  This paper studies the beamforming design problem of a multi-user downlink
network, assuming imperfect channel state information known to the base
station. In this scenario, the base station is equipped with multiple antennas,
and each user is wiretapped by a specific eavesdropper where each user or
eavesdropper is equipped with one antenna. It is supposed that the base station
employs transmit beamforming with a given requirement on sum transmitting
power. The objective is to maximize the sum secrecy rate of the network. Due to
the uncertainty of the channel, it is difficult to calculate the exact sum
secrecy rate of the system. Thus, the maximum of lower bound of sum secrecy
rate is considered. The optimization of the lower bound of sum secrecy rate
still makes the considered beamforming design problem difficult to handle. To
solve this problem, a beamforming design scheme is proposed to transform the
original problem into a convex approximation problem, by employing semidefinite
relaxation and first-order approximation technique based on Taylor expansion.
Besides, with the advantage of low complexity, a zero-forcing based beamforming
method is presented in the case that base station is able to nullify the
eavesdroppers' rate. When the base station doesn't have the ability, user
selection algorithm would be in use. Numerical results show that the former
strategy achieves better performance than the latter one, which is mainly due
to the ability of optimizing beamforming direction, and both outperform the
signal-to-leakage-and-noise ratio based algorithm.
