Diffusion Based Channel Gains Estimation in WSN Using Fractional Order Strategies

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.