Adaptive hybrid beamforming based on a convex combination of complex stochastic gradient filters

An adaptive hybrid beamforming (HB) based on the convex combination of two independent transversal adaptive filters is proposed and analyzed in this paper. It involves the use of the recursive least mean square (RLS) and the dual univariate filtering approach (DUAF). The main concept behind the hybrid beamforming stablishes that the adaptive structure is still able to generate a good radiation pattern, even though one of the filters fails. In order to prove this characteristic, two approaches have been analyzed in this paper: 1) both sub-filters have similar performance and 2) one of the filters has a bad steady-state error. In addition, general equations are derived for this beamforming in order to complete the analysis of the structure. Computer simulations have been performed to show the applicability and limitations that this structure has in its capacity of recovering the desired signal and generating the radiation pattern according to the desired direction-of-arrival (DOA) and nulls.