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This paper proposes a Bayesian approach for angle-based hybrid beamforming and tracking that is robust to uncertain or erroneous direction-of-arrival (DOA) estimation in millimeter wave (mmWave) multiple input multiple output (MIMO) systems. Because the resolution of the phase shifters is finite and typically adjustable through a digital control, the DOA can be modeled as a discrete random variable with a prior distribution defined over a discrete set of candidate DOAs, and the variance of this distribution can be introduced to describe the level of uncertainty. The estimation problem of DOA is thereby formulated as a weighted sum of previously observed DOA values, where the weights are chosen according to a posteriori probability density function (pdf) of the DOA. To alleviate the computational complexity and cost, we present a motion trajectory-constrained a priori probability approximation method. It suggests that within a specific spatial region, a directional estimate can be close to true DOA with a high probability and sufficient to ensure trustworthiness. We show that the proposed approach has the advantage of robustness to uncertain DOA, and the beam tracking problem can be solved by incorporating the Bayesian approach with an expectation-maximization (EM) algorithm. Simulation results validate the theoretical analysis and demonstrate that the proposed solution outperforms a number of state-of-the-art benchmarks.

Bayesian Beamforming for Mobile Millimeter Wave Channel Tracking in the Presence of DOA Uncertainty