﻿ 复杂电磁环境下基于信号稀疏表示的干扰抑制与通信信号重构方法
 计算机系统应用  2018, Vol. 27 Issue (11): 149-154 PDF

Interference Suppression and Communication Signal Reconstruction Method Based on Signal Sparse Representation in Complex Electromagnetic Environment
LIU Gao-Hui, ZHOU Xiong
Faculty of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, China
Foundation item: National Natural Science Foundation of China (61671375)
Abstract: In a complex electromagnetic environment, communication signals and interference overlap in the time-frequency domain, and they are difficult to be separated. To solve this problem, a method of interference suppression and communication signal reconstruction based on signal sparse representation is proposed. Firstly, the K-Singular Value Decomposition (K-SVD) algorithm is used to construct the over-complete sub-dictionaries of communication signals and interferences. Then, we build a joint dictionary by over-complete sub-dictionaries, and use the Orthogonal Matching Pursuit (OMP) algorithm to separate and reconstruct the signals. Finally, we simulate the interference suppression and reconstruction process of time-frequency overlapping 2ASK signal and 2PSK signal by computer, and verify the process of interference suppression and signal reconstruction of OFDM signal by experiments. The simulation experimental results show that this method can realize the interference suppression and signal reconstruction of communication signals under the condition of time-frequency overlapping.
Key words: time-frequency overlapping     interference suppression     signal reconstruction     sparse representation     joint dictionary

1 基于K-SVD算法的联合字典构造

1.1 K-SVD字典学习算法

K-SVD是一种经典的字典学习算法[15], 依据误差最小原则, 对误差项进行SVD分解, 选择使误差最小的分解项作为更新的字典原子和对应的原子系数, 经过不断的迭代从而得到优化的解.

K-SVD算法的具体实现步骤:

1) 字典初始化: 取待分解信号的部分数据作为训练样本组成初始字典.

2) 稀疏编码: 使用OMP算法近似求解稀疏系数, 即:

 ${x_i} = \arg \mathop {\min }\limits_x \left\| {{y_i} - {D_{k - 1}}x} \right\|_2^2,\;\;{\rm {s.t.}}\;\;{\left\| x \right\|_0} \leqslant {T_0}$ (1)

3) 逐列进行字典更新, 目标函数为:

 $\begin{array}{l}\left\| {Y - DX} \right\|_F^2 = \left\| {Y - \sum\limits_{j = 1}^k {{d_j}X_T^j} } \right\|_F^2\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; = \left\| {\left( {Y - \sum\limits_{j \ne k} {{d_j}X_T^j} } \right) - {d_k}X_T^k} \right\|_F^2\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; = \left\| {{E_k} - {d_k}X_T^k} \right\|_F^2\end{array}$ (2)

 $E_R^k = U\Sigma {V^{\rm T}}$ (3)

1.2 联合字典的构造

1) 复合信号 $y = {y_1} + {y_2}$ , 根据信号 ${y_1}$ 构造具有其特征成分的字典:

 $\phi = \left\{ {{\phi _i},i \in {\Gamma _1}} \right\},{\Gamma _1} = 1,2, \cdot \cdot \cdot ,l$ (4)

2) 根据信号 ${y_2}$ 构造具有其特征成分的字典:

 $\varphi = \left\{ {{\varphi _j},j \in {\Gamma _2}} \right\},{\Gamma _2} = 1,2, \cdot \cdot \cdot ,k$ (5)

3) 构建联合过完备字典:

 $D = \left\{ {\phi ,\varphi } \right\} = \left\{ {{\phi _1},{\phi _2}, \cdot \cdot \cdot ,{\phi _l},{\varphi _1},{\varphi _2}, \cdot \cdot \cdot ,{\varphi _k}} \right\}$ (6)

2 联合字典下信号的稀疏分解与重构

 ${\rm{min}}{\left\| x \right\|_0}\;\;\;{\rm {s.t.}}\;\;y = Dx$ (7)

(1) 首先从过完备字典中分别选出与待分解信号 $y$ 最为匹配的两个字典原子, 其中一个字典原子为 $\phi = \left\{ {{\phi _i},i = 1,2, \cdot \cdot \cdot ,l} \right\}$ , 另一个最为匹配的字典原子 $\varphi = \left\{ {{\varphi _j},j \in 1,2, \cdot \cdot \cdot ,k} \right\}$ , 且分别满足:

 $\left| {\left\langle {{\phi _{i0}},{R_0}} \right\rangle } \right| = \mathop {\sup }\limits_{i \in {\Gamma _1}} \left| {\left\langle {{\phi _i},{R_0}} \right\rangle } \right|$ (8)
 $\left| {\left\langle {{\varphi _{j0}},{R_1}} \right\rangle } \right| = \mathop {\sup }\limits_{j \in \Gamma 2} \left| {\left\langle {{\varphi _j},{R_1}} \right\rangle } \right|$ (9)

(2) 由于字典 $\phi$ 根据信号 ${y_1}$ 的特征信息构建, 字典 $\varphi$ 根据信号 ${y_2}$ 的特征信息构建, 故它们求出的最佳原子一定包含各自的主要成分. 通过OMP算法继续迭代可得到重叠信号 $y$ 的稀疏表达式为:

 $y = \sum\limits_{i = 0}^{m - 1} {\left\langle {{\phi _i},{R_i}} \right\rangle } {\phi _i} + \sum\limits_{j = 0}^{k - 1} {\left\langle {{\varphi _j},{R_j}} \right\rangle } {\varphi _j}$ (10)

3 仿真分析与实验验证 3.1 仿真信号分析

 图 1 联合字典下时频重叠信号的稀疏系数

 图 3 信干比与误码率关系图

3.2 OFDM信号分析

 图 4 OFDM信号16QAM调制后的星座图

 图 5 OFDM信号分解前与重构后的星座图

4 结论

 图 6 信干比与误码率关系图

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