Coherent signal DOA estimation method based on multi-beam frequency scanning leaky-wave antenna

Abstract

The application discloses a kind of based on the coherent signal DOA estimation method of multi-beam frequency scanning leaky-wave antenna, for solving the coherent signal DOA estimation problem of multi-beam FBS-LWA receiving model.Process as follows:First, based on the signal data matrix of multi-beam FBS-LWA receiving model, according to signal data matrix calculation frequency-space spectrum, select the angle corresponding to frequency-space spectrum peak point to obtain candidate angle set, interpolation is carried out to candidate angle set to obtain the super-complete angle set of pruning, then based on signal data matrix, using singular value decomposition method obtains the signal data matrix of pruning, finally based on the super-complete angle set of pruning and the signal data matrix of pruning, using SBL algorithm obtains the coherent signal DOA estimation result.The method disclosed in the application can successfully estimate the coherent signal DOA of multi-beam FBS-LWA receiving model with higher accuracy and lower running time.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of DOA estimation and leaky-wave antenna, and particularly relates to a coherent signal DOA estimation method based on a multi-beam frequency scanning leaky-wave antenna. BACKGROUND

[0002] The beam direction of a frequency beam scanning leaky-wave antenna (FBS-LWA) changes with the working frequency, and the beam scanning can be realized without any complex feed network or active devices such as phase shifters. In a direction-of-arrival (DOA) estimation system, the multi-beam FBS-LWA is used to take advantage of its high directivity, small bandwidth and low cost, greatly simplifying the system design and reducing the hardware complexity.

[0003] In an actual wireless communication environment, especially in the case of significant multipath propagation, the signals received by the antenna are mostly coherent signals. Therefore, the research on the coherent signal DOA estimation method for the FBS-LWA is particularly crucial. Xu et al. successfully solved the coherent signal DOA estimation problem of the single-beam FBS-LWA by interpolating the steering matrix of the single-beam FBS-LWA into the Vandermonde structure, and then using the decorrelation technique and subspace algorithm, but the method has a high requirement for the initial estimation accuracy. However, when the multi-beam FBS-LWA receives the incoming signal through multiple beams, parasitic direction responses will occur, making it difficult to obtain accurate initial estimation angle values, so that the above idea is no longer applicable. On the other hand, similar to the idea of spatial smoothing, Xu et al. successfully estimated the DOA of the partially coherent signal received by the multi-beam FBS-LWA by grouping different frequencies of the received partially coherent signal to partially restore the rank of the covariance matrix, but the method has a high requirement for the signal-to-noise ratio, and the performance of the method sharply decreases under the condition of full coherence. Therefore, the coherent signal DOA estimation problem based on the multi-beam FBS-LWA remains to be solved. SUMMARY

[0004] The purpose of the present application is to solve the above-mentioned defects in the prior art, and to provide a coherent signal DOA estimation method based on a multi-beam frequency scanning leaky-wave antenna, which can estimate the DOA of the coherent signal received by the multi-beam FBS-LWA with high accuracy and low running time.

[0005] The purpose of the present application can be achieved by adopting the following technical solutions:

[0006] A coherent signal DOA estimation method based on a multi-beam frequency scanning leaky-wave antenna, the DOA estimation method comprising the following steps:

[0007] S1, obtaining a signal data matrix based on a multi-beam FBS-LWA receiving model, wherein FBS-LWA is an abbreviation of frequency beam scanning leaky wave antenna;

[0008] S2, calculating a frequency-space spectrum based on the signal data matrix, selecting a candidate angle set corresponding to a frequency-space spectrum peak point, and performing interpolation on the candidate angle set to obtain a pruned super-complete angle set;

[0009] S3, using a singular value decomposition method to obtain a pruned signal data matrix based on the signal data matrix;

[0010] S4, using an SBL algorithm to obtain a coherent signal DOA estimation result based on the pruned super-complete angle set and the pruned signal data matrix. When a multi-carrier scheme such as orthogonal frequency division multiplexing modulated coherent signals hit the multi-beam FBS-LWA, it is assumed that the signals on each subcarrier are the same, which can be approximated as a narrowband signal,

[0011] Further, the step S1 process is as follows:

