Efficient Beamforming Training for 60-GHz Millimeter-Wave Communications: A Novel Numerical Optimization Framework

In this paper, we formulate realistic beamforming (BF) training (or beam steering) in the emerging 60-GHz millimeter-wave communications as a numerical optimization problem. To maximize the receiving SNR, it aims to identify the optimal beam pair from a prescribed codebook using as little overhead as possible. Being a promising numerical method that excludes a functional derivative, the Rosenbrock numerical search may be of great significance to such applications. Nevertheless, for the encountered nonsmooth objective function, a search failure is inevitable due to the local optimum. To meet this challenge, we further present an appealing global numerical algorithm inspired by simulated annealing (SA) mechanics. In sharp contrast to classical schemes, numerical probes that lead to reward improvement are always accepted, and search moves toward worse solutions are also permitted, with a probability associated with an external temperature parameter. By relying on a newly designed two-level annealing schedule, the temperature decreases; thereby, permitting movements to worse solutions is progressively restricted. Consequently, it can basically escape from the local optimum. We then apply this new numerical search to beam switching of 60-GHz communications. Experimental simulations have demonstrated that the developed beam-switching scheme can efficiently discover the optimal beam pair by considerably reducing protocol overhead and energy consumption.