  The mobile relaying technique is a critical enhancing technology in wireless
communications due to a higher chance of supporting the remote user from the
base station (BS) with better quality of service. This paper investigates
energy-efficient (EE) mobile relaying networks, mounted on an unmanned aerial
vehicle (UAV), while the unknown adversaries try to intercept the legitimate
link. We aim to optimize robust transmit power both UAV and BS along, relay
hovering path, speed, and acceleration. The BS sends legitimate information,
which is forwarded to the user by the relay. This procedure is defined as
information-causality-constraint (ICC). We jointly optimize the worst case
secrecy rate (WCSR) and UAV propulsion energy consumption (PEC) for a finite
time horizon. We construct the BS-UAV, the UAV-user, and the UAV-adversary
channel models. We apply the UAV PEC considering UAV speed and acceleration. At
last, we derive EE UAV relay-user maximization problem in the adversarial
wireless networks. While the problem is non-convex, we propose an iterative and
sub-optimal algorithm to optimize EE UAV relay with constraints, such as ICC,
trajectory, speed, acceleration, and transmit power. First, we optimize both BS
and UAV transmit power, and hovering speed for known UAV path planning and
acceleration. Using the optimal transmit power and speed, we obtain the optimal
trajectory and acceleration. We compare our algorithm with existing algorithms
and demonstrate the improved EE UAV relaying communication for our model.
