Interference Alignment: From Degrees-of-Freedom to Constant-Gap Capacity Approximations

Interference alignment is a key technique for communication scenarios with multiple interfering links. In several such scenarios, interference alignment was used to characterize the degrees-of-freedom of the channel. However, these degrees-of-freedom capacity approximations are often too weak to make accurate predictions about the behavior of channel capacity at finite signal-to-noise ratios (SNRs). The aim of this paper is to significantly strengthen these results by showing that interference alignment can be used to characterize capacity to within a constant gap. We focus on real time-invariant frequency-flat X-channels. The only known solutions achieving the degrees-of-freedom of this channel are either based on real interference alignment or on layer-selection schemes. Neither of these solutions is sufficient for a constant-gap capacity approximation. In this paper, we propose a new communication scheme and show that it achieves the capacity of the Gaussian X-channel to within a constant gap. To aid in this process, we develop a novel deterministic channel model. 1 This deterministic model depends on the 2 log SNR most-significant bits of the channel coefficients rather than only the single most-significant bit used in conventional deterministic models. The proposed deterministic model admits a wider range of achievable schemes that translate to a simple solution for the Gaussian channel. For this deterministic model, we find an approximately optimal communication scheme. We then translate the solution for the deterministic channel to the original Gaussian X-channel and show that it achieves capacity to within a constant gap.