Quadratic Detection in Noncoherent Massive SIMO Systems over Correlated Channels

TL;DR

This work addresses noncoherent, one-shot wireless links in a massive SIMO setting with correlated Rayleigh fading and statistical CSI at the receiver. It extends energy-detection by introducing a family of quadratic detectors that exploit channel second-order statistics, including the BQUE and QMMSE estimators, and derives an analytic, Gaussian-based approximation for error probability. A unified framework shows ED, HSNR, and BQUE as special cases, with ABQUE offering near-ML performance with reduced complexity; extensive simulations confirm advantages in outage and SER, particularly under channel hardening. The findings have practical impact for ultra-reliable, low-latency IIoT scenarios, enabling efficient noncoherent detection with massive antenna arrays and correlated channels. Future directions include constellation optimization for quadratic detectors, coding across multiple channel uses, and extending the framework to OFDM and index-modulation schemes.

Abstract

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.

Figures (6)

• Figure 1: Monte Carlo results of the ser for the ml detector in terms of snr. Various numbers of antennas have been considered under a correlated Rayleigh channel with $\rho=0.8$ with a uniform unipolar 4-ask modulation (see Section \ref{['sec:numerical_results']} for a detailed channel model description).
• Figure 2: Scatter plot to assess the relevance of the channel norm as an indicator of ser performance. The bque error probability for $10^4$ different channels at $\mathrm{SNR} = 10dB$ is depicted.
• Figure 3: Outage probability for a ser threshold at $\mathrm{SNR} = 10dB$ for $N=64$ (solid lines), $N=128$ (dashed lined) and $N=256$ (dotted lines).
• Figure 4: ser of the presented detectors in terms of snr for $N=512$.
• Figure 5: Floor level (i.e. ser at $\mathrm{SNR}=30dB$) of the presented detectors in terms of $N$.

Theorems & Definitions (2)

• Theorem 1
• Theorem 2