Robust secrecy rate optimisations for multiuser multiple-input-single-output channel with device-to-device communications

In the present study, the authors investigate robust secrecy rate optimisation problems for a multiple-input-single-output secrecy channel with multiple device-to-device (D2D) communications. The D2D communication nodes access this secrecy channel by sharing the same spectrum, and help to improve the secrecy communications by confusing the eavesdroppers. In return, the legitimate transmitter ensures that the D2D communication nodes achieve their required rates. In addition, it is assumed that the legitimate transmitter has imperfect channel state information of different nodes. For this secrecy network, the authors solve two robust secrecy rate optimisation problems: (a) robust power minimisation problem, subject to the probability based secrecy rate and the D2D transmission rate constraints; (b) robust secrecy rate maximisation problem with the transmit power, the probabilistic based secrecy rate and the D2D transmission rate constraints. Owing to the non-convexity of robust beamforming design based on two statistical channel uncertainty models, the authors present two conservative approximation approaches based on `Bernstein-type´ inequality and `S-Procedure´ to solve these robust optimisation problems. Simulation results are provided to validate the performance of these two conservative approximation methods, where it is shown that `Bernstein-type´ inequality based approach outperforms the `S-Procedure´ approach in terms of achievable secrecy rates.