Merging diversity and beamforming perceptions in spatial signal processing

We study the performance of optimal spatial filters in flat fading channels by means of antenna and diversity gains, by which we denote an amplification of mean signal levels and a reduction of fading-related fluctuation, respectively. For these gain variables, we introduce mathematical expressions by considering the transformation of short-term SINR probability density functions between the antenna inputs and the output of the antenna array. We evaluate the improvements for various prototypical propagation and array scenarios in the single user case, i.e., the case where all interferences are approximated as additive white Gaussian noise. It is shown analytically that under these conditions and under the assumption of perfect channel estimation, the antenna gain is always given by the number of antenna elements - regardless of wave incidence and array geometries. Moreover. the fading reduction capabilities in a given situation are found to be a matter of the orientation of multipath steering vectors in the signal space: a high diversity gain is achieved if the wave and array geometries are such that the inner products between all possible pairs of steering vectors of the desired signal are small. It is clarified how these observations are reflected in the time-variant beampattern behaviour of the array. In particular, the occurrence of grating lobes with larger spacings can be used to resolve directional multipath in order to achieve fading reduction without sacrificing antenna gain. Finally. we illustrate the impact of the two distinguishable gain contributions on typical bit error rate versus SNR plots.