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 omni-directional (non-sectorized) cells and consider the practical scenario where users have $2$ antennas, and base-stations have $2$, $3$ or $4$ antennas. In particular, we provide linear one-shot IA schemes for the $2\times 2$, $2\times3$ and $2\times 4$ 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 challenging optimization problem into a tractable linear program (LP) with significantly fewer variables. This approach is used to show that the achievable $3/4$ DoFs per user are indeed optimal for a large (extended) cellular network with $2\times 2$ links.