阅读说明：本技术 一种基于增强嵌套阵的doa估计方法 (DOA estimation method based on enhanced nested array ) 是由 周凡 徐政五 廖强 甘露 于 2021-08-03 设计创作，主要内容包括：本发明属于信号处理技术领域,涉及一种基于增强嵌套阵的DOA估计方法。本发明首先得到增强嵌套阵的输出信号,其次使用求和求差的方法得到输出信号的协方差矩阵,然后利用矩阵填充的方法补全求和求差虚拟阵元的孔洞,最后进行DOA估计。该发明相对传统的DOA估计方法,提高了一倍的自由度,拥有更高的角度分辨率和更高的DOA估计精度。(The invention belongs to the technical field of signal processing, and relates to a DOA estimation method based on an enhanced nested array. According to the method, firstly, an output signal of the enhanced nested array is obtained, secondly, a covariance matrix of the output signal is obtained by using a sum and difference method, then, holes of a sum and difference virtual array element are filled by using a matrix filling method, and finally DOA estimation is carried out. Compared with the traditional DOA estimation method, the DOA estimation method has the advantages that the DOA estimation method has one time of freedom degree, and has higher angular resolution and higher DOA estimation precision.)

1. A DOA estimation method based on an enhanced nested array is characterized by comprising the following steps:

s1, making the received signal of the enhanced nested array be:

x(t)＝As(t)+n(t)

wherein, A represents an array signal direction matrix, s (t) represents a source signal matrix, and n (t) represents a noise matrix;

s2, obtaining second-order statistics of the received signals through the array:

R_x2＝E[x(t)x^T(t)]＝AR_sA^T+n(t)n^T(t)

R_x3＝E[x^*(t)x^H(t)]＝A^*R_sA^H+n^*(t)n^H(t)

wherein, E [. C]Indicates expectation of R_sRepresenting second order statistics Es (t) s of the source signal s (t)^H(t)]，(·)^HIt is shown that the conjugate transpose is solved,representing the noise power, I_NRepresenting an identity matrix of order N, (.)^*Indicating to make conjugation (·)^TIndicating to solve the transposition;

s3, adding R_x1，R_x2，R_x3Vectorizing to obtain y₁，y₂，y₃，y₁，y₂，y₃Virtual array elements corresponding to received signal sum and difference:

y₂＝B₂r+vec(n(t)n^T(t))，B₂＝A⊙A

y₃＝B₃r+vec(n^*(t)n^H(t))，B₃＝A^*⊙A^*

wherein [ ] indicates the Khatri-Rao product of the matrix, vec (-) indicates the vectorization of the matrix,e_i∈R^M×1except that the ith element is 1, the other elements are 0, i is 1, …, M and M are the number of array elements of the enhanced nested array;

s4, mixing y₁，y₂，y₃Three received data vectors are reintegrated into one data vectorIts array manifold matrix

S5, carrying out redundancy elimination rearrangement on z to obtain a virtual summation difference optimization array receiving signal model;

s6, complementing the missing part of the array elements in the received signals of the summation and difference-finding optimization array by using a matrix filling method;

and S7, applying MUSIC algorithm to the completed matrix to perform DOA estimation.

Technical Field

The invention belongs to the technical field of signal processing, and relates to a DOA estimation method based on an enhanced nested array.

Background

Array signal processing can play a very important role in many areas, such as navigation, communications and radar. Traditionally, researchers have focused on Uniform Line Arrays (ULA), where the spacing between adjacent Array elements must not exceed λ/2, to avoid spatial aliasing. Traditional ULA increases the aperture of the array by increasing the number of array elements, but results in higher computational complexity and higher hardware cost. In order to obtain a larger degree of freedom and smaller mutual coupling between Array elements, a non-uniform linear Array (NLA) receives more attention, and research on the NLA can be traced back to a Minimum-redundancy Array (MRAs) at the earliest time, so that the NLA has good direction-finding performance, but has no closed expression, and is inconvenient to apply to engineering.

