DOA estimation method for eliminating mutual coupling influence based on mixed modulus structure

Abstract

The invention relates to a DOA estimation method for eliminating mutual coupling influence based on a mixed modulus structure, and aims to solve the influence of limited number of radio frequency chains and mutual coupling effect of antenna arrays on DOA estimation precision. The method comprises a DOA estimation framework in two stages: in the first stage, a spatial covariance matrix is reconstructed by selecting a middle subarray and combining a diagonal loading technology, DOA is preliminarily estimated, and a mutual coupling effect is relieved; and in the second stage, the DOA estimation precision is further improved by using full-array data and a super-resolution algorithm, and high-resolution DOA estimation is realized by compensating a mutual coupling effect. The invention also provides a corresponding system design, which comprises a switching network, an amplifier and a phase shifter and is used for dynamically adjusting the array to realize optimized signal receiving and processing. Compared with a traditional method, the method has the advantages that high DOA estimation precision can still be achieved under low radio frequency chain configuration, and the method has remarkable performance advantages and practical application value.

Description

Technical Field

[0001] The present invention relates to the technical field of array signal DOA estimation, and in particular to a DOA estimation method for eliminating the influence of mutual coupling under a hybrid analog-digital structure. Background Art

[0002] In modern wireless communication systems, direction-of-arrival (DOA) estimation is one of the key technologies, which is widely used in many scenarios such as base station downlink beamforming, integrated sensing and communication, interference suppression, etc. Most traditional DOA estimation methods are based on the full-digital structure (FDS), that is, 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 problem of large-scale arrays under FDS makes it impractical.

[0003] As an alternative, the hybrid analog-digital structure (HADS) has received extensive attention because it can balance low power consumption and reliable communication performance. However, due to the significant reduction in the number of RF chains in HADS and the existence of mutual coupling (MC) in the array, traditional FDS-based DOA estimation methods cannot be directly applied, which poses a great challenge to achieving high-performance DOA estimation. Mutual coupling in the array will introduce uncertainty in the array manifold, distort signal correlation, reduce the array response, making it difficult to accurately reconstruct the full-dimensional spatial covariance matrix (SCM) required for super-resolution DOA estimation methods, resulting in deviation and reduced resolution in angle estimation by traditional methods.

[0004] Therefore, there is an urgent need for a DOA estimation method and system that can effectively solve the limitations of the number of RF chains in HADS and the influence of mutual coupling in the array. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a DOA estimation method for eliminating the influence of mutual coupling under a hybrid analog-digital structure, which can improve the accuracy of DOA estimation, reduce the computational complexity while ensuring the estimation accuracy, and improve the operating efficiency of the system, and has stronger adaptability and practicality in actual communication scenarios.

[0006] The technical solution adopted by the present invention is a DOA estimation method for eliminating the influence of mutual coupling under a hybrid analog-digital structure, and the method includes the following steps:

[0007] Step 1. Establish a signal model: Assume that L far-field narrowband signals impinge on the antenna array from different angles. The antenna array adopts a hybrid analog-digital structure, which includes M antennas and N radio frequency (RF) chains, where N < M. Each antenna is equipped with an analog-domain auxiliary unit, which includes 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 one are sequentially connected to each antenna starting from the first antenna.

[0008] Step 2. Obtain the initial DOA estimate: Set a switch matrix S w , an amplitude adjustment matrix W a and a phase adjustment matrix H p in the hybrid analog-digital structure, and select the M - 2P antennas in the middle of the antenna array by setting the switch 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 subjected to analog-to-digital conversion processing on the first RF chain and then the signal z1(k) is output. Based on the signal z1(k), an overdetermined system of equations is constructed, and a spatial covariance matrix is constructed using the diagonal loading technique. The real-valued subspace technique is used to process the spatial covariance matrix to obtain the initial DOA estimate.

