Improper Gaussian signaling scheme for the two-users X-interference channel

Different from conventional proper Gaussian signalling (PGS), whose achievable rate depends on the input signals' covariances only, the capacity of channels with improper Gaussian signalling (IGS) is a function with the signals' covariances and pseudo-covariances. Thus, the additional degree of freedom provided by pseudo-covariance is available to improve the achievable rate. In this study, the authors investigate the achievable rate region of two-users X-interference channel (IC) in the condition of applying IGS. By treating the interference as additive Gaussian noise, the authors analyze the mathematical expression of capacity based on Shannon's theorem. Specifically, for the two-users simple input, simple output (SISO)-IC, they propose two optimal signalling schemes to achieve the Pareto boundary in situations of employing PGS and IGS, respectively. In these optimal signalling schemes, the transparent geometric model which takes less computational complexity is applied to calculate the optimal transmission parameters for the Pareto boundary. Numerical simulation results show that the proposed IGS strategies can achieve larger achievable rate region and a greater sum rate. Finally, the authors give an in-depth discussion about the structure of the Pareto boundary, which is characterised by the degree of impropriety measured by the covariance and the pseudo-covariance of signals.