. To address these challenges, an efficient DOA estimation method specifically designed for HADS is proposed, which effectively mitigates the influence of MC by adopting a two-stage framework.

[0035] The present invention relates to a DOA estimation method for eliminating the influence of mutual coupling under a hybrid analog-digital structure, and the method comprises the following steps:

[0036] Step 1, as shown in Figure 1 , establish a signal model: it is set that L far-field narrowband signals are incident on an antenna array from different angles, the antenna array adopts a hybrid analog-digital structure, the hybrid analog-digital structure comprises M antennas and N RF chains, wherein N<M; each of the antennas is equipped with an analog domain auxiliary unit, and the analog domain auxiliary unit comprises a switch, an amplifier and a phase shifter; among the N RF chains, the first RF chain is connected to all antennas, and the remaining RF chains except the first RF chain are sequentially connected to each antenna starting from the first antenna;

[0037] Step 2, obtain an initial DOA estimation value; the process is as follows: set a switch matrix S in the hybrid analog-digital structure w , an amplitude adjustment matrix W a and a phase adjustment matrix H pThe M-2P antennas in the middle of the antenna array are selected by setting the switching matrix as a block diagonal matrix, where M represents the total number of antennas in the antenna array and P represents the length of the unknown mutual coupling coefficient. The output signals of the M-2P antennas are processed by analog-to-digital conversion on the first RF chain to output signal z1(k). An overdetermined system of equations is constructed based on the signal z1(k), and a spatial covariance matrix is ​​constructed using diagonal loading technology. The initial DOA estimate is obtained by processing the spatial covariance matrix using real-valued subspace technology.

[0038] Step 3: Obtain the enhanced DOA estimate. The process is as follows: Obtain the output signal z(k) from the second RF chain to the nth RF chain, where n = 1, 2, 3, ..., N; Based on the output signal z(k), estimate the cross-coupling coefficient using the initial DOA estimate obtained in Step 2, and reconstruct the spatial covariance matrix based on the cross-coupling coefficient to obtain the reconstructed spatial covariance matrix. Then, process the reconstructed spatial covariance matrix using real-valued subspace techniques to obtain the enhanced DOA estimate.

[0039] Preferably, in step 1, the output signal of the hybrid modular structure at time t is expressed as:

[0040] y(t)=S w W a H p x(t)=S w W a H p (CA(θ)S(t)+n(t));

[0041] Where, x(t)=CA(θ)S(t)+n(t), x(t) represents the signal output by the antenna array itself after L far-field narrowband signals are incident on the antenna array from different angles; S w This represents a switch matrix, where 1 indicates the switch corresponding to the antenna is closed, and 0 indicates it is closed otherwise; W a H represents the amplitude adjustment matrix. p W represents the phase adjustment matrix. a =diag(ρ1,...,ρ M ), ρ M and Let s(t) represent the amplifier gain and phase shift at time t, respectively, where j is the imaginary unit; s(t) = [s1(t),...,s...] L (t)] T Let s(t) represent the set of L far-field narrowband signals incident from different angles at time t, and n(t) = [n1(t),...,n M (t)] Tn(t) represents the Gaussian white noise vector; A(θ) = [a(θ1),...,a(θ)] L )], A(θ) represents the M×L antenna array manifold matrix, where, w l = -πsinθ l θ l This represents the DOA estimate to be calculated. C represents an M×M matrix with a symmetric Toeplitz structure, i.e., a mutual coupling matrix, C = Toeplitz{[c0,c1,...c...}}. p ,0 1×(M-P-1) ]}; where c i The coefficient of mutual coupling between the two antennas is represented by , and P represents the length of the unknown coefficient of mutual coupling.

