Blind Source Separation of Complex Signals Based on Improved Pigeon-Inspired Optimization

doi:10.3969/j.issn.1009-086x.2023.02.012

Abstract

Abstract:

Blind source separation of complex signals composed of reconnaissance， interference， detection， and communication signals is the first step in the processing of received signals in the integrated reconnaissance， interference， detection， and communication system， which requires higher accuracy of blind source separation. The traditional blind source separation method based on independent component analysis has such defects as the easy acquisition of local optimums and poor separation performance. To solve these problems， this paper proposes an improved pigeon-inspired optimization algorithm for blind source separation of complex signals. A location factor is added to the map and compass operators of the pigeon-inspired optimization algorithm， and a compression factor is added to the landmark operator. In this way， the global exploration ability in the early stage and the local search accuracy in the later stage of the algorithm are balanced， and the problems of the easy fall into local optimums and premature convergence are solved. The optimization ability and convergence speed of the algorithm are improved. Simulations show that the algorithm proposed in this paper can better separate complex signals under low and strong noise. Compared with the traditional independent component analysis method， the algorithm has better separation performance and convergence speed.

Key words: blind source separation, integrated reconnaissance， interference， detection， and communications, improved pigeon-inspired optimization, location factor, compression factor

摘要：

由各类侦察、干扰、探测、通信信号构成的复杂信号盲源分离是侦干探通一体化系统接收信号处理的第一步，对盲源分离准确度要求更高。传统独立成分分析的盲源分离方法，存在容易求得局部最优解、分离性能较差等缺陷。针对这些问题，提出了一种改进鸽群算法的复杂信号盲源分离方法，通过在鸽群算法的地图和指南针算子中添加位置因子，以及在地标算子中添加压缩因子2种方式，平衡了算法前期全局探索能力以及后期局部搜索准确度，解决了易陷入局部最优以及早熟收敛的问题，提升了算法的寻优能力，同时该算法在收敛速度上也有所提升。仿真实验结果表明，该算法在低噪声和高噪声情况下均能较好地分离出复杂信号，对比传统独立成分分析的方法，具有更好的分离性能和收敛速度。

关键词: 盲源分离, 侦干探通一体化, 改进鸽群算法, 位置因子, 压缩因子

CLC Number:

TN957.5

Kangbo LIANG, Ruijuan YANG, Xiaobai LI, Weilin LUO, Kai YUAN. Blind Source Separation of Complex Signals Based on Improved Pigeon-Inspired Optimization[J]. Modern Defense Technology, 2023, 51(2): 100-108.

梁康博, 杨瑞娟, 李晓柏, 骆伟林, 袁凯. 改进鸽群算法的复杂信号盲源分离[J]. 现代防御技术, 2023, 51(2): 100-108.

Figures/Tables 17

Fig. 1 Principle of BSS

Fig. 2 Curve of function g（t）

Table 1 Change in population

变量	数值
$t$	1	2	3	4	5	6	7	8	…	$T 1$
$N p$	100	50	25	13	7	4	2	1	1	1

Table 1 Change in population

变量	数值
$t$	1	2	3	4	5	6	7	8	…	$T 1$
$N p$	100	50	25	13	7	4	2	1	1	1

Fig. 3 Flowchart of IPIO algorithm

Table 2 Source signal name and parameter settings

信号名称	参数设置
侦察信号 $s 1 (t)$	带宽为20 MHz，脉宽20 μs，载频为0 Hz
探测信号 $s 2 (t)$	Chirp函数，频率1~100 MHz，脉宽20 μs
干扰信号 $s 3 (t)$	Chirp函数，频率21~120 MHz，脉宽20 μs
通信信号 $s 4 (t)$	$s 4 (t) = v m g (t) c o s (2 π f c t + θ m)$ ， $v m = A m c 2 + A m s 2$ ， $θ m = a r c t a n A m s A m c$ ， $A m c$ 和 $A m s$ 是信号幅度， $f c = 1 ? H z$

