Feasibility Conditions for Relay-Aided Interference Alignment in Partially Connected Networks

In this paper, we investigate the feasibility conditions for relay-aided interference alignment in a class of partially connected networks. The considered scenario consists of several single-antenna communicating node pairs and multiple single-antenna amplify-and-forward relays. Some of the direct links between the source and the destination nodes may have zero gain. A two-hop transmission scheme is applied. The relays´ scaling factors, along with the transmit and receive filters, are adapted to the channel to null the interference signals at every destination node. However, this would also null the desired useful signal at certain destinations if the number of relays is insufficient. To avoid this, the required number of relays is studied. We show that the required number of relays depends on the rank of the incidence matrix of a graph defined by the topology of the direct links.