# Generalized Chirp Spread Spectrum for Underwater Acoustic Communications
## 1 Introduction  
For the flexible operation of various underwater systems needed for marine resource exploration, disaster monitoring, and military purposes such as harbor surveillance systems, underwater communication technology is essential [1, 2, 3, 4, 5]. Due to the characteristics of underwater communication media, radio frequency (RF) signals used on land experience strong transmission losses, making it difficult to transmit signals over a long range underwater [6, 7]. In underwater environments, both optical and acoustic communication methods are employed, with each having distinct characteristics [8, 9]. Specifically, acoustic signals experience less transmission loss compared with RF signals, making them relatively suitable for long range underwater communications. However, acoustic signals travel much more slowly than RF signals, and their speed can vary due to factors like water temperature and salinity [10, 11, 12, 13]. Due to non-uniformity in sound speed, the acoustic signals tend to bend rather than travel in straight lines. Moreover, the acoustic signals are reflected and refracted by the sea surface and seabed during transmission, resulting in the formation of a multipath channel with a long delay [14, 15]. The multipath channel causes frequency-selective fading and deep fading in the received signal, making it difficult to guarantee a stable communication performance [16, 17]. In addition, in cases where the transmitter or receiver is moving, such as in mobile underwatercommunication systems, the multipath channel varies over time, further degrading the communication performance. Unlike RF communication, underwater acoustic communication transmits signals via sound waves, leading to environmental constraints such as limited bandwidth, high signal attenuation, and interference caused by multipath. These characteristics demand approaches different from traditional terrestrial communication methods, particularly efficient modulation schemes and multiple access techniques to separate signals from multiple users. Orthogonal frequency division multiplexing (OFDM) is widely used in underwater communication because it is resilient to multipath fading and supports high data transmission rates in frequency-selective fading environments [18; 19]. OFDM divides the signal into multiple orthogonal subcarriers for transmission, minimizing interference caused by multipath delays and improving the demodulation performance. However, severe Doppler effects in underwater channels can compromise the orthogonality between subcarriers, leading to a significant performance degradation. Direct sequence spread spectrum (DSSS) exhibits robust characteristics against multipath interference and narrowband interference in underwater communications. However, in underwater environments, Doppler shifts occur due to the movement of transmitters or receivers, which can cause performance degradation by making it difficult to align DSSS spreading codes with signals. As DSSS spreads signals across a wide frequency band, the signal can be weakened under the same power conditions, and a high signal processing capability is required for signal detection. Due to its use of wide frequency bands, DSSS may have low spectral efficiency in underwater communication environments where frequency resources are limited [20; 21]. Code division multiple access (CDMA) is another spectrum spreading technique that uses orthogonality between codes to allow multiple users or data streams to share the same frequency band [22; 23]. CDMA is well-suited to underwater acoustic communication environments with significant multipath interference, as it can mitigate interference for each path and achieve array gain from orthogonal codes, ensuring a robust communication performance even in low SNR conditions. However, CDMA suffers from reduced transmission rates due to orthogonal codes, and in highly dynamic channels, such as those with Doppler shifts, channel estimation and compensation become challenging.