Degrees of Freedom of Wireless Networks With Relays, Feedback, Cooperation, and Full Duplex Operation

We find the degrees of freedom of 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. An outer bound to the capacity region of this network is obtained. Combining the outer bound with previous interference alignment based achievability results, we conclude that the techniques of relays, feedback, full-duplex operation and noisy cooperation do not increase the degrees of freedom of interference and X networks. As a second contribution, we show that for a network with K full-duplex nodes and K(K-1) independent messages with one message from every node to each of the other K-1 nodes, the total degrees of freedom are bounded above and below by [( K(K-1))/( (2K-2))] and [( K(K-1))/( (2K-3))], respectively.