Robust Masked Beamforming for MISO Cognitive Radio Networks With Unknown Eavesdroppers

This paper studies a cognitive radio network (CRN), in which a multiple-input single-output (MISO) secondary transmitter (SU-Tx) aims to send confidential messages to its receiver (SU-Rx) in the presence of unknown eavesdroppers, while having to control its generated interference to the primary users (PUs) under a given threshold. Because the eavesdroppers are unknown, this paper considers the artificial noise (AN) approach or masked beamforming to provide the information secrecy. The objective of this paper is to maximize the power of AN in order to degrade the eavesdroppers, subject to the signal-to-interference-plus-noise ratio (SINR) constraint at the SU-Rx, as well as the interference temperature limits (ITLs) for the PUs. In the case of perfect channel state information (CSI), we reveal that the optimal strategy for the information-bearing signal is beamforming. Imperfect CSI cases of bounded and stochastic uncertainties are investigated. In the case of ellipsoid-bounded errors, we derive the equivalent forms for the SINR and ITL constraints and then transform the optimization problem into a form of semidefinite programming (SDP). For the case of probabilistic CSI uncertainties, we propose an outage-constrained robust formulation where the CSI errors are Gaussian distributed. With the aid of two kinds of Bernstein-type inequalities, we reexpress the probabilistic constraints into deterministic forms, which results in a safe approximate solution.