Constellation Design in an Energy-based Noncoherent Massive SIMO System

An uplink system with a single antenna transmitter and a single receiver with a large number of antennas is considered. We propose an average energy-detection-based single-shot noncoherent communication scheme which does not use the instantaneous channel state information, but uses only the knowledge of the channel distribution. The suggested system uses a transmitter that modulates information on the power of the symbols, and a receiver which exploits only the average energy across the antennas to decode the transmitted symbols. We present three different scenarios with the channel knowledge known to varying degrees of certainty. Specifically, we consider constellation designs for the cases when the transmitter and receiver have knowledge of (1) the channel fading distribution, (2) the first, second and fourth moments of the channel fading distribution, and (3) the moments of the channel distribution with some bounded uncertainty. We present numerical results on how these designs perform in typical scenarios, and show specific examples where each design should be employed. Our analysis shows that an optimized constellation for a specific channel distribution makes it very sensitive to uncertainties in the channel statistics. Furthermore, overestimating, rather than underestimating, the channel conditions could lead to significant performance loss.