  In this paper, based on directional modulation (DM), robust beamforming
matrix design for sum secrecy rate maximization is investigated in multi-user
systems. The base station (BS) is assumed to have the imperfect knowledge of
the direction angle toward each eavesdropper, with the estimation error
following the Von Mises distribution. To this end, a Von Mises distribution-Sum
Secrecy Rate Maximization (VMD-SSRM) method is proposed to maximize the sum
secrecy rate by employing semi-definite relaxation and first-order
approximation based on Taylor expansion to solve the optimization problem. Then
in order to optimize the sum secrecy rate in the case of the worst estimation
error of direction angle toward each eavesdropper, we propose a maximum angle
estimation error-SSRM (MAEE-SSRM) method. 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
method. Simulation results show that our two proposed methods have better sum
secrecy rate than zero-forcing (ZF) method and signal-to-leakage-and-noise
ratio (SLNR) method. Furthermore, the sum secrecy rate performance of our
VMD-SSRM method is better than that of our MAEE-SSRM method.
