# Low-Resolution Quantization in Phase Modulated Systems: Optimum Detectors and Error Rate Analysis

arXiv: https://arxiv.org/abs/1902.10896 · HTML: https://mlsanity.com/paper/1902.10896/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2019.

## Built on by (most cited first, 2 of 2)

- [On the Capacity-Achieving Input of the Gaussian Channel with Polar Quantization](https://mlsanity.com/paper/2205.05850/) (2022)
- [Quantized Signal Recovery with Interference via Parametrized Look-Up Tables](https://mlsanity.com/paper/2507.18370/) (2025)

## Abstract (arXiv)

This paper considers a wireless communication system with low-resolution quantizers, in which transmitted signals are corrupted by fading and additive noise. For such wireless systems, a universal lower bound on the average symbol error probability (SEP), correct for all M-ary modulation schemes, is obtained when the number of quantization bits is not enough to resolve M signal points. In the special case of M-ary phase shift keying (M-PSK), the optimum maximum likelihood detector for equi-probable signal points is derived. Utilizing the structure of the derived optimum receiver, a general average SEP expression for M-PSK modulation with n-bit quantization is obtained when the wireless channel is subject to fading with a circularly-symmetric distribution. Adopting this result for Nakagami-m fading channels, easy-to-evaluate expressions for the average SEP for M-PSK modulation are further derived. It is shown that a transceiver architecture with n-bit quantization is asymptotically optimum in terms of communication reliability if n is greater than or equal to log_2(M +1). That is, the decay exponent for the average SEP is the same and equal to m with infinite-bit and n-bit quantizers for n is greater than or equal to log_2(M+1). On the other hand, it is only equal to half and 0 for n = log_2(M) and n < log_2(M), respectively. An extensive simulation study is performed to illustrate the derived results and energy efficiency gains obtained by means of low-resolution quantizers.