## 1 Introduction  
Maritime communication technologies achieve information exchange between ships and between ships and shore, and have always played an important role in ensuring the efficient and stable operation of maritime activities. Various modern maritime activities, such as offshore aquaculture as well as maritime search and rescue, require the transmission of real-time video information and other broadband services, requiring maritime communication systems to have a higher data transmission rate while being able to cover long distances. In addition, with the concept of marine Internet of Things, more maritime infrastructure, such as ships, buoys, unmanned ships, drones, etc., will have access to the maritime communications system and network, requiring maritime communication technology to have a higher spectral efficiency to accommodate more maritime communication users. Therefore, the establishment of a maritime communication technology with both a higher data transmission rate and higher spectral efficiency is important for the current and future operation of maritime activities. In open-sea regions, satellite communication is the main data transmission approach, and common satellite communication systems include the Iridium system [1], the VerySmall Aperture Terminal (VSAT) [2] and the Inmarsat system [3; 4]. In satellite communication systems, the available bandwidth is divided into multiple separate frequency sub-channels, and frequency guard bands are set between sub-channels to avoid interferences. For each sub-channel, Quadrature Phase Shift Keying (QPSK) is the most widely used modulation technology, and 8-Phase Shift Keying (8 PSK) and 16-Amplitude Shift Keying (16 ASK) are utilized in the fifth-generation Inmarsat satellite communication system to provide higher data rates. Meanwhile, communications between vessels in open-sea regions can also be implemented in the medium-frequency/high-frequency/very-high-frequency (MF/HF/VHF) band, and typical technologies include navigation telex (NAV-TEX), the automatic identification system (AIS) [5] and the VHF data exchange system (VDES) [6]. According to the standard [6], a 100 kHz VDES demo utilizes multi-carrier modulation, which comprises 32 equal-power subcarriers with 16-QAM modulation of each subcarrier, provides a data rate of 307.2 kbit/s, and has a frequency interval between sub-channels of 2.7 kHz (not orthogonal), indicating that the spectrum of sub-channels can be slightly overlapped. As offshore regions can be covered by base stations on the coast, various terrestrial communication technologies can be utilized to support data transmission between vessels and the coast. From 2010, many projects have been implemented, such as TRITON [7], Marcom [8], NANET [9] and BLUECOM+ [10; 11], and the involved technologies are mainly WiFi [12], WiMAX [13; 14; 15; 16], LTE [17; 18; 19], etc. For these technologies, orthogonal frequency division multiplexing (OFDM) is the most widely used technology, in which frequencies of sub-channels are orthogonal to each other, and spectrums of sub-channels can be overlapped to achieve higher spectral efficiency. For each sub-channel, 16/64/256-QAM modulation is used to realize a high data rate and support multi-user access. Although 4G/5G-based wireless communications can achieve a high data transmission rate, their base stations can only be constructed on land along the coastline, and the communication services can therefore only cover offshore regions. The VHF Data Exchange System (VDES) is a third-generation maritime communication system established by the World Radiocommunication Conference. AIS, VDES adds ASM and VDE can not only meet the requirement of close-range bi-direction data exchange between ships and ships, but can also achieve long-distance data exchange between ships and coasts on a global scale through satellites. However, the peak communication rate of the VDES is only 307.2 kbps, which means that it cannot meet the current and even future communication rate requirements for maritime services.