Outage analysis for two-user parallel Gaussian interference channels

We address outage analysis for a two-user parallel Gaussian interference channel consisting of two sub-channels. Each sub-channel is modelled by a two-user Gaussian interference channel with quasi-static and flat fading. Both users employ single-layer Gaussian codebooks and maintain a statistical correlation ρ between the signals transmitted over the underlying sub-channels. If the receivers treat interference as noise (TIN) or cancel interference (CI), the value of ρ minimizing the outage probability approaches 1 as the signal-to-noise ratio (SNR) approaches infinity, while ρ = 0 is optimum under joint decoding (JD) regardless of the value of SNR. Motivated by these observations, we let ρ = 1 under TIN and CI and ρ = 0 under JD and compute the outage probability in finite SNR assuming 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, we show that the outage probability scales as 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.