Optimal time invariant and widely linear spatial filtering for radiocommunications

The classical optimal array filtering problem assumes stationary signals and consists to implement a complex linear and Time Invariant (TI) filter, optimizing a second order criterion at the output under some possible constraints. Optimal for stationary signals this approach is sub-optimal for non stationary signals for which the optimal complex filters are Time Variant (TV) and, under some conditions of non circularity, Widely Linear (WL). The purpose of this paper is to present the interest of WL structures of spatial filtering with respect to linear ones in non stationary radiocommunications environments.