A Hybrid Distributed Source DOA Estimation Method Based on the Rank Deficit Principle

Abstract

This invention discloses a hybrid distributed source DOA estimation method based on the rank deficiency principle. First, a distributed source model is established where circular and non-circular signals are simultaneously incident on an array antenna. Second, the received signal is augmented using the conjugate of the received signal, and its covariance matrix is ​​calculated. Next, eigenvalue decomposition is performed on the covariance matrix to obtain the noise subspace under hybrid source conditions. Finally, based on the rank deficiency principle, a cost function is derived, and direction-of-arrival estimation is completed through one-dimensional spectral peak search. This method is applicable to scenarios where both circular and non-circular sources exist simultaneously in space. Compared to algorithms requiring two-dimensional search, this algorithm effectively reduces computational complexity while maintaining good angle estimation performance.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and in particular to a hybrid distributed source DOA estimation method based on the rank deficiency principle. Background Technology

[0002] Traditional Direction-of-Arrival (DOA) estimation algorithms, to simplify theoretical derivations, typically model the signal source as an ideal point source. However, in practical applications, reflective or scattering objects around the source cause a portion of the radiated signal to be reflected or scattered before reaching the array antenna. The signal observed at the array exhibits spatial diffusion, thus requiring the source to be modeled as a distributed source. Distributed sources can be classified according to the correlation between their different signal components. A distributed source where the signal components are completely coherent is called a coherent distributed source, while one where the signal components are completely incoherent is called an incoherent distributed source. In wireless communication, when the observation period is much shorter than the channel's coherence time, the channel exhibits slow time-varying characteristics, and the distributed source should be modeled as a coherent distributed source. Conversely, sources in fast time-varying channels should be modeled as incoherent distributed sources.

[0003] Signals can be categorized into circular and non-circular signals based on their non-circularity coefficients. In practical applications, it's sometimes difficult to ensure that all signal sources transmit the same type of signal. Therefore, DOA estimation algorithms for scenarios where circular and non-circular signals coexist are of practical significance. The MUSIC-like algorithm, developed by Feifei Gao et al. in 2008 based on Multiple Signal Classification (MUSIC), is one of the most representative DOA estimation algorithms for mixed circular and non-circular signal scenarios. While this algorithm boasts excellent angle estimation accuracy, it also inherits the high complexity of MUSIC-like algorithms. Extending it to distributed source scenarios further increases its complexity. Summary of the Invention

[0004] The technical problem to be solved by this invention is to address the deficiencies mentioned in the background technology by providing a hybrid distributed source DOA estimation method based on the rank deficiency principle. Based on the rank deficiency principle of the rank-reducing (RARE) operator and the orthogonality between the direction vector and the noise subspace, the method can complete the DOA estimation and type discrimination of circular and non-circular sources, which can greatly reduce the computational complexity.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

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

[0007] Step 1) Construct a uniform linear array containing an odd number of array elements and construct a coherent distributed source scene model in which circular and non-circular signals are incident together, so that the uniform linear array receives the circular and non-circular signals from the coherent distributed source scene model.

[0008] Step 1.1): Construct a uniform linear array containing an odd number of elements, using the center element of the uniform linear array as the reference element. The index position vector of the array is denoted as z = [z1, z2, ..., z2]. N ] T = [-M, -M+1, ..., M] T N = 2M + 1 is the number of array elements;

[0009] Step 1.2) Construct a coherent distributed source scenario model with both circular and non-circular signals incident;

[0010] Let there be a total of K signal sources in space, and let the received signal at time t be 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, and B = [b(η1), b(η2), ..., b(ηn)]. K )] is the direction matrix of the coherent distributed source, b(η) i Let η be the direction vector of the signal transmitted by the i-th source, i = 1, 2, ..., K. i =[θ i ,σ i [θ is the center angle of arrival of the i-th source] i and angular diffusion σ i The parameter vector formed; b(η) i The expression for the m-th element of ) is Among them, f R (θ i ,σ i ,z m ) is the center wave arrival angle θ i Angular diffusion σ i Array element index position z m Let f be a function of the variable, and f R (θ i ,σ i ,z m ) is about z m The even function, j is the imaginary unit, λ is the signal wavelength, and d0 is the element spacing. Usually, the element spacing d0 is set to half the wavelength.

[0011] If s(t) is sorted in the order of non-circular signals first and circular signals last, then in, L is a vector composed of non-circular signals. R The number of non-circular information sources. It is a vector composed of circular signals. The remaining real-valued portion after extracting the non-circular phase of a non-circular signal; and has in, It is a diagonal matrix that includes non-circular phases, and I is the identity matrix;

[0012] Step 1.3) Receive circular and non-circular signals from the coherent distributed source scene model using a uniform linear array;

[0013] Step 2), the received signal is augmented by combining it with its conjugate signal. x * (t) is the conjugate of the received signal matrix x(t), x e (t)=B e s e (t)+n e (t), It is the equivalent direction matrix, L C Let K = L be the number of circular sources. R +L C ,

[0014] Solve for x e The covariance matrix of (t), and for x e Perform eigenvalue decomposition on the covariance matrix of (t), and take the smallest (2N-(L)). R +2L C The eigenvectors corresponding to the eigenvalues ​​form the noise subspace E. n ;

[0015] Step 3), according to B e Based on the orthogonality with the noise subspace and the rank deficiency principle, cost functions are constructed for non-circular and circular signals respectively.

