Cascaded RLS Adaptive Filters Based on a Kronecker Product Decomposition

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.