[0012] It is assumed that the number of coherent sources is K, the DOA angle of the kth coherent source is θ k ,k=1,2,..,K, the minimum working frequency of the multi-beam FBS-LWA is f min , the maximum working frequency is f max , the frequency sampling number is N f , and the received signal data matrix is X=[x(1);x(2);...;x(t);...;x(T)], t=1,2,...,T, T is the total number of snapshots, X is an N f ×T matrix, the tth column x(t) of X is the signal data vector received by the tth snapshot, and the expression is as follows:

[0013] x(t)=A w s(t)+e(t) (1)

[0014] In the formula, x(t) is an N f ×1 vector, s(t) is a K×1 source signal vector, e(t) is an N f ×1 noise vector; A w =[a w (θ1),a w (θ2),...,a w (θ k ),...,a w (θ K )... is an N f ×K matrix, is the Nf A × 1-dimensional guiding vector, a wn (θ k ) is a w (θ k The nth element in the array, where n = 1, 2, ..., N f That is, the multi-beam FBS-LWA at the nth sampling frequency f n The response at the location is expressed as follows:

[0015]

[0016] In the formula, l represents the length of the multibeam FBS-LWA, j represents the imaginary sign, exp[·] represents the exponential function, and sinc[·] represents the non-normalized Singer function; m=m back ,m back +1,...,m forw Denotes the spatial harmonic order, M = m forw -m back +1 represents the total spatial harmonic number, m back and m forw Let be the harmonic orders radiated from the rear and front endpoints, respectively, as expressed below:

[0017]

[0018] In the formula, p represents the spatial period of modulation, c represents the speed of light, and ε r Represents the relative permittivity. W represents the cutoff frequency. g Denotes the waveguide width; k0(n) = 2πf n / c represents the free space wavenumber, k zm (n) represents the longitudinal wave number inside the waveguide structure corresponding to the m-th spatial harmonic order, as shown in the following expression:

[0019] k zm (n)=β m (n)-jα n k0(n) (5)

[0020] In the formula, β m (n) = β0(n) + 2πm / p is the phase constant of the higher-order mode. Let α be the phase constant of the fundamental guided mode. n This represents the attenuation constant that indicates radiation leakage and loss.

[0021] The grid-based DOA estimation algorithm selects the angles corresponding to the first K maximum peak points of the spatial spectrum spectrum value of the whole field of view as the DOA estimation value. The smaller the grid of the field of view is divided, the more candidate angles are contained, and the more accurate the estimation result is, but the higher the calculation complexity of the algorithm is. Therefore, the application clips the angle set searched by the DOA estimation algorithm to improve the estimation efficiency and reduce the running time.

[0022] As shown in formula (2), the direction of arrival of the multi-beam FBS-LWA received signal is coupled with the operating frequency. For a specific direction of arrival, the energy of the signal data matrix on some frequencies is higher than that on other frequencies. Moreover, when the multi-beam FBS-LWA receives multiple coherent waves through multiple spatial harmonics, the antenna response in formula (2) corresponding to each wave has about M peaks, therefore, the frequency-space spectrum of the signal data matrix may contain KM peaks, which contain the real DOA and spurious angle response. The application selects the angles corresponding to these peak points as the candidate angle set, which greatly reduces the number of angles to be searched.

[0023] Further, the step S2 process is as follows:

[0024] S21, calculating the frequency-space spectrum:

[0025]

[0026] In the formula, θ represents any wave angle in the field of view range Θ FoV g θ represents the division grid of Θ FoV z is the multi-beam FBS-LWA response when the given wave angle and the sampling frequency f n n is the nth row data vector of the 1×T-dimensional signal data matrix X;

[0027] S22, selecting the angles corresponding to the δKM frequency-space spectrum peak points as the candidate angle set δ is a positive integer, and the value is 1, 2, 3 or 4;

[0028] S23, using a grid θ g smaller than the specified grid θ s to interpolate Θ ini to obtain the clipped super-complete angle set Θ var , which is specifically as follows:

[0029]

[0030] and rewrite the above formula as ​​​​ P = 3δKM.

[0031] The signal received by the multi-beam FBS-LWA is a wide frequency signal, and the number of frequency sampling points is large. Singular value decomposition is performed on the signal data matrix, the dimension of the signal data matrix is reduced, and the calculation complexity of the method disclosed in the subsequent DOA estimation can be effectively reduced.

[0032] Generally, large singular values correspond to main components of the signal, and small singular values correspond to noise or interference. By retaining large singular values and discarding small singular values, the signal data matrix can be trimmed, and the influence of noise on the estimation performance of the method disclosed in the application can be suppressed to a certain extent.

