Design of Optimal Noncoherent Constellations for SIMO Systems

In this paper, we consider a single-input multiple-output (SIMO) system, in which a single-antenna transmitter communicates with a receiver having multiple antennas. It is assumed that the channel coefficients keep constant during two consecutive time slots, after which they become new independent values. For such a system, we focus on the concept of uniquely factorable constellations (UFCs) in the design of noncoherent coding schemes under two communication scenarios. The first scenario is the massive SIMO system, in which only the first and second order channel statistical information is available. The second is the traditional Rayleigh fading SIMO system. First, parameterized massive UFC (MUFC) and unitary UFC (UUFC) are designed for each scenario. It is proved that these designs ensure the unique identification of the transmitted signals when there is no additive Gaussian white noise. Second, using the Riemannian distance (RD) metric for the RD-based detector and coding gain criterion for generalized likelihood ratio test receiver, the optimal MUFCs and UUFCs of various sizes are constructed, respectively. Finally, we exploit the structures of our proposed designs to reduce the decoding complexities compared to the exhaustive search methods. Comprehensive computer simulations show that our proposed schemes outperform the current designs in literature.