Closed form solution and useful signal power maximization for interference alignment in multi-pair two-way relay networks

In this paper, bidirectional pair-wise communication between 2K nodes is considered. Each node has N antennas and wants to transmit d data streams to its communication partner. A single non-regenerative half-duplex relay with R antennas supports the communication. In this scenario, the process of interference alignment can be decomposed into partial signal alignment (PSA), partial channel alignment (PCA) and zero forcing (ZF). PSA and PCA are dual problems and we focus on PSA in this paper. PSA is a bilinear problem. A closed form solution is possible only when there is a sufficient number of variables in the system. In this paper, a closed form solution is proposed and the condition for the feasibility of the closed form solution is derived in terms of K;N;R; and d. Besides this, in order to improve the performance at low and medium signal to noise ratios (SNRs), a gradient based algorithm to maximize the useful signal power is also proposed. It is shown through simulations that in some cases, it is better to serve less node pairs and utilize the additional degrees of freedom in the system to maximize the useful signal power.