Pair-Aware Interference Alignment in Multi-User Two-Way Relay Networks

In this paper, K bidirectionally communicating node pairs with each node having N antennas and one amplify and forward relay having R antennas are considered. Each node wants to transmit d data streams to its communication partner. Taking into account that each node can perform self interference cancellation, a new scheme called Pair-Aware Interference Alignment is proposed. In this scheme, the transmit precoding matrices and the relay processing matrix are chosen in such a way that at any given receiver all the interfering signals except the self interference are within the interference subspace and the useful signal is in a subspace linearly independent of the interference subspace. If the number of variables is larger than or equal to the number of constraints in the system, the system is classified as proper, else as improper. Through simulations it is shown that for a proper system (2Kd≤2N+R-d), interferences can be perfectly aligned and the useful signals can be decoded interference-free at the receivers. An iterative algorithm to achieve the interference alignment solution is proposed. Also for the proper system fulfilling a certain additional condition, which will be derived in this paper, a closed form solution is proposed.