Optimal array processing for non-stationary signals

The optimal array filtering problem consists mainly of implementing a complex linear and time invariant (TI) filter, optimizing a second order criterion at the output, under some possible constraints and assuming stationary signals. This approach is optimal for stationary signals, but becomes sub-optimal for non-stationary signals for which the optimal complex filters an time variant (TV) and, under some conditions of non-circularity, widely linear (WL). The purpose of this paper is to demonstrate these results, to touch lightly on the implementation problems of TV filters, to give a sense to the classical approach for non-stationary signals and to show, on a particular example borrowed from the radiocommunications field, the interest of WL structures with respect to linear ones in non-stationary environments