近场非圆信号参数快速估计算法

宋嘉奇; 陶海红

doi:10.12000/JR20053

近场非圆信号参数快速估计算法

DOI: 10.12000/JR20053

宋嘉奇,
陶海红^,

西安电子科技大学雷达信号处理国家重点实验室西安 710071

基金项目: 国家自然科学基金(61971355)，国家部委基金

详细信息

作者简介:
宋嘉奇(1992–)，2013年于西安电子科技大学获工学学士学位，现为西安电子科技大学雷达信号处理国家重点实验室博士研究生，主要研究方向为阵列信号处理。E-mail: theo_song@163.com

陶海红(1976–)，女，西安电子科技大学教授，博士生导师，主要研究领域为雷达信号处理与检测、高速实时信号处理、阵列信号处理。E-mail: hhtao@xidian.edu.cn

通讯作者:
陶海红 hhtao@xidian.edu.cn

责任主编：魏玺章 Corresponding Editor: WEI Xizhang
中图分类号: TN911.7
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出版历程
- 收稿日期: 2020-05-02
- 修回日期: 2020-07-17
- 网络出版日期: 2020-08-28

A Fast Parameter Estimation Algorithm for Near-field Non-circular Signals

SONG Jiaqi,
TAO Haihong^,

National Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, China

Funds: The National Natural Science Foundation of China (61971355), The National Ministries Foundation

More Information

Corresponding author: TAO Haihong, hhtao@xidian.edu.cn

摘要

摘要: 该文基于对称的均匀线阵提出了一种近场非圆信号参数的快速估计算法，算法基于信号的非圆特性以及阵列的对称性对近场导向矢量进行解耦，并利用多项式求根取代传统的谱峰搜索对近场源的角度及距离参数进行快速估计。基于给定的阵列结构，建立非圆信号参数估计的多项式数学模型，然后对其进行求根即可获得近场信号源位置参数。所提算法采用多项式求根的方法有效地降低了运算复杂度，同时利用信号的非圆特性提高了参数估计的自由度(DOF)。通过性能分析和计算机仿真实验可以看出该算法能够分辨更多的近场非圆信号，并且参数估计性能有所提升，更接近于近场源参数估计的克拉美罗界(CRB)。
- 近场参数估计 /
- 非圆信号 /
- 降秩定理 /
- 多项式求根 /
- 克拉美罗界
Abstract: In this paper, a fast parameter estimation algorithm for near-field non-circular signals is proposed, which is based on symmetric, uniform, and linear array, that decouple the near-field steering vector via non-circularity and symmetry. Then, the position parameters are estimated based upon polynomial rooting technique instead of traditional spectral search. After fixing the array structure, the parameters for estimation equation are ascertained. Then the values of position parameters are obtained by solving the polynomial equations; consequently, computational difficulty is alleviated effectively. In addition, the Degree-Of-Freedom (DOF) is increased by utilizing the non-circularity characteristics of the impinging sources. It can be seen from the performance analysis and computer simulation experiments that the proposed algorithm can resolve more near-field non-circular signals and can improve parameter estimation performance, which is closer to the Cramer–Rao Bound (CRB) estimation.
- Near-field parameter estimation /
- Non-circular signal /
- Rank reduction theory /
- Polynomial rooting technique /
- Cramer-Rao Bound (CRB)

