## 1 Introduction  
In recent years, underwater communications and networking technologies for underwater wireless sensor networks (UWSNs) and the Internet of Underwater Things (IoUT) have been studied and developed actively by academia and industrial researchers due to their challenges and applications [1; 2; 3; 4]. [PERSON] et al. [1] provided a comprehensive survey on UWSN applications including water quality monitoring, habitat monitoring, fish farming, natural resource explorations, oil and gas pipeline monitoring, disaster forecasting (such as volcanoes and earthquakes), military surveillance, mine detection, and assistive navigation. [PERSON] et al. [2] presented a comprehensive study on IoUT applications, challenges for IoUT, and UWSN channel models. For the main challenges for IoUT, they discussed the differences between UWSNs and territorial (or terrestrial) wireless sensor networks (TWSNs) including transmission media, rate, range, and propagation speed. [PERSON] et al. [3] provided a survey on localization protocols and enabling technologies for UWSNs and IoUT including magneto-inductive communications and acoustic communications. In [3], the magneto-inductive communications can be used for short range and high data rate while the acoustic communications can be used for long range and low data rate. [PERSON] et al. [4] presented a survey of technical issues and future directions for electromagnetic, optical, and acoustic communications in underwater environments. They also presented related issues of UWSNs and emerging technologies in underwater environmental communications. There have been many studies on medium access control (MAC) protocols in TWSNs. IEEE 802.11 standard [5] has presented the distributed coordination function (DCF) based on carrier sense multiple access with collision avoidance (CSMA/CA) for wireless local area networks (WLANs). [PERSON] et al. [6] proposed a modeling approach to analyze the throughput and delay performance of IEEE 802.11 DCF. In [7], an analytical model of IEEE 802.11 DCF with a back-off freezing mechanism was proposed for WLANs. [PERSON] and [PERSON] [8] proposed an implicit block acknowledgment (ACK) scheme that does not use the explicit block ACK request frame for WLANs. In [9], a method to optimize the number of aggregated MAC protocol data units was proposed for maximizing the system throughput with considering delay requirements in IEEE 802.11 ac. In IEEE 802.15.4 standard [10] for low-rate wireless networks, the MAC protocol based on the slotted CSMA/CA mechanism is used in a contention access period. In [11], a method to estimate the number of active devices was proposed for the slotted CSMA/CA without acknowledgment in IEEE 802.15.4. To consider the differences between TWSNs and UWSNs such as transmission media, rate, range, and propagation speed, there have been many studies on MAC protocols in UWSNs. [PERSON] et al. [12] provided a survey on MAC protocols including contention-free, contention-based, and hybrid MAC protocols for UWSNs. [PERSON] [13] provided a survey on MAC protocols for underwater acoustic networks based on a MAC reference model. A slotted floor acquisition multiple access (FAMA) was presented by [PERSON] and [PERSON] [14]. Slotted FAMA uses time slotting, carrier sensing, and a handshake of request to send (RTS) and clear to send (CTS) control packets. [PERSON] et al. [15] proposed the MACA-U protocol by adapting terrestrial multiple access collision avoidance (MACA) for underwater acoustic networks. [PERSON] et al. [16] proposed MACA-MN protocol based on MACA with packet train for multiple neighbors in underwater acoustic networks. As our previous study [17], an underwater CSMA/CA protocol with multi-RTS and multi-DATA receptions was proposed and analyzed in terms of throughput and delay. For underwater acoustic networks, [PERSON] and [PERSON] [18] formulated an optimization problem to minimize the fractional idle time in a frame for unslotted variable packet duration schedules. [PERSON] et al.