Hybrid distributed information source DOA estimation method based on rank deficiency principle

Abstract

The invention discloses a hybrid distributed information source DOA (direction of arrival) estimation method based on a rank deficiency principle, which comprises the following steps of: firstly, establishing a distributed information source model in which circular and non-circular signals are incident to an array antenna together; secondly, augmenting a received signal by using conjugate construction of the received signal, and solving a covariance matrix of the received signal; carrying out characteristic decomposition on the covariance matrix to obtain a noise subspace under a mixed information source condition; and finally, deducing a cost function based on a rank deficiency principle, and completing direction-of-arrival estimation through one-dimensional spectrum peak search. The method is suitable for a scene in which a circular information source and a non-circular information source exist in the space at the same time, and compared with an algorithm needing two-dimensional search, the algorithm has the advantages that the calculation complexity is effectively reduced, and meanwhile the good angle estimation performance is kept.

Description

Technical Field

[0001] The present invention relates to the technical field of array signal processing, and in particular, to a method for estimating the direction of arrival (DOA) of hybrid distributed sources based on the rank deficiency principle. Background Art

[0002] In order to simplify theoretical derivation, traditional direction-of-arrival (DOA) estimation algorithms usually model the source as an ideal point source model. However, in actual application scenarios, due to the presence of reflectors or scatterers around the source, a part of the signal components radiated by the source are incident on the array antennas after reflection or scattering, and the signals observed at the array show a certain spatial diffusion. At this time, the source should be modeled as a distributed source. According to the correlation between different signal components from the source, distributed sources can be classified. A distributed source with completely coherent signal components is called a coherent distributed source, and conversely, when the signal components are completely incoherent, the source is called an incoherent distributed source. In wireless communication, when the observation period is much smaller than the coherence time of the channel, the channel exhibits slow time-varying characteristics, and the distributed source at this time should be modeled as a coherent distributed source; conversely, the source under a fast time-varying channel should be modeled as an incoherent distributed source.

[0003] Signals can be classified into circular signals and non-circular signals according to the non-circularity coefficient. In actual application scenarios, it is sometimes difficult to ensure that the signal types transmitted by all sources are the same. Therefore, a DOA estimation algorithm for the scenario where circular signals and non-circular signals coexist has practical significance. The MUSIC-like algorithm proposed by Feifei Gao et al. in 2008 based on the Multiple Signal Classification (MUSIC) algorithm is one of the most representative DOA estimation algorithms in the scenario of mixed circular and non-circular signals. Although this algorithm has excellent angle estimation accuracy, it also inherits the high complexity of the MUSIC-like algorithms. If it is extended to the distributed source scenario, the complexity will be further increased. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for estimating the DOA of hybrid distributed sources based on the rank deficiency principle, aiming at the defects involved in the background art. Based on the rank deficiency principle of the Rank-Reducing (RARE) operator and the orthogonality between the direction vector and the noise subspace, the DOA estimation and type discrimination of circular sources and non-circular sources can be completed, which can greatly reduce the computational complexity.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] A hybrid distributed source DOA estimation method based on the rank deficiency principle, comprising the following steps:

[0007] Step 1), construct a uniform linear array containing an odd number of array elements and construct a coherent distributed source scenario model for the co-incidence of circular signals and non-circular signals, and use the uniform linear array to receive the circular signals and non-circular signals from the coherent distributed source scenario model;

[0008] Step 1.1), construct a uniform linear array containing an odd number of array elements, use the central array element of the uniform linear array as the reference array element, and denote the index position vector of the array as z = [z 1 , z 2 ,..., z N T = [-M, -M + 1,..., M] T , where N = 2M + 1 is the number of array elements;

[0009] Step 1.2), construct a coherent distributed source scenario model for the co-incidence of circular signals and non-circular signals;

[0010] Let there be a total of K sources in space, and the received signal at time t is denoted as x(t) = Bs(t) + n(t), where s(t) is the signal waveform arriving at the reference array element, n(t) is additive white Gaussian noise, B = [b(η 1 ), b(η 2 ),..., b(η K )] is the direction matrix of the coherent distributed source, b(η i ) is the direction vector of the signal emitted by the i-th source, i = 1, 2,..., K, η i = [θ i , σ i is the parameter vector composed of the central angle of arrival θ i and the angle spread σ i of the i-th source; the expression of the m-th element of b(η i ) is where f R (θ i , σ i , z m ) is a function with the central angle of arrival θ i , the angle spread σ i , and the array element index position z m as variables, and f R (θ i , σ i , z m ) is an even function of z m , j is the imaginary unit, λ is the signal wavelength, d 0 is the array element spacing, and usually the array element spacing d 0 ​Set to half - wavelength;

