# A Novel Fractional Fourier Transform-Based ASK-OFDM System for Underwater Acoustic Communications  
[PERSON]  
1 Department of Electronics and Communications Engineering, College of Engineering and Technology, Arab Academy for Science, Technology & Maritime Transport (AASTMT), Alexandria 1029, Egypt; [EMAIL_ADDRESS]  
2 Department of Computer Engineering, College of Engineering and Technology, Arab Academy for Science, Technology & Maritime Transport (AASTMT), Alexandria 1029, Egypt; [EMAIL_ADDRESS]  
Electromagnetic waves can propagate only at low frequencies, which in turn require large antennas and high transmission power. Furthermore, optical transmission is greatly influenced by scattering, high levels of absorption and ambient noise [1,2]. The underwater environment is a very challenging channel due to its unparalleled physical properties and specifications [3]. It is mainly characterized by path loss, multipath fading, large extent of Doppler spread and ambient noise [1,2,4]. It is also known that the UWA channel suffers from high propagation delay due to the relatively low-transmission speed (1500 m/s), limited bandwidth, and high transmission power requirements. Moreover, different temperature degrees, salinity and pressure levels between multiple layers of sea water, add to the complexity of the UWA channel [1,2]. Orthogonal Frequency Division Multiplexing (OFDM) has dominated in recent underwater wireless communication systems. This is motivated by the success of OFDM in cellular communications. OFDM is characterized by its high spectral efficiency and low equalization complexity in the presence of frequency selective channels. However, OFDM suffers from the effect of Doppler spread due to the movement of the transmitter or the receiver, which consequently creates non-uniform carrier frequency offset (CFO). This poses great complexity for the channel equalizer and receiver, which in turn limits any fundamental improvement in terms of data rate. The commonly used digital modulation techniques with OFDM include quadrature amplitude modulation (QAM) and phase shift keying (PSK). The application of amplitude shift keying (ASK) to OFDM in cellular systems has been proposed in [5], and its performance was evaluated in the additive white Gaussian noise (AWGN) channel in [6], and in [7] the performance was evaluated in the Rayleigh fading channel. ASK-OFDM requires \(1/2T\) as the minimum frequency spacing for maintaining the orthogonality between sub-carriers, which is half the spacing required by PSK-OFDM and QAM-OFDM schemes. This bandwidth saving is traded for a higher peak-average-power-ratio (PAPR). However, there are many solutions which exist in the literature that reduce PAPR [7]. Generally, OFDM is efficiently implemented by fast Fourier transform (FFT), and it is effective in the underwater communication channel since it transforms the frequency selective channel into several narrow flat fading sub-channels. This in turn makes the system robust against inter-symbol-interference (ISI) induced by large channel delay spread. Though OFDM is better than single carrier transmission techniques, it still cannot be used for long range transmissions over UWA channels due to its poor BER performance. Similar to wireless communications, OFDM-based communications for UWA channels have been extensively studied in the literature. These studies included channel charectarization and measurements [8, 9, 10], system design and performance evaluation [11, 12], synchronization and channel estimation [13, 14, 15], inter-carrier-interference (ICI) cancellation [16], and the investigation of multiple-input-multiple-output (MIMO)-OFDM [17]. The commonly used modulation schemes with OFDM systems in UWA channels are Quadrature Phase Shift Keying (QPSK), equivalent to 4-QAM, and 16-QAM [11, 12, 18, 19].