Sparsity-aware learning in the context of echo cancelation: A set theoretic estimation approach

In this paper, the set-theoretic based adaptive filtering task is studied for the case where the input signal is nonstationary and may assume relatively small values. Such a scenario is often faced in practice, with a notable application that of echo cancellation. It turns out that very small input values can trigger undesirable behaviour of the algorithm leading to severe performance fluctuations. The source of this malfunction is geometrically investigated and a solution complying with the set-theoretic philosophy is proposed. The new algorithm is evaluated in realistic echo-cancellation scenarios and compared with state-of-the-art methods for echo cancellation such as the IPNLMS and IPAPA algorithms.