Double Full Diversity Space Time Block Code for Massive Mimo System

This paper considers a flat fading noncoherent wireless communication system with two transmitter antennas and massive number of receiver antennas, in which the channel coefficients change every four time slots. For such a system, we systematically design a family of noncoherent unitary space-time codes. Then, within this family and using a noncoherent maximum likelihood (ML) detector, we propose the design of an optimal unitary space-time code that minimizes the worst-case pairwise error probability (PEP) subject to a total transmission bits constraint. A closed-form optimal solution is attained by first characterizing the optimal structure for any fixed bits on each parameter space and then, finding an optimal bit assignment that further minimizes the worst-case PEP. Asymptotic PEP performance analysis on such an optimal code further shows that it not only enables full receiver-diversity gain when the number of the receiver antennas goes to infinity, but also enables full diversity gain when SNR goes to infinity. Therefore, we call such a code double full diversity code. One of significant advantages of the proposed optimal design is that it enables a fast ML detector.