In recent years, the presentation and analysis of nested and co-prime arrays, both academic and industrial, have renewed a great deal of interest in array geometry for non-homogeneous arrays. The common point of the nested array and the co-prime array is composed of two uniform linear sub-arrays with different intervals, and the original array is subjected to differential optimization to obtain a uniformly distributed virtual differential optimization array. Thus, virtual array based can be used to implement many signal processing algorithms, such as direction of arrival estimation (DOA) and beamforming and sparse DOA recovery. Since the degree of freedom and array aperture of the array can be increased from O (N) to O (N2) using a differential co-array, a greater degree of freedom can be obtained while increasing spatial resolution.

The enhanced nested array is improved in array type on the basis of the nested array, the degree of freedom is increased, the mutual coupling is reduced, and the enhanced nested array has better direction-finding performance compared with the nested array. However, the traditional differential co-array method used for DOA estimation of the enhanced nested array only obtains differencing virtual array elements of the array, does not utilize summing virtual array elements of the array, and has smaller array freedom compared with the summing differencing array.

Disclosure of Invention

The invention provides a novel DOA estimation algorithm based on the DOA estimation of the enhanced nested array. Compared with the traditional differential co-array method, the method has the advantages that the degree of freedom is increased by one time, higher angular resolution and higher DOA estimation precision are achieved, and therefore better direction finding performance is achieved.

For ease of understanding, the techniques employed in the present invention are described as follows:

the receiving array used in the invention is an enhanced Nested array, and the array arrangement mode of the enhanced Nested array (ANA) is to split a dense uniform subarray of the traditional Nested array, wherein the split subarrays are respectively arranged at two sides of a sparse uniform subarray and are called as a left subarray and a right subarray. The position of an array element normalized by a dense uniform subarray of an original traditional nested array is specified to start from 1, then the dense uniform subarray is divided into two subarrays, the subarrays are named as a subarray 1 and a subarray 2, the position of the subarray 1 is unchanged, the subarray 2 is converted to the right side of the sparse uniform subarray, and a corresponding array element set is called as a right subarray after the position is converted.

The configuration of the enhanced nested array used is ANAI-1, which will be described below. In the traditional nested array, a dense uniform sub-array has M array elements, and a sparse uniform sub-array has N array elements. The ANAI-1 can be divided into three Sub-Array portions, i.e., (L, M, R), where the Left Sub-Array (Left Sub-Array) is denoted by L, the Middle Sub-Array (Middle Sub-Array) is denoted by M, and the Right Sub-Array (Right Sub-Array) is denoted by R.

Aiming at the problems to be solved, the technical scheme of the invention is as follows:

a DOA estimation method based on an enhanced nested array comprises the following steps:

s1, obtaining the enhanced nested array receiving signal

x(t)＝As(t)+n(t)

Wherein, A represents an array signal direction matrix, s (t) represents a source signal matrix, and n (t) represents a noise matrix;

s2, obtaining second-order statistics of the received signals through the array:

R_x2＝E[x(t)x^T(t)]＝AR_sA^T+n(t)n^T(t)

R_x3＝E[x^*(t)x^H(t)]＝A^*R_sA^H+n^*(t)n^H(t)

wherein, E [. C]Indicates expectation of R_sRepresenting second order statistics Es (t) s of the source signal s (t)^H(t)]，(·)^HIt is shown that the conjugate transpose is solved,representing the noise power, I_NRepresenting an identity matrix of order N, (.)^*Indicating to make conjugation (·)^TIndicating to solve the transposition;

s3, adding R_x1，R_x2，R_x3Vectorizing to obtain y₁，y₂，y₃，y₁，y₂，y₃Virtual array element corresponding to summation and difference of received signals

y₂＝B₂r+vec(n(t)n^T(t))，B₂＝A⊙A

y₃＝B₃r+vec(n^*(t)n^H(t))，B₃＝A^*⊙A^*

Wherein [ ] indicates the Khatri-Rao product of the matrix, vec (-) indicates the vectorization of the matrix,e_i∈R^M×1(i-1, …, M) except the ith element is 1, the rest elements are 0, and M is the number of array elements of the enhanced nested array.

