Statistical analysis of single-beam interference alignment schemes

In this work, we derive analytical approximate expressions for the user rates achievable by interference alignment (IA) algorithms in single-beam multiple-input multiple-output (MIMO) networks for a fixed channel realization. Unlike previous works that perform a large-system analysis in which the number of users, antennas, or streams is required to tend to infinity, in this paper we only require that the number of different IA solutions (precoders and decoders) for the given scenario is sufficiently high, which typically happens even for moderate-size feasible networks. Based on the assumption that the IA beamformers for a given channel realization are random vectors isotropically distributed on the complex unit sphere, we characterize the user rates by averaging over the (possible finite) set of IA solutions. Some simulation results show the accuracy of the proposed rate expressions.