An uplink system with a single antenna transmitter and a single receiver with a large number of antennas is considered. For this system we propose an average energy-detection-based one-shot noncoherent communication scheme which does not use the instantaneous channel state information at either the transmitter or the receiver. We provide a constellation design that is asymptotically optimal in terms of achievable error exponent (in the number of receiver antennas) with an increasing constellation size. We also present numerical results on how this design performs in non-asymptotic regimes. Since the channel statistics may not be precisely known, we present a robust constellation design scheme which takes into account possible uncertainty in the large scale statistics and compare numerically its performance with the constellation design assuming perfect knowledge of channel and noise statistics. In terms of achievable symbol error rates, the robust constellation design is shown to perform almost as well as the scheme designed with perfectly known statistics despite mismatch in the channel statistics.