Signal incoming wave direction estimation method based on random subspace capturing technology

Abstract

The invention provides a signal incoming wave direction estimation method based on a random subspace capturing technology, and belongs to the technical field of signal processing. The technical problem that in the prior art, the response speed is not high enough under the high-dimensional condition is solved. According to the technical scheme, the method comprises the following steps of 1, calculating a covariance matrix according to a received signal; 2, rapidly extracting a signal subspace by using a random capture technology; step 3, determining a noise subspace projection operator; and 4, solving a specific optimization problem to obtain signal incoming wave direction estimation. The method has the advantages that the robustness is good, the method can adapt to a complex communication environment, the method has obvious advantages in calculation complexity and implementation difficulty, and the method can be easily applied to an actual communication system.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and in particular to a method for estimating the direction of a signal wave based on a random subspace capture technology. Background Art

[0002] In array signal processing, it is of great significance to accurately estimate the direction of arrival (DOA) of the signal. Although traditional DOA estimation methods such as beamforming and CAPON minimum variance unbiased estimator can achieve good results in some cases, they often face the problem of insufficient accuracy when dealing with complex environments or multipath effects. In recent years, subspace-based methods such as the MUSIC method proposed in the paper A signal subspace approach to multiple emitter location and spectral estimation, and the improved MUSIC method proposed in the paper Modified musical algorithm for estimating DOA of signals and the research and implementation of MUSIC and its improved algorithms, have improved the resolution and accuracy of DOA estimation by utilizing the orthogonality of signal subspace and noise subspace. However, such methods need to calculate the eigenvalue decomposition of the matrix when estimating the direction of arrival of the signal, which undoubtedly increases the computational complexity and weakens the energy intensity of each incoming signal, which is bound to affect the estimation of the direction of arrival. In order to avoid calculating the eigenvalue decomposition, the present invention introduces random technology to improve the operation speed, especially in high-dimensional situations, it can respond quickly to the signal arrival. Summary of the invention

[0003] The purpose of the present invention is to provide a signal wave direction estimation method based on random subspace capture technology. In order to avoid eigenvalue decomposition, the present invention quickly obtains the signal subspace by utilizing random signal subspace capture technology, and obtains the noise subspace by combining orthogonality, which makes it more advantageous in computational complexity and implementation difficulty, and is easy to apply in actual communication systems.

[0004] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is specifically: a method for estimating the direction of a signal wave based on a random subspace capture technology, comprising the following steps:

[0005] Step 1: Calculate the covariance matrix R based on the received signal XX ;

[0006] Step 2: Use random crawling technology to quickly extract the signal subspace U S ;

[0007] Step 3: Determine the noise subspace projection operator in Indicates U S The conjugate transpose of ;

[0008] Step 4: According to the following optimization problem:

[0009]

[0010] Get the signal direction estimate where a(θ)=(1,e -j2πdsinθ / λ ,…,e -j(L-1)2πdsinθ / λ ) T is the direction vector, d is the distance between adjacent array elements, λ is the signal wavelength, and θ is the signal arrival direction.

[0011] Furthermore, in step 1, the covariance matrix R XX for:

[0012] R XX =E(X(t)X H (t)) = AR SS A H +σ 2 I,

[0013] Where X(t) = (X 1 (t),X 2 (t),…,X L (t)) T is the received signal vector, X(t)=A(θ)S(t)+N(t), S(t) is the signal vector, N(t) is the noise vector, A(θ)=(a(θ 1 ),a(θ 2 ),…,a(θ M )) is a L×M spatial array steering vector array, where is the direction vector, θ i is the arrival direction of the ith signal, R SS =E(S(t)S H (t)), σ 2 is the noise variance, and I is the identity matrix.

[0014] Furthermore, in step 2, the signal subspace U S The extraction steps are as follows:

[0015] Step (1) Randomly generate an L×l matrix Ω i ,0 <l<L;

[0016] Step (2) Calculate U i =orth(R XXΩ i ), where orth(·) represents orthonormalization of the column space;

[0017] Step (3) performs orthogonality correction

[0018] Step (4) calculates the projection matrix

[0019] Step (5) calculates the remainder R XX = R XX - U i B i ;

[0020] Step (6) If ||R XX || 2 is less than the given threshold ∈, then terminate the calculation, otherwise return to Step (1). The signal subspace U S = [U 1 , U 2 , …, U i .

[0021] Furthermore, in Step 4, the optimization problem can be transformed into calculating the following optimization problem:

[0022]

[0023] Obtain the estimation of the signal arrival direction

[0024] Furthermore, in Step (6) of extracting the signal subspace U S , the threshold ∈ is determined according to the specific situation of the interference signal and is controlled between 10 -1 and 10 -4 .

[0025] Furthermore, in the optimization problem (2), the estimation of the signal arrival direction can be searched for spectral peaks by an equal-step method, and the step size is controlled at about 1 degree.

