A switching antenna array DOA estimation method based on orthogonal matching pursuit joint tracking

Abstract

The present application belongs to the field of array signal processing, and relates to a switched antenna array DOA estimation method based on orthogonal matching pursuit joint tracking. In view of the problem of algorithm performance distribution imbalance in traditional switched antenna array DOA estimation, a switched antenna array DOA estimation method based on orthogonal matching pursuit joint tracking is provided. The present application takes a sparse reconstruction algorithm as a starting point, converts the DOA estimation problem into a sparse representation problem of a dynamic dictionary by constructing a spatially over-complete dictionary, utilizes the characteristic that the sparse solutions of various observation values correspond to the same support set, and jointly solves all sampling data by using an orthogonal matching pursuit joint tracking algorithm, so that the structural characteristics of the switched antenna array are fully utilized, the DOA estimation precision is improved, and high-precision and low-complexity switched antenna array DOA estimation is realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of array signal processing, and relates to a switched antenna array DOA estimation method based on orthogonal matching pursuit. BACKGROUND

[0002] In the field of spatial spectrum sensing, switched antenna arrays using exchange network multiplexing radio frequency chains are widely used due to their low cost and high flexibility. In the process of receiving and restoring array signals, the direction of arrival (DOA) of signals is a crucial measurement parameter, and its accurate measurement directly affects the positioning accuracy and signal reconstruction quality of the system, and further determines the effectiveness and performance level of the overall system.

[0003] Currently, the DOA estimation methods for switched antenna array structures mainly include maximum likelihood estimation-based methods and matrix completion-based methods. The maximum likelihood estimation algorithm models the array as a time-varying array with structural parameters, combines machine learning to search for the angle of signal arrival, and can provide high-precision estimation results. However, the computational complexity of this algorithm increases significantly with the increase of array size, and it is not efficient in the context of large-scale antenna arrays. On the other hand, the matrix completion algorithm regards the signal data received by the switched antenna array as an incomplete matrix, and then fills and completes the signal matrix through a low-rank matrix recovery algorithm and estimates the DOA. This algorithm reduces the computational complexity but does not fully utilize the structural characteristics of the switched antenna array, resulting in a loss of estimation performance and the need for improved direction finding accuracy. In order to overcome the performance limitations of traditional technologies and balance the accuracy and efficiency of DOA estimation methods, it is necessary to further study the signal arrival angle measurement method for switched antenna arrays. SUMMARY

[0004] The purpose of the present application is to address the problem of algorithm performance imbalance in traditional switched antenna array DOA estimation, and to provide a switched antenna array DOA estimation method based on orthogonal matching pursuit. This method uses a sparse reconstruction algorithm to convert the DOA estimation problem into a sparse representation problem of a dynamic dictionary, and establishes an orthogonal matching pursuit algorithm to find the corresponding support set, thereby completing the DOA estimation of the switched antenna array.

[0005] The technical solution adopted by the present application is as follows:

[0006] A switched antenna array DOA estimation method based on orthogonal matching pursuit, K signals are incident on the switched antenna array from unknown angles, and at any time, the exchange network randomly selects N array element data from M antenna elements for output (M>N). The algorithm proposed in this paper includes the following steps:

[0007] S1, obtain the receiving data y[l] = Φ[l]A(θ)s[l] + e[l] at the first snapshot, wherein Φ[l] is a switching matrix, only the corresponding position of the received element of the radio frequency link is 1, the rest is 0, the signal array manifold A(θ) is to be estimated, s[l] and e[l] are signals and noises respectively.

[0008] S2, uniformly divide the spatial angle [-π / 2, π / 2] according to to form a DOA grid with Q grid points Construct a spatially over-complete dictionary Where the steering vector of the sparse signal Spatial phase Sine function sin(·), element spacing d, λ is the wavelength of the signal.