[0011] Sort \(s(t)\) in the order of non - circular signals first and circular signals second, then where, is a vector composed of non - circular signals, \(L\) R is the number of non - circular signal sources, is a vector composed of circular signals, is the real - valued part remaining after removing the non - circular phase for the non - circular signal; and there is where, is a diagonal matrix containing the non - circular phase, \(I\) is the identity matrix;

[0012] Step 1.3), receive circular signals and non - circular signals from the coherent distributed source scenario model with a uniform linear array;

[0013] Step 2), construct the augmented received signal by multiplying the received signal with its conjugate as \(\mathbf{x}\) * \((t)\) is the conjugate of the received signal matrix \(\mathbf{x}(t)\), \(\mathbf{x}\) e (t)=\(\mathbf{B}\) e \(\mathbf{s}\) e (t)+\(\mathbf{n}\) e (t), is the equivalent direction matrix, \(L\) C is the number of circular signal sources, \(K = L\) R +\(L\) C ,

[0014] Solve the covariance matrix of \(\mathbf{x}\) e (t), and perform eigenvalue decomposition on the covariance matrix of \(\mathbf{x}\) e (t), take the eigenvectors corresponding to the smallest \((2N-(L\) R +\(2L\) C )) eigenvalues to form the noise subspace \(\mathbf{E}\) n ;

[0015] Step 3), construct cost functions for non - circular signals and circular signals respectively according to the orthogonality between \(\mathbf{B}\) e and the noise subspace and based on the rank - deficiency principle;

[0016] Step 3.1), for non - circular signals, there is an orthogonality relationship Decompose the direction vector \(\mathbf{b}(\eta)\) of the non - circular signal as \(\mathbf{b}(\eta)=\mathbf{W}(\theta)\mathbf{g}(\eta)\), \(\eta = [\theta,\sigma]\) is the parameter vector composed of the central angle of arrival \(\theta\) and the angle spread \(\sigma\) of the non - circular signal,

[0017] \(\mathbf{g}(\eta)=[f\) R (\theta,\sigma,M),f\)R (θ, σ, M - 1),..., f R (θ, σ, 0)] T ;

[0018] Step 3.2), let Then the cost function of the non - circular signal is:

[0019]

[0020] Step 3.3), partition the noise subspace E n into two matrices of the same size E and E n1 and E n2 , then Construct the cost function of the circular signal:

[0021]

[0022] Step 4), perform one - dimensional spectral peak search on the cost functions of the non - circular signal and the circular signal respectively to complete the direction - of - arrival estimation of the signal sources and the judgment of the signal source type;

[0023] Analyze the orthogonality relationship and If the cost function designed for the non - circular signal can estimate the DOA of the circular signal, then first perform one - dimensional spectral peak search on the cost function F MIX-RARE-NC (θ) in the interval θ ∈ [-90°, 90°] to obtain the central DOA of K signal sources; perform one - dimensional spectral peak search on F MIX-RARE-C (θ) in the interval θ ∈ [-90°, 90°] to obtain the central DOA of all circular signal sources among the K signal sources; and then obtain the central DOA of all non - circular signal sources among the K signal sources.

[0024] Compared with the prior art, the present invention adopts the above technical solutions and has the following technical effects:

[0025] 1. The present invention can realize the direction - of - arrival estimation of distributed signal sources in the scenario where circular and non - circular signal sources coexist, can make full use of non - circular phase information, has a wider application range, and is applicable to more complex signal scenarios;

[0026] 2. The present invention has a lower computational complexity for the direction - of - arrival estimation of hybrid - type distributed signal sources, and at the same time, compared with the generalized two - dimensional spectral peak search algorithm, it still maintains excellent estimation accuracy. Generally, it has good direction - of - arrival estimation accuracy while reducing the complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is the flow chart of the present invention;

[0028] Figure 2 This is the root mean square error curve of the present invention and the comparative algorithm under different signal-to-noise ratios;

[0029] Figure 3 This is the root mean square error curve of the present invention and the comparative algorithm under different numbers of snapshots;

[0030] Figure 4 This is the complexity curve of the present invention and the comparative algorithm under different numbers of array elements. Detailed implementation manners

[0031] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings:

[0032] The present invention can be implemented in many different forms and should not be considered limited to the embodiments described herein. On the contrary, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the present invention to those skilled in the art. In the drawings, components are enlarged for clarity.