[0033] Further, the step S3 is as follows: S31, singular value decomposition is performed on the signal data matrix X:

[0034] X = UDV H (8)

[0035] In the formula, U is an N f ×N f dimension left singular matrix, D is an N f ×L dimension singular value matrix, and V is an L×L dimension right singular matrix.

[0036] S32, a trimmed signal data matrix X SVD is calculated based on the right singular matrix V.

[0037] X SVD = XVB (9)

[0038] In the formula, X SVD is an N f ×K dimension matrix, B = [I1, 0] T is an L×K dimension auxiliary matrix, I1 is a K×K dimension unit matrix, and 0 is a K×(L-K) dimension zero matrix.

[0039] A common method for estimating coherent signals is to first apply a decorrelation technique, and then use a subspace-based algorithm for estimation. However, the steering matrix of the multi-beam FBS-LWA is not a Vandermonde structure, and because the multi-beam FBS-LWA receives signals, a parasitic angle response is generated, making it difficult to obtain a suitable initial estimate for interpolating the steering matrix into a Vandermonde structure. The SBL algorithm does not require the response matrix of the receiving antenna to be a Vandermonde structure, and has good performance in estimating coherent signals. Therefore, the SBL algorithm is used to estimate the DOA of the coherent signals received by the multi-beam FBS-LWA.

[0040] Further, the step S4 is as follows:

[0041] S41, Overcomplete Angle Set Θ Based on Clipping var The overcomplete steering matrix is ​​calculated.

[0042]

[0043] In the formula, For N f A ×P-dimensional matrix N is the i-th complete angle f A 1-dimensional guiding vector;

[0044] S42. Initialize the incident source in the clipped overcomplete angle set Θ var The power distribution γ on the surface is expressed as follows:

[0045]

[0046] In the formula, γ=[γ1,γ2,...,γ i ,...,γ P Let ] be a P×1 dimensional vector, with the i-th element γ i This indicates that the incident source is at a perfect angle. On power, This indicates taking the k-th element of the matrix within the parentheses "()". * The calculation is performed on the row, k * =1,2,...,K, |·| denotes the absolute value function;

[0047] S43, Initialize noise power σ 2 The expression is as follows:

[0048]

[0049] In the formula, σ 2 For 1×1 dimensional numerical values, Var[·] denotes the variance function;

[0050] S44. Calculate the variance Σ of the posterior distribution, as shown in the following expression:

[0051]

[0052] In the formula, Σ is a P×P dimensional matrix, and the i-th diagonal element represents the distribution in the complete angle. The variance of Γ = diag(γ) is a P×P dimensional diagonal matrix, where the i-th diagonal element is γ. i diag(·) represents diagonalizing a vector into a matrix. For N f ×N f A matrix of dimension I2, where I2 is N f ×Nf An identity matrix of dimension (·) -1 This represents the inverse operation;

[0053] S45. Calculate the mean of the posterior distribution. The expression is as follows:

[0054]

[0055] In the formula, It is a P×T dimensional matrix;

[0056] S46. Using the power distribution γ as a hyperparameter, calculate the updated value of γ. new The expression is as follows:

[0057]

[0058] In the formula, (γ i ) new γ is 1×1 dimension new The i-th element represents the complete angle of the incident source after the update. On power, ρ is a value on the order of 10. -2 For positive values, ||·||2 is a 2-norm operation. Let Σ be a P×T dimensional matrix. ii Let Σ be the i-th diagonal element of matrix Σ;

[0059] S47, The noise power σ 2 As a hyperparameter, σ is calculated. 2 Updated value (σ) 2 ) new The expression is as follows:

[0060]

[0061] In the formula, For N f A matrix of dimension ×L, ||·|| F For F-norm operations, c and d take values ​​on the order of 10. -4 The positive value;

[0062] S48. Update hyperparameters γ and σ 2 That is, let γ = γ new , σ 2 =(σ 2 ) new Repeat steps S46 and S47 until the convergence condition is met, as shown in the following expression:

[0063]

[0064] In the formula, τ is a value on the order of 10. -3 Or 10 -4 A positive value of Θ indicates the convergence threshold; at this point, Θ var The K maxima of the pseudospectrum obtained by searching within the range are the DOA estimation results.

