﻿ 基于非圆信号的单次快拍二维DOA新算法
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1. 海军航空工程学院 研究生管理大队, 烟台 264001;
2. 北京航空航天大学 航空科学与工程学院, 北京 100191

New method for single-snapshot two-dimensional direction of arrival estimation based on noncircular signals
Li Lei1, Li Guolin1, Ma Yunpeng2
2. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:To resolve the problem of fast estimating two-dimensional direction of arrival (DOA) in coherent signals environment with two parallel linear arrays, a new method for single-snapshot two-dimensional DOA estimation was presented based on noncircular signals. New coordinate system was established and array received data was changed to its conjugate data. Pseudo snapshot data was made and array aperture was doubled by reconnecting data. The coherence between the signals was solved and two-dimensional DOA can be estimated only by using singular values decomposition (SVD) for extended matrix which was made of three pseudo snapshot matrix. The method has low complex degree and high estimation accuracy, so it is suitable for DOA estimation of high real-time attribution background. Simulation indicates that the method is effective.
Key words: noncircular signals     single-snapshot     singular values decomposition (SVD)     direction of arrival (DOA) estimation     coherent signals

 图 1 阵列模型Fig. 1 Array model

Ax(α)为(M+1)×N维阵列流型矩阵;a(αk)为对应的方向向量;Nx(t)=[nx0(t),nx1(t),…,nxM(t)]T为阵列X的噪声矢量,且有

X(t)和Y(t)分别进行共轭处理,则有

 图 2 扩展后的虚拟阵列系统模型Fig. 2 Dummy array model after expansion

Gx(t)的行数为2M+2,且第M+1行数据与第M+2行数据相同,即阵列孔径扩展后存在重复阵元(编号为0的阵元).为消除重复阵元,令Gx(t)=[GxT(t)(1:M,:),GxT(t)(M+2:2M+2,:)]T.同理,为消除子阵Y′重复阵元,令Gy(t)=[GyT(t)(1:M,:),GyT(t)(M+2:2M+2,:)]T,则Gx(t)和Gy(t)满足以下关系:

2.2 基于奇异值分解的单次快拍DOA估计

Φ2Φ3Η的形式可知,Φ2只和信源入射角α有关,Φ3只和信源入射角β有关,分别对Ψ1Ψ2进行特征分解即可得到入射信号的二维波达方向.理论上,对Ψ1Ψ2进行特征分解可得到同样的特征向量矩阵T,但实际运算中两次特征分解是独立进行的,导致两次特征分解的特征向量矩阵T1T2的排序可能不同,但同一信号在两次特征分解中的特征向量强相关,可构造式(29)所示排序矩阵R,依据矩阵R每列的最大值来调整β的顺序,即可实现二维角度参数匹配.
3 数值仿真分析

 图 3 不相关信源估计结果的星座图Fig. 3 Constellation diagram of uncorrelated signal estimation result

 图 4 相干信源估计结果的星座图Fig. 4 Constellation diagram of coherent signal estimation result

 图 5 过载环境下的DOA估计(本文算法)Fig. 5 DOA estimation in the presence of overload by the proposed algorithm

 图 6 均方根误差随信噪比变化曲线Fig. 6 Root mean square error vs signal-to-noise ratio
4 结 论

1) 利用信号的非圆特性,对阵列接收数据进行共轭重排,使阵列孔径扩展1倍,阵列自由度增大1倍,信息利用率及谱分辨力得到提高.与SS-ESPRIT算法相比,本文算法具有更好的估计性能,仿真结果证明了该算法的均方根误差相对较小.

2) 仅需对阵列单次快拍数据构造的扩展矩阵进行一次奇异值分解即可实现信号的完全解相干及二维DOA估计,计算复杂度低,实时性好.

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#### 文章信息

Li Lei, Li Guolin, Ma Yunpeng

New method for single-snapshot two-dimensional direction of arrival estimation based on noncircular signals

Journal of Beijing University of Aeronautics and Astronsutics, 2014, 40(11): 1609-1614.
http://dx.doi.org/10.13700/j.bh.1001-5965.2013.0770