[0009] Step 3. Obtain the enhanced DOA estimate: Obtain the output signals z(k) of the second RF chain to the nth RF chain, where n = 1, 2, 3, ..., N. Based on the output signals z(k), the mutual coupling coefficient is estimated using the initial DOA estimate obtained in Step 2, and the spatial covariance matrix is reconstructed according to the mutual coupling coefficient to obtain the reconstructed spatial covariance matrix. The real-valued subspace technique is used to process the reconstructed spatial covariance matrix to obtain the enhanced DOA estimate.

[0010] Preferably, in Step 1, the output signal of the hybrid analog-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] where x(t) = CA(θ)S(t) + n(t), and x(t) represents the signal output by the antenna array itself after L far-field narrowband signals impinge on the antenna array from different angles; S w represents the switch matrix, which is 1 when the switch corresponding to the antenna is closed and 0 otherwise; W a represents the amplitude adjustment matrix, and H pDenote the phase adjustment matrix as \(W\). a =\(diag(\rho_1,...,\rho\) M ). \(\rho\) M and respectively represent the amplifier gain and phase shift at time \(t\), where \(j\) is the imaginary unit; \(s(t)=[s_1(t),...,s\) L (t)] T , \(s(t)\) represents the set of \(L\) far - field narrow - band signals incident from different angles at time \(t\), \(n(t)=[n_1(t),...,n\) M (t)] T , \(n(t)\) represents the Gaussian white noise vector; \(A(\theta)=[a(\theta_1),...,a(\theta\) L )], \(A(\theta)\) represents the \(M\times L\) antenna array manifold matrix, where \(w\) l =-\(\pi\sin\theta\) l , \(\theta\) l represents the DOA estimate value to be calculated. \(C\) represents an \(M\times M\) matrix with a symmetric Toeplitz structure, that is, the mutual coupling matrix, \(C = Toeplitz\{[c_0,c_1,...c\) p ,0 1×(M-P-1) \}\); where \(c\) i represents the mutual coupling coefficient between two antennas, and \(P\) represents the length of the unknown mutual coupling coefficient.

[0012] Preferably, the specific process of step 2 includes the following steps:

[0013] S2.1. Set \(S\) w as the block - diagonal matrix \(S\) w =blkdiag(0 P×P ,I M-2P ,0 P×P ), where \(I\) M-2P represents the identity matrix of dimension \(M - 2P\times M - 2P\); select the middle \(M - 2P\) antennas, and the amplitude adjustment matrix of the \(M - 2P\) antennas is \(W\) a =I M , where \(I\) M represents the identity matrix of dimension \(M\times M\); the phase adjustment matrix of the \(M - 2P\) antennas is \(H\) p =diag(1,e -jπsinθ ,...,e -j(M-1)πsinθ ), where \(\theta\) represents the preset angle in the phase shift observation space to compensate for the phase distortion caused by mutual coupling at different angles.

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

[0015] S2.3. With the help of the operations and definitions, where vec(.) represents the vectorization operation symbol, represents the kronecker product operation symbol, and E, F, G represent any multiplicable matrices, represents the covariance matrix of the middle M-2P antennas, from which the average power can be obtained and adjust the phase shift in the phase adjustment matrix to obtain a series of average powers at different phase shifts: and from the series of average powers P 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. According to the overdetermined system of equations obtained in step S2.3, use the diagonal loading technique to solve for the estimated vector and construct the spatial covariance matrix corresponding to the middle M-2P antennas to obtain where unvec(.) represents the inverse quantization process; use the real-valued subspace technique to process the spatial covariance matrix to obtain the initial DOA estimate value.

[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. Convert the spatial covariance matrix into a real-valued matrix, and define the Hermitian supersymmetric matrix as where denotes the reverse-order matrix, (.) * denotes conjugation, denotes the covariance matrix obtained by receiving signals using partial antennas; then define the unitary transformation matrix The unitary transformation matrix has different definitions according to the parity of When is even, When is odd,

[0019] S2.42. Use the unitary transformation matrix to transform the Hermitian supersymmetric matrix to construct the real-valued spatial covariance matrix Perform eigenvalue decomposition on to obtain the noise subspace matrix E n , and obtain the initial DOA estimate by searching for the L peaks of the function where l = 1,..., L, is the steering vector matrix.

