# Orthogonal Chirp Division Multiplexing for Underwater Acoustic Communication
## 1 Introduction  
UWAC has multiple applications ranging from military to commercial fields, including scientific uses. However, the severe characteristics of the underwater acoustic channel such as time variation, high ambient noise, limited bandwidth and extended multipath effect make data transmission through underwater acoustic signals very challenging [1; 2; 3; 4]. By the use of frequency sweep signals, which are resistant to the detrimental effects of the UWAC channel, the Chirp Spread Spectrum (CSS) modulation technique offers robust performance with a very simple matched filtering-based decoder that makes such a communication scheme particularly adapted to the UWAC channel [5; 6]. In the CSS system, a broad spectrum is occupied to modulate the information in order to achieve high processing gain and multipath resolution to the detriment of the spectral efficiency. As a result, CSS is very attractive for a low and medium data rate UWAC link when reliability is considered as a priority factor. In order to optimize data rates with respect to the occupied bandwidth, research works in the 1990s focused on Single Carrier (SC) coherent Phase Shift Keying (PSK) and Quadrature Amplitude Modulation (QAM) signaling for UWAC. These modulation methods offer high spectral efficiencies, but require complex receivers that need to equalize extensive Channel Impulse Response(CIR) while tracking time variations and phase distortions. Nowadays, turbo-equalization approaches in the time [7; 8; 9] or frequency domain [9; 10] are often preferred for UWAC since these algorithms provide a good trade-off between performance and complexity. On the other hand, in the last decade, the conversion of OFDM modulation [11] to UWAC has been deeply investigated in the literature in order to improve the data rate of underwater telemetry while keeping a one tap equalizer at the reception side. OFDM-based UWAC modulation systems have demonstrated high spectral efficiencies in real undersea experiments, but also sensitivity to Doppler spread that breaks the subcarriers orthogonality, yielding to Inter-Carrier Interference (ICI). Thus, UWAC systems based on OFDM often require advanced ICI compensation algorithms [12; 13]. Very recently, a new modulation scheme called OCDM has been introduced in the field of optical fiber communications [14]. The basic principle of OCDM consists of multiplexing a number of chirp waveforms that are mutually orthogonal with each other and sharing the same bandwidth and time slot. With respect to single chirp modulation, OCDM increases the transmitted data rate by overlapping data in both the time and chirp domain. On the other hand, the OCDM approach shares many similarities with the OFDM system like orthogonal waveform multiplexing, which is based on the Fresnel transform [15], instead of the Fourier transform, as in OFDM. In a previous paper [16], the use of OCDM for UWAC was experimented with, yielding very promising results, but the study was limited to a simulated UWAC channel. The purpose of this paper is to extend the results of [16] to more realistic transmission channels in order to illustrate the feasibility of the OCDM system in real scenarios and its advantages against the conventional OFDM system. This paper is organized as follows: Section 2 describes the OCDM concept and its formulation. In Section 3, the detailed transmission structure is presented, which includes the modulator and receiver algorithms and the experimental channel. Section 4 provides the experimental performance over a static tank channel and replayed dynamic experimental channels, where OCDM is demonstrated to outperform conventional OFDM under certain circumstances. Finally, Section 5 presents the conclusion of this paper. Notation: \(\left(\cdot\right)^{*}\) stands for conjugate, \(\left(\cdot\right)^{T}\) for transpose and \(\left(\cdot\right)^{H}\) for Hermitian transpose. \(\mathbf{x}\) denotes a column vector, and \(\mathbf{X}\) is a matrix.