[0033] As Figure 1 shown, the present invention proposes a hybrid distributed source DOA estimation method based on the rank deficiency principle. Based on the orthogonality between the direction vector and the noise subspace and the rank deficiency principle, the direction of arrival estimation of distributed sources in a mixed scenario of non-circular sources and circular sources is completed. The specific steps are as follows:

[0034] Step 1), construct a uniform linear array containing an odd number of array elements, use the central array element of the uniform linear array as the reference array element, and record the index position vector of the array as z = [z 1 , z 2 ,..., z N T = [-M, -M + 1,..., M] T , where N = 2M + 1 is the number of array elements;

[0035] Construct a coherent distributed source scenario model where circular signals and non-circular signals are incident together;

[0036] Let there be a total of K sources in space, and the received signal at time t is denoted as x(t) = Bs(t) + n(t), where s(t) is the signal waveform arriving at the reference array element, n(t) is additive white Gaussian noise, B = [b(η 1 ), b(η 2 ),..., b(η K )] is the direction matrix of the coherent distributed sources, b(η i ) is the direction vector of the signal emitted by the i-th source, i = 1, 2,..., K, and η i = [θ i , σ i is the central angle of arrival θ of the i-th source​i and the angular spread σ i constitute a parameter vector; the m-th element of b(η i ) is expressed as where f R (θ i , σ i , z m ) is a function with the central angle of arrival θ i , the angular spread σ i , and the array element index position z m as variables, and f R (θ i , σ i , z m ) is an even function of z m , j is the imaginary unit, λ is the signal wavelength, and d 0 is the array element spacing. Usually, the array element spacing d 0 is set to half a wavelength;

[0037] Sort s(t) in the order of non-circular signals first and circular signals second, then where is a vector composed of non-circular signals, L R is the number of non-circular signal sources, is a vector composed of circular signals, is the real part remaining after removing the non-circular phase from the non-circular signal; and there is where is a diagonal matrix containing the non-circular phase, and I is the identity matrix;

[0038] Receive circular and non-circular signals from the coherent distributed source scenario model with a uniform linear array;

[0039] Step 2), form the augmented received signal by taking the conjugate of the received signal as x * (t) is the conjugate of the received signal matrix x(t), and x e (t) = B e s e (t) + n e (t), is the equivalent direction matrix, L C is the number of circular signal sources, K = L R + L C ,

[0040] Solve the covariance matrix of x e (t), and perform eigenvalue decomposition on the covariance matrix of x e (t), and take the smallest (2N - (LR +2L C ) The eigenvectors corresponding to the eigenvalues form the noise subspace E n ;

[0041] Step 3), for non-circular signals, there is an orthogonality relationship Decompose the direction vector b(η) of the non-circular signal as b(η) = W(θ)g(η), where η = [θ, σ] is the parameter vector composed of the central arrival angle θ and the angular spread σ of the non-circular signal,

[0042] g(η) = [f R (θ, σ, M), f R (θ, σ, M - 1),..., f R (θ, σ, 0)] T ;

[0043] Let Then the cost function of the non-circular signal is:

[0044]

[0045] Partition the noise subspace E n into two matrices E and E n1 of the same size, then n2 Construct the cost function of the circular signal:

[0046]

[0047] Step 4), analyze the orthogonality relationship and The cost function designed for non-circular signals can estimate the DOA of circular signals. First, perform a one-dimensional spectral peak search on the cost function F MIX-RARE-NC (θ) in the interval θ ∈ [-90°, 90°] to obtain the central DOA of K sources; perform a one-dimensional spectral peak search on F MIX-RARE-C (θ) in the interval θ ∈ [-90°, 90°] to obtain the central DOA of all circular sources among the K sources; and then obtain the central DOA of all non-circular sources among the K sources.

[0048] Figure 2 is the Root Mean Squared Error (RMSE) curve of the present invention and the comparative algorithm under different signal-to-noise ratio conditions; Figure 3 is the Root Mean Squared Error curve of the present invention and the comparative algorithm under different numbers of snapshots; Figure 4 is the complexity curve of the present invention and the comparative algorithm under different numbers of array elements.

[0049] Figure 2 and Figure 3 The scenario setting contains three signal sources, two of which are non-circular signal sources and one is a circular signal source. Figure 4 The scenario setting contains one circular signal source and one non-circular signal source. The several algorithms in the legend are as follows: 1) MIX-RARE-NC: The algorithm based on the cost function F MIX-RARE-NC (θ) in the algorithm proposed by the present invention; 2) MIX-RARE-C: The algorithm based on the cost function F MIX-RARE-C (θ) in the algorithm proposed by the present invention; 3) MIX-DSPE-NC: The spectral peak search algorithm of the distributed signal parameter estimator (DSPE) for non-circular signals in the mixed source scenario; 4) MIX-DSPE-C: The DSPE spectral peak search algorithm for circular signals in the mixed source scenario; 5) ESPRIT: The DOA estimation algorithm based on rotational invariance (Estimation of Signal Parameter via Rotational Invariance Technique, ESPRIT).

