Constellation Design for Noncoherent Massive SIMO Systems in URLLC Applications

In this paper, we concern the uplink of a massive single-input multiple-output enabled ultra-reliable low-latency communication system, in which a single-antenna transmitter aims to timely and reliably send data to a receiver equipped with a large number of antennas over Rayleigh fading channels. For such a scenario, to eliminate the considerable overhead caused by channel estimation, we adopt a noncoherent maximum-likelihood (ML) receiver, which is known to be optimal in terms of average symbol-error rate for equiprobable discrete input signals. We propose a two-dimensional noncoherent constellation design framework to enhance the reliability of the considered system. Specifically, our design principle is to maximize the minimum Kullback-Leibler divergence between the conditional distributions induced by different transmitted signals under average power constraint for any given transmission rate. The resulting optimization problem is shown to be a challenging mixed discrete-continuous problem. We manage to solve the problem by deliberately designing optimal bit allocation and optimal constellation structure as a function of signal-to-noise ratios. We then unveil that the proposed constellation can facilitate efficient ML detection with low computational complexity. Finally, simulation results illustrate that the proposed scheme has a superior error performance than conventional training-based schemes and existing energy detection designs.