Phase Modulation for Discrete-time Wiener Phase Noise Channels with Oversampling at High SNR

TL;DR

This paper investigates a discrete-time Wiener phase noise channel with oversampling at high SNR, demonstrating that increasing samples per symbol enhances capacity pre-log, with phase modulation achieving a significant portion of the theoretical maximum.

Contribution

It introduces a new channel model with oversampling, derives a lower bound on capacity, and shows how oversampling improves the capacity pre-log compared to single-sample scenarios.

Findings

Capacity pre-log is at least 3/4 with oversampling growing with sqrt(SNR)

Amplitude modulation achieves a pre-log of 1/2

Phase modulation achieves a pre-log of at least 1/4

Abstract

A discrete-time Wiener phase noise channel model is introduced in which multiple samples are available at the output for every input symbol. A lower bound on the capacity is developed. At high signal-to-noise ratio (SNR), if the number of samples per symbol grows with the square root of the SNR, the capacity pre-log is at least 3/4. This is strictly greater than the capacity pre-log of the Wiener phase noise channel with only one sample per symbol, which is 1/2. It is shown that amplitude modulation achieves a pre-log of 1/2 while phase modulation achieves a pre-log of at least 1/4.