Training Beam Sequence Design for Multiuser Millimeter Wave Tracking Systems

In this paper, a novel training beam sequence design for multiuser millimeter wave tracking systems is proposed. For each receiver, a single-path channel model is firstly investigated, where we introduce a maximum a posteriori (MAP) criterion to estimate the time-varying angle of departure (AoD), followed by an extended Kalman filter to update the stale complex path gain. We then employ training beam sequence design to minimize the estimated AoD's average mean squared error (AMSE), which however has no explicit expression. We firstly derive a closed-form upper bound for the AMSE and then simplify this upper bound into a tractable form, based on which a nonlinear optimization problem (NLP) is formulated. By solving this NLP optimally using its corresponding Karush-Kuhn-Tucker conditions, we obtain an efficient training beam sequence. The proposed MAP criterion and its associated training beam sequence design are further extended to multi-path scenarios, where a joint estimation of the multiple paths is firstly discussed, followed by a sequential estimation as a low-complexity alternative. Numerical results demonstrate the superiority of our proposed scheme over the existing benchmark methods, especially in the case when the receivers' channels change rapidly.