A general derivation of Wave-Domain Adaptive Filtering and application to acoustic echo cancellation

Wave-domain adaptive filtering (WDAF) was introduced as an efficient spatio-temporal generalization of the popular frequency-domain adaptive filtering (FDAF). Through the incorporation of the mathematical foundations on wavefields, WDAF is suitable even for massive MIMO systems with highly cross-correlated broadband input signals. In this paper, we present a new rigorous derivation of WDAF leading to a whole class of powerful MIMO adaptation algorithms within a compact matrix framework. We show efficient approximations which provide both new efficient WDAF realizations and interesting links to well-known algorithms (including the various FDAF algorithms). Due to the rigorous approach, we obtain important practical design rules.