Constrained beamforming for cyclostationary signals

The classical linearly constrained minimum variance (LCMV) beamformer corresponds, in the general case, to the linear, time invariant (TI) and spatio-temporal (ST) complex filter, the output power of which is minimized under some linear constraints. Optimal for stationary signals, this beamformer becomes sub-optimal for (quasi)-cyclostationary observations for which the optimal complex filters are (poly)-periodic (PP) and, under some conditions of widely linear non-circularity. Using these results and the fact that PP filtering is equivalent to FREquency SHifted (FRESH) filtering, the purpose of this paper is to present a first extension of the classical LCMV beamformer, taking into account the potential (quasi)-cyclostationarity and non-circularity properties of the observations. This new cyclic LCMV beamformer is shown to have an equivalent cyclic generalized sidelobe canceller (GSLC) structure. The performance computation of this new cyclic beamformer shows the interest of the latter in cyclostationary contexts and opens a reflection about the optimal constraint choice.