﻿ 基于改进的SOMP水声通信信道联合估计方法
 舰船科学技术  2020, Vol. 42 Issue (2): 140-143 PDF

Research on the improved joint estimation method of SOMP for underwater acoustic communication channel
GE Hui-lin, LIANG Shi-jie
Jiangsu University of Science and Technology, Zhenjiang 212002, China
Abstract: Underwater acoustic communication channel usually show the feature of time-varying. However, under certain communication conditions, the change of the underwater acoustic channel rate is still slower than the sending OFDM symbol cycle. The whole presents a slow time-varying characteristic and the channel structure within the adjacent time slot has strong time correlation. How to use the slow - changing characteristics of the channel to design the suitable OFDM channel estimation method is of great significance to further improve the underwater acoustic communication channel estimation performance. Distributed Compressed Sensing (DCS) theory can further improve the performance of sparse reconstruction by joint reconstruction using the common sparsity of multiple signals. On this basis, this article will build a time domain channel estimation method with joint structure in the DCS theory framework by improving the synchronous Orthogonal Matching Pursuit (Simultaneous Orthogonal Matching Pursuit, SOMP) algorithm and be compared with other similar algorithms on performance through the simulation.
Key words: the channel estimation     compressed sensing     joint sparse model     orthogonal frequency division multiplexing(OFDM)     simultaneous orthogonal matching pursuit algorithm
0 引　言

1 分布式压缩感知理论及联合稀疏模型

DCS理论的研究对象是具有联合稀疏特性的信号集，通过挖掘各稀疏信号之间的相关性结构，采取联合恢复信号的策略，因此能够获得更好的稀疏信号重构效果。联合稀疏模型（Joint Sparsity Models，JSM）中常用的主要有JSM-1型和JSM-2型。

1）JSM-1型

2）JSM-2型

2 基于联合稀疏模型的CS信道估计 2.1 系统模型

 ${{{Y}}_P} = {{{X}}_P}{{{F}}_P}{{h}} + {{{W}}_P} = {{Ah}} + {{{W}}_P} {\text{。}}$ (1)

 $\left\{ {\begin{array}{*{20}{c}} {{{Y}}_P^{(1)} = {{A}}{{{h}}^{(1)}} + {{W}}_P^{(1)}}{\text{，}} \\ {{{Y}}_P^{(2)} = {{A}}{{{h}}^{(2)}} + {{W}}_P^{(2)}} {\text{，}}\\ \vdots \\ {{{Y}}_P^{(T)} = {{A}}{{{h}}^{(T)}} + {{W}}_P^{(T)}} {\text{。}} \end{array} } \right.$ (2)

 $\begin{array}{l} {\hat{ H}} = \arg \min \sum\limits_{t = 1}^T {{{\left\| {{{{h}}^{(t)}}} \right\|}_1}} {\text{，}} \\ {\rm s.t.}\sum\limits_{t = 1}^T {\left\| {Y_P^{(t)} - A{h^{(t)}}} \right\|} _2^2 \leqslant \varepsilon {\text{。}} \\ \end{array}$ (3)

2.2 基于改进SOMP算法的OFDM信道估计

SOMP算法作为一种在OMP算法基础上改进的贪婪算法，主要应用与JSM-2模型。SOMP算法在每次迭代中同样仅选取与残差最匹配的原子进行支撑集的更新，通过多次快速迭代完成对信号集的联合恢复。

1）输入

2）公共信道抽头检测

 ${{\bf{\Lambda }}_0} = SOMP({{{Y}}_P},{{A}},K) {\text{。}}$ (4)

3）动态信道抽头检测

 $\begin{array}{*{20}{l}} {\lambda _t^{(i)} = \arg {{\max }_j}\left| {\left\langle {{{{A}}_j},{{r}}_{t - 1}^{(i)}} \right\rangle } \right|} {\text{，}}\\ {{{\varGamma }}_t^{(i)} = {{\varGamma }}_{t - 1}^{(i)} \cup \lambda _t^{(i)}} {\text{，}}\\ {{{\varPhi }}_t^{(i)} = {{\varPhi }}_{t - 1}^{(i)} \cup {{{A}}_{\lambda _t^{(i)}}}} {\text{。}} \end{array}$ (5)

 ${\hat{ h}}_t^{(i)} = \arg \min {\left\| {{{Y}}_P^{(i)} - {\bf{\Phi }}_t^{(i)}{{{h}}^{(i)}}} \right\|_2} {\text{。}}$ (6)

 ${{r}}_t^{(i)} = Y_P^{(i)} - {\bf{\Phi }}_t^{(i)}{\hat{ h}}_t^{(i)} {\text{。}}$ (7)

4）输出

3 实验仿真与分析 3.1 参数设置

3.2 结果分析

1）不同信道长度对估计算法性能影响

 图 1 不同信道长度下的归一化均方误差 Fig. 1 The NMSE with different channel lengths

2）公共信道抽头数对信道估计算法性能影响

 图 2 不同时间相关度下的归一化均方误差 Fig. 2 The NMSE with different temporal correlation degree L

3）不同信噪比下多种算法的NMSE及BER曲线

 图 3 不同信噪比下的归一化均方误差 Fig. 3 The NMSE with different SNR

 图 4 不同信噪比下的误比特率 Fig. 4 The BER with different SNR

 图 5 所提算法信道估计结果与原信道对比 Fig. 5 The comparison between channel estimation result of the proposed algorithm and the original channel
4 结　语

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