基于部分解耦合的非线性数字干扰对消算法

doi:10.12305/j.issn.1001-506X.2023.04.05

摘要/Abstract

摘要：

针对数字对消器中基于并行Hammerstein(parallel Hammerstein, PH)模型的非线性最小均方(least mean square, LMS)算法基函数之间的强相关性而存在收敛速度变慢、收敛稳定性变差、稳态误差增大的问题, 提出了一种采用部分解耦合策略的改进算法。通过引入带约束的正则方程, 实现各个非线性阶次独立的迭代步长设定。并且对基于部分解耦合干扰对消算法进行解析分析, 给出了平均和均方意义下的收敛条件。仿真结果表明, 所提方法在几乎不损失稳态误差性能的前提下, 提升了非线性LMS算法收敛速度, 改善了收敛性能, 并且针对滤波器非线性阶数和记忆长度变化具有良好的鲁棒性。在1 MHz带宽二进制相移键控(binary phase shift keying, BPSK)干扰和加性高斯白噪声情况下干噪比设置为20 dB, 相较于传统非线性LMS算法, 所提算法可以实现最大0.5倍迭代步长上界、最高非线性阶次9以及最大记忆长度12的设定。

关键词: 数字干扰对消, 最小均方算法, 非线性, 部分解耦合, 收敛特性分析

Abstract:

In view of the strong correlation between the basis functions of the nonlinear least mean square (LMS) algorithm based on the parallel Hammerstein (PH) model in the digital canceller, which has the problems of slow convergence speed, poor convergence stability and increased steady-state error, an improved algorithm using the partial decoupling strategy is proposed. By introducing a regular equation with constraints, the iterative step size of each nonlinear order can be set independently. The algorithm of interference cancellation based on partial decoupling is analyzed analytically, and the convergence conditions in the mean and mean square sense are given. The simulation results show that the proposed method improves the convergence speed and performance of nonlinear LMS algorithm without losing the steady-state error performance, and has good robustness against the change of nonlinear order and memory length of the filter. In the case of 1 MHz bandwidth binary phase shift keying (BPSK) interference and additive white Gaussian noise, the interference to noise ratio is set to 20 dB. Compared with the traditional nonlinear LMS algorithm, the proposed algorithm can achieve the setting of the upper bound of the maximum 0.5 times of iteration step length, the maximum nonlinear order 9 and the maximum memory length 12.

Key words: digital interference cancellation, least mean square (LMS) algorithm, nonlinearity, partially decouple, convergence property analysis

中图分类号:

TN911.7

崔中普, 葛松虎, 李亚星, 郭宇, 邢金岭, 孟进. 基于部分解耦合的非线性数字干扰对消算法[J]. 系统工程与电子技术, 2023, 45(4): 973-981.

Zhongpu CUI, Songhu GE, Yaxing LI, Yu GUO, Jinling XING, Jin MENG. Partially decoupling based nonlinear digital interference cancellation algorithm[J]. Systems Engineering and Electronics, 2023, 45(4): 973-981.

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阶次	线性模型维纳解			非线性模型维纳解			部分解耦合模型维纳解
阶次	0 dB	10 dB	20 dB	0 dB	10 dB	20 dB	0 dB	10 dB	20 dB
k=1	-19.394 1	-16.018 1	-7.937 4	-19.384 1	-16.018 1	-7.937 4	-19.384 1	-16.018 1	-7.937 4
k=3	-19.413 9	-16.034 8	-7.944 5	-20.015 9	-20.015 9	-19.992 1	-19.553 2	-19.7116	-19.051 1
k=5	-19.398 9	-15.987 7	-7.993 3	-19.983 1	-19.983 1	-20.026 0	-19.565 5	-19.806 8	-19.348 0
k=7	-19.383 9	-16.009 7	-7.985 8	-20.019 4	-20.019 4	-19.983 1	-19.555 1	-19.884 3	-19.408 6
k=9	-19.379 1	-16.006 6	-7.955 7	-19.970 0	-19.970 0	-19.969 6	-19.551 4	-19.886 5	-19.411 9

阶次	方法
阶次	线性LMS	非线性LMS	部分解耦合LMS
k=1	1.078 0	1.078 0	1.078 0
k=3	1.078 0	0.639 6	1.385 6
k=5	1.078 0	0.485 1	1.734 8
k=7	1.078 0	0.407 9	2.115 8
k=9	1.078 0	0.362 1	2.515 5

阶次	方法
阶次	线性LMS	非线性LMS	部分解耦合LMS
k=1	0.768 5	0.768 5	0.768 5
k=3	0.768 5	0.431 9	0.986 0
k=5	0.768 5	0.317 9	1.204 7
k=7	0.768 5	0.259 2	1.404 8
k=9	0.768 5	0.222 6	1.572 4

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