The usage of unmanned aerial vehicles (UAVs) as aerial base station (BS) or relay are becoming increasingly important in the yield of wireless communications. An UAV-based relay can greatly support the transmission between the mobile ground user (MGU) and the base station. In this paper, we study the optimum altitude of a decode-and-forward (DF) relaying UAV system. In particular, we analyze two different communication scenarios, i.e., BS-UAV-MGU (BUM) and MGU-UAV-MGU (MUM) scenarios, respectively. For the BUM scenario, the optimum altitude of UAV-based relay over Mixed-Rayleigh fading channel is studied. For the MUM scenario, we analyze the performance of a two-hop network over the Double-Rayleigh fading channel with the assistance of a DF relay. Moreover, the average end-to-end bit error rate (BER) and outage probability of the proposed UAV-relay system are analyzed for both BUM and MUM scenarios. Additionally, we provide closed-form expressions of outage probability and BER for BPSK modulation and demonstrate the accuracy of proposed expressions via Monte-Carlo simulations.