基于压缩感知理论的宽带信号波达方向估计

doi:10.13229/j.cnki.jdxbgxb20200694

摘要/Abstract

摘要：

针对一维宽带信号波达方向（DOA）估计中聚焦变换算法需要角度预估值的问题，在双边相关变换算法基础上设计了一种无需角度预估值的DOA估计算法。首先，利用离散傅里叶变换（DFT）变换将宽带信号分解为若干个不同频点处的窄带数据模型。然后，通过本文改进的聚焦矩阵将不同频点处的窄带数据聚焦到同一参考频点，得到单一频率点处窄带信号模型。最后，采用改进阵列协方差矩阵稀疏迭代估计算法进行求解。理论研究和仿真实验结果表明，该方法在低信噪比和多快拍条件下比传统算法具有更高的估计精度和分辨率，且结合压缩感知理论有效降低了算法的运算量。

关键词: 信号与信息处理, 波达方向估计, 压缩感知, 聚焦变换

Abstract:

In order to solve the problem that the Direction of Arrival (DOA) estimation of one-dimensional wideband signal needs angle estimation, a DOA estimation algorithm without angle estimation is designed on the basis of bilateral correlation transform algorithm. Firstly, the wideband signal is decomposed into several narrow-band data models at different frequency points by using Discrete Fourier Transform (DFT). Secondly, the narrow-band data at different frequency points are focused on the same reference frequency point by the improved focusing matrix, thus, the narrow-band signal model at a single frequency point is obtained. Finally, the improved array covariance matrix sparse iterative estimation algorithm is used to solve the problem. Theoretical research shows that the proposed method has higher estimation accuracy and resolution than the traditional algorithm under the condition of low SNR and multiple snapshots, and the computational complexity of the algorithm is effectively reduced by combining with compressed sensing theory. The simulation results verify the reliability of the above conclusions.

Key words: signal and information processing, direction of arrival（DOA） estimation, compressive sensing, focusing transformatio

中图分类号:

TN911.7

窦慧晶,丁钢,高佳,梁霄. 基于压缩感知理论的宽带信号波达方向估计[J]. 吉林大学学报(工学版), 2021, 51(6): 2237-2245.

Hui-jing DOU,Gang DING,Jia GAO,Xiao LIANG. Wideband signal direction of arrival estimation based on compressed sensing theory[J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(6): 2237-2245.

图/表 9

表1

聚焦变换准则与聚焦矩阵对照表"

TCT算法	聚焦变换准则	$T (f j) ? A (f j, θ) S (f j) = A (f 0, θ) S (f 0)$
TCT算法	聚焦矩阵	$T (f j) = Q (f 0) Q H (f j)$
RSS算法	聚焦变换准则	$T (f j) ? A (f j, θ) = A (f 0, θ)$
RSS算法	聚焦矩阵	$T (f j) = V (f j, θ) U H (f j, θ)$
MTLS-CSSM 算法	聚焦变换准则	$T (f j) ? A (f j, θ) = A (f 0, θ)$
MTLS-CSSM 算法	聚焦矩阵	$T (f j) = A 0 (A 0 H A 0) - 1 / 2 (A j H A j) - 1 / 2 A j H$

表1

图1

图2

图3

图4

图5

图6

图7

表2

不同算法的运行时间对比"

算法	复杂度	运行时间/s
TCT	$O (M 3 + 2 N 3 M 3 + N 2 M 3)$	2.735 147
l₁-SRACV	$O (M 3 N 3)$	2.290 214
本文	$O (k N 3 M 3 + M 2)$	2.435 238

表2

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