Time modulation array DOA estimation method based on GPH matrix

Abstract

The invention relates to the field of array signal processing, in particular to a method for estimating DOA in a time modulation array based on a GPH matrix scheme. In order to reduce energy dispersion of antenna radiation and expand a direction finding range, the invention provides a DOA estimation method of a time adjustment array based on a GPH scheme. Based on the GPH matrix, the complete complementary set is obtained through recursive derivation of the Hardman matrix, the mutually paired sequences with the same number of conducted radio frequency switches are selected from the complete complementary set, the time modulation array is obtained through design, the direction finding range is expanded, the DOA estimation performance is improved, and high-precision and low-complexity switching antenna array DOA estimation is achieved.

Description

Technical Field

[0001] The present invention relates to the field of array signal processing, and particularly to a method for estimating DOA in a time-modulated array based on a GPH matrix. Background Art

[0002] In the field of spatial spectrum sensing, switched antenna arrays are widely used due to their many advantages such as low cost and high flexibility. This technology reduces the computational complexity and hardware cost by randomly selecting the array element outputs. In a conventional antenna array, three parameters, namely the spatial position, excitation amplitude, and excitation phase of the antenna element, are usually variable, and these parameters are determined to meet the radiation characteristic requirements of the antenna array, so that the array radiation pattern is the same as expected. However, in the feeding network of a time-modulated array, there are high-speed RF switches, and time modulation is achieved by periodically turning on and off the RF switches, so that there is a design freedom in the "time" dimension for the array.

[0003] Currently, the time modulation schemes in time-modulated arrays can be mainly classified into four types: Variable Aperture Sizes (VAS), Unidiretional Phase Center Motion (UPCM), Bidiretional Phase Center Motion (BPCM), and Pulse Shifting (PS). The time-modulated array can achieve the switching between patterns by using different time modulation methods, which greatly simplifies the design of the feeding network and has greater design flexibility in the combined pattern compared with the conventional antenna array. However, in the antenna radiation pattern, it is observed that there are large beam depressions at angles of ±30° and ±90° for both UPCM and BPCM schemes. The estimation performances of VAS and PS schemes are relatively stable, but there are estimation errors in the case of fewer sidebands. Therefore, a more efficient and accurate time modulation method needs to be designed during the DOA estimation process.

[0004] In order to overcome the performance limitations of traditional technologies and balance the accuracy and efficiency of the DOA estimation method, a DOA estimation method for a time-modulated array based on a Golay paired Hadmard (GPH) matrix scheme can make full use of the frequency components under different sidebands, improve the measurement accuracy while reducing the influence of the number of sidebands and beam depressions. Summary of the Invention

[0005] The object of the present invention is to provide a method for estimating the direction of arrival (DOA) in a time-modulated array based on the GPH matrix scheme, aiming at the problems of low estimation accuracy and limited direction-finding range in traditional time-modulation methods. This method utilizes the complementarity and orthogonality of the GPH matrix for the working timing sequence of radio frequency switches, optimizes the antenna radiation pattern, and combines with the Multiple Signal Classification (MUSIC) algorithm to complete the DOA estimation of the time-modulated array.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A method for estimating the DOA in a time-modulated array based on the GPH matrix scheme can reduce the energy dispersion of antenna radiation and expand the direction-finding range based on the complementarity and orthogonality in the GPH matrix. The time-modulated array function design method includes:

[0008] S1. Configure the antenna array. Specifically, design a high-speed radio frequency switch sequence based on the GPH matrix. Consider a linear array of isotropic array elements with equal spacing. Each array element is controlled by a high-speed radio frequency switch. The array is numbered from 1 to N from left to right. First, the element selected at the leftmost side is turned on for one time step according to the first sequence corresponding to the selected GPH matrix where T p is the time modulation period. Then, the element corresponding to the second sequence is turned on in the next time step, and so on. According to the GPH matrix scheme, the time modulation function is U k (t):

[0009]

[0010] where the time series matrix of the time-modulated array designed based on the GPH matrix O(k,j) represents the k-th row and j-th column of the array.

[0011] S2. After the signal passes through the antenna configured as in S1, the output signal of the time-modulated array is x(t):

[0012]

[0013] where L is the number of signals, N is the number of array elements, f0 is the signal center frequency, θ l represents the azimuth angle of the l-th signal, s l (t) is the l-th far-field signal with the incident angle of θ l , d is the array element spacing, c is the speed of light in free space, n k (t) represents zero-mean Gaussian white noise with variance σ 2 , and U k(t) is the time modulation function corresponding to the k-th array element.