[0009] S3, construct the sparse representation form of the array signal receiving data y[l] Sparse signal vector, at the index corresponding to the K signal incident angle The remaining Q-K values are 0.

[0010] S4, convert the DOA estimation problem into the following sparse solution problem of the dynamic dictionary:

[0011]

[0012]

[0013]

[0014] Where, ||·|| represents the number of non-zero rows of the matrix, the sparse signal matrix row,0

[0015] S5, solve S4 by establishing the combined synchronous orthogonal matching algorithm: input the number of signals K, the received signal matrix Y = [y[1], y[2], …, y[L]], the spatially over-complete dictionary D, and the switching matrix Φ[l]. At the same time, initialize the residual R0 = Y, and let the support set be empty, that is Let the iteration step number t = 1.

[0016] Calculate the corresponding index of the tth observation signal and update the support set: calculate the dynamic dictionary of the lth snapshot Where d q Indicates the qth column of the over-complete dictionary D, according to the residual R[l] at the lth snapshot, calculate the index of the tth observation signal Update the support set

[0017] ​Solving the sparse signal solution using least square method denotes the matrix pseudo-inverse, denotes the first Λ t column constitutes a set, update the residual And let the iteration number t=t+1.

[0018] When the iteration number is less than or equal to the signal number, that is, t<=K, the arrival angle estimation value of the total K signals is repeatedly calculated; when the iteration number t=K+1, the iteration is stopped, and the DOA estimation result is output according to the DOA grid point corresponding to the support set index

[0019] The beneficial effects of the present application are that: the present application takes the sparse reconstruction algorithm as the starting point, converts the DOA estimation problem into the sparse representation problem of the dynamic dictionary by constructing the spatially over-complete dictionary, utilizes the characteristics that the sparse solutions of each observation value correspond to the same support set, and jointly solves all sampling data through the orthogonal matching pursuit algorithm, fully utilizes the structural characteristics of the switched antenna array, improves the DOA estimation precision, and realizes the high-precision, low-complexity switched antenna array DOA estimation. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 It is a switched antenna array DOA estimation method flow chart based on the orthogonal matching pursuit algorithm.

[0021] Figure 2 It is a system structure schematic diagram of the switched antenna array.

[0022] Figure 3 It is the DOA estimation precision change of the matrix completion method and the method of the present application under different signal-to-noise ratios.

[0023] Figure 4 It is the DOA estimation precision change of the matrix completion method and the method of the present application under different output channel numbers.

[0024] Figure 5 It is the DOA estimation precision change of the matrix completion method and the method of the present application under different snapshot numbers. DETAILED DESCRIPTION

[0025] The present application provides a switched antenna array DOA estimation method based on the orthogonal matching pursuit, aiming at the random switched antenna array, and the algorithm flow chart is referred to Figure 1 . The technical scheme of the present application will be further described below in combination with the drawings and simulation, and the performance of the algorithm in the DOA estimation aspect is verified.

[0026] In an optional embodiment: a certain random switched antenna array such as Figure 2As shown, a total of M=80 array elements are uniformly arranged with an element spacing of d=λ / 2, and N=40 array elements are randomly selected for data output at each moment, five uncorrelated signals are incident at azimuth angles of -40°, -20°, 10°, 40° and 50° respectively, and the number of snapshots L=30.

[0027] The DOA estimation algorithm of the application has the following calculation process:

[0028] (1) At an arbitrary moment, the system randomly selects 40 array elements for data output among the 80 array elements, and the signal data y[l] received by the system at the lth sampling snapshot is y[l]=Φ[l]A(θ)s[l]+e[l], and the signal matrix Y received by the system under the total number of 30 snapshots is Y=[y[1], y[2], …, y

[30] ].

