阵列信号降采样低秩矩阵的恢复方法

doi:10.3969/j.issn.1001-2400.2014.05.006

J4 ›› 2014, Vol. 41 ›› Issue (5): 30-35.doi: 10.3969/j.issn.1001-2400.2014.05.006

阵列信号降采样低秩矩阵的恢复方法

杨东¹;廖桂生¹;朱圣棋¹;王凯²

(1. 西安电子科技大学雷达信号处理国家重点实验室，陕西西安 710071;
2. 中国人民解放军61251部队，河北秦皇岛 066102)

收稿日期:2013-05-29 出版日期:2014-10-20 发布日期:2014-11-27
通讯作者: 杨东
作者简介:杨东(1988-)，男，西安电子科技大学博士研究生，E-mail：yangdongxd@gmail.com．
基金资助:
国家自然科学基金资助项目(61231017)；国家973 计划资助项目(2010CB731903)

Improved low-rank recovery method for sparsely sampling data in array signal processing

YANG Dong¹;LIAO Guisheng¹;ZHU Shengqi¹;WANG Kai²

(1. National Key Lab. of Radar Signal Processing, Xidian Univ., Xi'an 710071, China;
2. Unit 91251, PLA, Qinhuangdao 066102, China)

Received:2013-05-29 Online:2014-10-20 Published:2014-11-27
Contact: YANG Dong

摘要/Abstract

摘要：

矩阵填充可以有效恢复阵列信号降采样数据，从而得到等效的全采样回波信号．然而，现有基于矩阵填充的阵列波达方向估计方法要求回波数据在不同快拍下随机选择采样序列，以满足采样数据的随机性．当部分阵元在整个观测时间内关闭或损坏时，上述方法将失效．因此，笔者提出了一种改进的降采样数据恢复方法，利用阵元间的相关特性，将单快拍下的信号矢量变换到一个等效的低秩矩阵，继而通过求解该矩阵的最小核范数，实现对缺失数据的有效估计．仿真结果表明，该方法可以有效恢复降采样数据，抑制噪声，提高波达方向的估计性能．

关键词: 阵列信号, 矩阵填充, 低秩矩阵, 波达方向估计

Abstract:

Matrix Completion (MC) theory can recover the under-sampled data in the array signal processing, further estimating the direction of arrival (DOA) as the fully sampled data does. However, it is required that the data should be under-sampled randomly in different snapshots which satisfy the randomness of MC theory. When some sensors are unsampled or broken in the whole observing time, the previous method would fail. To address this problem, a new processing method is proposed in this paper. The inner relationship among sensors is used, and then we reshape the signal vector in a single snapshort into an equivalent low-rank matrix, which can be recovered effectively by minimizing the nuclear norm. Simulation results validate the effectiveness of the proposed method. Meanwhile, the method can lower the noie power, and improve the performance of the DOA.

Key words: array signal processing, matrix completion, low rank matrix, direction of arrival

杨东;廖桂生;朱圣棋;王凯. 阵列信号降采样低秩矩阵的恢复方法[J]. J4, 2014, 41(5): 30-35.

YANG Dong;LIAO Guisheng;ZHU Shengqi;WANG Kai. Improved low-rank recovery method for sparsely sampling data in array signal processing[J]. J4, 2014, 41(5): 30-35.

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阵列信号降采样低秩矩阵的恢复方法

Improved low-rank recovery method for sparsely sampling data in array signal processing

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