Asymptotic capacity of randomly-failing relay networks with DF strategy

In this paper, we investigate the asymptotic 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 subject to independent random failures (e.g., due to fatal random physical attacks) with probability p. With a total power constraint on all the nodes, we examine the performance of the decode-and-forward (DF) strategy when N tends to infinity, assuming zero or perfect forward link channel state information (CSI) at the relays, respectively. For the noncoherent relay scheme, we study the e-outage capacity. The multiple access (MAC) cut-set upper bound and the achievable rate (i.e, the lower bound) are derived with the optimal power allocation between the source and relays. It is proved that the DF strategy is asymptotically optimal as the outage probability goes to zero. Given the random attacks, it is shown that there is less than a p-fraction achievable rate loss in the low SNR regime and a constant loss in the high SNR regime. For the coherent relay scheme, we study the ergodic capacity. It is shown that the capacity upper bound scales as O (log (SNRN)), while the DF achievable rate scales as O (log (SNRlog(N))). Finally, we discuss the optimal power allocation strategy among the relays.