Research on Suppressing Co-channel Interference of Passive Radar Based on Blind Source Separation Using Second Order Statistics
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摘要:
针对基于长期演进(LTE)信号的无源雷达存在同频基站干扰的问题，该文提出一种基于2阶统计量的盲源分离算法，该算法是在卷积混合模型下，通过多通道最小均方(LMS)算法实现分离信号之间的相关性最小。由于各发射基站信号之间统计不相关，当分离信号之间的相关性达到最小时，完成观测信号的分离。在此基础上，改进了传统无源雷达信号处理的流程，增加了分离同频干扰基站直达波和多径杂波的步骤，实现了对同频干扰基站杂波的抑制。通过仿真分析，验证了算法的有效性，为基于LTE信号的无源雷达数据处理提供了参考。
Abstract:For the problem of co-frequency base station interference in passive radar based on Long Term Evolution (LTE) signal, an algorithm based on blind source separation using second order statistics is proposed. The presented algorithm is based on convolution mixed model, and achieves the minimum correlation among separated signals through multi-channel Least-Mean-Square (LMS) algorithm. Without statistical correlation among the signals of each transmitting base station, the separation of the observed signals is completed when the separated signals achieve the minimum correlation. On this basis, the traditional signal processing for passive radar is improved. The steps of separating co-frequency interference clutter consisting of both direct-path and multipath clutter are added, which can suppress the clutter interference of co-channel base station. Simulation and analysis verify the effectiveness of the algorithm. The algorithm provides a reference for data processing of passive radar based on LTE signal.
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表 1 多通道LMS算法总结
参数：$N$= 源数目，$M$= 观测信号数目
一般假设$N = M$
${K_i}$= 分离滤波器阶数，$i = 1,2, ··· ,N$
${\mu _{ij}}$= 步长，$i,j = 1,2, ··· ,N$，且$i \ne j$输入：${x_i}\left( t \right) = $观测信号，$i = 1,2, ··· ,N$ 初始化：${ {{W} }_{ {{ij} } } }\left( 0 \right) = { {{{\textit{0}}} }_{ {{Kj} } } }$, $i,j = 1,2, ··· ,N$，且$i \ne j$
${ {{Y} }_i}\left( t \right) = { {{{\textit{0}}} }_{Ki} }$, $i = 1,2, ··· ,N$
${K_i}$选取$K \ge \max \left\{ {{K_i},i = 1,2, ··· ,N} \right\}$
${\mu _{ij}}$根据输入数据进行调整计算：对$t = 1,2, ··· $，迭代计算：
${y_i}\left( t \right) = {x_i}\left( t \right) - \displaystyle\sum\nolimits_{j \ne i,j = 1}^N { {{W} }_{ij}^{\rm{T} }\left( {t - 1} \right){ {{Y} }_j}\left( t \right)} $
${{{W}}_{ij}}\left( t \right) = {{{W}}_{ij}}\left( {t - 1} \right) + {\mu _{ij}}{y_i}\left( t \right){{{Y}}_j}\left( t \right)$
${{{Y}}_i}\left( t \right) = {\left[ {{y_i}\left( {t - 1} \right),{y_i}\left( {t - 2} \right), ··· ,{y_i}\left( {t - {K_i}} \right)} \right]^{\rm{T}}}$
$i,j = 1,2, ··· ,N,i \ne j$终止条件：前后两次分离信号之间相关性系数的变化量小于所设
的误差门限输出：${y_i}\left( t \right) = $分离信号，$i = 1,2, ··· ,N$ 
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表 2 回波通道1仿真参数
主基站信号 同频干扰基站信号 时延(μs) 衰减(dB) 时延(μs) 衰减(dB) 直达波 0 0 0.07 –1 多径1 0.13 –8 0.20 –9 多径2 0.29 –11 0.36 –12 多径3 0.42 –15 0.59 –15 弱多径 0.16～1.95 –20～>–30 0.16～1.95 –20～>–30 目标1 11.39 –30 目标2 17.15 –37
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表 3 回波通道2仿真参数
主基站信号 同频干扰基站信号 时延(μs) 衰减(dB) 时延(μs) 衰减(dB) 直达波 0.03 –2 0 –1 多径1 0.19 –8 0.16 –9 多径2 0.35 –14 0.36 –13 多径3 0.46 –19 0.49 –14 弱多径 0.16～1.95 –20～–30 0.16～1.95 –20～–30
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