Cellular Interference Alignment: Omni-Directional Antennas and Asymmetric Configurations

Although interference alignment (IA) can theoretically achieve the optimal degrees of freedom (DoFs) in the K-user Gaussian interference channel, its direct application comes at the prohibitive cost of precoding over exponentially many signaling dimensions. On the other hand, it is known that practical one-shot IA precoding (i.e., linear schemes without symbol expansion) provides a vanishing DoFs gain in large fully connected networks with generic channel coefficients. In our previous work, we introduced the concept of cellular IA for a network topology induced by hexagonal cells with sectors and nearest-neighbor interference. Assuming that neighboring sectors can exchange decoded messages (and not received signal samples) in the uplink, we showed that linear one-shot IA precoding over M transmit/ receive antennas can achieve the optimal M/2 DoFs per user. In this paper, we extend this framework to networks with omnidirectional (non-sectorized) cells and consider a limited practical scenario where users have 2 antennas, and base-stations have 2, 3, or 4 antennas. We provide linear one-shot IA schemes for the 2 × 2, 2 × 3, and 2 × 4 cases, and show the achievability of 3/4, 1, and 7/6 DoFs per user, respectively. DoFs converses for one-shot schemes require the solution of a discrete optimization problem over a number of variables that grows with the network size. We develop a new approach to transform such optimization problem into a tractable linear program with significantly fewer variables. This approach is used to show that 3/4 DoFs per user are indeed optimal for one-shot schemes over large (extended) cellular network with 2 × 2 links.