[0020] Preferably, the specific process of step 3 includes the following steps:

[0021] S3.1. Reset S w = W a = H P = I M , and obtain the output signals from the second RF chain to the nth RF chain as: where corresponds to the mutual coupling effect between the first N - 1 antennas and has a symmetric Toeplitz structure similar to the overall mutual coupling matrix C; represents a matrix transformation, c = [1, c1, c2,..., c p T denotes the vector of mutual coupling parameters;

[0022] S3.2. Use the initial DOA estimate obtained in step 2 to construct another overdetermined system of equations Ξ T c = 0 L(N-1-L)×1 , where​ Denote the noise subspace matrix, and solve the overdetermined equation system to obtain the estimated value of the mutual coupling coefficient and reconstruct the mutual coupling matrix therefrom

[0023] S3.3. Reconfigure S w = I M , Calculate the average power of the digital sampling signal z1(k) again, and use the diagonal loading technique again to reconstruct the spatial covariance matrix corresponding to the middle M - 2P antennas Finally, adopt the real - valued subspace technique for the reconstructed spatial covariance matrix process, and obtain the enhanced DOA estimated value by searching for the L peaks of the function .

[0024] The beneficial effects of the present invention are as follows: Through the two - stage design of the present invention, in the first stage, by reasonably setting the matrix and adopting the diagonal loading technique, the influence of array mutual coupling is effectively reduced, and a relatively accurate initial DOA estimate is obtained; in the second stage, the initial DOA estimated value is used to further estimate and compensate the mutual coupling coefficient, making full use of the data of the entire array, realizing the enhanced DOA estimate, and significantly improving the accuracy of the arrival angle estimate. The method proposed by the present invention can effectively utilize the limited RF chain resources in the hybrid analog - digital structure, has stronger adaptability and practicability in actual communication scenarios, and provides strong support for applications such as realizing efficient downlink beamforming. By introducing the real - valued subspace technique, while ensuring the estimation accuracy, the computational complexity is reduced, and the operation efficiency of the system is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is the structural schematic diagram of the hybrid analog - digital structure of the present invention;

[0026] Figure 2 is the flowchart of a DOA estimation method for eliminating the influence of mutual coupling based on a hybrid analog - digital structure according to the present invention;

[0027] Figure 3 is the schematic diagram of the relationship between the mean square error and the signal - to - noise ratio of the method proposed by the present invention;

[0028] Figure 4 is the schematic diagram of the relationship between the mean square error and the number of samples of the method proposed by the present invention;

[0029] Figure 5 is the schematic diagram of the relationship between the mean square error and the number of antennas of the method proposed by the present invention;

[0030] Figure 6 is the schematic diagram of the relationship between the estimation success rate and the signal - to - noise ratio of the method proposed by the present invention;

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

[0032] Figure 8 It is a schematic diagram showing the relationship between the estimated success rate of the method proposed by the present invention and the number of antennas. Detailed implementation manner

[0033] The following further describes the invention with reference to the accompanying drawings and in combination with the detailed implementation manner, so that those skilled in the art can implement it according to the text of the specification. The protection scope of the present invention is not limited to this detailed implementation manner.

[0034] The hybrid analog-digital structure (HADS) has become an effective solution for reducing transmission losses and system overhead in multiple-input multiple-output (MIMO) systems. However, the limited number of radio frequency (RF) chains and the presence of mutual coupling (MC) in the array pose significant challenges to achieving high-performance direction-of-arrival (DOA) estimation, thus hindering effective downlink beamforming. To address these challenges, an efficient DOA estimation method specifically designed for HADS is proposed, which effectively mitigates the impact 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 includes the following steps:

[0036] Step 1: As shown in Figure 1 , establish a signal model: Assume that L far-field narrowband signals are incident on the antenna array from different angles. The antenna array adopts a hybrid analog-digital structure, and the hybrid analog-digital structure includes M antennas and N RF chains, where N < M; each antenna 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 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 estimate value; the process is as follows: Set a switch matrix S 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, where M represents the total number of antennas in the antenna array, and P represents the length of the 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 and output the signal z1(k), construct an overdetermined system of equations according to the signal z1(k), construct a spatial covariance matrix using the diagonal loading technique, and use the real-valued subspace technique to process the spatial covariance matrix to obtain an initial DOA estimate value;