[0065] The present invention has the following advantages and effects compared with the prior art:

[0066] (1) The coherent signal DOA estimation method disclosed in this invention successfully eliminates the influence of parasitic direction, and can successfully estimate the coherent signal DOA received by multi-beam FBS-LWA with high accuracy and low running time. Moreover, the method has low requirements for signal-to-noise ratio.

[0067] (2) The coherent signal DOA estimation method disclosed in this invention does not require the steering matrix to be interpolated into a Vandermonde structure. It is applicable to DOA estimation or time delay estimation of antennas or antenna arrays with other steering matrices that are not Vandermonde structures, and has a wide range of applications.

[0068] (3) The coherent signal DOA estimation method disclosed in this invention uses the SBL algorithm to estimate the DOA of coherent signals received by multi-beam FBS-LWA, taking advantage of its estimation advantages under coherent conditions without needing to combine any decoherence techniques, thus simplifying the processing. In addition, this method utilizes the frequency response characteristics of multi-beam FBS-LWA, interpolates the angles corresponding to the frequency-space spectrum peak points to obtain a clipped overcomplete angle set, and uses singular value decomposition to clip the signal data matrix, which can effectively reduce the computational complexity of the SBL algorithm and reduce the DOA estimation time of coherent signals. Attached Figure Description

[0069] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0070] Figure 1 This is a flowchart of the coherent signal DOA estimation method based on a multi-beam frequency scanning leaky wave antenna disclosed in this invention.

[0071] Figure 2 This is the frequency-space spectrum diagram in Embodiment 1 of the present invention;

[0072] Figure 3 This is the pseudospectral diagram of the SBL algorithm in Embodiment 1 of the present invention;

[0073] Figure 4 This is the RMSE diagram in Embodiment 1 of the present invention;

[0074] Figure 5is the running time diagram of the coherent signal DOA estimation method in Embodiment 1 of the present application;

[0075] Figure 6 is the frequency-space spectrum diagram in Embodiment 2 of the present application;

[0076] Figure 7 is the SBL algorithm pseudo-spectrum diagram in Embodiment 2 of the present application;

[0077] Figure 8 is the RMSE diagram in Embodiment 2 of the present application;

[0078] Figure 9 is the running time diagram of the coherent signal DOA estimation method in Embodiment 2 of the present application. DETAILED DESCRIPTION

[0079] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described below in connection with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the present application.

[0080] Embodiment 1

[0081] The present embodiment provides a coherent signal DOA estimation method based on a multi-beam frequency scanning leaky wave antenna.

[0082] The method obtains a signal data matrix based on a multi-beam FBS-LWA receiving model, calculates a frequency-space spectrum based on the signal data matrix, selects candidate angles corresponding to frequency-space spectrum peak points to obtain a candidate angle set, and performs interpolation on the candidate angle set to obtain a pruned super-complete angle set. Then, based on the signal data matrix, a pruned signal data matrix is obtained by using a singular value decomposition method. Finally, based on the pruned super-complete angle set and the pruned signal data matrix, a coherent signal DOA estimation result is obtained by using an SBL algorithm. Specifically, the method comprises the following steps:

[0083] S1, obtaining a signal data matrix based on a multi-beam FBS-LWA receiving model;

[0084] Suppose the number of coherent sources is K = 3, the DOA angles of the coherent sources are [-5.3°, 15.4°, 38.4°], the minimum working frequency of the multi-beam FBS-LWA is f min = 25.5 GHz, the maximum working frequency is f max = 27.5 GHz, and the frequency sampling number is N f= 100, the received signal data matrix is X = [x(1); x(2);...; x(t);...; x(T)], t = 1, 2,..., T, T = 100 is the total number of snapshots, X is an N f × T matrix, the t-th column x(t) of X is the signal data vector received in the t-th snapshot, and is expressed as follows:

[0085] x(t) = A w s(t) + e(t) (1)

[0086] In the formula, x(t) is an N f × 1 vector, s(t) is a K × 1 source signal vector, e(t) is an N f × 1 noise vector; A w = [a w (θ1), a w (θ2),..., a w (θ k ),..., a w (θ K )] is an N f × K steering matrix, is the N f × 1 steering vector of the k-th incoming wave to the multi-beam FBS-LWA, a wn (θ k ) is the n-th element in a w (θ k ), n = 1, 2,..., N f , that is, the response of the multi-beam FBS-LWA at the n-th sampling frequency f n , and is expressed as follows:

