• DOI:10.1109/TCOMM.2021.3102131
• Corpus ID: 235593299

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

@article{Bernardo2021OnMS,
  title={On Minimizing Symbol Error Rate Over Fading Channels With Low-Resolution Quantization},
  author={Neil Irwin Bernardo and Jingge Zhu and Jamie S. Evans},
  journal={IEEE Transactions on Communications},
  year={2021},
  volume={69},
  pages={7205-7221}
}

• N. I. Bernardo, Jingge Zhu, Jamie S. Evans
• Published 22 June 2021
• Computer Science
• IEEE Transactions on Communications

We analyze the symbol error probability (SEP) of <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-ary pulse amplitude modulation (<inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-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 <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-PAM receivers is obtained when Nakagami-<inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-PAM receiver reveals the existence of error floor which decays at a double exponential rate with increasing quantization bits, <inline-formula> <tex-math notation="LaTeX">$b$ </tex-math></inline-formula>. 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 <inline-formula> <tex-math notation="LaTeX">$b$ </tex-math></inline-formula>. Lastly, we demonstrate that the decay exponent of a quantized receiver can be complemented by receive antenna diversity techniques.