Capacity of a Class of Symmetric SIMO Gaussian Interference Channels within O(1)

The N + 1 user, 1 x N single input multiple output (SIMO) Gaussian interference channel where each transmitter has a single antenna and each receiver has N antennas is studied. The symmetric capacity within 0(1) is characterized for the symmetric case where all direct links have the same signal-to-noise ratio (SNR) and all undesired links have the same interference-to-noise ratio (INR). The gap to the exact capacity is a constant which is independent of SNR and INR. On the achievability side, an interesting conclusion is that the generalized degrees of freedom (GDOF) regime where treating interference as noise is found to be optimal in the 2 user interference channel, does not appear in the N + 1 user, 1 x N SIMO case. On the converse side, new multi-user outer bounds emerge out of this work that do not follow directly from the 2 user case. We also provide an outer bound on the capacity region of the 3 user SIMO Gaussian interference channel with 2 antennas at each receiver. This outer bound directly leads to the capacity region of this channel if the channel vectors satisfy certain conditions.