﻿ 一种特殊的非均匀水声阵列稀疏重构方法
 舰船科学技术  2018, Vol. 40 Issue (3): 132-136 PDF

1. 江苏科技大学 电子信息学院，江苏 镇江 212003;
2. 水声对抗技术重点实验室，北京 100094

A special method for non-uniform acoustic array with sparse reconstruction
YAN Yu-xia1, WANG Biao2
1. School of Electronic and Information, Jiangsu University of Science and Technology, Zhenjiang 212003, China;
2. Key Laboratory of Underwater Acoustic Warfare Technology, Beijing 100094, China
Abstract: For improving the utilization ratio of the array elements and the precision of underwater targets, a special sparse reconstruction approach for NULA are proposed. This NULA which composed of two linear uniform sub-arrays is used as the receiving array of signal. Flow pattern array of NULA which have divided angle is the observation matrix. Using the observation matrix for projection measurement of the signal to obtain observed value. The original signal is reconstructed from the observed value then getting the orientation information. The technology of Non-uniform acoustic array can use fewer elements to identify more underwater targets with the same resolution condition. So it greatly reducing the complexity of traditional underwater acoustic array. It also improve the direction-finding accuracy of underwater acoustic array in low SNR and low prior knowledge conditions.
Key words: non-uniform linear array (NULA)     compressed sensing     sparse reconstruction     estimation of the direction of arrival
0 引　言

1 阵列信号模型

 图 1 均匀线性子阵列 Fig. 1 Uniform linear sub-array

 图 2 非均匀线阵 Fig. 2 Non-uniform linear array

 $x\left( t \right) = \sum\limits_{k = 1}^K {a\left( {{\theta _k}} \right)} {s_k}\left( t \right) + n\left( t \right) = {{A}}\left( \theta \right)s\left( t \right) + n\left( t \right)\text{。}$ (1)

2 稀疏重构模型

 $y\left( t \right) = \varPhi x\left( t \right) = \varPhi {{A}}\left( \theta \right)s\left( t \right) + \varPhi n\left( t \right)\text{，}$ (2)

 $Y = \varPhi X = \varPhi {{A}}S + N,$ (3)

 $\min {\left\| S \right\|_{{l_1}}},\;{ s.t}\;{\left\| {Y - \Phi AS} \right\|_{{l_2}}} \leqslant \varepsilon \text{。}$ (4)
3 特殊的非均匀水声阵列稀疏重构方法 3.1 特殊的非均匀阵列分析

 $\begin{split}& {y_r} = E[{x_p}\left( t \right){x_q}^H\left( t \right)] = \sum\limits_{k = 1}^K {\sigma _k^2} {a_p}\left( {{\theta _k}} \right){a_p}^H\left( {{\theta _k}} \right) +\\& \sigma _n^2I = {{A}}P{{{A}}^{ H}} + \sigma _n^2I\text{。}\end{split}$ (5)

 $\widehat {{y_r}} = \frac{1}{L}\sum\limits_{l = 1}^L {{x_p}} \left( t \right){x_q}\left( t \right)\text{。}$ (6)
3.2 特殊的非均匀阵列稀疏重构方法

 $z = vec\left( {\widehat y} \right) = \widetilde A{ b} + \sigma _n^2\widetilde i\text{。}$ (7)

 $\widehat b = \arg \min {\left\| b \right\|_0}\text{，}\;\;{{subject}}\;{{to}}\;\;{\left\| {z - \widetilde Ab - \sigma _n^2\widetilde i} \right\|_2} < \varepsilon \text{。}$ (8)

 $\widehat r = \arg \;\mathop {\min }\limits_r {\left\| b \right\|_0}\text{，}\;\;{ subject \;to}\;\;{\left\| {z - Br} \right\|_2} < \varepsilon \text{。}$ (9)

 $B\left( \theta \right) = \left[ {a\left( {{\theta _1}} \right),a\left( {{\theta _2}} \right),\; \cdots ,a\left( {{\theta _Q}} \right)} \right]\text{。}$ (10)

4 仿真结果与分析

 图 3 实际阵列位置矢量信息 Fig. 3 Vector information of actual array position

 图 4 本文方法实现DOA估计 Fig. 4 Proposed method for DOA estimation

 图 5 不同参数条件下各种方法实现信号DOA估计比较结果 Fig. 5 The DOA estimation results of different method with different parameters

 图 6 可估计的最多信源数比较 Fig. 6 The estimated maximum number of source comparison

 图 7 两种估计方法均方根误差比较 Fig. 7 The RMSE comparison of the two estimation methods
5 结　语

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