[0042] As a preferred embodiment, step 2 includes the following steps:

[0043] S2.1, Setting S w S is a block diagonal matrix w =blkdiag(0 P×P ,I M-2P ,0 P×P ), where I M-2P Let W represent an identity matrix of dimension M-2P × M-2P; selecting the middle M-2P antennas, we obtain the amplitude adjustment matrix for the M-2P antennas. a =I M Among them, I M Represents an identity matrix of dimension M×M; the phase adjustment matrix for M-2P antennas is H. p =diag(1,e -jπsinθ ,...,e -j(M-1)πsinθ ), where θ represents a preset angle in the phase-shifted observation space to compensate for phase distortion caused by mutual coupling at different angles;

[0044] S2.2. Combine the output signals of the M-2P antennas on the first radio frequency chain to obtain a combined analog signal; digitally sample the combined analog signal to obtain a digital sampled signal z1(k), which is expressed as: k represents the sample time index, where each k value corresponds to a specific sampling time; q represents the candidate phase shift index, where Q represents the dimension of the phase shift observation space, and each q value corresponds to a specific candidate phase shift; H This is represented as the conjugate transpose; h q Let θ represent the phase shift of the q-th phase-shift observation space, P represent the length of the unknown mutual coupling coefficient, M represent the total number of antennas in the antenna array, and θ represent the phase shift of the q-th phase-shift observation space. q The preset angle for the q-th observation space; Let x(k) represent the M-2P elements in the middle, where x(k) represents the discrete-time representation of the original signal received by the M-2P antennas after analog processing; then calculate the average power of the digitally sampled signal z1(k). in, Let K represent the covariance matrix of the middle M-2P antennas, and K represent the number of samples relative to the candidate phase shift.

[0045] S2.3, using calculation and r = vec(R) x The definition of ), where vec(.) represents the vectorized operator, The symbols represent the Kronecker product operator, where E, F, and G represent any multiplyable matrices. This represents the covariance matrix of the M-2P antennas in the middle, from which the average power can be obtained. And adjust the phase shift in the phase adjustment matrix Adjustments were made to obtain a series of average powers under different phase shifts: And the average power P under a series of different phase shifts q Construct an overdetermined system of equations: P = [P1,...,P] Q ] T =Br; where B is Where r represents the vectorized covariance matrix;

[0046] S2.4. Based on the overdetermined system of equations obtained in step S2.3, the estimated vector is obtained by solving it using the diagonal loading technique. And construct the spatial covariance matrix corresponding to the intermediate M-2P root antennas. get Wherein, unvec(.) represents the inverse vectorization process; the initial DOA estimate is obtained after processing the spatial covariance matrix using real-valued subspace techniques.

[0047] Among them, the diagonal loading technique solves the vector. The specific process is as follows: the diagonal loading technique is an improved solution method, the core idea of ​​which is to load B... H Adding a positive constant λ multiplied by the identity matrix I to the diagonal of B improves the condition number of the matrix and enhances the stability of the solution. Specifically, the objective function after diagonal loading becomes... Ask about it Taking the derivative of and setting it to zero, we can obtain the equation satisfied by the optimal solution. Solving this equation yields an estimated vector. Wherein, λ is the diagonal loading coefficient, which is a pre-defined positive number. This term acts as a regularization mechanism, restricting the estimation vector. The norm is used to avoid excessive fluctuations in the solution.

[0048] Preferably, in step S2.4, the specific process of processing the spatial covariance matrix using the real-valued subspace technique is as follows:

[0049] S2.41, the aforementioned spatial covariance matrix Convert to a real-valued matrix, and define the Hermitian supersymmetric matrix as follows: in, Represents the reversed matrix. (.) * Indicates conjugate. This refers to the covariance matrix obtained by receiving signals using a portion of the antennas; then, the unitary transformation matrix is ​​defined. The unitary transformation matrix is ​​based on Parity has different definitions, when When it is even, when When it is an odd number,

[0050]

[0051] S2.42, through the unitary transformation matrix For Hermitian supersymmetric matrices Perform transformations to construct the real-valued space covariance matrix right Perform eigenvalue decomposition to obtain the noise subspace matrix E n Through search function The L peaks are used to obtain the initial DOA estimate. Where l = 1,...,L, This is the guiding vector matrix.

