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

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 ρ between the signals transmitted over the underlying sub-channels. When joint decoding (JD) is performed at the receivers, setting ρ = 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 ρ approaches 1 as SNR goes to infinity. Motivated by these observations, we let ρ = 0 under JD and ρ = 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 snr, it is shown that the outage probability scales like snr-(1-r) under both TIN and CI, while it vanishes at least as fast as snr-min{2-r,4(1-r)} log 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.