Sparse Channel Equalization for Direct-to-Satellite Smartphone Communications Using a Rational-Function Penalty

WANG Chengzhen; BIAN Dongming; ZHANG Gengxin

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Sparse Channel Equalization for Direct-to-Satellite Smartphone Communications Using a Rational-Function Penalty

更新时间：2026-05-20

- Sparse Channel Equalization for Direct-to-Satellite Smartphone Communications Using a Rational-Function Penalty
- Chinese Journal on Internet of Things (2026)
- 作者机构：
  
  南京邮电大学通信与信息工程学院，江苏南京210003
- 作者简介：
- 基金信息：
  
  Science and Technology Innovation Program of Xiongan New Area(2025XAGG0029)
- DOI：
  CLC： TN927.2
- Received：15 March 2026，
  
  Revised：2026-04-23，
  
  Accepted：09 May 2026，
- 稿件说明：
移动端阅览
WANG Chengzhen, BIAN Dongming, ZHANG Gengxin. Sparse Channel Equalization for Direct-to-Satellite Smartphone Communications Using a Rational-Function Penalty[J/OL]. Chinese Journal on Internet of Things, 2026.
DOI：

WANG Chengzhen, BIAN Dongming, ZHANG Gengxin. Sparse Channel Equalization for Direct-to-Satellite Smartphone Communications Using a Rational-Function Penalty[J/OL]. Chinese Journal on Internet of Things, 2026. DOI：

摘要

基于3GPP协议及ITU-R标准模型，手机直连卫星场景下，卫星信道受到视距（LoS，line of sight）径能量的主导，其时延扩展显著低于地面非视距（NLoS，non-line

of sight）场景，在离散时延域表现出极强的稀疏性，传统LMS算法由于缺乏结构约束，其稳态误差受零抽头噪声波动影响剧烈，存在收敛速度慢、稳态误差高的问题，因此，本文在零吸引LMS（ZA-LMS，zero-attracting least mean squares）、重加权零吸引LMS（RZA-LMS，reweighted zero-attracting least mean squares）的基础上，提出一种基于有理分式惩罚项的改进稀疏最小均方算法（Rational-LMS，rational least mean squares），推导了其权系数的随机梯度下降更新公式。该算法利用有理分式函数在原点附近的高灵敏度梯度以及在大系数区域的快速衰减特性，在有效滤除噪声分量的同时，实现了对均衡器系数的稳定收敛，从而在数学逻辑上更贴近

范数的理想约束；进一步地，引入参数自适应更新机制，使得算法能够根据误差动态调整稀疏惩罚系数，从而实现更低的稳态误差与更快的收敛速度。理论分析与仿真结果证明，在稀疏信道环境下，所提算法的收敛速率与稳态均方误差（MSE，mean squared error）性能均优于ZA-LMS和RZA-LMS算法。

Abstract

Based on the 3GPP specifications and ITU-R standardized channel models

in direct-to-satellite smartphone scenarios

the satellite channel is dominated by the energy of the line-of-sight (LoS) path. Consequently

its delay spread is significantly smaller than that in terrestrial non-line-of-sight (NLoS) environments

exhibiting strong sparsity in the discrete delay domain. Due to the lack of structural constraints

the conventional least mean squares algorithm is highly sensitive to noise fluctuations on zero taps in the steady state

resulting in slow convergence and high steady-state error. Therefore

building upon the zero-attracting LMS (ZA-LMS) and reweighted zero-attracting LMS (RZA-LMS)

this paper proposes an improved sparse least mean squares algorithm with a rational-function penalty

termed rational least mean squares (Rational-LMS)

and derives its stochastic gradient descent-based weight update equation. By exploiting the high-sensitivity gradient of the rational-function penalty near the origin and its rapid attenuation in the large-coefficient region

the proposed algorithm effectively suppresses noise components while ensuring stable convergence of the equalizer coefficients

thereby yielding a regularization effect

that is mathematically closer to the ideal

-norm constraint. Furthermore

an adaptive parameter update mechanism is introduced to dynamically adjust the sparsity penalty factor according to the instantaneous error

thereby achieving faster convergence and lower steady-state mean squared error (MSE). Theoretical analysis and simulation results demonstrate that

in sparse channel environments

the proposed Rational-LMS outperforms ZA-LMS and RZA-LMS in terms of both convergence rate and steady-state MSE performance.

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references

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