A data reusage algorithm based on incremental combination of LMS filters

Abstract

This work introduces a new data reuse algorithm based on the incremental combination of LMS filters. It is able to outperform the Affine Projection Algorithm (APA) in its standard form, another well-known data reuse adaptive filter. First, the so called true gradient data reuse LMS-sometimes referred to as data reuse LMS-is shown to be a limiting case of the regularized APA. Afterwards, an incremental counterpart of its recursion is inspired by distributed optimization and adaptive networks scenarios. Simulations in different scenarios show the efficiency of the proposed data reuse algorithm, that is able to match and even outperform the APA in the mean-square sense at lower computational complexity.

Combinations of adaptive filters.

“…Other solutions have been proposed, such as data reusing (DR) [22][23][24][25], mixed-norm updates [26][27][28][29], and variable step size (VSS) [30][31][32]. Combinations of AFs, however, have shown several advantages over these techniques in terms of performance and robustness [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. In some cases, it even provides a more general framework under which these adaptive algorithms can be cast (as argued in Chapter 8).…”

“…These citations are biased towards parallel combinations because they predate the incremental topology. Its introduction, however, has not changed this issue: "a set of AFs is aggregated via a supervisor, which attempts to achieve universal behavior" [41] or "aggregating a pool of AFs through mixing parameters, adaptive or not, and attempting to achieve universality" [73].…”

“…Hence, a direct approach to the study of these structures rapidly becomes intractable. However, two classes of topology have gained prominence in the literature, namely, the parallel and incremental topologies [33,35,41,73]. These categories can be distinguished in terms of the synchronicity of their components updates:…”

Hybrid convex combinations for IIR system identification.

“…Although ecient for combating the stagnation eect, the supervisor design is challenging, as the experts no longer evolve independently. However, it can be eciently explored as a technique to reduce complexity: an incremental combination of several LMS AFs was shown to outperform the Ane Projection Algorithm (APA) with less computational complexity in the FIR system identication scenario [87].…”

“…During the development of this thesis, several studies involving the incremental combination of FIR AFs and IIR AFs were conducted with very promising results (e.g., [87]). However, in the techniques developed in the next chapters, we focus on parallel structures in which at least one of the components is IIR.…”