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In this paper, we propose a codebook-based beam tracking strategy for mobile millimeter-wave (mmWave) systems, where the temporal variation of the angle of departure (AoD) is considered. A closed-form upper bound of the average tracking error probability (ATEP) is derived and further optimized. We first consider a slow-varying scenario where narrow training beams implemented by single radio-frequency (RF) chain are employed. We show that the ATEP can be reduced by optimizing the power allocation strategy over these training beams, which is formulated and transformed into a second-order cone programming. The fast-varying scenario is further considered where the use of narrow training beams becomes inefficient due to the rapid variations of AoD. In order to reduce the training time, multiple RF chains generating wide beams are employed to track the AoD's variations, and the associated beam pattern design problem is shown to be a 0 - 1 nonlinear optimization problem (NLP). A sequential quadratic programming method is used to solve this binary NLP. To reduce the complexity, a progressive edge-growth algorithm is further introduced by associating the binary NLP with a bipartite graph. Numerical results demonstrate significant gains of the proposed beam tracking strategy over existing benchmarks for both scenarios.
Zhang et al. (Thu,) studied this question.