MISO interference channel with improper Gaussian signaling

This paper studies the achievable rate region of the K-user Gaussian multiple-input single-output interference channel (MISO-IC) with interference treated as noise, when improper or circularly asymmetric complex Gaussian signaling is applied. By exploiting the separable rate expression with improper Gaussian signaling, we propose a separate covariance and pseudo-covariance optimization algorithm, which is guaranteed to improve the users' rates over the conventional proper or circularly symmetric complex Gaussian signaling. In particular, for the pseudo-covariance optimization, the semidefinite relaxation (SDR) technique is applied to provide a high-quality approximate solution. For the special case of two-user MISO-IC, the SDR technique yields the optimal pseudo-covariance solution.