[0087]

[0088] In the formula, l = 20 cm represents the length of the multi-beam FBS-LWA, j represents the imaginary symbol, exp[·] represents the exponential function, and sinc[·] represents the non-normalized sinc function; m = m back ,m back +1,..., m forw represent the spatial harmonic order, M = m forw -m back +1 represents the total number of spatial harmonics, m back = -4 and m forw = 1 are the backward end-point and forward end-point radiation harmonic orders, respectively, and are expressed as follows:

[0089]

[0090] In the formula, p = 3.13 cm represents the spatial period of modulation, c represents the speed of light, and ε r =2.94 represents the relative permittivity. W represents the cutoff frequency. g =2.2mm represents the waveguide width; k0(n) = 2πf n / c represents the free space wavenumber, k zm (n) represents the longitudinal wave number inside the waveguide structure corresponding to the m-th spatial harmonic order, as shown in the following expression:

[0091] k zm (n)=β m (n)-jα n k0(n) (5)

[0092] In the formula, β m (n) = β0(n) + 2πm / p is the phase constant of the higher-order mode. Let α be the phase constant of the fundamental guided mode. n The attenuation constant representing radiation leakage and loss is taken as α in this embodiment. n / k0(n)=0.01.

[0093] S2. Calculate the frequency-space spectrum based on the signal data matrix, select the angles corresponding to the peak points of the frequency-space spectrum to obtain a candidate angle set, and interpolate the candidate angle set to obtain a cropped supercomplete angle set.

[0094] S21. Calculate the frequency-space spectrum:

[0095]

[0096] In the formula, Indicates the field of view Θ FoV =-70°:θ g θ is any incoming wave angle within 70°. g =1° represents Θ FoV The grid division, Given the angle of arrival and sampling frequency f n Multi-beam FBS-LWA response at time, z n The nth row of the signal data matrix X is a data vector.

[0097] S22. Select the corresponding angles of the frequency-space spectrum peak points of δKM. Forming a candidate angle set In this embodiment, δ = 2;

[0098] S23, Using a grid θ specified by the grid g small grid θ s =0.5° to Θini Interpolation is performed to obtain the pruned overcomplete angle set Θ var , which is shown as follows:

[0099]

[0100] and the above equation is rewritten as P = 3δKM.

[0101] S3, based on the signal data matrix, a pruned signal data matrix is obtained using a singular value decomposition method;

[0102] S31, singular value decomposition is performed on the signal data matrix X:

[0103] X = UDV H (8)

[0104] In the equation, U is an N f ×N f dimensional left singular matrix, D is an N f ×L dimensional singular value matrix, and V is an L×L dimensional right singular matrix;

[0105] S32, based on the right singular matrix V, a pruned signal data matrix X SVD is calculated:

[0106] X SVD = XVB (9)

[0107] In the equation, X SVD is an N f ×K dimensional matrix, B = [I1, 0] T is an L×K dimensional auxiliary matrix, I1 is a K×K dimensional unit matrix, and 0 is a K×(L-K) dimensional zero matrix.

[0108] S4, based on the pruned overcomplete angle set and the pruned signal data matrix, a coherent signal DOA estimation result is obtained using an SBL algorithm;

[0109] S41, based on the pruned overcomplete angle set Θ var , an overcomplete steering matrix is calculated

[0110]

[0111] In the equation, is an N f ×P dimensional matrix, is an N f ×1 dimensional steering vector of the i-th complete angle;

[0112] S42. Initialize the incident source in the clipped overcomplete angle set Θ var The power distribution γ on the surface is expressed as follows:

[0113]

[0114] In the formula, γ is a P×1 dimensional vector. This indicates taking the k-th element of the matrix within the parentheses "()". * The calculation is performed on the row, k * =1,2,...,K, |·| denotes the absolute value function;

[0115] S43, Initialize noise power σ 2 The expression is as follows:

[0116]

[0117] In the formula, σ 2 For 1×1 dimensional numerical values, Var[·] denotes the variance function;

[0118] S44. Calculate the variance Σ of the posterior distribution, as shown in the following expression:

[0119]

[0120] In the formula, Σ is a P×P dimensional matrix, Γ=diag(γ) is a P×P dimensional diagonal matrix, and diag(·) denotes the transformation of a vector into a matrix. For N f ×N f A matrix of dimension I2, where I2 is N f ×N f An identity matrix of dimension (·) -1 This represents the inverse operation;

