A closed-form solution to implement interference alignment and cancellation for a gaussian interference multiple access channel

For interference alignment (IA) with no channel extension, determining the existence of IA solution for general system parameters is still an open problem. This same problem also exists in interference alignment and cancellation (IAC), which combines IA with interference cancellation in the receivers, involving a new receiver architecture associated with signaling over backhaul links among them. As IAC is expected to achieve more degrees of freedom (DoF) than IA, the existence of IAC solution would be another interesting, yet challenging issue to investigate. In this paper, we have proposed a specific alignment scheme, which allows for the derivation of closed-form IAC solution. Furthermore, we establish and prove the general necessary and sufficient condition to determine the existence of closed-form IAC solution for a Gaussian interference multiple access channel (MAC) with K receivers and J users, each with M antennas.