[0038] Step 3, obtain an enhanced DOA estimate value; the process is as follows: obtain the output signals z(k) from the second radio frequency chain to the nth radio frequency chain, where n = 1, 2, 3,..., N; according to the output signal z(k), estimate the mutual coupling coefficient using the initial DOA estimate value obtained in Step 2, reconstruct the spatial covariance matrix according to the mutual coupling coefficient to obtain the reconstructed spatial covariance matrix, and use the real-valued subspace technique to process the reconstructed spatial covariance matrix to obtain an enhanced DOA estimate value.

[0039] Preferably, in Step 1, the output signal of the hybrid analog-to-digital 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 incident from different angles to the antenna array; S w represents the switch matrix, which is 1 when the switch corresponding to the antenna is closed and 0 otherwise; W a represents the amplitude adjustment matrix, H p represents the phase adjustment matrix, W a = diag(ρ1,..., ρ M ), ρ M and respectively represent the amplifier gain and phase shift at time t, j is the imaginary unit; s(t) = [s1(t),..., s L (t)] T , s(t) represents the set of L far-field narrowband signals incident from different angles at time t, n(t) = [n1(t),..., n M (t)] T, n(t) represents a Gaussian white noise vector; A(θ) = [a(θ1),..., a(θ L )], A(θ) represents an M×L antenna array manifold matrix, where, w l = -πsinθ l , θ l represents the DOA estimation value to be calculated. C represents an M×M matrix with a symmetric Toeplitz structure, i.e., the mutual coupling matrix, C = Toeplitz{[c0, c1,... c p , 0 1×(M-P-1)}; where, c i represents the mutual coupling coefficient between two antennas, and P represents the length of the unknown mutual coupling coefficient.

[0042] Preferably, the specific process of step 2 includes the following steps:

[0043] S2.1. Set S w as a block diagonal matrix S w = blkdiag(0 P×P , I M-2P , 0 P×P ), where, I M-2P represents an identity matrix of dimension M - 2P×M - 2P; select the middle M - 2P antennas, and the amplitude adjustment matrix for the M - 2P antennas is W a = I M , where, I M represents an identity matrix of dimension M×M; the phase adjustment matrix for the M - 2P antennas is H p = diag(1, e -jπsinθ ,..., e -j(M-1)πsinθ ), where, θ represents a preset angle in the phase shift observation space to compensate for the 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; perform digital sampling on the combined analog signal to obtain a digital sampling signal z1(k), which is expressed as: k represents the sample time index, each k value corresponds to a specific sampling moment, q represents the candidate phase shift index, Q represents the dimension of the phase shift observation space, and each q value corresponds to a specific candidate phase shift; (.) H represents conjugate transpose; h q represents the phase shift amount of the qth phase shift observation space, P represents the length of the unknown mutual coupling coefficient, M represents the total number of antennas in the antenna array, θ q is the preset angle of the qth observation space; Denote the M - 2P elements in the middle of x(k), where x(k) represents the expression of the original signal received by M - 2P antennas in the discrete - time domain after analog processing; then calculate the average power of the digital sampling signal z1(k). Among them, Denote the covariance matrix of the middle M - 2P antennas, and K represents the number of samples relative to the candidate phase shifts.

[0045] S2.3. By means of the operation and the definition of r = vec(R x ), where vec(.) represents the vectorization operation symbol, Denote the kronecker product operation symbol, and E, F, G represent any multiplicable matrices. Denote the covariance matrix of the middle M - 2P antennas, from which the average power can be obtained, and adjust the phase shifts in the phase - adjustment matrix to obtain the average powers under a series of different phase shifts: And from the average powers P q under the series of different phase shifts, construct an over - determined system of equations: P = [P1,..., P Q T = Br; where B is Among them, r represents the vectorized covariance matrix.

