Achievable Degrees of Freedom for Closed-form Solution to Interference Alignment and Cancellation in Gaussian Interference Multiple Access Channel

A combined technique of interference alignment (IA) and interference cancellation (IC), known as interference alignment and cancellation (IAC) scheme, has been proposed to improve the total achievable degrees of freedom (DoFs) over IA. Since it is NP-hard to solve the transceiver under a given tuple of DoFs or to maximize the total achievable DoFs in the general system configuration by IA (or IAC), the optimal transceiver cannot be obtained in polynomial time. Meanwhile, it has been known that a closed-form yet suboptimal transceiver can be designed for IAC by employing a symbol-to-symbol (STS) alignment structure. As its performance has not been known yet, we aim to derive the total DoFs that can be achieved by such suboptimal but closed-form IAC transceivers for Gaussian interference multiple access channels with K receivers and J users (transmitters), each with M antennas. Our analysis shows that the closed-form IAC transceivers under consideration can achieve a maximum total achievable DoFs of 2M, which turns out to be larger than those achieved in classical IA, e.g., 2MK/(K+1) DoFs by a specific configuration where each link has the same target DoFs. Moreover, considering the NP-hardness of deriving the maximum total achievable DoFs with the optimal IAC transceiver, its upper bound has been derived for comparison with the results of our closed-form IAC transceiver. Numerical results illustrate that its performance can be guaranteed within 20% of the upper bound when the number of multiple access channels are relatively small, e.g., K <=4.