Signaling Over Two-User Parallel Gaussian Interference Channels: Outage Analysis

Abstract

This paper presents an outage analysis for a two-user parallel Gaussian interference channel consisting of two sub-channels. Each sub-channel is modeled as a two-user Gaussian interference channel with quasi-static and flat fading. Both users employ single-layer Gaussian code-books and maintain a statistical correlation $\rho $ between the signals transmitted over the underlying sub-channels. When joint decoding (JD) is performed at the receivers, setting $\rho =0$ minimizes the outage probability, regardless of the value of the signal-to-noise ratio (SNR). It is shown, however, that if the receivers treat interference as noise (TIN) or cancel interference (CI), the value of optimum $\rho $ approaches 1 as SNR goes to infinity. Motivated by these observations, we let $\rho =0$ under JD and $\rho =1$ under TIN and CI and compute the outage probability in finite SNR, assuming that the direct and crossover channel coefficients are independent zero-mean complex Gaussian random variables with possibly different variances. In the asymptote of large SNR and assuming the transmission rate per user is $r\log \mathrm {snr}$ , it is shown that the outage probability scales like $\mathrm {snr}^{-(1-r)}$ under both TIN and CI, while it vanishes at least as fast as $\mathrm {snr}^{-\min \{2-r,4(1-r)\}}\log \mathrm {snr}$ under JD. This paper is concluded by extending some of the results to a two-user parallel Gaussian interference channel with an arbitrary number of sub-channels.