A probe-then-refine beam tracking algorithm for millimeter wave MISO systems

This paper is concerned with beam tracking problem in millimeter wave communication systems. We use a Markov process to describe the evolution of the beam steering angle, and its temporal correlation is characterized by a transition probability matrix. A two-stage beam tracking algorithm, termed probe-then-refine (PTR), is proposed. In the probing stage, a coarse range of the beam steering angle is determined via a set of training beams with a fixed beamwidth. In the refining stage, the attained coarse range is further divided using a multi-stage hierarchical codebook-based approach. The successful tracking probability, average required number of measurements and average energy consumption of the proposed PTR algorithm are derived, respectively. By exploiting the a priori transition probabilities, the optimal probing beamwidth that can minimize the average number of measurements of the PTR algorithm is obtained. Numerical results show that our PTR algorithm significantly reduces the required number of measurements and achieves a much better tracking performance relative to the benchmark scheme.