## 1 Introduction  
The upcoming 5G communication standard has been an active area of research in recent years, focusing on terrestrial communications. However, progress in underwater communications has been comparatively much slower. The underwater acoustic environment is much more challenging, with far greater dispersion and multipath effects, limiting the potential use of the classical 5G scheme in the underwater domain [1]. Some research in developing underwater technology has taken place with a focus on orthogonal frequency division multiplexing (OFDM) and single-carrier frequency division multiple access (SC-FDMA) schemes [2; 3]. In general, the underwater acoustic communication community has focused on increasing transmission distance, improving bandwidth efficiency, and reducing the rate of error in the complex time-space-varying underwater channel [4; 5]. Covert underwater acoustic communication has been studied for military purposes to hide positioning information or data information. Although it is not an acoustic signal, underwater optical communication using a blue-green laser has also been aimed at enhancing covertness through the use of the strong directivity of lasers [6]. In addition, biomimetic signaling has been studied as a scheme for underwater acoustic communications, but the subject is in the early stages [7; 8]. On the other hand, the spread spectrum schemes are widely used in the field to achieve covert communication. There are two typical spread spectrum schemes. One is a direct-sequence spread spectrum (DSSS) method in which the data are multiplied by a spread factor [9; 10; 11; 12]. The other is a frequency-hopping spread spectrum (FHSS) method in which the frequency band is shifted using a spread code [13]. The FHSS method is randomly hopped according to the hopping pattern. By this method, an interceptor who does not know the hopping pattern cannot recover the signal. Furthermore, if any jamming is executed with malicious intent, the signal performance will be maintained because the center frequency will be continuously changed. This capability is called anti-jamming [14; 15]. A simple multiple-access underwater acoustic communication protocol called JANUS was designed and tested as a NATO standard. It was a binary frequency shift keying (BFSK)-based FH method [16]. A covert underwater acoustic communication scheme between an unmanned underwater vehicle (UUV) and a distant mother platform using an OFDM had been studied [17]. However, the previous FHSS method was of the form in which a single center frequency was hopped. A chirp-based method utilizes a data-modulated signal, which has its energy spread over a bandwidth that is greater than the rate of information being sent, like all spread spectrum systems. The chirp-based method is one in which the binary information modulates the slope of a linear chirp, with chirps representing zeros or ones. This method alone can be considered a covert underwater acoustic communication technology. Due to the wide bandwidth in the chirp-based method, immunity against various frequency-selective fading and a frequency diversity effect may be expected [18; 19]. Fractional Fourier transform (FrFT) is a generalized analysis method of the existing Fourier transform concept [20; 21]. In particular, when a chirp signal has a linear characteristic in the time-frequency domain, robust detection is possible in a noisy or reverberant environment, as the FrFT results can obtain a concentrated energy spectrum. The FrFT has been applied in various fields, such as radar, image processing and communication [22; 23; 24; 25]. Since underwater acoustic communication signals must typically pass through poor underwater channels, the coherent methods that are sensitive to phase shifts complicate the structure of the receiver. On the other hand, the non-coherent methods, such as the FrFT, can mitigate the fading effects with a relatively simple receiver structure. The chirp signal combined with FHSS and demodulated by the FrFT method was studied in recent times [26].