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Based on directional modulation (DM), robust beamforming matrix design for sum secrecy rate maximization is investigated in this article in multiuser systems. First, in case of random estimation error of direction angles toward eavesdroppers, a Von Mises distribution-sum secrecy rate maximization (VMD-SSRM) method is proposed to maximize the sum secrecy rate. Semidefinite relaxation and first-order approximation based on Taylor expansion are employed to solve the optimization problem in VMD-SSRM. Then in order to optimize the sum secrecy rate in the case of the worst estimation errors of direction angles, a maximum angle estimation error-SSRM (MAEE-SSRM) method is proposed. The optimization problem is constructed based on the upper and lower bounds of the estimated eavesdropping channel related coefficient and then solved by the change of the variable. Simulation results show that our two proposed methods have better sum secrecy rates than the state-of-the-art methods. Furthermore, when the estimation error of direction angle toward each eavesdropper is random but within a certain range, the secrecy performance of our VMD-SSRM method is better than that of our MAEE-SSRM method. On contrary, when the direction angle estimation error reaches its maximum, our MAEE-SSRM method performs better.

Robust Directional Modulation Design for Secrecy Rate Maximization in Multiuser Networks