# Generalized Chirp Spread Spectrum for Underwater Acoustic Communications
## 1 Introduction
For military purposes, such as submarine communication, long range communication is required compared to the distance required in civilian areas. As the communication range increases, the signal-to-noise power ratio (SNR) decreases, making it more difficult to estimate and compensate for the underwater acoustic channel, which makes overcoming channel-related impacts even more challenging [24; 25]. Therefore, in long range underwater acoustic communication, where channel estimation and compensation are difficult, frequency shift keying (FSK) modulation shows a better communication performance than phase shift keying (PSK) [26; 27]. The FSK modulation transmits single tones with different frequencies sequentially according to the bits to be transmitted, and the demodulation is performed simply by measuring the energy of the frequency bin for each symbol [28; 29]. The FSK modulation and demodulation do not require channel estimation or compensation because demodulation is based on energy detection. However, if interference occurs due to multipath or deep fading happens at the frequency corresponding to the FSK basis, the demodulation performance can significantly deteriorate. In underwater acoustic environments, chirp signals offer a powerful solution to the interference problems caused by multipath. In wireless communication, synchronization of communication signals is often achieved by transmitting a synchronization chirp signal before the data symbols, followed by cross-correlation to perform synchronization. Crosscorrelation produces as many peaks as the number of paths caused by multipath, allowing for an estimation of the number of paths and their delays. Chirp signals are resilient to frequency-selective fading due to their time-varying frequency. Even when multiple paths are received, these signals can be distinguished and combined, leading to an improved demodulation performance. This approach not only mitigates the effects of multipath and inter-symbol interference (ISI), but also eliminates the need for channel estimation and compensation through energy detection [30, 31]. To overcome the impact of multipath in underwater environments, chirp-based modulation/demodulation techniques have been developed for long range communication, which are robust to multipath [32, 33, 34, 35, 36, 37, 38, 39, 40, 41]. Up/down-chirp spread spectrum (CSS) modulates signals into up-chirp or down-chirp signals based on the transmitted bit, and as up-chirp and down-chirp satisfy quasi-orthogonality, energy detection is performed by multiplying the conjugate chirp of each up or down-chirp [34, 35, 36]. However, because up/down-CSS is limited to a modulation order of 2 (up or down), the symbol length must be shortened to increase the transmission rate, which reduces the chirp orthogonality and the symbol's energy, thus lowering the demodulation performance. Long range-chirp spread spectrum (LoRa-CSS) modulates signals by circularly shifting the chirp signal according to the bits to be transmitted, distinguishing them by the starting frequency. Demodulation is performed by multiplying the received signal with a down-chirp signal to cancel the frequency change over time, followed by fast Fourier transform (FFT) to extract the frequency components corresponding to each symbol. However, as the modulation order increases, the circular shift intervals become narrower, reducing the symbol orthogonality. In addition, due to the limitations of FFT resolution, the demodulation performance deteriorates [37, 38, 39, 40, 41]. In this paper, we propose a generalized-CSS (G-CSS) that supports various modulation orders to improve the communication performance, including transmission rate and BER, of chirp-based modulation and demodulation schemes. While conventional LoRa-CSS and up/down-CSS methods offer advantages in terms of a simple implementation structure, they suffer from performance degradation due to reduced symbol orthogonality as the modulation order increases.