Fast Beam Tracking for Millimeter-Wave Systems under High Mobility

In this paper, we propose a fast beam tracking strategy for mobile millimeter-wave systems, where the temporal variations of the angle of departure (AoD) are considered and modeled as a discrete Markov process. In contrast to most existing works that rely on the slow-fading assumption, we consider a more practical scenario in which the AoD can vary rapidly due to blockage and other environmental obstructions. In this case, the use of narrow training beams becomes inefficient, and therefore we propose to employ multiple radio-frequency chains generating wide beams to reduce the training time. By optimizing the selected training beams, we aim to minimize the average tracking error probability (ATEP). However, since the exact expression for ATEP is difficult to obtain, we derive its upper bound in a closed form, and aim to minimize this upper bound instead. The associated training beam sequence design problem is transformed into the construction of a bipartite graph that does not contain cycles of length 4, which is implemented with the progressive edge-growth algorithm. Numerical results demonstrate significant gains of the proposed beam tracking strategy over the existing benchmark methods.