Robust Transmit Design for MISO Gaussian Broadcast Channel with Integrated Services

We consider the problem of physical layer service integration for the multiple-input single-output (MISO) Gaussian Broadcast Channel (BC). In particular, we study a scenario with two receivers and two messages: one common message intended for both receivers and one confidential message for only receiver 1 which needs to be kept perfectly secure from receiver 2. With partially known Channel state information (CSI), we aim to study the robust design of the input covariance matrices to maximize the worst-case secrecy rate region. To this end, we adopt a Quality of Service (QoS) constrained method, and we recast the original nonconvex optimization problem as a sequence of convex ones. Moreover, we study the rank of the optimal solutions. It proves that, generally, the rank of the optimal input covariance matrix associated with the confidential message is 1, while the rank of the optimal input covariance matrix associated with the common message is less than 4. Further, we prove that for the case of perfect CSI, beamforming is optimal for both common message and confidential message. Numerical results are presented to show the efficacy of the proposed method.