On A Special Structured Robust Optimization Problem

This thesis considers a special structured robust optimization problem derived from the physical layer security of wireless communications.Consider a relay assisted wiretap channel with one pair of users,several relays and an eavesdropper.We jointly design the relay beamforming weights and minimize the total relay transmit power,while ensuring users'quality of services and preventing the information being eavesdropped at the same time.Because the channel state information(CSI)from users and relays to the eavesdropper is imperfect,the problem can be reduced to a robust optimization problem.We propose two methods to solve this problem.In the third chapter,we eliminate some robust parameters by tightening the robust constraint.Thus,it leads to a robust optimization problem with only one type of robust parameters.S-lemma is applied,and the robust constraint is transformed into a finite number of linear matrix inequalities constraint.Then we use the semi-definite relaxation method to obtain the optimal solution of the tightened problem.Next in the fourth chapter,we simplify the original problem by neglecting the high order terms and cross product terms of robust parameters in the robust constraint.Different from the tighten problem in the third chapter,the simplified robust optimization problem preserves all the robust parameters.An iteration method based on the line search framework is proposed.In each iteration,we obtain the line search direction and step size by solving two quadratic constrained quadratic programming subproblems and a one-dimensional subproblem,respectively.The convergence is guaranteed under certain conditions.And the global optimality conditions of the simplified problem are shown,too.Simulation results show that the performance of our model is close to that with perfect CSI,and is much better than that with no CSI.The proposed algorithm outperforms the state of arts.