On the Non-Coherent Wideband Multipath Fading Relay Channel

TL;DR

This paper models the non-coherent wideband multipath fading relay channel using a hypergraph approach and demonstrates that a peaky frequency binning scheme achieves its capacity, matching upper bounds in some cases.

Contribution

It introduces a hypergraph model for the non-coherent wideband relay channel and shows that a peaky frequency binning scheme achieves the channel capacity.

Findings

The min-cut of the hypergraph model is achieved by a non-coherent peaky frequency binning scheme.

The lower bound on capacity matches the block-Markov lower bound for the FD-AWGN relay channel.

In certain cases, the achievable rate reaches the channel's capacity, matching the cut-set upper bound.

Abstract

We investigate the multipath fading relay channel in the limit of a large bandwidth, and in the non-coherent setting, where the channel state is unknown to all terminals, including the relay and the destination. We propose a hypergraph model of the wideband multipath fading relay channel, and show that its min-cut is achieved by a non-coherent peaky frequency binning scheme. The so-obtained lower bound on the capacity of the wideband multipath fading relay channel turns out to coincide with the block-Markov lower bound on the capacity of the wideband frequency-division Gaussian (FD-AWGN) relay channel. In certain cases, this achievable rate also meets the cut-set upper-bound, and thus reaches the capacity of the non-coherent wideband multipath fading relay channel.