On the feasibility of beamforming in millimeter wave communication systems with multiple antenna arrays

The use of the millimeter (mm) wave spectrum for next generation (5G) mobile communication has gained significant attention recently. The small carrier wavelengths at mmwave frequencies enable synthesis of compact antenna arrays, providing beamforming gains that compensate the increased propagation losses. In this work, we investigate the feasibility of employing multiple antenna arrays to obtain diversity/multiplexing gains in mmwave systems, where each of the arrays is capable of beamforming independently. Considering a codebook based beamforming system (e.g., to facilitate limited feedback), we observe that the complexity of \emph{jointly} optimizing the beamforming directions across the multiple arrays is highly prohibitive, even for very reasonable system parameters. To overcome this bottleneck, we develop reduced complexity algorithms for optimizing the choice of beamforming directions, premised on the sparse multipath structure of the mmwave channel. Specifically, we reduce the cardinality of the joint beamforming search space, by restricting attention to a small set of dominant candidate directions. To obtain the set of dominant directions, we develop two complementary approaches: (a) based on computation of a novel spatial power metric; a detailed analysis of this metric shows that, in the limit of large antenna arrays, the selected candidate directions approach the channel's dominant angles of arrival and departure, and (b) precise estimation of the channel's (long-term) dominant angles of arrival, exploiting the correlations of the signals received across the different receiver subarrays. Our methods enable a drastic reduction of the optimization search space (a factor of 100 reduction), while delivering close to optimal performance, thereby indicating the potential feasibility of achieving diversity and multiplexing gains in mmwave systems.