Table 2 Source signal name and parameter settings

信号名称	参数设置
侦察信号 $s 1 (t)$	带宽为20 MHz，脉宽20 μs，载频为0 Hz
探测信号 $s 2 (t)$	Chirp函数，频率1~100 MHz，脉宽20 μs
干扰信号 $s 3 (t)$	Chirp函数，频率21~120 MHz，脉宽20 μs
通信信号 $s 4 (t)$	$s 4 (t) = v m g (t) c o s (2 π f c t + θ m)$ ， $v m = A m c 2 + A m s 2$ ， $θ m = a r c t a n A m s A m c$ ， $A m c$ 和 $A m s$ 是信号幅度， $f c = 1 ? H z$

Fig. 4 Waveforms of four source signals

Fig. 5 Observation signal waveforms under low noise

Fig. 6 Sorted signal under low noise （EASI algorithm）

Fig. 7 Sorted signal under low noise （PIO algorithm）

Fig. 8 Sorted signal under low noise （IPIO algorithm）

Table 3 Similarity coefficients and number of iterations under low noise

算法	EASI	PIO	IPIO
相似系数	0.991 9	0.991 5	0.999 9
	0.991 5	0.990 1	0.999 5
	0.983 0	0.990 3	0.999 6
	0.969 2	0.988 3	0.999 3
平均值	0.983 9	0.990 1	0.999 6
迭代次数	402	164	112

Fig. 9 Histogram of similarity coefficients under low noise

Fig. 10 Sorted signal under strong noise （EASI）

Fig. 11 Sorted signal under strong noise （PIO）

Fig. 12 Sorted signal under strong noise （IPIO）

Table 4 Similarity coefficient and number of iterations under strong noise

算法	EASI	PIO	IPIO
相似系数	0.934 4	0.978 2	0.998 2
	0.936 2	0.972 6	0.997 6
	0.919 8	0.978 7	0.997 9
	0.901 2	0.975 3	0.997 5
平均值	0.922 9	0.976 2	0.997 8
迭代次数	586	199	122

