# A Study on the Maximum Reliability of Multi-UAV Cooperation Relay Systems
###### Abstract  
This paper studies the maximum reliability of multi-hop relay UAVs, in which UAVs provide wireless services for remote users as a coded cooperative relay without an end-to-end direct communication link. In this paper, the analytical expressions of the total power loss and total bit error rate are derived as reliability measures. First, based on the environmental statistical parameters, a LOS probability model is proposed. Then, the problem of minimizing the bit error rate of static and mobile UAVs is studied. The goal is to minimize the total bit error rate by jointly optimizing the height, elevation, power and path loss and  
that tethered UAVs use cables to transmit electricity and signals solves the major problems of flight duration, safety, and reliability. China's three major operators have conducted joint exercises and tests many times and have purchased tethered UAV aerial base stations for emergency communications. At the same time, extensive research in academia has been dedicated to the use of UAVs in different types of air communication platforms, such as mobile base stations (MBSs) and mobile relays (MRs). In order to realize the potential of air communication platforms, allocating resources to UAV-assisted communication networks is crucial, which has also sparked research on the joint optimization of communication resource allocation [5; 6; 7; 8; 9]. The authors of [5] studied energy-efficient UAV communications and optimized resource allocation to maximize the energy efficiency of a UAV relay. The authors of [6] applied multiple UAVs to extend the duration of communications via UAV collaboration and optimized resource allocation to maximize end-to-end throughput. In [7], the authors considered a single UAV launched from a fixed initial location to a final location and optimized resource allocation to minimize the average outage probability of the system. In [8], the authors optimized resource allocation to maximize the service time duration of a UAV while simultaneously ensuring adequate coverage. In [9], the authors studied the use of a multi-hop UAV relaying network, and optimized resource allocation to maximize the total system throughput between two source nodes. Little of the existing research has focused on the effective deployment of UAVs as MRs, and the maximum reliability problem to be addressed by optimizing resource allocation is even less studied. However, the challenging fact concerns utilizing the mobility of UAVs, and the future research direction of UAV-assisted ground communications is in multi-UAV cooperative communications. In this paper, we consider a multi-source, multi-destination and multi-hop communication model in which the UAV acts as the coding cooperation (CC) relay, which can realize an air-to-air (AtA) relay to expand wireless coverage, as shown in Figure 1. This paper studies the problem of minimizing the BER of static and mobile UAVs, which is constrained by the maximum allowable path loss, the transmission power allocation, the UAV altitude and elevation, and minimizes the total path loss to achieve maximum communication coverage. However, the formulated optimization problem is nonconvex and generally difficult to solve. Firstly, two subproblems, namely, the height and elevation subproblem of given power and path loss, and the power and path loss subproblem of given height and elevation, are studied, which are processed by applying the gradient descent method and interior point method. Then, an effective joint optimization iteration algorithm is proposed, which can effectively update the optimization variables in each iteration and ensure the convergence of the algorithm. Finally, the effectiveness of the proposed algorithm is proved, which shows its superiority in the interrupted performance of mobile UAVs. Notations: In this paper, scalars are denoted using italic letters, while vectors and matrices are, respectively, denoted using bold-face lower-case and upper-case letters.