[0029] (2) The spatial angle is discretely divided according to a grid of 0.01° to form a DOA network with Q=1801 grid points. Construction of a spatially over-complete dictionary

[0030] (3) The sparse expression form of the signal receiving data at the lth snapshot is obtained:

[0031] (4) The DOA estimation problem is converted into a sparse solution problem of a dynamic dictionary:

[0032]

[0033]

[0034]

[0035] (5) The problem in (4) is solved by combining the synchronous orthogonal matching algorithm. According to the array receiving data, the input signal number K=5, the receiving signal matrix Y, the spatially over-complete dictionary D and the switching matrix Φ[l]. At the same time, the residual R0=Y is initialized, and the support set is an empty set, i.e. Let the iteration step number t=1.

[0036] (6) The dynamic dictionary of the lth snapshot is calculated and combined with the residual R[l] of the lth snapshot to calculate the index of the tth observation signal under all snapshots Update the support set

[0037] (7) The sparse signal solution is solved by using the least square method Update the residual and let the iteration number t=t+1.

[0038] (8) when t≤5, repeat steps (6) and (7) to calculate the arrival angle estimation values of all 5 signals; when the iteration number t=6, stop iteration, and output the DOA estimation result according to the DOA grid point corresponding to the support set index

[0039] In order to compare the DOA estimation accuracy of the method and the matrix completion method proposed in the application, the DOA estimation accuracy of the same signal under the condition of different signal-to-noise ratios, the number of radio frequency chains and the number of sampling shots is made, and the DOA estimation accuracy comparison chart of the two algorithms is as shown in Figures 3-5

[0040] The simulation results show that with the improvement of the simulation conditions, the DOA estimation accuracy of the matrix completion method and the method proposed in the application is improved, and under the same simulation conditions, the method proposed in the application has better performance in angle estimation accuracy, which clearly verifies the excellent performance of the method in the application in the DOA estimation performance.​

Claims

1. A method for estimating the DOA of a switched antenna array based on orthogonal matching joint tracking, defining K signals incident on the switched antenna array from unknown angles, and at any given time, the switching network randomly selects N array data elements from M antenna elements for output, characterized in that... The DOA estimation method includes: S1. The received data at the l-th snapshot is y[l]=Φ[l]A(θ)s[l]+e[l], where Φ[l] is the switching matrix, which is 1 only at the corresponding position of the array element received by the radio frequency link, and 0 at the rest. The signal array manifold A(θ) needs to be estimated, and s[l] and e[l] are the signal and noise, respectively. S2, arranging the spatial angle [-π / 2, π / 2] according to... The intervals are uniformly divided to form a DOA grid with Q grid points. Constructing an overcomplete dictionary for the spatial domain The steering vector of the sparse signal Spatial phase sin(·) is the sine function, d is the spacing between array elements, and λ is the wavelength of the signal; S3. Construct a sparse representation of the array signal received data y[l]. Given a sparse signal vector, at the indices corresponding to the K signal incident angles, we have: The remaining QK values ​​are 0; S4. Transform the DOA estimation problem into a sparse solution problem for the following dynamic dictionary: In the formula, ||·|| row,0 The number of non-zero rows in a matrix, sparse signal matrix. S5. Establish a joint synchronous orthogonal matching algorithm to solve the problem in S4: the number of input signals K, the received signal matrix Y = [y[1], y[2], ..., y[L]], the spatial overcomplete dictionary D, and the switching matrix Φ[l]; at the same time, initialize the residual R0 = Y, and set the support set to an empty set, i.e. Let the iteration step number t = 1; Calculate the corresponding index of the t-th observed signal and update the support set; calculate the dynamic dictionary of the l-th snapshot. Where d q Let q be the index of the t-th observed signal calculated from the residual R[l] at l snapshots in the overcomplete dictionary D. Update support set The sparse signal solution is obtained using the least squares method. Indicates the pseudo-inverse of a matrix. Denotes the Λth of D t The set of columns is used to update the residuals. Let the iteration number t = t + 1; The iteration stops when the number of iterations is t = K+1, and the DOA estimation result is output based on the DOA grid points corresponding to the support set index.

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