Abstarct: Relays are important factors to improve the performance of the system in wireless communication networks. In fact, relays have a significant role in increasing the system rate and improvement of system power. In this thesis, unmanned aerial vehicles are employed as relays. We aim to benefit the mobility of UAV and using it as a mobile relay. Since UAVs have batteries with limited capacity, we define the problem as finding the optimal trajectory for the UAV and optimal power allocation for the network, while having maximum data transmission rate for each communication. In order to find the optimal trajectory and power, we consider information rate factor for two scenarios with one and multiple pairs of users. In expressing the problem in this way, our target is to maximize the information rate through one or several communication lixnk between the k-th transmitter and receiver subject to some constraints on the power of source and UAV and also trajectory of UAV. So we face a constrained optimization problem which is not convex. Due to difficulty of solving such non-convex problem, we convert the main problem to some sub-problems by fixing some constraints and solve them with successive convex optimization which is an iterative algorithm and reach the solution for main problem by solving the sub-problems iteratively. Simulation results show the efficiency of proposed algorithm.