[0052] As a preferred embodiment, step 3 includes the following steps:

[0053] S3.1, Reset S w =W a =H P =I M The output signals from the second RF chain to the nth RF chain are obtained as follows: in, Corresponding to the mutual coupling effect between the first N-1 antennas, it has a symmetric Toeplitz structure similar to the overall mutual coupling matrix C; Let c = [1, c1, c2, ..., c] represent a matrix transformation. p ] T A vector representing the mutual coupling parameters;

[0054] S3.2 Using the initial DOA estimate obtained in step 2 Construct another overdetermined system of equations Ξ T c = 0 L(N-1-L)×1 ,in, Denotes the noise subspace matrix, and solving this overdetermined system of equations yields the estimated values ​​of the mutual coupling coefficients. And thereby reconstruct the mutual coupling matrix

[0055] S3.3, Reconfigure S w =I M , The average power of the digital sampled signal z1(k) is calculated again, and the spatial covariance matrix corresponding to the middle M-2P antennas is reconstructed again using the diagonal loading technique. Finally, the real-valued subspace technique is used to analyze the spatial covariance matrix. Processed, and through a search function The L peaks are used to obtain an enhanced DOA estimate.

[0056] The following experiments demonstrate the effectiveness of the DOA estimation method based on a hybrid modular structure for eliminating mutual coupling effects, as proposed in this invention.

[0057] Experimental setup: The lengths of the unknown MC coefficients are set to P = 2, C1 = 0.4045 + 0.2939j, and C2 = 0.2898 - 0.0776j. The number of phase shifts in the first-stage algorithm and the number of phase shifts in the second-stage algorithm are Q = 181 and Q = 30, respectively.

[0058] Figure 3 The system has 10 antennas (M) and 5 RF chains (N). It has 2 signal sources with angles of -32.7° and 24.1° respectively, 1000 sampling samples (K), and a signal-to-noise ratio (SNR) ranging from -5dB to 15dB. Figure 4 The system has 10 antennas, 5 radio frequency chains, 2 signal sources, angles of -32.7° and 24.1°, a signal-to-noise ratio of 10dB, and a sampling number K ranging from 100 to 3000. Figure 5 The number of antennas M is set to 8 to 20, the number of radio frequency chains N = 5, the number of signal sources is 2, the angles are θ = -32.7° and θ = 24.1° respectively, the signal-to-noise ratio is 10dB, and the number of samples K = 1000.

[0059] Figure 6 , Figure 7 as well as Figure 8The system has 10 antennas (M) and 5 RF chains (N). It has two signal sources with angles of -32.7° and -27.7° respectively, a sampling rate of K = 1000, and a signal-to-noise ratio of 5dB.

[0060] exist Figures 3-8 In the above, the all-digital multiple signal classification algorithm 1 is: a fully digital multiple signal classification algorithm based on M sensors with known mutual coupling, where M>N;

[0061] The all-digital multiple signal classification algorithm 2 is: a fully digital multiple signal classification algorithm based on N sensors with known mutual coupling, where M>N;

[0062] The algorithm without handling mutual coupling is: a multi-signal classification algorithm based on covariance matrix reconstruction for unknown mutual coupling;

[0063] Cramer-Rao bound is defined as the lower bound of the variance of an unbiased estimate.

[0064] Experimental Results: Through simulation experiments, under different signal-to-noise ratio conditions, the DOA estimation method based on a hybrid modulus structure proposed in this invention can obtain relatively accurate DOA estimates. Figure 3 It can be clearly seen that as the SNR increases, the RMSE gradually decreases, indicating that the method of the present invention has better performance in high signal-to-noise ratio environments and can accurately estimate the angle of arrival of the signal, thus verifying the effectiveness of the algorithm.

