# Performance Analysis of a WPCN-Based Underwater Acoustic Communication System
## 1 Introduction
### Motivation and Contributions  
So far, the research on UWAC systems still focuses on improving the communication qualities of the system, such as communication reliability, information transmission rate, communication distance, coverage, etc., while the research on how to solve the energy-limited problem of the nodes in UWAC systems is rather insufficient. WPCN is a promising and attractive scheme for the energy-limited problem of underwater acoustic nodes in UWAC systems. As shown in Figure 1, by applying the WPCN technology to UWAC systems, underwater vehicles with sufficient power supply can serve as energy replenishment devices for long-distance energy transfer to the sensor nodes in the downlink. The sensor nodes can harvest the energy and use it to transmit information to the underwater vehicles in the uplink. Compared to the current power transfer schemes that can only operate within a few meters [28; 29] or are environmentally susceptible and unreliable [21; 22; 24], a WPCN-based UWAC system can stably and comparably controllably power the sensor nodes at a much farther distance of hundreds or even thousands of meters.  
Motivated by the above observations, in this paper, we present the application of WPCN to the UWAC systems and investigate the performance of the WPCN-based UWAC systems. To the best knowledge of the authors, except for the work of [6], where an overview was provided for the wireless information and power transfer (WIPT)-based UWAC and networks, there is no other research on the WPCN-based UWAC systems. Our main contributions are as follows:  
* We present an application of WPCN to the UWAC systems to provide an auxiliary and convenient energy supplement for solving the energy-limited problem of underwater acoustic nodes, where the H-AP transfers energy to the terminal node in the downlink while the hydrophone of the terminal node exploits the received acoustical signal and ambient noise for energy harvesting. The harvested energy at the terminal node is then used for the information transmission in the uplink;
* We analyze the average BER, outage probability, and achievable rate performance for the WPCN-based UWAC systems in the frequency-selective sparse channel and non-white noise environments. We first derive the closed-form expression for the probability density function (PDF) of the received signal-to-noise ratio (SNR) at the H-AP in the uplink. Based on this, we further derive closed-form expressions of the average BER and outage probability of the systems, which are used in the discussion for the effects of system and channel parameters on the system performance;
* We investigate the impacts of the transmission distance, signal frequency, spreading factor, and time allocation factor on the system's performance. It is demonstrated that there exist optimal signal frequency and time allocation factors to minimize the average BER and maximize the achievable information rate for the system, respectively. Moreover, a larger optimal time allocation factor is preferred for a smaller H-AP transmit power or a larger transmission distance, while a smaller optimal signal frequency is required for a larger transmission distance.  
The rest of the paper is organized as follows. In Section 2, we present and introduce the model of the WPCN-based UWAC system. In Section 3, the performance of the system in terms of the average BER and the outage probability is analyzed. In Section 4, the analytical and simulation results, along with the discussion, are presented. Finally, the conclusion is given in Section 5.