[0121] S45. Calculate the mean of the posterior distribution. The expression is as follows:

[0122]

[0123] In the formula, It is a P×T dimensional matrix;

[0124] S46. Using the power distribution γ as a hyperparameter, calculate the updated value of γ. new The expression is as follows:

[0125]

[0126] In the formula, (γ i ) new γ is 1×1 dimension new The i-th element, ρ is a small positive value, which is 0.01 in this embodiment. ||·||2 is the 2-norm operation. Let Σ be a P×T dimensional matrix. ii Let Σ be the i-th diagonal element of matrix Σ;

[0127] S47, The noise power σ 2 As a hyperparameter, σ is calculated. 2 Updated value (σ) 2 ) new The expression is as follows:

[0128]

[0129] In the formula, For N f A matrix of dimension ×L, ||·|| F For F-norm operations, c and d are small positive values, both of which are 10 in this embodiment. -4 ;

[0130] S48. Update hyperparameters γ and σ 2 That is, let γ = γ new , σ 2 =(σ 2 ) new Repeat steps S46 and S47 until the convergence condition is met, as shown in the following expression:

[0131]

[0132] In the formula, τ represents the convergence threshold, which is taken as 10 in this embodiment. -3 At this time, in Θ var The K maxima of the pseudospectrum obtained by searching within the range are the DOA estimation results.

[0133] To evaluate the performance of this invention, 200 Monte Carlo experiments were conducted using MATLAB within a signal-to-noise ratio (SNR) range of -10:5:15 dB, following the steps described above. The frequency-space spectrum calculated at SNR = 5 dB was plotted using MATLAB as follows. Figure 2 As shown, since the grid of the frequency-space spectrum is θ g =1°, resulting in the candidate angle set Θ ini The initial estimate of the true DOA is the closest grid angle value [-5°, 15°, 39°]. It can be seen that... Figure 2The angles corresponding to the mid-frequency-space spectrum peaks also include parasitic directions such as -54° and 70°, and the peak at angle -54° is similar in height to the peak at [-5°, 15°, 39°]. In other words, when estimating the DOA of the coherent signal received by a multi-beam FBS-LWA, the estimation performance will be affected by some parasitic angles. The pseudospectral of the SBL algorithm calculated when SNR = 5dB is plotted using MATLAB as shown below. Figure 3 As shown, the SBL algorithm can eliminate the influence of parasitic directions -54° and 70°, estimating the true DOA. Furthermore, since the SBL algorithm is a grid-based algorithm, the final estimation result is the grid angle value [-5.5°, 15.5°, 38.5°] closest to the true DOA, for the candidate angle set Θ. ini The interpolation makes the estimated value obtained by the method disclosed in this invention closer to the true DOA, thus improving the estimation accuracy. The RMSE and running time of the estimation results are respectively within [timeframe missing]. Figure 4 and Figure 5 As shown in the figure, the RMSE curve decreases with increasing SNR, but remains below 10dB. This indicates that the present invention can successfully estimate the DOA of the coherent signal received by multi-beam FBS-LWA at low SNR. At medium to high SNR, the RMSE remains stable below -8dB, demonstrating the high accuracy of the method. Furthermore, compared to… Figure 4 and Figure 5 The simulation results show that the pruning of the overcomplete angle set and signal data matrix greatly reduces the running time of the SBL algorithm, making the running time of the method disclosed in this invention within an acceptable range.

[0134] Example 2

[0135] This embodiment specifically discloses a method for estimating the DOA of coherent signals based on a multi-beam frequency scanning leaky antenna. The specific implementation steps of this method are as follows:

[0136] T1, the number of coherent sources is set to K=4, the incident angle is [-45.6°, -5.3°, 15.4°, 23.9°], ε r =2.94, W g =2.2mm, l=20cm, α n / k0(n)=0.01, p s =3.13cm, ρ=10 -2 c = 10 -4 d=10 -4 Θ FoV =-70°:θ g 70°, θ g =1°, δ=2, θ s= 0.5°, snapshot number T = 100. Based on the above parameters, referring to step S1 of embodiment 1, the signal data matrix X is obtained based on the multi-beam FBS-LWA receiving model.

