Asymptotic Capacity of Large Fading Relay Networks with Random Node Failures

TL;DR

This paper analyzes the asymptotic capacity of large fading relay networks under random node failures, comparing amplify-and-forward and decode-and-forward strategies, and finds the conditions under which each strategy is optimal.

Contribution

It derives outage capacity bounds for large relay networks with random failures and shows the asymptotic optimality of the decode-and-forward strategy as outage probability approaches zero.

Findings

DF strategy is asymptotically optimal as outage probability approaches zero.

AF strategy is less suboptimal than DF at high SNR.

DF strategy is more robust at low SNR.

Abstract

To understand the network response to large-scale physical attacks, we investigate the asymptotic capacity of a half-duplex fading relay network with random node failures when the number of relays $N$ is infinitely large. In this paper, a simplified independent attack model is assumed where each relay node fails with a certain probability. The noncoherent relaying scheme is considered, which corresponds to the case of zero forward-link channel state information (CSI) at the relays. Accordingly, the whole relay network can be shown equivalent to a Rayleigh fading channel, where we derive the $\epsilon$-outage capacity upper bound according to the multiple access (MAC) cut-set, and the $\epsilon$-outage achievable rates for both the amplify-and-forward (AF) and decode-and-forward (DF) strategies. Furthermore, we show that the DF strategy is asymptotically optimal as the outage probability $\epsilon$ goes to zero, with the AF strategy strictly suboptimal over all signal to noise ratio (SNR) regimes. Regarding the rate loss due to random attacks, the AF strategy suffers a less portion of rate loss than the DF strategy in the high SNR regime, while the DF strategy demonstrates more robust performance in the low SNR regime.