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

TL;DR

This paper characterizes the symmetric capacity within a constant gap for the N+1 user, 1 x N SIMO Gaussian interference channel, using deterministic models and generalized degrees of freedom analysis.

Contribution

It extends deterministic interference channel models to multi-antenna scenarios and derives new outer bounds for the capacity region.

Findings

Capacity within O(1) of the true value is established.

Treating interference as noise is not optimal in the N+1 user case.

New outer bounds and strong interference regimes are identified.

Abstract

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 O(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. To get this result, we first generalize the deterministic interference channel introduced by El Gamal and Costa to model interference channels with multiple antennas. We derive the capacity region of this deterministic interference channel. Based on the insights provided by the deterministic channel, we characterize the generalized degrees of freedom (GDOF) of Gaussian case, which directly leads to the O(1) capacity approximation. 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. In addition to the GDOF region, the outer bounds identify a strong interference regime where the capacity region is established.