Asynchronous Communication over a Fading Channel and Additive Noise

TL;DR

This paper analyzes the impact of fading and noise on asynchronous frame synchronization, deriving thresholds for different channel models and showing how energy can replace frame length in synchronization criteria.

Contribution

It extends prior work by characterizing synchronization thresholds for fading channels, including Rayleigh fading and AWGN, and introduces energy-based synchronization analysis.

Findings

Synchronization threshold for ON-OFF fading channel derived.

Threshold for Rayleigh fading and AWGN channels characterized.

Trade-off between sync frame length and channel parameters established.

Abstract

In \cite{Chandar2008}, Chandar et al studied a problem of sequential frame synchronization for a frame transmitted randomly and uniformly among $A$ slots. For a discrete memory-less channel (DMC), they showed that the frame length $N$ must scale as $e^{\alpha(Q)N}>A$ for the frame detection error to go to zero asymptotically with $A$. $\alpha(Q)$ is the synchronization threshold and $Q$ is channel transition probability. We study the sequential frame synchronisation problem for a fading channel and additive noise and seek to characterise the effect of fading. For a discrete ON-OFF fading channel (with ON probability $p$) and additive noise (with channel transition probabilities $Q_n$), we characterise the synchronisation threshold of the composite channel $\alpha(Q)$ and show that $\alpha(Q)\leq p\,\alpha(Q_n)$. We then characterize the synchronization threshold for Rayleigh fading and AWGN channel as a function of channel parameters. The asynchronous framework permits a trade-off between sync frame length, $N$, and channel, $Q$, to support asynchronism. This allows us to characterize the synchronization threshold with sync frame energy instead of sync frame length.