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In this paper, we present a priori-aided beam alignment scheme for time-varying millimeter wave multiple-input multiple-output (MIMO) systems, where the temporal correlations of the angle of departure (AoD) and angle of arrival (AoA) of the propagation path are exploited. Specifically, the variations of AoD and AoA between two consecutive channel realizations are described by a set of transition probabilities, respectively, which characterize the temporal correlations. We aim to maximize the average successful estimation probability (ASEP) by jointly optimizing the selected transmitting-receiving training beam pairs and their associated transmit power. When the transition probabilities are known, this problem is formulated as a mixed integer nonlinear programming (MINLP). Due to the non-convex nature of the formulated MINLP, we propose a semi-exhaustive search algorithm (SESA) to obtain a suboptimal solution. Moreover, in order to achieve maximum ASEP, we prove that the training beam pairs corresponding to the directions which have higher transition probabilities should be used more times than those with lower transition probabilities. Numerical results show that the proposed joint optimization with the SESA can achieve a higher ASEP than the existing works.
Zhang et al. (Sat,) studied this question.