[0137] T2, referring to step S2 of embodiment 1, the frequency-space spectrum is calculated based on the signal data matrix X. The candidate angle set Θ is obtained by selecting the angle corresponding to the peak point of the frequency-space spectrum. ini The pruned super-complete angle set Θ is obtained by interpolating the candidate angle set. var .

[0138] T3, referring to step S3 of embodiment 1, the pruned signal data matrix X is obtained based on the signal data matrix X using the singular value decomposition method. SVD .

[0139] T4, referring to step S4 of embodiment 1, the coherent signal DOA estimation result is obtained based on the pruned super-complete angle set Θ var and the pruned signal data matrix X SVD using the SBL algorithm.

[0140] Based on the above parameters and steps, 200 times of Monte Carlo experiments are performed in the signal-to-noise ratio SNR = -10:5:15 dB range based on MATLAB. The frequency-space spectrum calculated when SNR = 5 dB is drawn based on MATLAB as shown in Figure 6 , it can be seen that the peak point of the frequency-space spectrum contains the closest grid value [-46, -5°, 16°, 24°] to the true DOA and the remaining spurious directions, and the peak values of these spurious directions are close to the peak value of the true DOA. The SBL algorithm pseudospectrum calculated when SNR = 5 dB is drawn based on MATLAB as shown in Figure 7 , it can be seen that the SBL algorithm can exclude the influence of the spurious directions, and the final estimation result is the value [-45.5°, -5.5°, 15.5°, 24°] closest to the true DOA in the candidate set Θ var . The RMSE and running time of the estimation result are given in Figure 8 and Figure 9 , it can be seen that when SNR = -10 dB, the pruning of the signal data matrix affects the estimation accuracy of the disclosed method, but the RMSE of the disclosed method is still lower than 10 dB, which shows that the estimation result is still close to the true DOA value. The RMSE curve of the method tends to be stable as the SNR increases, and the running time decreases as the SNR increases, and is much lower than the running time when the signal data matrix and the super-complete angle set are not pruned ('SBL').

[0141] In conclusion, the DOA estimation method disclosed by the application successfully estimates the DOA of the coherent signals received by the multi-beam FBS-LWA with high accuracy and low running time.

[0142] The above embodiments are preferred embodiments of the application, but the embodiments of the application are not limited to the above embodiments, and any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the application shall be equivalent replacement modes and shall be included in the protection scope of the application.

Claims

1. A method for coherent signal DOA estimation based on multi-beam frequency scanning leaky-wave antenna, characterized in that, The DOA estimation method comprises the following steps: S1, obtaining a signal data matrix based on a multi-beam FBS-LWA receiving model, wherein FBS-LWA is a short name of a frequency beam scanning leaky wave antenna; S2, calculating a frequency-space spectrum based on the signal data matrix, selecting a candidate angle set corresponding to a frequency-space spectrum peak point, and performing interpolation on the candidate angle set to obtain a pruned super-complete angle set; the process is as follows: S21, calculating the frequency-space spectrum: wherein represents a field of view range Θ FoV represents any incoming wave angle, θ g represents a partition grid of Θ FoV is a multi-beam FBS-LWA response for a given incoming wave angle and sampling frequency f n n is a dimensional signal data matrix is an nth row data vector of​​ S22, selecting corresponding angles of δKM frequency-space spectrum peak points composing a candidate angle set δ is a positive integer, and takes values 1, 2, 3 or 4; S23, use the specified grid θ g Small grid θ s For Θ ini Interpolation to get the cropped super-complete angle set Θ var , as follows: and rewrite the above equation as i = 1, 2, 3,..., P, P = 3δKM; S3, obtaining a pruned signal data matrix by using a singular value decomposition method based on the signal data matrix; S4, obtaining a coherent signal DOA estimation result by using an SBL algorithm based on the pruned super-complete angle set and the pruned signal data matrix.