Fig. 13 Histogram of similarity coefficients under strong noise

References 19

1	付卫红，刘乃安，杨小牛，等. 基于相对梯度的鲁棒的盲源分离算法［J］. 系统工程与电子技术， 2010， 32（2）： 226-228.
	FU Weihong， LIU Naian， YANG Xiaoniu， et al. Robust Blind Source Separation Algorithm Based on Relative-Gradient［J］. Systems Engineering and Electronics， 2010， 32（2）： 226-228.
2	FERREIRA A E A， ALARCÃO D. Real-Time Blind Source Separation System with Applications to Distant Speech Recognition［J］. Applied Acoustics， 2016， 113： 170-184.
3	CERRILLO-CUENCA E， SEPÚLVEDA M， GUERRERO-BUENO Z. Independent Component Analysis （ICA）： A Statistical Approach to the Analysis of Superimposed Rock Paintings［J］. Journal of Archaeological Science， 2021， 125： 105269.
4	LI Yancang， XU Peidong. Improved Wolf Pack Algorithm for Optimum Design of Truss Structures［J］. Civil Engineering Journal， 2020， 6（8）： 1411-1427.
5	WU Feng. Contactless Distribution Path Optimization Based on Improved ant Colony Algorithm［J］. Mathematical Problems in Engineering， 2021， 2021： 5517778.
6	席志红，边峦剑，晋野，基于改进粒子群的盲源分离算法研究［J］.应用科技， 2010， 37（1）： 12-14，22.
	XI Zhihong， BIAN Luanjian， JIN Ye. A Novel Blind Source Separation Method Based on Improved Particle Swarm Optimization［J］. Applied Science and Technology， 2010， 37（1）： 12-14，22.
7	罗涛华，张聪. 带有梯度加速粒子群算法的盲源分离［J］. 计算机仿真， 2010， 27（10）： 112-115.
	LUO Taohua， ZHANG Cong. Blind Source Separation Using the Particle Swarm Optimization Algorithm with Gradient Acceleration［J］. Computer Simulation， 2010， 27（10）： 112-115.
8	WANG Rongjie， ZHAN Yiju， ZHOU Haifeng. A Class of Sequential Blind Source Separation Method in Order Using Swarm Optimization Algorithm［J］. Circuits， Systems， and Signal Processing， 2016， 35（9）： 3220-3243.
9	DUAN Haibin， QIAO Peixin. Pigeon-Inspired Optimization： A New Swarm Intelligence Optimizer for Air Robot Path Planning［J］. International Journal of Intelligent Computing and Cybernetics， 2014， 7（1）： 24-37.
10	WANG Cheng， HUANG Haiyang， ZHANG Yiwen， et al. Variable Learning Rate EASI-Based Adaptive Blind Source Separation in Situ Ation Of Nonstationary Source and Linear Time-Varying Systems［J］. Journal of Vibroengineering， 2019， 21（3）： 627-638.
11	WANG Dong， ZHONG Jingjing， LI Chuan， et al. Box-Cox Sparse Measures： A New Family of Sparse Measures Constructed from Kurtosis and Negative Entropy［J］. Mechanical Systems and Signal Processing， 2021， 160： 107930.
12	YI Tinghua， WEN Kaifang， LI Hongnan. A New Swarm Intelligent Optimization Algorithm： Pigeon Colony Algorithm （PCA）［J］. Journal of Technology & Science， 2016， 18（3）： 425-448.
13	GUILFORD T， ROBERTS S， BIRO D， et al. Positional Entropy During Pigeon Homing II： Navigational Interpretation of Bayesian Latent State Models［J］. Journal of Theoretical Biology， 2004， 227（1）： 25-38.
14	DU Shuxing， CUI Jiashan. An Improved Strategy of PSO for Solving Multimodal and Higher Dimensional Complicated Optimization Problems［C］∥2015 International Conference on Computational Intelligence and Communication Networks （CICN）. Jabalpur， India. IEEE， 2015： 1229-1234.
15	赵远东，方正华.带有权重函数学习因子的粒子群算法［J］.计算机应用，2013，33（8）：2265-2268.
	ZHAO Yuandong， FANG Zhenghua. Particle Swarm Optimization Algorithm with Weight Function’s Learning Factor［J］. Journal of Computer Applications， 2013， 33（8）： 2265-2268.
16	ZHANG Bo， DUAN Haibin. Predator-Prey Pigeon-Inspired Optimization for UAV Three-Dimensional Path Planning［C］∥Advances in Swarm Intelligence， Hefei， 2014： 96-105.
17	CHEN Lin， DUAN Haibin， FAN Yanming， et al. Multi-objective Clustering Analysis via Combinatorial Pigeon Inspired Optimization［J］. Science China Technological Sciences， 2020， 63（7）： 1302-1313.
18	WATKINS D S. Fundamentals of Matrix Computations［M］. Hoboken， NJ， USA： John Wiley & Sons， Inc.， 2002.
19	邵堃，雷迎科.对武器制导数据链灵巧干扰技术［J］.弹箭与制导学报，2020，40（3）：17-22.
	SHAO Kun， LEI Yingke. Smart Jamming Technology for Weapon Guidance Data Link［J］. Journal of Projectiles， Rockets， Missiles and Guidance， 2020， 40（3）： 17-22.

[1]	Zhen-yu JIA, Hua-xing KUANG. Research on Blind Source Separation in Subarray Domain Applied to Anti-Main Lobe Jamming Algorithm [J]. Modern Defense Technology, 2022, 50(4): 132-139.
[2]	ZHANG Jian-zhong, WEN Shu-liang, TAN Cheng, ZHOU Bao-liang. Radar Main-Lobe Jamming Suppression Based on the Method of BSS-BM Union [J]. Modern Defense Technology, 2018, 46(1): 135-140.