SEP Analysis of Quantized SIMO Systems with M-PSK over Correlated Fading Channels
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 independent and identically distributed Rayleigh fading, we extend the analysis to the spatially correlated case 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.