2. The method of claim 1, wherein, The step S1 process is as follows: Assume that the number of coherent sources is K, and the DOA angle of the kth coherent source is θ k , k = 1, 2,..., K, the minimum working frequency of the multi-beam FBS-LWA is f min , the maximum working frequency is f max , the frequency sampling number is N f , and the received signal data matrix is , the total number of snapshots is , is a matrix of dimensions, , and the tth column of x(t) is the signal data vector received in the tth snapshot, expressed as follows: x(t) = A w s(t) + e(t) (1) In the formula, x(t) is N f A K×1 dimensional vector, s(t) is the source signal vector, and e(t) is the N×1 dimensional vector. f A ×1 dimensional noise vector; w =[a w (θ1),a w (θ2),...,a w (θ k ),...,a w (θ K )] is N f ×K-dimensional guiding matrix, It is the kth incoming wave incident on the multi-beam FBS-LWA. f A × 1-dimensional guiding vector, a wn (θ k ) is a w (θ k The nth element in the array, where n = 1, 2, ..., N f That is, the multi-beam FBS-LWA at the nth sampling frequency f n The response at the location is expressed as follows: where l denotes the length of the multi-beam FBS-LWA, j denotes the imaginary unit, exp[·] denotes the exponential function, sinc[·] denotes the non-normalized sinc function; m = m back ,m back +1,...,m forw denotes the spatial harmonic order, M = m forw -m back +1 denotes the total spatial harmonic number, m back and m forw are the harmonic orders of the backward and forward end-point radiation, respectively, and are expressed as follows: where p represents a spatial period of modulation, c represents the speed of light, ε r represents a relative dielectric constant, represents a cutoff frequency, W g represents a waveguide width; k0(n) = 2πf n / c is a free space wave number, k zm (n) is a longitudinal wave number inside the waveguide structure corresponding to the mth spatial harmonic order, expressed as follows: k zm (n) = β m (n) - jα n k0(n) (5) where β m (n) = β0(n) + 2πm / p is the phase constant of the high order mode, is the phase constant of the fundamental guided mode, and α n represents the attenuation constant of the radiation leakage and loss.

3. The method of claim 2, wherein, The step S3 is performed as follows, S31, singular value decomposition is performed on the signal data matrix S32, the singular values are sorted in descending order where U is N f x N f where U is N f x L and V is L x L S32, obtain a pruned signal data matrix based on the right singular matrix V wherein is N f is a K-dimensional matrix, B = [I1, 0] T is a L x K-dimensional auxiliary matrix, I1is a K x K-dimensional identity matrix, and 0 is a K x (L - K)-dimensional zero matrix.

4. The method of claim 3, wherein, The step S4 process is as follows: S41, the super-complete angle set Θ based on pruning var The super-complete steering matrix is calculated wherein is N f a matrix of dimension N is the N f a steering vector of dimension 1 S42. Initialize the incident source in the clipped overcomplete angle set Θ var The power distribution γ on the surface is expressed as follows: In the formula, γ=[γ1,γ2,...,γ i ,...,γ P Let ] be a P×1 dimensional vector, with the i-th element γ i This indicates that the incident source is at a perfect angle. On power, This indicates taking the k-th element of the matrix within the parentheses "()". * The calculation is performed on the row, k * =1,2,...,K, |·| denotes the absolute value function; S43, initialize noise power σ 2 The expression is as follows: where σ 2 is a 1 x 1 vector of values, and Var[•] denotes the variance function. S44, calculating a variance Σ of a posterior distribution, and the expression is as follows: where Σ is a P x P matrix, the i-th diagonal element represents the variance of the distribution over the complete angle Θi, Γ = diag(γ) is a P x P diagonal matrix, the i-th diagonal element is γ i , diag(·) denotes diagonalizing a vector into a matrix, is an N f x N f matrix, I2 is an N f x N f identity matrix, (·) -1 denotes the inverse operation; S45, compute mean of posterior distribution The expression is as follows: In the formula, is a matrix of the vector S46, taking the power distribution γ as a hyperparameter, calculating an updated value γ of γ new , the expression is as follows: where (γ i ) new is the i-th element of the 1x1 vector γ new , which represents the power of the updated incident source over the complete angle , ρ is a positive value of order 10 -2 , ||·||2 is the 2-norm operation, is the i-th diagonal element of the matrix Σ is a matrix of dimension N ii ; S47, the noise power σ 2 As a hyperparameter, compute σ 2 the update value of (σ 2 ) new , the expression is as follows: wherein is N f is a matrix of dimension L x L, ||·||F F is the F-norm operation, and d are positive values of order 10 -4 ​ S48, updating the hyperparameters γ and σ 2 i.e., γ = γ new , σ 2 = (σ 2 ) new , repeating steps S46 and S47 until a convergence condition is met, expressed as follows: wherein is a positive value with magnitude of 10 -3 or 10 -4 , representing the convergence threshold, at this time, the K maximum values of the pseudo spectrum obtained in the range of Θ var are the DOA estimation results.

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