We consider the problem of active sensing and sequential beam tracking at mmWave frequencies and above. We focus on the setting of aerial communications between a quasi-stationary receiver and mobile transmitter, for example, a gateway array tracking a small agile drone, where we formulate the problem to be equivalent to actively sensing and tracking an optimal beamforming vector along the single dominant (often line-of-sight) path. In this setting, an ideal beam points in the direction of the angle of arrival (AoA) with sufficiently high resolution to ensure high beamforming gain. However, narrow beams are inherently sensitive to stochastic mobility. Without active sensing, narrow beam alignment can only be maintained in the case of highly predictive mobility with low prediction error. We pose the problem of active beam tracking and communication as a partially observed Markov decision problem (POMDP) with an expected average cost constraint. We establish the existence of a solution to the dynamic programming equation under reasonable technical assumptions. Drawing on the insight obtained from this solution, we propose an active joint sensing and communication algorithm for tracking the AoA through evolving a Bayesian posterior probability belief which is utilized for a sequential beamforming selection. Our algorithm relies on an integrated strategy of adaptive allocation of pilot versus data symbols as well as an active selection of beamforming vectors that trades off mutual information between the AoA and measurements (sensing) against spectral efficiency (communication). Through extensive numerical simulations, we analyze the performance of our proposed algorithm under various stochastic mobility models and demonstrate significant improvements over existing strategies. We also consider the impact of model mismatch on the performance of our algorithm which shows a good degree of robustness to model mismatch.
