Interference alignment in partially connected multi-user two-way relay networks

In this paper, a partially connected ad-hoc network with relays is considered. Partially connected means that not all nodes are connected to all relays, but each node may be connected to one or multiple relays. This leads to multiple partially connected subnetworks, where each subnetwork includes a single relay and all nodes connected to this relay. The most challenging part of such a partially connected network is the handling of the nodes which are connected to multiple relays. In this paper, a new closed-form solution to achieve interference alignment in partially connected networks with relays is proposed. It is shown that local channel state information (CSI) is sufficient to perform interference alignment in such a network. The properness condition for the proposed algorithm is derived using the method of counting the dimensions of signal spaces. The new algorithm to perform interference alignment is decomposed into what we call simultaneous signal alignment, simultaneous channel alignment and transceive zero forcing. The simulation results show that the degrees of freedom increase for the considered network in comparison with our reference scheme.