On Minimizing Symbol Error Rate Over Fading Channels with Low-Resolution Quantization

TL;DR

This paper derives exact symbol error probability expressions for low-resolution quantized M-PAM receivers over fading channels, optimizing quantizer design and constellation to minimize errors, and analyzes the impact of diversity techniques.

Contribution

It provides a closed-form SEP expression for quantized M-PAM over Nakagami-m fading, revealing error floor behavior and the effects of constellation and diversity optimization.

Findings

Error floor decays double exponentially with quantization bits

Optimized constellation can eliminate the error floor but reduces decay rate

Diversity techniques improve decay exponent of quantized receiver

Abstract

We analyze the symbol error probability (SEP) of $M$-ary pulse amplitude modulation ($M$-PAM) receivers equipped with optimal low-resolution quantizers. We first show that the optimum detector can be reduced to a simple decision rule. Using this simplification, an exact SEP expression for quantized $M$-PAM receivers is obtained when Nakagami-$m$ fading channel is considered. The derived expression enables the optimization of the quantizer and/or constellation under the minimum SEP criterion. Our analysis of optimal quantization for equidistant $M$-PAM receiver reveals the existence of error floor which decays at a double exponential rate with increasing quantization bits, $b$. Moreover, by also allowing the transmitter to optimize the constellation based on the statistics of the fading channel, we prove that the error floor can be eliminated but at a lower decay exponent than the unquantized case. Characterization of this decay exponent is provided in this paper. We also expose the outage performance limitations of SEP-optimal uniform quantizers. To be more precise, its decay exponent does not improve with $b$. Lastly, we demonstrate that the decay exponent of a quantized receiver can be complemented by receive antenna diversity techniques.