Interference Alignment in Dual-Hop MIMO Interference Channel

With interference alignment in the spatial domain, the achievable degrees of freedom (DoF) of a single-hop multiple-input multiple-output (MIMO) interference channel (IC) are limited by the number of antennas at the sources and destinations. The use of relays introduces additional freedoms to manage the interference and can enhance the DoF performance. However, the characterization of the DoF regions with relays is much more complicated and is not available in the literature. In this paper, we shall investigate the DoF of the dual-hop MIMO IC via interference alignment. Based on the solvability of the alignment conditions, the upper bound for the maximum achievable DoF tuple is obtained. To evaluate the tightness of the derived bound, we further propose an iterative algorithm to determine the processing matrices at the sources, relays, and destinations for a given feasible DoF tuple. It is shown that the proposed algorithm can achieve the upper bound for the sum DoF in the low and high DoF regions, where the achievability indicates that the upper bound indeed gives the maximum sum DoF. It is also found that despite the DoF loss caused by the half-duplexity assumption, the dual-hop IC with sufficient number of relays can still outperform the conventional single-hop IC under most circumstances.