S4, reintegrating the three received data vectors into one data vectorIts array manifold matrix

S5, performing redundancy elimination rearrangement on z to obtain a virtual summation and difference calculation optimization array receiving signal model;

s6, complementing the missing part of the array elements in the received signals of the summation and difference-finding optimization array by using a matrix filling method;

and S7, applying MUSIC algorithm to the completed matrix to perform DOA estimation.

The invention provides a novel DOA estimation algorithm based on the DOA estimation of the enhanced nested array. And obtaining a received signal sum and difference array virtual array element by adopting a sum and difference method for the received signal, then completing the holes of the sum and difference array virtual array element by using a matrix filling method, and finally performing DOA estimation by using an MUSIC algorithm. Compared with the traditional differential optimization algorithm, the algorithm provided by the invention has the advantages that the degree of freedom is doubled, and higher angular resolution and higher estimation precision are realized.

Drawings

FIG. 1 is a flow chart of a process for implementing the present invention;

FIG. 2 is a diagram of an enhanced nested array architecture;

FIG. 3 is a diagram showing the results of the degree of freedom experiment;

FIG. 4 is a graph of experimental results of resolution;

FIG. 5 is a graph of the result of the algorithm estimated accuracy RMSE;

Detailed Description

The technical solution of the present invention will be further explained with reference to the accompanying drawings and examples.

Example 1

The purpose of this example is to compare the conventional method with the proposed method, and to verify that the proposed method of the present invention has a higher degree of freedom than the conventional method. In the embodiment, an enhanced nested array of 8 array elements is used for receiving signals, and the array element positions are {1, 5, 10, 15, 20, 21, 22, 23} d, wherein d is a half wavelength. Considering the case of multiple incident signals, the incident angle is set to-70: 5:70, 29 angles in total, the experimental signal-to-noise ratio is 15, and the snapshot number is 1000. At this time, the conventional differential optimization algorithm has failed, and the experimental result is shown in fig. 3. The algorithm provided by the invention can well expand the array aperture and improve the utilization rate of the array elements, can estimate 44 angles at most under the condition of 8 array elements, and the traditional differential optimization algorithm can estimate 22 incident angles at most under the condition of 8 array elements, which is far higher than the traditional algorithm.

An example DOA estimation method is shown in FIG. 1. Fig. 2 shows a structure diagram of an enhanced nested array used in this embodiment, and fig. 3 shows a simulation result of this embodiment, when a traditional differential optimization algorithm fails. The algorithm provided by the invention can well expand the array aperture and improve the utilization rate of the array elements, can estimate 44 angles at most under the condition of 8 array elements, and the traditional differential optimization algorithm can estimate 22 incident angles at most under the condition of 8 array elements, which is far higher than the traditional algorithm.

Example 2

The purpose of this example is to compare the conventional method with the proposed method, and to verify that the proposed method of the present invention has a higher angular resolution than the conventional method. The number of incident signals is 8, the angle is 0:3:21, the experimental signal-to-noise ratio is 15, and the snapshot number is 1000.

An example DOA estimation method is shown in FIG. 1. Fig. 2 shows a structure diagram of an enhanced nested array used in this embodiment, and fig. 4 shows a simulation result of this embodiment, the proposed algorithm can accurately estimate 8 angles of 0:3:21, whereas the conventional algorithm only has 6 peaks in the range of 0-30 degrees and cannot correctly estimate the angles.

Example 3

The purpose of this embodiment is to compare the conventional method with the proposed method, and to verify that the proposed method of the present invention has higher estimation accuracy than the conventional method. In order to measure the estimation accuracy of the algorithm, the method adopts a root mean square error criterion (RMSE) criterion, and the RMSE of DOA estimation under the conditions of different signal-to-noise ratios is tested by carrying out 100 Monte Carlo experiments on the assumption that an incident signal is-40: 10:40 and has 9 angles, and the number of fast beats of the experiments is 1000.

An example DOA estimation method is shown in FIG. 1. Fig. 2 shows a structure diagram of an enhanced nested array used in this embodiment, and fig. 5 shows a simulation result of this embodiment, and the estimation accuracy of the algorithm provided by the present invention is improved to a certain extent compared with the conventional algorithm.