On Capacity of Non-Coherent Diamond Networks.

There is a vast body of work on the capacity bounds for a "coherent" wirelessnetwork, where the network channel gains are known, at least at thedestination. However, there has been much less attention to the case where thenetwork parameters (channel gains) are unknown to everyone, i.e., thenon-coherent wireless network capacity. In this paper, we study the generalizeddegrees of freedom (gDoF) of the block-fading non-coherent diamond (parallelrelay) network with asymmetric distributions of link strengths, and a coherencetime of T symbol duration. We first derive an outer bound for this channel andthen derive the optimal signaling structure for this outer bound. Using theoptimal signaling structure we solve the outer bound optimization problem forgDoF. Using insights from our outer bound signaling solution, we devise anachievability strategy based on a novel scheme that we call train-scalequantize-map-forward. This uses training in the links from source to relays,scaling and quantizing at relays combined with non-training based schemes. Weshow the optimality of this scheme with respect to the outer bound in terms ofgDof. In non-coherent point-to-point MIMO, where the fading channel is unknownto transmitter and receiver, an important trade-off between communication andchannel learning was revealed by Zheng and Tse, by demonstrating that not allantennas available might be used as it is sub-optimal to learn all theirchannel parameters. Our results in this paper for the diamond networkdemonstrates that in certain regimes the optimal scheme uses a sub-network,demonstrating a similar trade-off between channel learning and communications.However, in other regimes it is useful to use the entire network and not usetraining at all in the signaling, as traditional training based schemes aresub-optimal in these regimes.