In this paper, we design the precoding matrices at the base station side andthe combining matrices at the user terminal side for initial downlinksynchronization in millimeter wave massive multiple-input multiple-outputsystems. First, we demonstrate two basic requirements for the precoding andcombining matrices, including that all the entries therein should have constantamplitude under the implementation architecture constraint, and the averagetransmission power over the total K time slots taking for synchronizationshould be constant for any spatial direction. Then, we derive the optimalsynchronization detector based on generalized likelihood ratio test. Byutilizing this detector, we analyze the effect of the precoding and combiningmatrices to the missed detection probability and the false alarm probability,respectively, and present the corresponding conditions that should besatisfied. It is shown that, both of the precoding and combining matricesshould guarantee the perfect omnidirectional coverage at each time slot, i.e.,the average transmission power at each time slot is constant for any spatialdirection, which is more strict than the second basic requirement mentionedabove. We also show that such omnidirectional precoding matrices andomnidirectional combining matrices exist only when both of the number oftransmit streams and the number of receive streams are equal to or greater thantwo. In this case, we propose to utilize Golay complementary pairs andGolay-Hadamard matrices to design the precoding and combining matrices.Simulation results verify the effectiveness of the propose approach.
展开▼
