Cascaded RLS Adaptive Filters Based on a Kronecker Product Decomposition

Constantin Paleologu,Alexandru-George Rusu,Jacob Benesty,Silviu Ciochină

doi:10.3390/electronics11030409

Abstract

The multilinear system framework allows for the exploitation of the system identification problem from different perspectives in the context of various applications, such as nonlinear acoustic echo cancellation, multi-party audio conferencing, and video conferencing, in which the system could be modeled through parallel or cascaded filters. In this paper, we introduce different memoryless and memory structures that are described from a bilinear perspective. Following the memory structures, we develop the multilinear recursive least-squares algorithm by considering the Kronecker product decomposition concept. We have performed a set of simulations in the context of echo cancellation, aiming both long length impulse responses and the reverberation effect.

Highlights

In the field of system identification, many applications involve adaptive filtering algorithms [1,2]
We have introduced various memoryless and memory structures described by a bilinear input-output relation
We have obtained a single-input single-output (SISO) system from a multiple-input single-output (MISO) system, which is a cascade of shorter length filters

Summary

Introduction

In the field of system identification, many applications involve adaptive filtering algorithms [1,2]. Based on the input-output relation, a dynamic system should be determined (i.e., the echo path), considering various parameters and external factors that must be estimated These dynamic systems are modeled linearly through an adaptive filter with a finite-impulse-response (FIR) structure [5,6]. In our previous work [14], we introduced a new approach of splitting a long length impulse response into several impulse responses of shorter lengths, aiming to reduce the computational complexity by maintaining the overall performance. Another challenge arises when the echo path produces multiple reflections, and this effect is called reverberation.

Bilinear Structures without Memory

Bilinear Structures with Memory

Cascaded Multilinear RLS Algorithm Using Kronecker Product Decomposition

Simulation Results

Conclusions