正则化选择在LMS稀疏多径信道估计中的应用

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"LMS类型稀疏多径信道估计的正则化选择方法" 本文主要探讨了在无线通信系统中，特别是在多径信道估计领域，如何利用LMS（Least Mean Square）类型的自适应算法进行稀疏信道的高效估计。多径信道由于其在传播过程中信号经过多个路径反射、折射，会产生频率选择性衰落，对通信系统的性能产生重大影响。而稀疏多径信道（Sparse Multipath Channel，SMPC）的特点是信道响应大多数元素为零，只有少数几个元素非零，这为利用稀疏恢复理论进行高效信道估计提供了可能。 LMS算法因其低计算复杂度和良好的稳定性，被广泛应用于自适应滤波和信道估计中。为了适应SMPC的特性，研究者提出了两种增强型LMS算法：Zero-Attracting LMS (ZA-LMS) 和 Reweighted Zero-Attracting LMS (RZA-LMS)。这两种算法通过引入了L1范数的稀疏约束函数，能够更好地寻找信道响应中的非零元素，从而提高信道估计的准确性。然而，信道估计的性能在很大程度上取决于正则化参数的选择。正则化参数在L1范数约束中起到了平衡信道估计误差和稀疏惩罚强度的作用。如果正则化参数选择不当，可能会导致过度平滑或欠拟合的问题，从而影响到信道估计的精度和恢复效果。目前，ZA-LMS和RZA-LMS算法尚未考虑正则化参数的最优选择问题。文章基于压缩感知理论（Compressive Sensing Theory），深入研究了正则化参数选择对于LMS类型稀疏信道估计的影响。压缩感知理论指出，如果一个信号是稀疏的，那么只需要远少于信号维度的观测样本就能重构该信号。这一理论为解决正则化参数选取问题提供了新的视角。作者 Zhengxing Huang, Guan Gui, Anmin Huang, Dong Xiang 和 Fumiyuki Adachi 分别来自清华大学软件工程系、东北大学通信工程系以及井冈山大学电子与信息工程系。他们通过理论分析和仿真验证，提出了一种正则化参数选择的新方法，旨在优化LMS类型的自适应算法在SMPC中的性能，提高信道估计的准确性和效率。本文的研究成果对于理解和改进无线通信系统中的信道估计具有重要意义，特别是对于那些需要处理稀疏信道环境的系统，如5G和未来的6G通信网络。通过优化正则化参数，可以进一步提升通信系统的数据传输速率、降低误码率，从而提高整体通信质量。

Regularization Selection Method for LMS-Type

Sparse Multipath Channel Estimation

Zhengxing Huang⋆, Guan Gui †, Anmin Huang ‡, Dong Xiang⋆, and Fumiyki Adachi †

⋆ Department of Software Engineering, Tsinghua University, Beijing, China

† Department of Communication Engineering, Tohoku University, Sendai, Japan

‡ Department of Electronics and Information Engineering, Jinggangshan University, Jian, China

Abstract—Least mean square (LMS)-type adaptive sparse

algorithms have been attracting much attention on sparse

multipath channel estimation (SMPC) due to their two

advantages: low computational complexity and reliability. By

introducing 



-norm sparse constraint function into LMS

algorithm, both zero-attracting least mean square (ZA-LMS) and

reweighted zero-attracting least mean square (RZA-LMS) have

been proposed for SMPC. It is well known that the performance

of the SMPC is decided by regularization parameter which

balances channel estimation error and sparse penalty strength.

However, optimal regularization parameter selection has not yet

considered in the two proposed algorithms. Based on the

compressive sensing theory, in this paper, we explain the

mathematical relationship between Lasso and LMS-type adaptive

sparse algorithms. Later, an approximate optimal regulation

parameter selection method is proposed for ZA-LMS and RZA-

LMS, respectively. Monte Carlo based computer simulations are

presented to show the effectiveness of our propose method.

Keywords—regularization parameter selection, least mean

square (LMS); adaptive sparse channel estimation; zero-attracting

least mean square (ZA-LMS); reweighted zero-attracting least

mean square (RZA-LMS).

I. INTRODUCTION

The demand for high-speed data services is getting more

insatiable due to the number of wireless subscribers roaring

increase in the next generation wireless communication

systems. Various portable wireless devices, e.g., smart phones

and laptops, have generated rising massive data traffic [1]. It is

well known that the broadband transmission is an

indispensable technique for realizing Gigabit wireless

communication [2][3]. However, the broadband signal is

susceptible to interference by frequency-selective channel

fading. In the sequel, the broadband channel is described by a

sparse channel model in which multipath taps are widely

separated in time, thereby create a large delay spread [4]. In

other words, unknown channel impulse response (CIR) in

broadband wireless communication system is often described

by sparse channel model, supporting by a few large

coefficients. In other words, most of channel coefficients are

zero or close to zero while only a few channel coefficients are

dominant (large value) to support the channel. A typical

example of sparse channel is shown in Fig. 1, where the

number of dominant channel taps is 4 while the length of

channel is 16.

Traditional least mean square (LMS) algorithm is one of the

most popular methods for adaptive system identification [5],

e.g. channel estimation. Indeed, LMS-based adaptive channel

estimation can be easily implemented by LMS-based filter due

to its low computational complexity or fast convergence speed.

However, the standard LMS-based method never takes

advantage of channel sparse structure as prior information and

then it may loss some estimation performance.

Recently, many algorithms have been proposed to take

advantage of sparse structure of the channel. For example,

based on the theory of compressive sensing (CS) [6], [7],

various sparse channel estimation methods have been

proposed in [8–13]. For one thing, these CS-based sparse

channel estimation methods require that the training signal

matrices satisfy the restricted isometry property (RIP) [14].

However, design these kinds of training matrices is non-

deterministic polynomial-time (NP) hard problem [21]. For

another thing, some of these methods achieve robust

estimation at the cost of high computational complexity, e.g.,

sparse channel estimation using least-absolute shrinkage and

selection operator (LASSO) [15]. To avoid the high

computational complexity on sparse channel estimation, a

variation of the LMS algorithm with ℓ

-norm penalty term in

the LMS cost function has also been developed in [16], [17].

The ℓ

-norm penalty was incorporated into the cost function

Fig. 1. A typical example of sparse multipath channel.

The 19th Asia-Pacific Conference on Communications (APCC2013), Bali - Indonesia

655

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