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图 1 近场参数估计示意图

Figure 1. Schematic diagram of near-field parameter estimation

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图 2 RMSE-信噪比曲线图

Figure 2. RMSE-signal to noise ratio curve

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图 3 RMSE-快拍数曲线图

Figure 3. RMSE-snapshots curve

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图 4 三种算法的运算时间比较

Figure 4. Comparison of operation time of three algorithms

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表 1 矩阵M中的元素

Table 1. Elements of matrix M

元素位置	表达式	元素位置	表达式
${m_{11}}(z)$	$\displaystyle\sum \nolimits_i {\displaystyle\sum \nolimits_j { {{L} }({ {{u} }_i},{ {{u} }_j}){z^{ { {{u} }_i} - { {{u} }_j} } } } }$	${m_{12}}(z)$	$\displaystyle\sum \nolimits_i {\displaystyle\sum \nolimits_j { {{L} }({ {{u} }_i},{ {{v} }_j}){z^{ { {{u} }_i} - { {{v} }_j} } } } }$
${m_{13}}(z)$	$\displaystyle\sum \nolimits_i { {{S} }({ {{u} }_i},{ {{u} }_i}){z^{2{ {{u} }_i} - 4} } + } \underbrace {\displaystyle\sum \nolimits\nolimits_i {\displaystyle\sum \nolimits\nolimits_j { {{S} }({ {{u} }_i},{ {{u} }_j})} } }_{i \ne j}$	${m_{14}}(z)$	$\displaystyle\sum \nolimits_i {\displaystyle\sum \nolimits_j { {{S} }({ {{u} }_i},{ {{v} }_j})} } {z^{ { {{u} }_i} - { {{v} }_j} } }$
${m_{21}}(z)$	$\displaystyle\sum \nolimits_i {\displaystyle\sum \nolimits_j { {{L} }({ {{v} }_i},{ {{u} }_j}){z^{ { {{v} }_i} - { {{u} }_j} } } } }$	${m_{22}}(z)$	$\displaystyle\sum \nolimits_i {\displaystyle\sum \nolimits_j { {{L} }({ {{v} }_i},{ {{v} }_j}){z^{ { {{v} }_i} - { {{v} }_j} } } } }$
${m_{23}}(z)$	$\displaystyle\sum \nolimits_i {\displaystyle\sum \nolimits_j { {{S} }({ {{v} }_i},{ {{u} }_j}){z^{ - { {{v} }_i} + { {{u} }_j} } } } }$	${m_{24}}(z)$	$\displaystyle\sum \nolimits_i {\displaystyle\sum \nolimits_j { {{S} }({ {{v} }_i},{ {{v} }_j}){z^{ { {{v} }_i} - { {{v} }_j} } } } }$
${m_{31}}(z)$	$\displaystyle\sum \nolimits_i { {{Y} }({ {{u} }_i},{ {{u} }_i}){z^{ - 2{ {{u} }_i} + 4} } + } \underbrace {\displaystyle\sum \nolimits\nolimits_i {\displaystyle\sum \nolimits\nolimits_j { {{Y} }({ {{u} }_i},{ {{u} }_j})} } }_{i \ne j}$	${m_{32}}(z)$	$\displaystyle\sum \nolimits_i {\displaystyle\sum \nolimits_j { {{Y} }({ {{u} }_i},{ {{v} }_j}){z^{ - { {{u} }_i} + { {{v} }_j} } } } }$
${m_{33}}(z)$	$\displaystyle\sum \nolimits_i {\displaystyle\sum \nolimits_j { {{W} }({ {{u} }_i},{ {{u} }_j}){z^{ - { {{u} }_i} + { {{u} }_j} } } } }$	${m_{34}}(z)$	$\displaystyle\sum \nolimits_i {\displaystyle\sum \nolimits_j { {{W} }({ {{u} }_i},{ {{v} }_j}){z^{ - { {{u} }_i} + { {{v} }_j} } } } }$
${m_{41}}(z)$	$\displaystyle\sum \nolimits_i {\displaystyle\sum \nolimits_j { {{Y} }({ {{v} }_i},{ {{u} }_j})} } {z^{ { {{v} }_i} - { {{u} }_j} } }$	${m_{42}}(z)$	$\displaystyle\sum \nolimits_i {\displaystyle\sum \nolimits_j { {{Y} }({ {{v} }_i},{ {{v} }_j}){z^{ { {{v} }_i} - { {{v} }_j} } } } }$
${m_{43}}(z)$	$\displaystyle\sum \nolimits_i {\displaystyle\sum \nolimits_j { {{W} }({ {{v} }_i},{ {{u} }_j}){z^{ - { {{v} }_i} + { {{u} }_j} } } } }$	${m_{44}}(z)$	$\displaystyle\sum \nolimits_i {\displaystyle\sum \nolimits_j { {{W} }({ {{v} }_i},{ {{v} }_j}){z^{ { {{v} }_i} - { {{v} }_j} } } } }$

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表 2 算法运算复杂度比较

Table 2. Algorithm complexity comparison

算法	统计量矩阵	特征值分解	谱峰搜索
GESPRIT	$O(2{N^2}/L)$	$8{N^3}/3$	$K{N^2}/{\Delta _r}({R_{\max } } - {R_{\min } }) + 360{N^2}/{\Delta _\theta }$
NCGESPRIT	$O(4{N^2}/L)$	$32{N^3}/3$	$4K{N^2}/{\Delta _r}({R_{\max } } - {R_{\min } }) + 720{N^2}/{\Delta _\theta }$
本文算法	$O(4{N^2}/L)$	$32{N^3}/3$

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