[0046] S2.4. According to the over - determined system of equations obtained in step S2.3, use the diagonal loading technique to solve for the estimated vector and construct the spatial covariance matrix corresponding to the middle M - 2P antennas to obtain Among them, unvec(.) represents the inverse quantization process; use the real - valued subspace technique to process the spatial covariance matrix to obtain the initial DOA estimate value.

[0047] Among them, the specific process of using the diagonal loading technique to solve the vector is as follows: The diagonal loading technique is an improved solution method, and its core idea is to add a positive constant λ times the identity matrix I to the diagonal of B H B, so as to improve the condition number of the matrix and enhance the stability of the solution. Specifically, the objective function after diagonal loading becomes Take the derivative of it with respect to and set the derivative to zero, and the equation satisfied by the optimal solution can be obtained Solving this equation can obtain the estimated vector Among them, λ is the diagonal loading coefficient, which is a preset positive number. ​This term plays a role in regularization, which restricts the norm of the estimated vector 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. Convert the spatial covariance matrix into a real-valued matrix, and define the Hermitian supersymmetric matrix as where represents the reverse matrix, (.) * represents conjugation, refers to the covariance matrix obtained by receiving signals using some antennas; then define the unitary transformation matrix The unitary transformation matrix has different definitions according to the parity of When is even, When is odd,

[0050]

[0051] S2.42. Use the unitary transformation matrix to transform the Hermitian supersymmetric matrix to construct a real-valued spatial covariance matrix Perform eigenvalue decomposition on to obtain the noise subspace matrix E n , and obtain the initial DOA estimate value by searching for the L peaks of the function where l = 1,..., L, and is the steering vector matrix.

[0052] Preferably, the specific process of step 3 includes the following steps:

[0053] S3.1. Reset S w = W a = H P = I M , and obtain the output signals from the second RF chain to the nth RF chain as: where corresponds to the mutual coupling effect between the first N - 1 antennas and has a symmetric Toeplitz structure similar to the overall mutual coupling matrix C; represents a matrix transformation, c = [1, c1, c2,..., c p T represents the vector of mutual coupling parameters;​

[0054] S3.2. Use the initial DOA estimation value obtained in Step 2 to construct another overdetermined equation system Ξ T c = 0 L(N-1-L)×1 , where represents the noise subspace matrix, solve this overdetermined equation system to obtain the mutual coupling coefficient estimation value and reconstruct the mutual coupling matrix therefrom

[0055] S3.3. Reconfigure S w = I M , calculate the average power of the digital sampling signal z1(k) again, and use the diagonal loading technique to reconstruct the spatial covariance matrix corresponding to the middle M - 2P antennas again Finally, use the real-valued subspace technique to process the said spatial covariance matrix and obtain the enhanced DOA estimation value by searching for the L peaks of the function .

[0056] The effectiveness of a DOA estimation method based on eliminating the influence of mutual coupling under a hybrid analog-digital structure according to the present invention is demonstrated by the following experiments

[0057] Experiment settings: The length of the unknown MC coefficient is set to P = 2, C1 = 0.4045 + 0.2939j, C2 = 0.2898 - 0.0776j. The number of phase shifts of the first-stage algorithm and the second-stage algorithm are Q = 181 and Q = 30 respectively

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

[0059] Figure 6 、 Figure 7 and Figure 8The number of antennas M = 10, and the number of RF chains N = 5. The number of signal sources is 2, with angles θ = -32.7° and θ = -27.7° respectively. The number of sampling samples K = 1000, and the signal-to-noise ratio is set to 5 dB.

[0060] In Figures 3 to 8 the full-digital multiple signal classification algorithm 1 is: a full-digital multiple signal classification algorithm using M sensors with known mutual coupling, where M > N;

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

[0062] The algorithm without processing mutual coupling is: a multiple signal classification algorithm based on covariance matrix reconstruction with unknown mutual coupling;

[0063] The Cramer-Rao bound is: the lower limit 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 the hybrid analog-digital structure proposed by the present invention can obtain relatively accurate DOA estimation values. In 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 a high signal-to-noise ratio environment, can accurately estimate the arrival angle of the signal, and verifies the effectiveness of the algorithm.

