A family of diffusion normalized subband adaptive filter algorithms over distributed networks

Abstract

Summary This paper solves the problem of distributed estimation in the diffusion networks based on the family of normalized subband adaptive filters (NSAFs). The diffusion NSAF (DNSAF), the diffusion selective partial update NSAF (DSPU‐NSAF), the diffusion fix selection NSAF (DFS‐NSAF), and the diffusion dynamic selection NSAF (DDS‐NSAF) are established based on the general formalism. In DSPU‐NSAF, the weight coefficients are partially updated rather than the entire weights at each node during the adaptation. The DFS‐NSAF selects a subset of subbands and uses them to update the weights. The dynamic selection of subbands is performed in DDS‐NSAF at each node during the weigh coefficients update. In comparison with DNSAF, the DSPU‐NSAF, the DFS‐NSAF, and the DDS‐NSAF have lower computational complexity while the convergence speed of them is close to the DNSAF. Also, by combination of SPU with FS and DS approaches, the DSPU‐FS‐NSAF and the DSPU‐DS‐NSAF are established, which are computationally efficient. In the following, based on the spatial‐temporal energy conservation relation, a unified framework for mean‐square performance analysis of the family of DNSAF algorithms in stationary and nonstationary environments is presented, and the theoretical expressions for learning curve and steady‐state error are derived for entire network. The validity of the theoretical results and the good performance of introduced algorithms are demonstrated by several computer simulations.

A Class of Diffusion Proportionate Subband Adaptive Filters for Sparse System Identification over Distributed Networks

“…A detailed analysis of DNSAF algorithm (including steady-state and convergence analysis) has been reported in [43].…”

“…where b k,K denotes a column vector of the diagonal matrix I K in kth position. Substituting σ σ σ = r k or σ σ σ = m k in (43), the transient response associated with two learning curves, i.e. mean square deviation (MSD) and excess mean square error (EMSE), respectively, is estimated.…”

“…According to (43), when n approaches infinity, the final values of EMSE and MSD at each node can be calculated respectively as:…”

Two Low Computational Complexity Improved Multiband Structured Subband Adaptive Filter Algorithms

“…To improve the convergence behavior of LMS, various adaptive algorithms such as the affine projection algorithm (APA) and multiband-structured subband adaptive filter (MSAF) were proposed [5], [6], [7], [8], [9], [10]. The APA is one of the important family of adaptive filter algorithm.…”