Invited Speech Abstract:
Widely linear adaptive filters have been recently developed in the complex domain due to their generalized framework to take into account the full second-order signal statistics, namely, the covariance matrix and the complementary covariance matrix, when processing improper data. However, their current performance evaluations still directly inherit the conventional mean square analysis from the real domain and provide limited physical insights into theseadaptive filters, since they omit the complementary second-order statistics of the estimation errors – a key feature of improper data. Therefore, in this talk, we propose a novel complementary second-order performance analysis of widely linear adaptive filters by investigating the transient and steady-state behaviors of the complementary mean square errors(CMSEs), which are used to represent the degree of improperness of estimation errors. In this way, the proposed complementarymean square analysis augments the standard mean square convergenceanalysis of widely linear adaptive filters, and they togetherequip us with an additional insight intoMSE evolutions along the real part (I channel) and imaginary part (Q channel)ofwidely linear adaptive filters, independently.This usefulness of the proposed full second-order performance analysis will be illustrated when applying adaptive filters in the compensation of I/Q imbalanced OFDM transceivers, a typical scenario where improper complex-valued signalsoccur.