[0065] In addition, from Figure 3 , Figure 4 and Figure 5 the curves in it can be clearly seen that the root mean square error under the second-stage algorithm is smaller than that under the first-stage algorithm. Thus, the effectiveness of the two-stage estimation strategy is verified. Compared with the case without compensation, the RMSE after mutual coupling compensation is significantly reduced, especially at low signal-to-noise ratios, indicating that the mutual coupling compensation algorithm proposed in this paper can effectively improve the estimation accuracy. As the signal-to-noise ratio increases, the accuracy of mutual coupling coefficient estimation becomes the main factor affecting the DOA estimation performance.

[0066] Figure 6 , Figure 7 and Figure 8 Analyzing the simulation results from the perspective of performance, it can be seen from the figure that as the signal-to-noise ratio and the number of samples increase, the performance under each algorithm is improved. The proposed second-stage algorithm exhibits super-resolution ability, 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 full-digital multiple signal classification algorithm 2, it cannot resolve the two sources in the entire observation area.

Claims

1. A DOA estimation method based on a hybrid modulus structure to eliminate mutual coupling effects, characterized by: The method comprises the following steps: Step 1, establish a signal model: Assume that L far-field narrowband signals are incident on the antenna array from different angles. The antenna array adopts a hybrid analog-digital structure, and the hybrid analog-digital structure includes M antennas and N radio frequency chains, where 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 connected to each antenna in turn starting from the first antenna. Step 2: Get the initial DOA estimate. The process is: Set the switch matrix S in the hybrid analog-digital structure. w , amplitude adjustment matrix W a and the phase adjustment matrix H p , and select M-2P antennas in the middle of the antenna array by setting the switch matrix to 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 subjected to analog-to-digital conversion processing on the first RF chain to output a signal z1(k), an overdetermined set of equations is constructed based on the signal z1(k), a spatial covariance matrix is ​​constructed using a diagonal loading technique, and the spatial covariance matrix is ​​processed using a real-valued subspace technique to obtain an initial DOA estimate; Step 3: Obtain enhanced DOA estimation value; the process is: set S w =W a =H P =I M , where I M Representing a unit matrix, and obtaining an output signal z(k) from the second RF chain to the nth RF chain, wherein n=1, 2, 3, ..., N; estimating a mutual coupling coefficient according to the output signal z(k) using the initial DOA estimation value obtained in step 2, and reconstructing the spatial covariance matrix according to the mutual coupling coefficient to obtain a reconstructed spatial covariance matrix, and processing the reconstructed spatial covariance matrix using a real-valued subspace technique to obtain an enhanced DOA estimation value.

2. The DOA estimation method based on eliminating mutual coupling effect under a hybrid analog-digital structure according to claim 1 is characterized in that: In Step 1, the output signal of the hybrid analog-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)); 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 Represents the switch matrix, which is 1 when the switch corresponding to the antenna is closed, otherwise it is 0; W a represents the amplitude adjustment matrix, H p represents the phase adjustment matrix, W a =diag(ρ1, ..., ρ M ), ρ M and denote the amplifier gain and phase shift at time t, respectively, j is an imaginary unit; s(t) = [s1(t), ..., s L (t)] T , s(t) represents the set of L far-field narrowband signals incident from different angles at time t, 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 θ l represents the DOA estimate to be calculated. C represents an M×M matrix with a symmetric Toeplitz structure, i.e., the mutual coupling matrix, C=Toeplitz{[c0,c1,...c p ,0 1×(M-P-1) ]}; where c i represents the mutual coupling coefficient between the two antennas, and P represents the length of the unknown mutual coupling coefficient.

3. The DOA estimation method based on eliminating mutual coupling influence under a hybrid analog-digital structure according to claim 2 is characterized in that: The specific process of Step 2 includes the following steps: S2.

