Optimizing the number of relays for energy efficient multi-hop covert underwater acoustic cooperative networks

Abstract

Multi-hop underwater acoustic (UWA) cooperative networks can effectively reduce the energy consumption of the system, yet the covertness of communication is also greatly reduced since a spatial diversity gain can be obtained by both the intended receiver and the intercept detector. In this paper, we investigate how to select the optimal number of relays for multi-hop UWA cooperative networks, by considering both the low probability of detection (PD) and energy consumption. We derive the relationship between PD and the number of relays and then analyze the relationship between energy consumption and the number of relays for the system. To address the joint PD and energy consumption optimal problem, we define the energy consumption rate for multi-hop UWA systems by normalizing the energy consumed in single-hop UWA systems at the same source-to-destination distance. Then, we derive the range number of relays under the given PD and energy consumption rate. Moreover, we construct the objective function and derive the optimal number of relays by jointly addressing PD and the energy consumption rate. Finally, we simulate and analyze the impact of several parameters on PD and energy consumption, including the signal-to-noise ratio, working distance, position angle of interceptor and data length. The simulation results show that the number of relays for multi-hop covert UWA cooperative networks can take the value between 2 and 6 under a given condition, which can meet the covert communication requirement with a PD < 0.5, while the system energy consumption is relatively low.