Relay-Assisted Opposite Directional Interference Alignment: Feasibility Condition and Achievable Degrees of Freedom

This letter proposes an opposite directional interference alignment (ODIA) algorithm for the general K-user Gaussian interference channel with a half-duplex MIMO relay, where the numbers of transmit and receive antennas are arbitrary. By exploiting the additional space dimensions introduced by the MIMO relay, the algorithm requires only global channel state information (CSI) available at the relay to align the interference from the relay link along the opposite direction of the interference from the direct link. The ODIA feasibility involves the solvability of a linear system. We then derive a sufficient and necessary feasibility condition by using the properties of Kruskal-rank of Khatri-Rao product, and give a closed-form solution. Furthermore, the exact expression of the sum degrees of freedom (DoF) achieved through ODIA is provided and is also verified by simulation results.