1. Setting S w is a block diagonal matrix S w =blkdiag(0 P×P ,I M-2P ,0 P×P ), where I M-2P Represents the unit matrix of dimension M-2P×M-2P; select the middle M-2P antennas, and the amplitude adjustment matrix of the M-2P antennas is W a =I M , where I M represents the unit matrix with dimension M×M; the phase adjustment matrix of M-2P antennas is H p =diag(1,e -jπsinθ ,...,e -j(M-1)πsinθ ), where θ represents a preset angle in the phase shift observation space to compensate for the phase distortion caused by mutual coupling at different angles; S2.2, the output signals of the M-2P antennas are combined on the first RF chain to obtain a combined analog signal; the combined analog signal is digitally sampled to obtain a digital sampling signal z1(k), which is expressed as: k represents the sample time index, each k value corresponds to a specific sampling time, q represents the candidate phase shift index, Q represents the dimension of the phase shift observation space, and each q value corresponds to a specific candidate phase shift; (.) H Expressed as conjugate transpose; h q represents the phase shift of the qth phase shift observation space, P represents the length of the unknown mutual coupling coefficient, M represents the total number of antennas in the antenna array, θ q is the preset angle of the qth observation space; represents the M-2P elements in the middle of x(k), where x(k) represents the original signal received by M-2P antennas after analog processing in the discrete time domain; then calculate the average power of the digital sampling signal z1(k) in, represents the covariance matrix of the middle M-2P root antennas, K represents the number of samples relative to the candidate phase shift; S2.3, with the help of calculation and The definition of , where vec(.) represents the vectorized operation symbol, represents the Kronecker product operator, E, F, and G represent any multiplyable matrices. represents the covariance matrix of the middle M-2P antennas, from which the average power can be obtained And adjust the phase shift in the phase adjustment matrix Adjust to get the average power at a series of different phase shifts: And the average power P under a series of different phase shifts is q Construct an overdetermined system of equations: P = [P1, ..., P Q ] T =Br; where B is Where r represents the vectorized covariance matrix; S2.4, according to the overdetermined equations obtained in step S2.3, the estimated vector is solved by using the diagonal loading technique And construct the spatial covariance matrix corresponding to the middle M-2P root antenna get Wherein, unvec(.) represents the inverse quantization process; the initial DOA estimation value is obtained after processing the spatial covariance matrix using the real-valued subspace technology.

4. The DOA estimation method based on eliminating mutual coupling influence under a hybrid analog-digital structure according to claim 3 is characterized in that: In Step S2.4, the specific process of processing the spatial covariance matrix using the real-valued subspace technique is: S2.41, the spatial covariance matrix Convert to a real-valued matrix and define the Hermitian supersymmetric matrix as in, represents the inverse matrix, (.) * represents conjugation, Represents the covariance matrix obtained by receiving signals using some antennas; then define the unitary transformation matrix The unitary transformation matrix is ​​based on There are different definitions of parity. When is an even number, when When is an odd number, S2.42, through the unitary transformation matrix For Hermitian supersymmetric matrices Transform to construct the real-valued space covariance matrix right Perform eigenvalue decomposition to obtain the noise subspace matrix E n , by searching for the function The L peaks of the initial DOA estimate are obtained Where l = 1, ..., L, represents the steering vector matrix.

5. The DOA estimation method based on eliminating mutual coupling effect under a hybrid analog-digital structure according to claim 4 is characterized in that: The specific process of Step 3 includes the following steps: S3.

1. Reset S w =W a =H P =I M , the output signal from the second RF chain to the nth RF chain is obtained as: in, Corresponding to the mutual coupling effect between the first N-1 antennas, it has a symmetrical Toeplitz structure similar to the overall mutual coupling matrix C; Represents a matrix transformation, c=[1,c1,c2,...,c p ] T A vector representing the mutual coupling parameters; 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, Represents the noise subspace matrix, and solving the overdetermined equations yields the estimated value of the mutual coupling coefficient And thus reconstruct the mutual coupling matrix S3.

3. Reconfigure S w =I M The average power of the digital sampling signal z1(k) is calculated again, and the spatial covariance matrix corresponding to the middle M-2P antennas is reconstructed using the diagonal loading technique again. Finally, the real-valued subspace technique is used to reconstruct the spatial covariance matrix Processing and searching through the function The L peaks of the image are obtained to obtain the enhanced DOA estimate.

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