Quadratic Detection in Noncoherent Massive SIMO Systems Over Correlated Channels

With the goal of enabling ultrareliable and low-latency wireless communications for industrial Internet of Things (IIoT), this paper studies the use of energy-based modulations in noncoherent massive single-input multiple-output (SIMO) systems. We consider a one-shot communication over a channel with correlated Rayleigh fading and colored Gaussian noise, in which the receiver has statistical channel state information (CSI). We first provide a theoretical analysis on the limitations of unipolar pulse-amplitude modulation (PAM) in systems of this kind, based on maximum likelihood detection. The existence of a fundamental error floor at high signal-to-noise ratio (SNR) regimes is proved for constellations with more than two energy levels, when no (statistical) CSI is available at the transmitter. In the main body of the paper, we present a design framework for quadratic detectors that generalizes the widely-used energy detector, to better exploit the statistical knowledge of the channel. This allows us to design receivers optimized according to information-theoretic criteria that exhibit lower error rates at moderate and high SNR. We subsequently derive an analytic approximation for the error probability of a general class of quadratic detectors in the large array regime. Finally, we numerically validate it and discuss the outage probability of the system.