Can feedback, cooperation, relays and full duplex operation increase the degrees of freedom of wireless networks?

We consider a fully connected network with S full duplex source nodes, D full duplex destination nodes and R relay nodes, perfect feedback to source and relay nodes, and noisy cooperation between all source, relay and destination nodes. We show that this network has SD/S+D-1 degrees of freedom if the channel gains are time-varying/frequency selective. The implication of the result is that, the techniques mentioned in the title (i.e relays etc.) can affect the capacity of a network only up to a o(log(SNR)) term and therefore cannot improve the degrees of freedom of a network. Certain communication scenarios excluded by our system model where these techniques improve the degrees of freedom are also identified. Bounds on the degrees of freedom of a fully connected K node network emerge as a by-product of our study.