# Secrecy Rate of Resource-Constrained Mobile Relay Model under Two-Way Wiretap Channel
## 1 Introduction  
It is well known that secure information transmission is an essential communication requirement. Resource-constrained two-way communication occurs in a four-node network, where two users exchange information through a relay station under the condition of an eavesdropper wiretapping the channels. This four-node relay-eavesdropper network has been widely studied [1; 2; 3; 4; 5], and with the help of relay, the network is able to adjust its uplink and downlink channels and thus improves the system security. With the rapid development of Internet of Things (IoT), huge numbers of long-distance sensors need to interact with each other to jointly complete tasks [6]. Resources such as time and energy in this type of cooperative sensor network are important factors that need to be carefully considered. Therefore, the resource-constrained relay-eavesdropper network is becoming a novel interesting research topic and is attracting considerable attention. Currently, most existing works focus on two-way communication systems with fixed relays [7; 8; 9; 10]. In particular, relay cooperative jamming has been studied extensively [7; 8; 9; 10] to protect confidential message from wiretapping. This type of method, although effectively improving the secrecy rate, may lead to harmful interference and additional energy consumption [7; 8]. Thus, to eliminate interference, interference cancellation techniques have to be taken into account [10]. On the other hand, in order to improve energy utilization efficiency, energy harvesting [7] or wireless energy transfer [8] is adopted to provide the relay and users with sufficient energy. Nowadays, there is a growing interest in deploying unmanned aerial vehicles (UAVs) in two-way relay systems [11; 12; 13]. UAV schemesindeed provide flexible mobile relays to implement air-to-ground or air-to-air wireless communication. However, for ground secure transmission, especially indoor, complicated pitches (e.g., warehouses), this beyond the reach of UAV-based relay system. Moreover, when an UAV serves as a flying relay, it requires large propulsion energy to keep itself aloft, which leads to a short life flight. This feature prevents the UAV from participating in many applications. Therefore, two-way secure relay system needs further investigation, and this paper presents an investigation of the secrecy rate region of a ground mobile vehicle-based relay system, which remains an open problem. To quantify the performance gain brought by our scheme, this paper proposes a two-way secure transmission and a graph mobility model, as well as formulating a secrecy rate maximization optimization problem with resource allocations incorporating path planning constraints, which represents a mixed integer nonlinear programming (MINLP) problem. The major challenges in solving this discrete problem are twofold. First, the path planning refers to a considerable number of discrete binary variables, and the solution space grows exponentially with the number of anchor points. This characteristic results in a substantial difference from the design of UAVs' trajectories, which only involve continues variables. Second, when the relay moves along an unknown path, finding the achievable secrecy rate becomes very challenging. This is because two major reasons. One is that the transmission time at different location point needs to be determined. The other is that the powers at relay and users at each location need to be jointly optimized. As a result, in contrast to the fixed relay case, the dimension of variables significantly increase, resulting in additional nonlinear coupling between time allocation and uplink-downlink power allocation. In order to overcome the above challenges, auxiliary and relaxation methods are adopted to transform the non-convex problem into a convex problem, and a local optimal solution is derived. Finally, numerical results show that our mobile relay scheme outperforms the fixed relay scheme, and the relay trajectory is highly dependent on noise power.