Capacity of Discrete-Time Wiener Phase Noise Channels to Within a Constant Gap

TL;DR

This paper derives bounds on the capacity of discrete-time Wiener phase noise channels, showing it can be approximated within a constant gap across different noise regimes, aiding understanding of phase noise effects on communication.

Contribution

The paper introduces novel inner and outer bounds on channel capacity, providing a unified analysis across various phase noise regimes with a constant gap of at most 6.65 bits.

Findings

Capacity bounds differ by at most 6.65 bits per channel use.

Channel behavior varies with frequency noise variance, from uniform phase noise to additive noise dominance.

Transmission strategies must adapt to phase noise regimes for optimal performance.

Abstract

The capacity of the discrete-time channel affected by both additive Gaussian noise and Wiener phase noise is studied. Novel inner and outer bounds are presented, which differ of at most $6.65$ bits per channel use for all channel parameters. The capacity of this model can be subdivided in three regimes: (i) for large values of the frequency noise variance, the channel behaves similarly to a channel with circularly uniform iid phase noise; (ii) when the frequency noise variance is small, the effects of the additive noise dominate over those of the phase noise, while (iii) for intermediate values of the frequency noise variance, the transmission rate over the phase modulation channel has to be reduced due to the presence of phase noise.