Training Beam Sequence Optimization for Millimeter Wave MIMO Tracking Systems

In this paper, we consider the design of training beam sequence for sparse millimeter wave (mmWave) multiple-input multiple-output (MIMO) tracking systems. We use Markov random walks to model the temporal variations of the beam steering angle of arrival (AoA) and angle of departure (AoD), respectively. By exploiting the MIMO virtual channel representation, the AoA/AoD tracking problem is equivalent to choosing a set of directional training beams to find the nonzero elements in a two-dimensional virtual channel matrix. Furthermore, in contrast to existing work that used each transmitting-receiving beam pair once only, we consider a more general case such that each beam pair might be adopted more than once in the tracking procedure. As the number of repetitions of each transmitting-receiving beam pair can only be integer, the training beam sequence design problem is then formulated as an integer nonlinear programming (INLP) problem. To resolve the formulated INLP problem, we derive a tractable lower bound of the successful tracking probability and then decompose it into a set of convex INLP subproblems, which are solved by implementing an iterative branch-and-bound (BB) method. Numerical results show that our proposed iterative BB algorithm significantly outperforms the benchmark schemes and achieves near-optimal tracking performance.