[0014] S3. Since U k (t) is a periodic function of time, its spatial and frequency responses can be obtained by decomposing it into a Fourier series. After time modulation by the RF switch, the received signal is Fourier-expanded to obtain the m-th order sideband signal corresponding to the frequency f0 + mf p on, which is denoted as x m (t):

[0015]

[0016] where the modulation frequency represents the Fourier coefficient of the corresponding harmonic component.

[0017] S4. Then, all sideband signals are subjected to mixing and filtering operations. In order to be able to use a filter to separate different sideband signals, the signals need to be down-converted to the same intermediate frequency (IF) stage, and the resulting output signal is denoted as y m (t):

[0018]

[0019] where represents the intermediate frequency signal of s l (t), Q is a positive integer representing the maximum order of the sideband. Substituting m = -Q, -Q + 1,..., 0,..., Q - 1, Q, the matrix expression of the output signal can be obtained as:

[0020] Y(n) = B T [AS(n) + N(n)], (n = 1, 2,..., NN)

[0021] where NN is the number of available snapshots, Y(n) = [y -Q (n), y -Q+1 (n), …, y Q (n)] T , N(n) = [n1(n), n2(n), …, n N (n)] T , A = [a(θ1), a(θ2), …, a(θ L )], The time modulation matrix B can be expressed as:

[0022]

[0023] S5. Estimate the signal arrival angle of the output signal according to the MUSIC algorithm:

[0024] S5.1. The output signal covariance matrix can be obtained as follows:

[0025]

[0026] where

[0027] S5.2. Perform eigenvalue decomposition on and arrange them in descending order. The eigenvectors corresponding to the first L largest eigenvalues form the signal subspace, and the eigenvectors corresponding to the subsequent (2Q + 1) - L smallest eigenvalues form the noise subspace E N = [v L+1 , v L+2 ,..., v 2Q , v 2Q+1 , and obtain the null spectrum based on the orthogonality of the signal subspace and the noise subspace.

[0028] S5.3. Obtain the estimated value of DOA through MUSIC spatial spectrum peak search. The spatial spectrum function P(θ) is expressed as:

[0029]

[0030] The beneficial effects of the present invention are as follows: Starting from the GPH matrix, through the recursive derivation of the Hadamard matrix, a complete complementary set is obtained, and a time - modulated array is designed. By using the orthogonality and complementarity of the matrix, the problem of the small direction - finding range caused by beam dips in the radiation pattern of the traditional time - modulated array antenna is compensated. By combining the time - modulated array with the MUSIC direction - finding method, the estimation accuracy and performance of the traditional time - modulated array antenna are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a flowchart of the method for estimating DOA in a time - modulated array based on the GPH matrix scheme of the present invention.

[0032] Figure 2 is the time series of an 8 - antenna TMLA.

[0033] Figure 3 is the change in the DOA estimation accuracy of the PS and VAS time - modulation schemes and the present scheme under different signal - to - noise ratios.

[0034] Figure 4 The change in the DOA estimation accuracy of the traditional time - modulation scheme and the present scheme at different azimuth angles. DETAILED DESCRIPTION OF THE INVENTION

[0035] The present invention provides a method for estimating DOA in a time - modulated array based on the GPH matrix scheme for a time - modulated array. For the algorithm flowchart, refer toFigure 1 Next, the technical solution of the present invention will be further described in conjunction with the accompanying drawings and simulations, and the performance of this solution in DOA estimation will be verified.

[0036] In an alternative embodiment: Consider a TMLA with N = 8 isotropic elements having a half-wavelength spacing according to the GPH matrix scheme. Three uncorrelated signals are incident at azimuth angles of -10°, 5°, and 45° respectively. The signal-to-noise ratio is changed, the number of snapshots NN = 500, and the sampling frequency f s = 5 GHz, the signal center frequency f0 = 1 GHz, and the modulation frequency f p = 60 MHz. Or the signal-to-noise ratio SNR = 10 dB, other parameters remain unchanged, the signal incident azimuth angle is changed, and the sampling data of 50 modulation periods are used to calculate the FFT, and the number of Monte Carlo times is 1000. The calculation process of the DOA estimation algorithm of this solution is as follows:

[0037] (1) Design the corresponding time modulation method according to the GPH matrix to generate the time modulation function U k (t).

