Towards the feasibility conditions for linear interference alignment with symbol extensions: A diversity constraint

We explore the feasibility of linear interference alignment using finite signaling dimensions and symbol extensions. In the non-zero total intersection regime, we show that the number of sources is upperbounded by a function of channel diversity. The available diversity places a fundamental constraint on the number of signal spaces that can overlap at one destination (where they are undesired) while maintaining the resolvability of a subset of those signals (desired signals) at another destination. Specifically, the number of such signal spaces cannot be larger than the channel diversity. This is the diversity constraint that we identify in this paper. Not only is the proposed method applicable for X channels, interference channels, and their rank-deficient counterparts, it can also be used for both circular symmetric signaling (CSS) and asymmetric complex signaling (ACS) over a combination of frequency and MIMO channels with arbitrary symbol extensions.