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Feasibility conditions of interference alignment with general alignment set

Interference alignment (IA) has received great recent attention for its breakthrough performance. Classical IA algorithms require infinite dimensional symbol extension. On the other hand, IA algorithms which draw on the finite signal dimension provided by multiple antennas, become infeasible when the network scales. To construct practical IA algorithms that are applicable to large-scale MIMO interference networks, it is essential to introduce flexible IA algorithms which selectively cancels the strongest interference perceived by the receivers (Rxs). In this work, we aim at understanding the feasibility conditions of such IA algorithms, which cancel interference selectively according to the alignment set. By exploiting methodologies from algebraic geometry and graph theory, we characterize the feasibility regions of IA schemes with general alignment set and obtain insights into how network configurations and alignment set affects the feasibility of IA schemes.