Improper Gaussian Signaling Scheme for the Z-Interference Channel

This paper studies improper Gaussian signaling in the Z-Interference-Channel (ZIC) for the case when the interference is treated as noise. The extra degree of freedom from improper signaling provides better interference management, which balances the trade-off between maximizing the direct link throughput and controlling the effect of interference, hence giving better achievable rate than the proper signaling counterpart. In this work, a closed form solution to the sum-rate maximizing real-composite transmit covariance matrix is derived for the ZIC. The structure of the real-composite covariance matrix reveals some interesting insights, such as the optimality of binary power control, the channel condition when improper signaling is strictly better than the proper signaling strategy, as well as the relationship between the choice of the real-composite transmit covariance matrix and the system parameters. The connection between the results obtained in this work and those available in the literature are also pointed out.