On Optimal Beam Steering Directions In Millimeter Wave Systems

In order to increase system capacity and transmission rates, fifth generation (5G) cellular and 802.11ad/ay wireless systems will use millimeter wave frequencies (24GHz-70GHz), which require large antenna arrays and narrow beamforming to mitigate the impact of substantial path-loss. While narrow beamforming maximizes array gain it also entails a significant increase in the number of beams needed to maintain the desired cell coverage. Consequently, there is a considerable increase in the complexity of beam management for initial user access and then tracking. This paper proposes a novel beam steering algorithm to maximize coverage given a prescribed size for the codebook of beam directions. The proposed approach leverages the observation that the problem of finding the optimal set of beam pointing angles can be mapped to the classical quantizer design problem in source coding, albeit with a somewhat unusual distortion measure. A variant of the Generalized Lloyd Algorithm is derived and employed to find the optimal codebook of beam placement angular directions. Numerical results show up to 2 dB gains in average power array factor, in comparison with the conventional uniformly spaced beam steering approach. These performance gains can be traded for codebook size reduction and a corresponding reduction in beam management complexity.