[0050] In summary, from the analysis of the simulation effect diagram, it can be seen that a method for estimating the DOA of a mixed distributed signal source based on the rank deficiency principle proposed by the present invention still maintains good estimation performance while reducing the computational complexity.

[0051] Those skilled in the art of the present technology can understand that, unless otherwise defined, all terms (including technical terms and scientific terms) used herein have the same meaning as the general understanding of those of ordinary skill in the art to which the present invention belongs. It should also be understood that terms defined in a general dictionary such as those should be understood to have a meaning consistent with the meaning in the context of the prior art, and will not be interpreted with an idealized or overly formal meaning unless defined as here.

[0052] The specific embodiments described above have further elaborated on the purpose, technical solutions, and beneficial effects of the present invention. It should be understood that the above description is only the specific embodiments of the present invention and is not used to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A hybrid distributed source DOA estimation method based on rank deficiency principle, characterized in that: The following steps are involved: Step 1), constructing a uniform linear array including an odd number of array elements and constructing a coherent distributed information source scene model in which circular signals and non-circular signals are incident together, and receiving the circular signals and non-circular signals from the coherent distributed information source scene model with the uniform linear array; Step 1.1), construct a uniform linear array with an odd number of array elements, take the central array element of the uniform linear array as the reference array element, and record the index position vector of the array as z = [z1, z2, ..., z N ] T =[-M,-M+1,...,M] T , N = 2M + 1 is the number of array elements; Step 1.2), constructing a coherent distributed source scenario model with circular and non-circular signals incident together; Assume that there are K signal sources in the space, and the received signal at time t is recorded as x(t)=Bs(t)+n(t), s(t) is the signal waveform reaching the reference array element, n(t) is the additive white Gaussian noise, B=[b(η1),b(η2),...,b(η K )] is the direction matrix of the coherent distributed source, b(η i ) is the direction vector of the signal transmitted by the i-th source, i = 1, 2, ..., K, η i =[θ i ,σ i ] is the central arrival angle θ of the i-th signal source i and the angular spread σ i The parameter vector formed by b(η i ) is expressed as Among them, f R (θ i ,σ i ,z m ) is the central arrival angle θ i , angular spread σ i , array element index position z m is a function of a variable, and f R (θ i ,σ i ,z m ) is about z m An even function of, j is an imaginary unit, λ is the signal wavelength, d0 is the array element spacing, usually the array element spacing d0 is set to half the wavelength; Sort s(t) in the order of non-circular signals first and circular signals last, then in, is a vector composed of non-circular signals, L R is the number of non-circular sources, is a vector consisting of circular signals, The real-valued part remaining after the non-circular phase is extracted for the non-circular signal; and in, is a diagonal matrix containing non-circular phases, and I is the identity matrix; Step 1.3), receiving circular signals and non-circular signals from a coherent distributed source scene model with a uniform linear array; Step 2), the received signal is conjugated with its augmented received signal to form x * (t) is the conjugate of the received signal matrix x(t), x e (t) = B e s e (t)+n e (t), is the equivalent direction matrix, L C is the number of circular information sources, K = L R +L C , Solving for x e (t) and the covariance matrix of x e The covariance matrix of (t) is decomposed by eigenvalues, and the smallest (2N-(L R +2L C The eigenvectors corresponding to the eigenvalues ​​constitute the noise subspace E n ; Step 3), according to B e Orthogonality with the noise subspace and based on the rank deficiency principle, cost functions are constructed for non-circular signals and circular signals respectively; Step 3.1), for non-circular signals, there is an orthogonal relationship The direction vector b(η) of the non-circular signal is decomposed into b(η)=W(θ)g(η), where η=[θ,σ] is the parameter vector composed of the central arrival angle θ and the angular spread σ of the non-circular signal. g(η)=[f R (θ,σ,M),f R (θ,σ,M-1),...,f R (θ,σ,0)] T ; Step 3.2), let Then the cost function of the non-circular signal is: Step 3.3), the noise subspace E n Block Divide into two matrices E of equal size n1 and E n2 ,but Construct the cost function of the circular signal: Step 4), performing one-dimensional spectrum peak search on the cost functions of non-circular signals and circular signals respectively, completing the direction of arrival estimation and signal source type judgment; Analyzing orthogonal relationships and The cost function designed for non-circular signals can estimate the DOA of circular signals. First, the cost function F MIX-RARE-NC (θ) Perform a one-dimensional spectrum peak search on the interval θ∈[-90°,90°] to obtain the central DOA of K sources; MIX-RARE-C (θ) Perform a one-dimensional spectrum peak search on the interval θ∈[-90°,90°] to obtain the central DOA of all circular sources among the K sources; and then obtain the central DOA of all non-circular sources among the K sources.

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