Improper Gaussian signaling for the K-user SISO interference channel

This paper studies the transmit optimization for the K-user Gaussian single-input single-output interference channel (SISO-IC), with the interference treated as Gaussian noise and by applying improper or circularly asymmetric complex Gaussian signaling. The transmit optimization with improper Gaussian signaling involves not only the signal covariance as in the conventional proper or circularly symmetric complex Gaussian signaling, but also the signal pseudo-covariance, which is conventionally set to zero in proper Gaussian signaling. By utilizing the rate-profile method, the achievable rate region of the K-user SISO-IC is characterized by solving a sequence of minimum-weighted-rate maximization (MinWR-Max) problems, which are non-convex and thus difficult to be solved globally optimally. By applying the semidefinite relaxation (SDR) technique, we propose an efficient approximate solution, which jointly optimizes the covariance and pseudo-covariance of the transmitted signals. Simulation results demonstrate the effectiveness of the proposed algorithm for the K-user SISO-IC with improper Gaussian signaling.