[0016] Step 3.1): For non-circular signals, there exists 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 center angle of arrival θ and the angular spread σ of the non-circular signal.

[0017] g(η)=[f R (θ,σ,M),f R (θ,σ,M-1),...,f R (θ,σ,0)] T ;

[0018] Step 3.2), let The cost function for a non-circular signal is:

[0019]

[0020] Step 3.3), the noise subspace E n Divide into blocks Divide into two matrices E of the same size. n1 and E n2 ,but Cost function for constructing a circular signal:

[0021]

[0022] Step 4) Perform one-dimensional spectral peak search on the cost functions of non-circular and circular signals respectively to complete the direction of arrival estimation and source type determination;

[0023] Analysis of orthogonality and The cost function designed for non-circular signals can estimate the DOA of circular signals. Therefore, the cost function F is first... MIX-RARE-NC (θ) Perform a one-dimensional spectral peak search on the interval θ∈[-90°,90°] to obtain the central DOAs of K sources; for F MIX-RARE-C (θ) Perform a one-dimensional spectral peak search on the interval θ∈[-90°,90°] to obtain the center DOA of all circular sources among the K sources; and then obtain the center DOA of all non-circular sources among the K sources.

[0024] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0025] 1. This invention can realize distributed source direction of arrival estimation in scenarios where circular and non-circular sources coexist. It can make full use of non-circular phase information, has a wider range of applications, and is suitable for more complex signal scenarios.

[0026] 2. This invention has lower computational complexity for estimating the direction of arrival (DOA) of mixed-type distributed sources, while maintaining excellent estimation accuracy compared to the generalized two-dimensional spectral peak search algorithm. Overall, it achieves good DOA estimation accuracy while reducing complexity. Attached Figure Description

[0027] Figure 1 This is a flowchart of the present invention;

[0028] Figure 2 The root mean square error curves of the present invention and the comparison algorithm under different signal-to-noise ratio conditions are shown.

[0029] Figure 3 The root mean square error curves of the present invention and the comparison algorithm under different snapshot numbers are shown.

[0030] Figure 4 The diagram shows the complexity curves of the present invention and the comparison algorithm under different array element numbers. Detailed Implementation

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

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

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

[0034] Step 1) Construct a uniform linear array containing an odd number of elements, using the center element of the uniform linear array as the reference element. The index position vector of the array is denoted as z = [z1, z2, ..., z2]. N ] T = [-M, -M+1, ..., M] T N = 2M + 1 is the number of array elements;

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

[0036] Let there be a total of K signal sources in space, and let the received signal at time t be 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, and B = [b(η1), b(η2), ..., b(ηn)]. K )] is the direction matrix of the coherent distributed source, b(η) i Let η be the direction vector of the signal transmitted by the i-th source, i = 1, 2, ..., K. i =[θ i ,σ i [θ is the center angle of arrival of the i-th source] i and angular diffusion σ i The parameter vector formed; b(η) i The expression for the m-th element of ) is Among them, f R (θ i ,σi ,z m ) is the center wave arrival angle θ i Angular diffusion σ i Array element index position z m Let f be a function of the variable, and f R (θ i ,σ i ,z m ) is about z m The even function, j is the imaginary unit, λ is the signal wavelength, and d0 is the element spacing. Usually, the element spacing d0 is set to half the wavelength.

[0037] If s(t) is sorted in the order of non-circular signals first and circular signals last, then in, L is a vector composed of non-circular signals. R The number of non-circular information sources. It is a vector composed of circular signals. The remaining real-valued portion after extracting the non-circular phase of a non-circular signal; and has in, It is a diagonal matrix that includes non-circular phases, and I is the identity matrix;

[0038] A uniform linear array is used to receive circular and non-circular signals from a coherent distributed source scene model.

[0039] Step 2), the received signal is augmented by combining it with its conjugate signal. x * (t) is the conjugate of the received signal matrix x(t), x e (t)=B e s e (t)+n e (t), It is the equivalent direction matrix, L C Let K = L be the number of circular sources. R +L C ,

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

[0041] Step 3), for non-circular signals, there exists 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 center angle of arrival 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] make The cost function for a non-circular signal is:

[0044]

[0045] The noise subspace E n Divide into blocks Divide into two matrices E of the same size. n1 and E n2 ,but Cost function for constructing a 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. Therefore, the cost function F is first... MIX-RARE-NC (θ) Perform a one-dimensional spectral peak search on the interval θ∈[-90°,90°] to obtain the central DOAs of K sources; for F MIX-RARE-C (θ) Perform a one-dimensional spectral peak search on the interval θ∈[-90°,90°] to obtain the center DOA of all circular sources among the K sources; and then obtain the center DOA of all non-circular sources among the K sources.

