Double Full Diversity Massive Unitary Space–Time Codes for MIMO Channels

In this paper, we consider a flat fading noncoherent wireless communication system with double transmitter antennas and massive multiple receiver antennas, in which the channel coherence time is divided into four orthogonal time slots, and these are used within a complete transmission cycle. For such a system, we systematically design a family of noncoherent unitary space–time codes. Then, within this family and with the 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 constraint on total transmission bits. 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. Also, asymptotic PEP performance analysis on such an optimal code further shows that it enables full receiver-diversity gain when the number of the receiver antennas goes to infinity, with the increasing rate of the coding gain in terms of signal-to-noise ratio (SNR) being the number of the transmitter antennas. In other words, it also provides full diversity gain, i.e., the product of the number of the receiver antennas and the number of the transmitter antennas, when SNR goes to infinity. Therefore, we call such a code double full diversity code. One of the significant advantages of the proposed optimal design for our considered massive multiple-input multiple-output system is that it has no error floor with SNR increasing. Another significant advantage is that it enables a fast ML detector.