## 1 Introduction  
In spite of their long and consolidated history, underwater acoustic communications (UWACs) have recently experienced a peak of interest from the scientific community, as they represent an effective technology for a wide range of applications [1]. Real-time control and communication with underwater remote instrumentation and autonomous vehicles [2], coastal surveillance [3] and shipping traffic management [4], environmental monitoring [5] and data collection [6] are some of the most widespread activities where the use of UWACs has been shown to be suitable. Regarding communication aspects, UWAC links are affected by several impairments that significantly limit the transmission rate. In fact, besides the intrinsic (technological) bandwidth limitation, due to transmitter capabilities, underwater acoustic channels are also characterized by severe multipath delays and highly selective frequency responses, as well as non-negligible propagation delays due to the relatively slow speed of sound in water [7]. The UWAC propagation scenario exhibits a peculiar time-varying behavior [8, 9], due to sea temperature and salinity gradients, sea stream, and wind speed, as well as relative positional changes due to motion of the terminals [10]. Multipath time delay and frequency-selective deep fading affect the UWAC channel in different ways, depending on the propagation environment, typically classified as shallow, medium or deep water [11]. The shallow water channel is characterized by several paths of comparable length, so the corresponding channel impulse response (CIR) presents a large number of close coefficientswith similar amplitudes. On the other hand, deep water CIR exhibits longer delays and small coefficients because of the long distances traveled by the signal echoes with respect to the line-of-sight wave. The medium water environment presents delay spread and path gain features between the above two cases. The mitigation of channel impairments is fundamental to provide a reliable communication link. Typical countermeasures consider the use of equalization [12; 13] in order to restore the quality of the received signal. Alternatively, adaptive modulation and coding schemes are developed in order to match the transmission parameters with the channel behavior [14; 15; 16]. In this regard, Orthogonal Frequency Division Modulation (OFDM) offers desirable features, like robustness to multipath delay spread, sufficiently high data rate, large bandwidth efficiency, and adaptivity of the modulation format to channel conditions [17]. In OFDM, modulated symbols are transmitted over different sub-carriers that, ideally, do not interfere with each other when propagating over frequency-selective and time-invariant channels, so that simple symbol-by-symbol detection can be adopted. In real cases, the potential inter-carrier interference can be mitigated through equalization [18]. Furthermore, it is worth highlighting that, in radio-frequency (RF) OFDM systems, the intersymbol interference (ISI) arising from multipath propagation is typically mitigated through the use of a cyclic prefix (CP), the length of which is set according to the channel delay spread [19]. On the other hand, the sudden variability of channel behavior, as well as the long CIR, make the use of a fixed CP impracticable in UWACs, since ISI may not be properly mitigated [20]. CP length optimization has also been investigated, but mainly in reference to RF OFDM scenarios [21; 22]. However, such solutions cannot be employed directly in UWACs, due to the significant differences between RF and underwater acoustic channels. Therefore, channel issues must be addressed in a different fashion. In this regard, OFDM adaptivity to the medium conditions is a relevant feature for the harsh propagation scenario offered by UWACs, allowing a significant increase in transmission rate. In [23], the authors propose an OFDM sub-carrier power optimization mechanism based on channel knowledge, achieved with a length-adaptive estimation technique.