SEP Analysis of Quantized SIMO Systems with M-PSK over Correlated Fading Channels

TL;DR

This paper derives analytical expressions for the symbol error probability of a quantized SIMO system with M-PSK over correlated fading channels, highlighting the effects of correlation and quantization on performance.

Contribution

It extends previous SEP analysis to correlated channels using an asymptotic MRC approach, providing explicit high-SNR formulas that include correlation, quantization, and modulation effects.

Findings

Channel correlation mainly reduces coding gain, causing an SNR penalty.

Diversity gain remains unaffected when the channel covariance is full-rank.

Analytical results closely match Monte Carlo simulations across SNRs.

Abstract

The average symbol error probability (SEP) of a phase-quantized single-input multiple-output system with M-ary phase-shift keying modulation and maximum ratio combining (MRC) is analyzed under correlated Rayleigh fading and additive white Gaussian noise. Building on our prior framework for the independent and identically distributed case, we extend the analysis to spatially correlated channels by introducing an asymptotically equivalent MRC combiner that enables tractable SEP characterization. Using this approach, we derive closed-form expressions at high signal-to-noise ratio (SNR) that explicitly characterize the diversity and coding gains as functions of the receive correlation structure, phase-quantization resolution, and modulation order, up to a scaling factor bounded between 1 and 2. The results show that channel correlation primarily degrades the coding gain, leading to an SNR penalty, while the diversity gain is preserved when the channel covariance matrix is full-rank. The analytical findings are validated through Monte Carlo simulations, demonstrating a tight match across a wide SNR range.