Performance Improvement of Subband Adaptive Filtering Algorithm based on Mean-Square Analysis and Its Extension to Distributed Estimation

Abstract

This dissertation presents study on performance improvement of subband adaptive filtering (SAF) algorithm and its extension to distributed estimation over network. The mean-square deviation (MSD) is analyzed in advance to examine the behavior of the SAF algorithm, where it gives us chance to improve the performance of the algorithm in terms of the convergence rate and the steady-state estimation errors as well as to improve the accuracy of the distributed estimation.

First, in Chapter 2, we propose the SAF algorithm which improves its performance by deriving optimal step sizes based on the MSD analysis. The proposed algorithm deals with the individual step sizes for each subband update instead of a common step size for multiple subband updates. The derivation of the step sizes is based on the MSD minimization with respect to the individual step size in order to achieve the fastest convergence at the instant. Furthermore, the individual step size contain the squared norm of the input vector at each subband update, so it leads to the regularization effect that helps the proposed algorithm work well in the case of badly-excited input signals. Simulation results show that the proposed algorithm achieves faster convergence rate and smaller steady-state estimation error than the existing algorithms for highly correlated input cases.

Second, in Chapter 3, the work of Chapter 2 is extended to distributed estimation over network by introducing a novel diffusion SAF algorithm. The MSD behavior of the diffusion SAF algorithm is analyzed and the performance improvement strategies are developed in two ways; the MSD-optimal variable step size for computation at each node (adaptation step) and the MSD-based combination method for communication among neighboring nodes (combination step). For the adaptation step, the upper bound of the MSD for the intermediate estimate is derived and the step size is adapted by minimizing it in order to attain the fastest convergence rate on every iteration. Furthermore, for the combination step realized by a convex combination of the neighboring-node estimates, the proposed algorithm uses the MSD, which contains information on the reliability of the estimates, to determine combination coefficients. Simulation results show that the proposed algorithm outperforms the existing diffusion adaptive filtering algorithms in terms of the convergence rate and the steady-state errors when the network has spatial variation of node profile including input coloredness and noise statistics.