We propose a thoroughly optimal signal design strategy to achieve the Pareto boundary （boundary of the achievable rate region） with improper Gaussian signaling （IGS） on the Z-interference channel （Z-IC） under th...We propose a thoroughly optimal signal design strategy to achieve the Pareto boundary （boundary of the achievable rate region） with improper Gaussian signaling （IGS） on the Z-interference channel （Z-IC） under the assumption that the interference is treated as additive Gaussian noise. Specifically, we show that the Pareto boundary has two different schemes determined by the two paths manifesting the characteristic of improperly transmitted signals. In each scheme, we derive several concise closed-form expressions to calculate each user＇s optimally transmitted power, covariance, and pseudo-covariance of improperly transmitted signals. The effectiveness of the proposed optimal signal design strategy is supported by simulations, and the results clearly show the superiority of IGS. The proposed optimal signal design strategy also provides a simple way to achieve the required rate region, with which we also derive a closed-form solution to quickly find the circularity coefficient that maximizes the sum rate. Finally, we provide an in-depth discussion of the structure of the Pareto boundary, characterized by the channel coefficient, the degree of impropriety measured by the covariance, and the pseudo-covaxiance of signals transmitted by two users.展开更多
基金Project supported by the National Natural Science Foundation of China （Nos. 61601477 and 61601482）
文摘We propose a thoroughly optimal signal design strategy to achieve the Pareto boundary （boundary of the achievable rate region） with improper Gaussian signaling （IGS） on the Z-interference channel （Z-IC） under the assumption that the interference is treated as additive Gaussian noise. Specifically, we show that the Pareto boundary has two different schemes determined by the two paths manifesting the characteristic of improperly transmitted signals. In each scheme, we derive several concise closed-form expressions to calculate each user＇s optimally transmitted power, covariance, and pseudo-covariance of improperly transmitted signals. The effectiveness of the proposed optimal signal design strategy is supported by simulations, and the results clearly show the superiority of IGS. The proposed optimal signal design strategy also provides a simple way to achieve the required rate region, with which we also derive a closed-form solution to quickly find the circularity coefficient that maximizes the sum rate. Finally, we provide an in-depth discussion of the structure of the Pareto boundary, characterized by the channel coefficient, the degree of impropriety measured by the covariance, and the pseudo-covaxiance of signals transmitted by two users.