[0065] In addition, from Figure 3 , Figure 4 as well as Figure 5 The curves clearly show that the root mean square error (RMSE) under the second-stage algorithm is smaller than that under the first-stage algorithm, thus verifying the effectiveness of the two-stage estimation strategy. Compared with the case without compensation, the RMSE after mutual coupling compensation is significantly reduced, especially at low signal-to-noise ratios (SNR), indicating that the proposed mutual coupling compensation algorithm can effectively improve estimation accuracy. As the SNR increases, the accuracy of mutual coupling coefficient estimation becomes the main factor affecting DOA estimation performance.

[0066] Figure 6 , Figure 7 as well as Figure 8 Analyzing the simulation results from a performance perspective, the figures show that the performance of each algorithm improves with increasing signal-to-noise ratio and number of samples. The proposed second-stage algorithm exhibits super-resolution capability, which can be attributed to its ability to fully utilize the aperture of the entire array. In contrast, due to the smaller effective array aperture of the all-digital multiple signal classification algorithm 2, it is unable to resolve the two sources across the entire observation area.

Claims

1. A DOA estimation method based on eliminating the influence of mutual coupling under a hybrid modular structure, characterized in that: The method comprises the following steps: Step 1, establishing a signal model: setting that L far-field narrowband signals are incident to an antenna array from different angles, the antenna array adopts a hybrid analog-digital structure, the hybrid analog-digital structure comprises M antennas and N radio frequency chains, wherein N<M; each of the antennas is equipped with an analog domain auxiliary unit, and the analog domain auxiliary unit comprises a switch, an amplifier and a phase shifter; among the N radio frequency chains, a first radio frequency chain is connected to all antennas, and the remaining radio frequency chains except the first radio frequency chain are sequentially connected to each antenna starting from a first antenna; Step 2: Obtain the initial DOA estimate; the process involves setting the switching matrix in the hybrid modular structure. Amplitude adjustment matrix and phase adjustment matrix And by setting the switch matrix to a block diagonal matrix, the center of the antenna array is selected.

1. Antenna, where M represents the total number of antennas in the antenna array, and P represents the length of the unknown mutual coupling coefficient; The output signal of the antenna is processed by analog-to-digital conversion on the first RF chain before being output as a signal. According to the signal An overdetermined system of equations is constructed, and a spatial covariance matrix is ​​built using diagonal loading techniques. The spatial covariance matrix is ​​then processed using real-valued subspace techniques to obtain an initial DOA estimate. Specifically, this includes: S2.1, Settings block diagonal matrix ,in, The dimension is The identity matrix; select the middle one. Root antenna, obtain The amplitude adjustment matrix of the root antenna is ,in, The dimension is The identity matrix; The phase adjustment matrix of the root antenna is ,in, This represents a preset angle in the phase-shifted observation space to compensate for phase distortion caused by mutual coupling at different angles; S2.2, will The output signals of the antennas are combined on the first radio frequency chain to obtain a combined analog signal; the combined analog signal is then digitally sampled to obtain a digital sampled signal. It is represented as: , Represents the sample time index, each The value corresponds to a specific sampling time, and q represents the candidate phase shift index. This indicates the dimension of the phase shift observation space, where each q value corresponds to a specific candidate phase shift; This is represented as the conjugate transpose; , Let P represent the phase shift of the q-th phase shift observation space, P represent the length of the unknown mutual coupling coefficient, and M represent the total number of antennas in the antenna array. The preset angle for the q-th observation space; express The middle There are elements, among which... This represents the discrete-time representation of the original signal received by the M-2P antenna after analog processing; then, the digitally sampled signal is calculated. average power ,in, Indicates the middle The covariance matrix of the root antenna, where K represents the number of samples relative to the candidate phase shift; S2.3, using calculation and The definition, in which, Indicates vectorized operators. The symbols represent the Kronecker product operator, where E, F, and G represent any multiplyable matrices. Indicates the middle The covariance matrix of the root antenna can be used to obtain the average power. And adjust the phase shift in the phase adjustment matrix. Adjustments were made to obtain a series of average powers under different phase shifts: ; and the average power under a series of different phase shifts Constructing an overdetermined system of equations: Where B is , where r represents the vectorized covariance matrix; S2.

