Diffusion Based Channel Gains Estimation in WSN Using Fractional Order Strategies

Nasir Mahmud Khokhar,Syed Muslim Shah,Muhammad Nadeem Majeed

doi:10.32604/cmc.2022.019120

Abstract

In this study, it is proposed that the diffusion least mean square (LMS) algorithm can be improved by applying the fractional order signal processing methodologies. Application of Caputo’s fractional derivatives are considered in the optimization of cost function. It is suggested to derive a fractional order variant of the diffusion LMS algorithm. The applicability is tested for the estimation of channel parameters in a distributed environment consisting of randomly distributed sensors communicating through wireless medium. The topology of the network is selected such that a smaller number of nodes are informed. In the network, a random sleep strategy is followed to conserve the transmission power at the nodes. The proposed fractional order modified diffusion LMS algorithms are applied in the two configurations of combine-then-adapt and adapt-then-combine. The average squared error performance of the proposed algorithms along with its traditional counterparts are evaluated for the estimation of the Rayleigh channel parameters. A mathematical proof of convergence is provided showing that the addition of the nonlinear term resulting from fractional derivatives helps adjusts the autocorrelation matrix in such a way that the spread of its eigenvalues decreases. This increases the convergence as well as the steady state response even for the larger step sizes. Experimental results are shown for different number of nodes and fractional orders. The simulation results establish that the accuracy of the proposed scheme is far better than its classical counterparts, therefore, helps better solves the channel gains estimation problem in a distributed wireless environment. The algorithm has the potential to be applied in other applications related to learning and adaptation.

Highlights

In this study, it is proposed that the diffusion least mean square (LMS) algorithm can be improved by applying the fractional order signal processing methodologies
fractional calculus (FC) relies on new feature space in comparison with the traditional integer order derivatives such as treatment of FO chaotic systems [19,20] and exploited for the solution of different problems arising in applied physics and engineering such as modified least mean square [21], complex domain LMS and NLMS algorithms for channel equalization [22], active noise control systems [23], Improved design of digital fractional-order differentiator [24], and chemotaxis model involving fractional operators [25]
We considered different cases of the random sleep strategy; using the average squared error as the performance metric, we found that the proposed algorithm has much superior performance than its conventional counterpart

Summary

Introduction

Adaptive algorithms provide solutions including learning and inference to a class of problems arising in signal processing, instrumentations, control systems, machine learning and evolutionary. Least Mean Square (LMS) based diffusion strategies have recently been applied to model adaptive networks These especially useful when there are limited number of informed agents involved to achieve an objective in a collaborative manner [11]. FC relies on new feature space in comparison with the traditional integer order derivatives such as treatment of FO chaotic systems [19,20] and exploited for the solution of different problems arising in applied physics and engineering such as modified least mean square [21], complex domain LMS and NLMS algorithms for channel equalization [22], active noise control systems [23], Improved design of digital fractional-order differentiator [24], and chemotaxis model involving fractional operators [25].

System Model and MSE Based Adaptive Algorithms

Fractional Diffusion LMS Algorithm for Distributed Channel Gains Estimation

Convergence Analysis

Simulation Results

Conclusions