Joint Optimization Design of UAV-Active RIS System Based on a Quadratic Transformation

Aiming at the problem of maximizing the average achievable rate (AAR) of users in the scenario of unmanned aerial vehicle (UAV) carrying an active reconfigurable intelligent surface (RIS) in the downlink communication system, a method based on quadratic transformation combined with semidefinite relaxation (SDR) and successive convex approximation (SCA) is proposed. Due to the characteristics of active RIS, its thermal noise cannot be ignored. The additive noise in the objective function makes its fractional form highly complex. To solve the nonconvex fractional programming problem with highly coupled multiple variables, the objective function is split into three sub-problems: the transmit power allocation of the base station, the phase shift of active RIS, and the trajectory optimization of the UAV. The quadratic transformation method is used to incorporate the influence of thermal noise into the optimization framework. By introducing auxiliary variables, the multi-fractional problem can be effectively dealt with. At the same time, the nonconvex quadratically constrained quadratic problem (QCQP) is transformed into a convex optimization problem with multiple single variables by combining the semidefinite relaxation method and the successive convex approximation method. Finally, the alternating iteration method is used to obtain the suboptimal solution of the original problem. The simulation results show that compared with the Taylor scheme, the traditional passive RIS scheme, and the random phase shift scheme, the optimized scheme improves the AAR by 10%-20%, 20%-40%, and 80%-240%, respectively.