4. Based on the overdetermined system of equations obtained in step S2.3, the estimated vector is obtained by solving it using the diagonal loading technique. And construct the spatial covariance matrix corresponding to the intermediate M-2P root antennas. ,get ;in, The inverse vectorization process is represented; the initial DOA estimate is obtained by processing the spatial covariance matrix using real-valued subspace techniques. Step 3: Obtain the enhanced DOA estimate; the process is as follows: Set ,in, Represent the identity matrix and obtain the output signals from the second RF chain to the nth RF chain. ,in, According to the output signal The cross-coupling coefficients are estimated using the initial DOA estimate obtained in step 2, and the spatial covariance matrix is ​​reconstructed based on the cross-coupling coefficients to obtain the reconstructed spatial covariance matrix. The reconstructed spatial covariance matrix is ​​then processed using real-valued subspace techniques to obtain an enhanced DOA estimate.

2. The DOA estimation method based on a hybrid modular structure for eliminating mutual coupling effects as described in claim 1, characterized in that: In step 1, the output signal of the hybrid modular structure at time t is expressed as: ;in, , This represents the signal output by the antenna array itself after L far-field narrowband signals are incident on the antenna array from different angles; This represents a switch matrix; the value is 1 when the switch corresponding to the antenna is closed, and 0 otherwise. Represents the amplitude adjustment matrix. Represents the phase adjustment matrix. ; and Let represent the amplifier gain and phase shift at time t, respectively, where j is the imaginary unit; , This represents the set of L far-field narrowband signals incident from different angles at time t. , Represents a Gaussian white noise vector; , Let M×L be the manifold matrix of the antenna array, where, , , This represents the DOA estimate to be calculated, and C represents an M×M matrix with a symmetric Toeplitz structure, i.e., a mutual coupling matrix. ;in, The coefficient of mutual coupling between the two antennas is represented by , and P represents the length of the unknown coefficient of mutual coupling.

3. The DOA estimation method based on a hybrid modular structure for eliminating mutual coupling effects as described in claim 1, characterized in that: In step S2.4, the specific process of processing the spatial covariance matrix by using a real-valued subspace technology is: S2.41, the aforementioned spatial covariance matrix Convert to a real-valued matrix, and define the Hermitian supersymmetric matrix as follows: ,in, Represents the reversed matrix. , Indicates conjugate. The covariance matrix is ​​represented by the signal received using a portion of the antennas; then the unitary transformation matrix is ​​defined. The unitary transformation matrix is ​​based on Parity has different definitions, when When it is even, ,when When it is an odd number, ; S2.42, through the unitary transformation matrix For Hermitian supersymmetric matrices Perform transformations to construct the real-valued space covariance matrix ,right Perform eigenvalue decomposition to obtain the noise subspace matrix. Through search function The L peaks are used to obtain the initial DOA estimate. ,in, , This represents the guiding vector matrix.

4. The DOA estimation method based on a hybrid modular structure for eliminating mutual coupling effects as described in claim 3, characterized in that: The specific process of step 3 comprises the following steps: S3.1, Reset The output signals from the second RF chain to the nth RF chain are obtained as follows: ;in, ; Corresponding to the mutual coupling effect between the first N-1 antennas, it has a mutual coupling matrix with the overall system. Similar symmetrical Toeplitz structures; To represent a matrix transformation, A vector representing the mutual coupling parameters; S3.2 Using the initial DOA estimate obtained in step 2 Another overdetermined system of equations was constructed. ,in, , Denotes the noise subspace matrix, and solving this overdetermined system of equations yields the estimated values ​​of the mutual coupling coefficients. And thereby reconstruct the mutual coupling matrix ; S3.3, Reconfiguration , , Calculate the digital sampled signal again The average power was then reconstructed using diagonal loading technology to obtain the intermediate power. The spatial covariance matrix corresponding to each antenna Finally, the real-valued subspace technique was used to reconstruct the spatial covariance matrix. Processed, and through a search function The L peaks are used to obtain an enhanced DOA estimate.

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