Asymptotic Capacity of Large Fading Relay Networks under Random Attacks

In this paper, we investigate the asymptotic e-outage capacity of a half-duplex large fading relay network, which consists of one source node, one destination node, and N relay nodes. The relay nodes are assumed to be randomly deployed in a given area and under fatal independent random attacks with probability p. With a total power constraint on all the nodes, we examine the e-outage rate of the amplify-and-forward (AF) strategy when N tends to infinity, assuming no channel state information at the relays. We further quantify the gap between the e-outage rate and the e-outage cut-set bound, which is determined by the attack probability p, the source vs. sum power allocation factor ¿, and the topology of the networks. Moreover, we examine the effect of random attacks on the eoutage rate, and calculate the relative losses in low and high SNR regimes, respectively. Finally, for general SNR, we show that it is a quasiconcave problem to determine the optimal power allocation between the source and the relays, and we could obtain the optimal ¿ efficiently.