[0038] (2) Perform Fourier transform on the time modulation function U k (t), calculate the Fourier series corresponding to different sideband numbers and different antennas, and generate the time modulation matrix B.

[0039] (3) Obtain the system received signal y(t) and perform fast Fourier transform on the received signal to extract the frequency domain components related to the target frequency f0 and the sideband frequencies f0 ± mf p (m = 0, ±1, ±2,..., ±∞).

[0040] (4) Sample the signal with the number of snapshots NN = 100, and calculate the output signal covariance matrix

[0041] (5) Perform eigenvalue decomposition on the covariance matrix to obtain the signal subspace and the noise subspace.

[0042] (6) Construct the spatial spectrum function according to the orthogonality relationship between the noise subspace and the signal vector Use the spatial spectrum function to perform spectral peak search.

[0043] (7) Find out that the angle corresponding to the maximum value point is the DOA estimation value of the signal.

[0044] In order to compare the DOA estimation accuracy of this solution with the traditional time modulation solution, a DOA estimation accuracy comparison diagram is made under the condition changes of different signal-to-noise ratio environments and sideband orders for the DOA estimation accuracy of the same signal, as Figures 3 - 4 shown.

[0045] The simulation results show that with the improvement of simulation conditions, the DOA estimation accuracies of both the traditional time modulation scheme and this scheme are improved. Under the same simulation conditions, the method proposed in the present invention has better performance in terms of angle estimation accuracy and estimation range, verifying that the DOA estimation performance of the method of the present invention is superior to the traditional time modulation scheme.

Claims

1. A DOA estimation method for time-modulated arrays based on the GPH matrix, characterized in that, Including the following steps: S1. Configure the antenna array. Specifically, design a high-speed radio frequency switch sequence based on the GPH matrix. For a linear array of isotropic elements with equal spacing, each element is controlled by a high-speed radio frequency switch. The array is numbered from 1 to N from left to right, and the leftmost element is turned on for one time step according to the first sequence corresponding to the selected GPH matrix. Where T p is the time modulation period; then, the element corresponding to the second sequence is turned on in the next time step, and so on. According to the GPH matrix, the time modulation function is U k (t): where num_cycles is the number of modulation cycles, and O is the time series matrix of the time modulation array, obtained from the GPH matrix, expressed as O(k,j) represents the k-th row and j-th column of the array; S2. After the signal passes through the antenna array configured as in S1, the output signal of the time modulation array is x(t): where L is the number of signals, N is the number of array elements, and θ l represents the azimuth angle of the l-th signal, s l (t) is the l-th far-field signal with the incident angle of θ l , d is the element spacing, f0 is the signal center frequency, c is the speed of light in free space, n k (t) represents white Gaussian noise with zero mean and variance of σ 2 , and U k (t) corresponds to the time modulation function of the k-th array element; S3. Fourier-expand the received signal to obtain the m-th order sideband signal at the corresponding frequency f0 + mf, denoted as x p (t): m (t): Among them, the modulation frequency represents the Fourier coefficient corresponding to the harmonic component; S4. Mix and filter all the sideband signals to down-convert the signals to the same intermediate frequency stage, and the resulting output signal is denoted as y m (t): Among them, represents the intermediate frequency signal of s l (t), Q is a positive integer representing the maximum order of the sideband; substituting m = -Q, -Q + 1,..., 0,..., Q - 1, Q, the matrix expression of the output signal can be obtained as follows: Y(n) = B T [AS(n) + N(n)], (n = 1, 2,..., NN) where NN is the number of available snapshots, Y(n)=[y -Q (n),y -Q+1 (n),…,y Q (n)] T , N(n)=[n1(n),n2(n),…,n N (n)] T , A=[a(θ1),a(θ2),…,a(θ L )], The time modulation matrix B is expressed as: S5. Estimate the signal arrival angle for the output signal according to the MUSIC algorithm: Calculate the covariance matrix of the output signal It is as follows: Among them Perform eigenvalue decomposition and sort them in descending order. The eigenvectors corresponding to the first L largest eigenvalues form the signal subspace, and the eigenvectors corresponding to the subsequent (2Q + 1) - L smallest eigenvalues form the noise subspace E N = [v L+1 , v L+2 , …, v 2Q , v 2Q+1 , and obtain the zero spectrum based on the orthogonality of the signal subspace and the noise subspace; Obtain the estimated value of DOA through MUSIC spatial spectrum peak search. The spatial spectrum function P(θ) is expressed as:

Images