Potential of improper-complex signaling in communications over two-user interference channel

In this paper, we show a potential of improper-complex signaling in multi-user proper-complex Gaussian noise channel. It is well known that improper-signaling does not increase the capacity of a single-user and some multi-user proper-complex Gaussian noise channels. As a baseline system, we apply the conventional iterative water filling (IWF) algorithm to two-user interference channel, where each user transmits proper-complex signal in order to maximize its own information rate. To demonstrate the potential of improper-complex signaling, we consider a special two-user interference channel, where each transmitter has single transmit antenna, each receiver also has single receive antenna, equal-gain direct links and general asymmetric-gain cross links. By using exhaustive search, we find the capacity region of this communication system and compares it with that obtained by the conventional IWF. It turns out that, depending on the magnitudes of the cross channel gains, the improper-complex signaling outperforms the selfish IWF algorithm that generates proper-complex signals. This warrants further research on the application of the improper-complex signaling to various channel models with constraints on the level of user cooperation.