# Link Connectivity and Coverage of Underwater Cognitive Acoustic Networks under Spectrum Constraint
## 1 Introduction  
There is a growing interest in exploring the underwater environment due to a diversity of underwater applications, including ocean environment monitoring, offshore structural health monitoring, mine reconnaissance, distributed tactical surveillance, target tracking, shipping safety, and fish farm monitoring [1; 2; 3]. A key technology to enable various underwater monitoring applications is underwater sensor networks (USNs), which can be deployed in various underwater environments such as reservoirs, lakes, rivers, and oceans. Due to the high attenuation of electromagnetic waves in underwater environments, acoustic communications are typically used in USNs. However, the underwater acoustic spectrum is becoming a scarce resource for the following reasons: (1) the high competition for acoustic spectrum between different users due to the proliferation of man-made underwater acoustic systems, including sonars, acoustic sensors, and unmanned underwater vehicles [4]; (2) the co-existence of _man-made acoustic systems and natural acoustic systems_ (e.g., marine animals like whales, dolphins, and sea lions) [1]. It is worth mentioning that we often ignore the interference caused by man-made acoustic systems to marine animals that may use the same frequencies as the human-made acoustic systems. Therefore, it is necessary to solve the spectrum scarcity problem in an environmentally-friendly and spectrum-efficient way. Cognitive acoustic communications are one of the most promising solutions to the acoustic spectrum scarcity problem. We name such underwater cognitive acoustic sensor networks as UCANs. In UCANs, there are two types of acoustic spectrum users: primary users (PUs) and secondary users (SUs). PUs (including both artificial and natural acoustic systems) have the higher priority to use the acoustic spectrum. SUs (usually only include artificial acoustic systems) have a lower priority to use acoustic spectrum only when the acoustic spectrum is idle or their communications do not hamper the communications of PUs; the awareness of the existence of PUs can be achieved by using spectrum-detecting technology [5]. In fact, cognitive radio technology has been well investigated in terrestrial wireless networks. However, underwater acoustic communications are significantly different from terrestrial wireless communication systems due to the unique features of underwater acoustic channels (e.g., frequency-dependent attenuation and long propagation delay). Therefore, UCANs bring new research challenges in investigating cognitive radio technology in underwater environments. Cognitive acoustic communications have recently received substantial attention. [PERSON] et al. [1] summarized the research challenges in underwater cognitive acoustic networks. A dynamic spectrum-borrowing algorithm was proposed in [6]. Most recently, a receiver-initiated spectrum management system for underwater acoustic networks was developed in [7]. However, few studies focus on the quality-of-service (QoS) of SUs in UCANs. Essentially, SUs are spectrum-constrained in UCANs compared with PUs who have a greater chance to access acoustic spectrum than SUs. Therefore, it is more difficult to guarantee the QoS of SUs than that of PUs. One of the most important QoS metrics is the link connectivity and the coverage probability; the former concerns the possibility of whether a pair of nodes can establish a communication link, and the latter concerns the probability that a user is able to achieve a certain threshold signal-to-noise ratio (SNR). _To the best of our knowledge, there is no study on the link connectivity and coverage probability of SUs in underwater cognitive acoustic networks._  
The main goal of this paper is to investigate the link connectivity and coverage of SUs in UCANs. It is non-trivial to analyze the link connectivity and the coverage probability of SUs because of the influence of various ambient factors caused by the complicated underwater acoustic channel and the activities of PUs.