# Phase Modulated Communication with Low-Resolution ADCs

## TL;DR

This paper analyzes the performance limits of low-resolution quantized wireless communication systems, deriving bounds and optimal detectors for M-ary modulation under fading, and shows that adding more quantization bits improves reliability.

## Contribution

It provides a universal lower bound on symbol error probability for low-resolution ADCs and derives the optimal detector for M-PSK in fading channels, with extensive simulation validation.

## Key findings

- n-bit quantization with n ≥ log2(M+1) achieves asymptotic optimality
- Error decay rate depends on the number of quantization bits and fading severity
- Adding an extra bit significantly improves reliability in severe fading environments

## Abstract

This paper considers a low-resolution wireless communication system in which transmitted signals are corrupted by fading and additive noise. First, 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. Second, in the special case of M-ary phase shift keying (M-PSK), the optimum maximum likelihood detector for equiprobable signal points is derived. Third, utilizing the structure of the derived optimum receiver, a general average SEP expression for the M-PSK modulation with n-bit quantization is obtained when the wireless channel is subject to fading with a circularly-symmetric distribution. Finally, an extensive simulation study of the derived analytical results is presented for general Nakagami-m fading channels. It is observed 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 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. Hence, for fading environments with a large value of m, using an extra quantization bit improves communication reliability significantly.