Capacity of Wireless Networks within o(log(SNR)) - the Impact of Relays, Feedback, Cooperation and Full-Duplex Operation

Recent work has characterized the sum capacity of time-varying/frequency-selective wireless interference networks and X networks within o(log(SNR)), i.e., with an accuracy approaching 100% at high SNR (signal to noise power ratio). In this paper, we seek similar capacity characterizations for wireless networks with relays, feedback, full duplex operation, and transmitter/receiver cooperation through noisy channels. First, we consider a network with S source nodes, R relay nodes and D destination nodes with random time-varying/frequency-selective channel coefficients and global channel knowledge at all nodes. We allow full-duplex operation at all nodes, as well as causal noise-free feedback of all received signals to all source and relay nodes. The sum capacity of this network is characterized as SD S+D−1 log(SNR) + o(log(SNR)). The implication of the result is that the capacity benefits of relays, causal feedback, transmitter/receiver cooperation through physical channels and full duplex operation become a negligible fraction of the network capacity at high SNR. Some exceptions to this result are also pointed out in the paper. Second, we consider a network with K full duplex nodes with an independent message from every node to every other node in the network. We find that the sum capacity of this network is bounded below by K(K−1) 2K−2 + o(log(SNR)) and bounded above by K(K−1) 2K−3 + o(log(SNR)).