[0048] Figure 2 The root mean squared error (RMSE) curves of the present invention and the comparison algorithm under different signal-to-noise ratio conditions are shown. Figure 3 The root mean square error curves of the present invention and the comparison algorithm under different snapshot numbers are shown. Figure 4 The diagram shows the complexity curves of the present invention and the comparison algorithm under different array element numbers.

[0049] Figure 2 , Figure 3 The scene setting includes three signal sources: two non-circular signal sources and one circular signal source. Figure 4The scene setup includes one circular signal source and one non-circular signal source. The algorithms shown in the illustrations are: 1) MIX-RARE-NC: The algorithm proposed in this invention is based on the cost function F. MIX-RARE-NC (θ) algorithm; 2) MIX-RARE-C: The algorithm proposed in this invention is based on the cost function F MIX-RARE-C (θ) algorithm; 3) MIX-DSPE-NC: Distributed Signal Parameter Estimator (DSPE) spectral peak search algorithm for non-circular signals in mixed source scenarios; 4) MIX-DSPE-C: DSPE spectral peak search algorithm for circular signals in mixed source scenarios; 5) ESPRIT: DOA estimation algorithm based on rotation invariance (Estimation of Signal Parameter via Rotational Invariance Technique, ESPRIT).

[0050] In summary, the analysis of the simulation results shows that the proposed hybrid distributed source DOA estimation method based on the rank deficiency principle maintains good estimation performance while reducing computational complexity.

[0051] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0052] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific 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 principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A hybrid distributed source DOA estimation method based on the rank deficiency principle, characterized in that, Includes the following steps: Step 1) Construct a uniform linear array containing an odd number of array elements and construct a coherent distributed source scene model in which circular and non-circular signals are incident together, so that the uniform linear array receives the circular and non-circular signals from the coherent distributed source scene model. Step 1.1): Construct a uniform linear array containing an odd number of elements, using the center element of the uniform linear array as the reference element. The array's index position vector is denoted as... , The number of array elements; Step 1.2) Construct a coherent distributed source scenario model with both circular and non-circular signals incident simultaneously; Let the total number of spaces be One source, The received signal at time is denoted as , The signal waveform that reaches the reference array element, It is additive white Gaussian noise. The direction matrix of a coherent distributed information source. For the first The direction vector of the signal emitted by each source. , For the first Center Point of the signal source and angular diffusion The parameter vector formed; The The expression for each element is ,in, With the center of the angle of arrival Angular diffusion Array element index position A function of variables, and It is about even functions, The imaginary unit, The wavelength of the signal; The element spacing is set to half a wavelength. According to the order of non-circular signals first, then circular signals... To sort, then ,in, It is a vector composed of non-circular signals. The number of non-circular information sources. It is a vector composed of circular signals. The remaining real-valued portion after extracting the non-circular phase of a non-circular signal; and has ,in, It is a diagonal matrix that includes non-circular phases. It is the identity matrix; Step 1.3) Receive circular and non-circular signals from the coherent distributed source scene model using a uniform linear array; Step 2), the received signal is combined with its conjugate to form an augmented received signal. , For the received signal matrix conjugate, , It is an equivalent direction matrix. The number of circular information sources. , , ; , ; , ; Solve The covariance matrix, and for Perform eigenvalue decomposition on the covariance matrix and take the minimum value. The eigenvectors corresponding to each eigenvalue form the noise subspace. ; Step 3), according to Based on the orthogonality with the noise subspace and the rank deficiency principle, cost functions are constructed for non-circular and circular signals respectively. Step 3.1) For non-circular signals, there exists an orthogonal relationship. The direction vector of the non-circular signal Decomposed into , The center angle of arrival for a non-circular signal and angular diffusion The parameter vector formed ; ； Step 3.2), let Then the cost function for the non-circular signal is: ; Step 3.3), the noise subspace Divide into blocks Divide into two matrices of the same size. and ,but , The cost function for constructing a circular signal: ; Step 4) Perform one-dimensional spectral peak search on the cost functions of non-circular and circular signals respectively to complete the direction of arrival estimation and source type determination; Analysis of orthogonality , and The cost function designed for non-circular signals can estimate the DOA of circular signals. Therefore, the first step is to design the cost function... In the interval A one-dimensional spectral peak search was performed to obtain The central DOA of each information source; for In the interval A one-dimensional peak search was performed to obtain... The center DOA of all circular sources in a given source; thus obtaining the... The center DOA of all non-circular sources in the information source.

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