## 3 Results  
In this section, the numerical simulation results are presented to evaluate the energy efficiency performance of different relaying schemes in supporting the communication between the BS and UE. All the results are obtained by averaging over 50,000 independent channel realizations. Unless stated otherwise, the simulation parameters listed in Table 1 are used to simulate the findings, which are based on [9; 18; 25; 26]. Specifically, the environment parameters are according to the dense urban scenarios. In addition, assuming that the UAV relays are equipped with only a single antenna, the number of reflecting elements in the active, hybrid, and passive RIS-UAVs is fixed at 256. The example size of the RIS operating at 2.3 GHz is about 800 mm \(\times\) 800 mm, as demonstrated by the prototype shown in [27]. This form factor is feasible to be mounted on a hexacopter, such as the Tarot X6. In order to study the fundamental performance of the proposed hybrid RIS-UAV, a hybrid RIS-UAV is equipped with only a single active element, and the remaining 255 elements are passive. Furthermore, all the channels are assumed to be uncorrelated in this paper; hence, there is no signal coupling in the reflection by the neighboring antenna or elements, and all the elements reflect the incident signal independently to the UE. The hardware-dissipated power at the BS, UAV, and UE, as well as the RIS elements are based on [9; 18; 26]. First, the energy efficiencies of the relaying schemes are compared in Figure 2 by varying the placement of the UAV such that the UAV moves its horizontal distance from the BS toward the UE, i.e., from coordinate (0, 0, 20) to coordinate (100, 0, 20). From Figure 2, it is revealed that the proposed active RIS-UAV achieves a higher energy efficiency than other relaying schemes, no matter if the UAV is placed close to the ground nodes or far away from them. This observation was validated with [26] that compared the achievable rate between the active and passive terrestrial RIS with the same total power budget. In [26], it is demonstrated that the active terrestrial RIS outperform the passive terrestrial RIS in all the terrestrial RIS deployments. In addition, the active RIS-UAV is more energy efficient when the UAV is placed in the middle point between the BS and UE due to the equal allocation of the transmit power between the BS and RIS. In contrast, the passive RIS-UAV suffers from the double path-loss problem when the UAV is placed near the middle point of the BS and UE, so it can be observed that the energy efficiency of the passive RIS-UAV drops significantly when the UAV is moving away from the BS and increases back again when it is approaching the UE. Meanwhile, the proposed hybrid RIS-UAV, which consists of a single active element and \(N-1\) passive elements, performs better than the passive RIS-UAV. It is revealed that the proposed active and hybrid RIS-UAV relaying schemes can provide up to 26 times and 14 times improvement in energy efficiency as compared to the passive RIS-UAV, respectively, when the UAV is placed in the middle between the BS and UE. When the UAV is placed close to the BS or UE, the performance of the proposed active and hybrid RIS-UAVs is about 187% and 18.9% higher than the passive RIS-UAV, respectively. This is because they can amplify the signal with the power amplifiers integrated with the active elements, hence improving the received signal at the UE. The amplification factor of the hybrid RIS-UAV is computed through the simulation in the range of \(2.67\times 10^{4}\) to \(1.28\times 10^{9}\). The amplification factor increases as the channel link between the BS and UAV becomes weaker.