[0026] Compared with the prior art, the beneficial effects of the present invention are:

[0027] 1. The present invention uses the random signal subspace capture technology to quickly obtain the signal subspace. Specifically: First, randomly generate an L×l matrix Ω i , 0 < l < L; then, through U i = orth(R XX Ω i ), randomly capture fragments of the orthogonal basis of the column space of the covariance matrix R XX , and continuously capture in the remainder until the column space is obtained. Obviously, this is faster thanXX The eigenvalue decomposition should be easy to implement, require little computation and respond quickly, especially when the dimension is large.

[0028] 2. The present invention obtains the signal subspace U S Then, the noise subspace projection operator is determined by combining the orthogonality It improves the accuracy of the noise subspace without the need for redundant eigenvalue information and has obvious advantages in terms of difficulty of implementation. It can adapt to complex communication environments and is easy to apply in actual communication systems.

[0029] 3. The present invention cleverly utilizes the unitary matrix property (U S ,U N )(U S ,U N ) H =I, from the signal subspace U S Rapid transition to the projection of the noise space enables rapid spectral peak search. This technical means greatly simplifies the implementation of the program and is particularly suitable for signal detection in large array systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0031] Figure 1 is a schematic diagram of a linear array model of the present invention, wherein S 1 (t) is the signal data, θ is the signal wave arrival direction, d is the distance between adjacent array elements, X i (t), i=1,2,…,L is the received signal data.

[0032] Figure 2 Schematic diagram of simulation results of Example 2 of the present invention.

[0033] Figure 3 Schematic diagram of simulation results of Example 3 of the present invention. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.

[0035] Example 1

[0036] The technical solution provided in this embodiment is a signal wave direction estimation method based on random subspace capture technology, which mainly performs random signal subspace fast extraction on the covariance matrix of the received signal, then uses the orthogonality of the signal subspace and the noise subspace to obtain the noise subspace, and finally performs spectrum peak search through the equal step method to obtain the signal wave direction estimation, including the following steps:

[0037] Setting R XX In order to receive the signal covariance matrix and obtain the signal wave direction estimation, the present invention proposes the following signal wave direction estimation method based on random signal subspace capture technology, which uses the random capture technology to quickly extract the signal subspace. The actual steps are:

[0038] Step (1) Randomly generate an L×l matrix Ω i ,0 <l<L;

[0039] Step (2) Calculate U i =orth(R XX Ω i ), where orth(·) represents the standard orthogonalization of the column space;

[0040] Step (3) Orthogonal correction

[0041] Step (4) Calculate the projection matrix

[0042] Step (5) Calculate the remaining R XX =R XX -U i B i ;

[0043] Step (6) If || R XX || 2 If it is less than the given threshold ∈, the calculation is terminated, otherwise return to step (1). The obtained signal subspace U S =[U 1 ,U 2 ,…,U i ].

[0044] Compute the noise subspace projection operator in Indicates U S The conjugate transpose of .

[0045] Compute the following optimization problem:

[0046]

[0047] Get the signal direction estimate

[0048] In the above solution process, the threshold ∈ is determined according to the specific situation of the interference signal and is controlled within 10 -1 Up to 10 -4 The signal direction is estimated The peak search can be performed using the equal step method, with the step size controlled at around 1 degree.

[0049] The signal direction estimation obtained by the above process has the advantages of low computational complexity and easy implementation, and is easy to be applied in actual communication systems.

[0050] Example 2

[0051] Considering the practical feasibility of the method of the present invention, in Example 2, the number of given spatial arrays is L=8, the number of signal sources is M=3, the angle to be estimated is θ=[-30,0,60], the number of sampling points in the time domain is K=512, the array element spacing is d=0.5, and the incident signal is randomly generated. In this example, S=randn(M,K), where randn(·) is a built-in function of MATLAB. Gaussian white noise is added by function awgn(·), the signal-to-noise ratio is set to 10, and the signal after adding noise is the received signal X(t).

[0052] Calculate the covariance matrix R according to the received signal in step 1 XX =E(X(t)X H (t)) = X(t)X H (t) / K; then the covariance matrix R XX To capture the signal subspace, the steps are as follows:

[0053] Step (1) Randomly generate an L×l matrix Ω i =randn(L,l), where l=5;

[0054] Step (2) Calculate U i =orth(R XX Ω i );

[0055] Step (3) Orthogonal correction

[0056] Step (4) Calculate the projection matrix

[0057] Step (5) Calculate the remaining R XX =R XX -U i B i ;

[0058] Step (6) If || R XX || 2If it is less than the given threshold ∈=0.01, the calculation is terminated, otherwise it returns to step (1). After i steps of this iterative process, the signal subspace U S =[U 1 ,U 2 ,…,U i ].

