基于复数支持向量回归机的盲均衡算法

doi:10.11959/j.issn.1000-436x.2019199

通信学报 ›› 2019, Vol. 40 ›› Issue (10): 180-188.doi: 10.11959/j.issn.1000-436x.2019199

基于复数支持向量回归机的盲均衡算法

杨凌, 陈亮, 赵膑, 张国龙, 李媛

兰州大学信息科学与工程学院，甘肃兰州 730000

修回日期:2019-08-06 出版日期:2019-10-25 发布日期:2019-11-07
作者简介:杨凌（1966- ），女，甘肃张掖人，兰州大学副教授、硕士生导师，主要研究方向为机器学习理论与通信系统智能信号处理。|陈亮（1992- ），男，山东临沂人，兰州大学硕士生，主要研究方向为机器学习理论与盲信号处理。|赵膑（1994- ），男，甘肃平凉人，兰州大学硕士生，主要研究方向为神经网络理论及其在盲均衡中的应用。|张国龙（1985- ），男，甘肃武威人，兰州大学硕士生，主要研究方向为水声通信系统盲均衡。|李媛（1994- ），女，山东烟台人，兰州大学硕士生，主要研究方向为极限学习机及其在卫星信道盲均衡中应用。
基金资助:
中央高校基本科研业务费专项资金资助项目(lzujbky-2019-91);甘肃省自然科学基金资助项目(20180322)

Blind equalization algorithm based on complex support vector regression

Ling YANG, Liang CHEN, Bin ZHAO, Guolong ZHANG, Yuan LI

School of Information Science and Engineering,Lanzhou University,Lanzhou 730000,China

Revised:2019-08-06 Online:2019-10-25 Published:2019-11-07
Supported by:
The Fundamental Research Fund for the Central Universities(lzujbky-2019-91);The Natural Science Foundation of Gansu Province(20180322)

摘要/Abstract

摘要：

基于复数支持向量回归机（CSVR）的框架，提出了一种针对复数信号的新的盲均衡算法，将多模算法的误差函数代入CSVR的惩罚项构造代价函数，利用广泛线性估计建立回归关系，并采用迭代重加权最小二乘方法确定均衡器系数。不同于支持向量回归机对复数信号的实数化处理方式，CSVR利用Wirtinger微积分，将复数信号直接在复数再生核希尔伯特空间进行解析。仿真实验表明，针对QPSK调制信号，在线性信道和非线性信道下，与基于SVR的盲均衡算法相比，通过选取合适的核函数和迭代优化方法，所提算法的均衡性能显著提升。

关键词: 复数支持向量回归机, 盲均衡, 多模算法, 希尔伯特空间, 核函数

Abstract:

A new blind equalization algorithm for complex valued signals was proposed based on the framework of complex support vector regression(CSVR).In the proposed algorithm,the error function of multi-modulus algorithm (MMA) was substituted into CSVR to construct the cost function,and the regression relationship was established by widely linear estimation,and the equalizer coefficients were determined by the iterative re-weighted least square (IRWLS) method.Different from spliting the complex valued signals into real valued signals used in support vector regression,the Wirtinger’s calculus was used in complex support vector regression to analyze the complex signals directly in the complex regenerative kernel Hilbert space.Simulation experiments show that for QPSK modulated signals,compared with the blind equalization algorithm based on support vector regression,the equalization performance of the proposed algorithm is significantly improved in linear channel and nonlinear channel by choosing appropriate kernel function and iterative optimization method.

Key words: complex support vector regression, blind equalization, multi-modulus algorithm, Hilbert space, kernel function

中图分类号:

TN911.5

杨凌, 陈亮, 赵膑, 张国龙, 李媛. 基于复数支持向量回归机的盲均衡算法[J]. 通信学报, 2019, 40(10): 180-188.

Ling YANG, Liang CHEN, Bin ZHAO, Guolong ZHANG, Yuan LI. Blind equalization algorithm based on complex support vector regression[J]. Journal on Communications, 2019, 40(10): 180-188.

图/表 9

图1

表1

图2

图3

表2

不同算法的复杂度比较"

算法	复杂度
CSVR-IRWLS	O(4 N ² L_w+10 N+2)
SVR-IRWQP^[10]	$O (N^{4} L_{w}^{2} + 16 N L_{w})$
SVR-IRWLS^[11,14]	$O (16 N L_{w} + 4 N L_{w}^{2} + L_{w}^{3})$

表2

图4

图5

图6

表4

CSVR-IRWLS（复高斯核）算法与SVR-IRWLS （高斯核）算法的复杂度比较"

算法	复杂度
CSVR-IRWLS	O(4N³+20N2+4 N ² L_w+10 N+2)
SVR-IRWLS^[11,14]	$O (N^{2} +16 N L_{w} + 4 N L_{w}^{2} + L_{w}^{3})$

表4

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输入序列长度N	C	ε	η	ρ
200	0.4～0.5	0～0.1	0.6～0.8	0.7～0.9
400	0.4～0.6	0～0.1	0.6～0.8	0.7～0.9
600	0.5～0.7	0～0.1	0.6～0.8	0.6～0.7
800	0.6～0.9	0～0.1	0.6～0.8	0.5～0.7
1 000	0.6～0.9	0～0.1	0.7～0.9	0.5～0.7

基于复数支持向量回归机的盲均衡算法

Blind equalization algorithm based on complex support vector regression

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