Linear transmitter with correlated noises

TL;DR

This paper analyzes a linear transmitter affected by correlated Gaussian noises and periodic signals, revealing how noise correlations influence signal transmission differently depending on whether the signal is additive or multiplicative.

Contribution

It provides analytical results for the effects of correlated noises on linear transmitters with additive and multiplicative signals, confirming previous findings and offering methods to compute expectations involving Gaussian processes.

Findings

Correlations weakly disrupt additive signals

Correlations strongly enhance multiplicative signals

Analytical methods align with previous approaches

Abstract

A linear transmitter with correlated Gaussian white additive and multiplicative noises and a periodic signal coupled either additively or multiplicatively is considered. The correlations have a weak destructive effect in case of the additive signal and a strong constructive effect in case of the multiplicative one. Analytical results for the linear transmitter with the additive signal agree with those obtained previously by a different approach. We also show how to analytically calculate certain expectation values involving exponentials of Gaussian processes.