[0059] Compute the noise subspace projection operator in Indicates U S The conjugate transpose of .

[0060] Search in steps of π / 180 radians The corresponding angle is the estimated value of the incoming wave direction. Figure 2 It can be seen that the signal direction estimation method based on random signal subspace capture technology and the classic MUSIC method can both accurately obtain the direction of the signal.

[0061] Example 3

[0062] In this embodiment, the number of spatial arrays is L=1024, the number of signal sources is M=7, the angle to be estimated is θ=[-30,-10,0,10,20,40,60], the number of sampling points in the time domain is K=512, the array element spacing is d=0.5, and the incident signal is randomly generated 6 times by S=randn(M,K). Gaussian white noise is also added, and the signal-to-noise ratio is set to 50. The signal after adding noise is the received signal X(t).

[0063] Calculate the covariance matrix R according to the received signal in step 1 XX =E(X(t)X H (t)) = X(t)X H (t) / K; then the covariance matrix R XX To capture the signal subspace, the steps are as follows:

[0064] Step (1) Randomly generate an L×l matrix Ω i = randn(L,l), where l = 10;

[0065] Step (2) Calculate U i =orth(R XX Ω i );

[0066] Step (3) Orthogonal correction

[0067] Step (4) Calculate the projection matrix

[0068] Step (5) Calculate the remaining R XX=R XX -U i B i ;

[0069] Step (6) If || R XX || 2 If it is less than the given threshold ∈=0.01, the calculation is terminated, otherwise it returns to step (1). After i steps of this iterative process, the signal subspace U S =[U 1 ,U 2 ,…,U i ].

[0070] Compute the noise subspace projection operator in Indicates U S The conjugate transpose of .

[0071] Search in steps of π / 180 radians The corresponding angle of the spectrum peak is the estimated value of the incoming wave direction. Figure 3 The simulation results based on the above model parameters show that both the signal direction estimation method based on random signal subspace capture technology and the classical MUSIC method can obtain accurate results, but the running time is significantly different. The operation time of the classical MUSIC method is about 3 times that of the present invention. For details, please refer to Table 1.

[0072] Table 1 Comparison of calculation time between the method proposed in this invention and the classic MUSIC method (unit: seconds / s)

[0073]

[0074] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for estimating the direction of a signal wave based on random subspace capture technology, characterized in that: The steps include: Step 1: Calculate the covariance matrix R based on the received signal XX ; Step 2: Use random crawling technology to quickly extract the signal subspace U S ; Step 3: Determine the noise subspace projection operator in Indicates U S The conjugate transpose of ; Step 4: According to the following optimization problem: Get the signal direction estimate where a(θ)=(1,e -j2πdsinθ / λ ,…,e -j(L-1)2πdsinθ / λ ) T is the direction vector, d is the distance between adjacent array elements, λ is the signal wavelength, and θ is the signal arrival direction.

2. According to claim 1, a method for estimating the direction of incoming signal based on random subspace capture technology is characterized in that: The covariance matrix R in step 1 XX for: R XX =E(X(t)X H (t))=AR SS A H +σ 2 I, Where X(t)=(X1(t),X2(t),…,X L (t)) T is the received signal vector, X(t)=A(θ)S(t)+N(t), S(t) is the signal vector, N(t) is the noise vector, A(θ)=(a(θ1), a(θ2),…, a(θ M )) is a L×M spatial array steering vector array, where is the direction vector, θ i is the arrival direction of the ith signal, R SS =E(S(t)S H (t)), σ 2 is the noise variance, and I is the identity matrix.

3. The method for estimating the direction of incoming signal based on random subspace capture technology according to claim 1, characterized in that: In step 2, the signal subspace U is extracted S The steps are as follows: Step (1) Randomly generate an L×l matrix Ω i ,0 <l<L; Step (2) Calculate U i =orth(R XX Ω i ), where orth(·) represents the standard orthogonalization of the column space; Step (3) Orthogonal correction Step (4) Calculate the projection matrix Step (5) Calculate the remaining R XX =R XX -U i B i ; Step (6) If || R XX If ||2 is less than the given threshold ∈, the calculation is terminated, otherwise return to step (1); Signal subspace U S =[U1,U2,…,U i ].

4. The method for estimating the direction of incoming signal based on random subspace capture technology according to claim 1, characterized in that: The optimization problem in step 4 is transformed into the following optimization problem: Get the signal direction estimate 5. The signal arrival direction estimation method based on random subspace capture technology according to claim 3 is characterized in that: The extracted signal subspace U S Step (6), the threshold ∈ is determined according to the specific situation of the interference signal and is controlled within 10 -1 Up to 10 -4 between.

6. The signal direction estimation method based on random subspace capture technology according to claim 4 is characterized in that: The optimization problem (2) is to estimate the direction of the signal The peak search can be performed using the equal step method, with the step size controlled at around 1 degree.

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