1 A Geometry-Based Underwater Acoustic Channel Model Allowing for Sloped Ocean Bottom Conditions Meisam Naderi, Student Member, IEEE, Matthias P¨ atzold, Senior Member, IEEE, Rym Hicheri, and N´ eji Youssef Abstract—This paper proposes a new geometry-based channel model for shallow-water ocean environments in which the ocean bottom can slope gently down/up. The need for developing such an underwater acoustic (UWA) channel model is driven by the fact that the standard assumption of a flat ocean bottom does not hold in many realistic scenarios. Starting from a geometrical model, we develop a stochastic channel model for wideband single-input single-output vehicle-to-vehicle UWA channels using the ray theory assuming smooth ocean surface and bottom. We investigate the effect of the ocean-bottom slope angle on the distribution of the channel envelope, instantaneous channel capacity, temporal autocorrelation function, frequency correlation function, Doppler power spectral density, and the power delay profile. Theoretical and simulation results show that even a relatively small slope angle influences considerably the statistical properties of UWA channels. The validation of the proposed UWA channel model has been performed by fitting its main characteristic quantities (average delay, delay spread, and coherence bandwidth) to measurement data. In comparison with the conventional UWA channel model, which has been developed on the assumption of a flat ocean bottom, it is shown that the proposed UWA channel model enables the modelling of measured channels with higher precision. Index terms — Shallow underwater acoustic channels, instan- taneous channel capacity, Doppler power spectral density, power delay profile, temporal correlation function. I. INTRODUCTION In recent years, underwater acoustic (UWA) communication systems have received considerable attention. UWA networks have been studied in various areas due to their potential applications in oceanography that involve the exploration of the ocean [1], support for underwater robots [2], offshore oil industry exploration [3], and pollution monitoring [4], just to name a few examples. Owing to the fact that electromagnetic waves and laser beams suffer from high path loss in ocean water, acoustic signals are being used, especially, in medium- and long-range underwater communications. For the design, test, and performance analysis of UWA communication sys- tems, realistic channel models are required. This calls for the statistical analysis of UWA channels in terms of the channel envelope distribution, instantaneous channel capacity, M. Naderi and M. P¨ atzold are with the Faculty of Engineering and Science, University of Agder, 4887 Grimstad, Norway (e-mails: {meisam.naderi, matthias.paetzold}@uia.no). R. Hicheri and N. Youssef are with the Ecole Sup´ erieure des Communi- cations de Tunis, Ariana 2083, Tunisia (e-mails: {rym.hicheri@supcom.tn, neji.youssef@supcom.rnu.tn). correlation functions, Doppler power spectral density (PSD), and power delay profile (PDP). UWA wave propagation in the ocean is described by the wave equation, but the development of a proper propagation model by solving the wave equation is well known to be a difficult problem [5]. To circumvent this problem, approxima- tions by means of the ray theory are often used to model the acoustic wave propagation phenomena in ocean environments [6]. By invoking the ray theory, the energy of sound propagates in shallow-water environments along straight lines like light rays, where the speed of sound is assumed to be constant (isovelocity assumption) [5], [7], [8]. Moreover, several stochastic channel models have been de- veloped for UWA communication systems under the assump- tion that the ocean bottom is flat [5], [9]–[13]. For example, in [5] and [9], the total distances that macro-eigenrays travel between the transmitter and the receiver have been computed by using the method of image projections, which has first been introduced in [6]. In both aforementioned papers, the reference channel models have been developed by combining the deterministic ray-tracing concept with statistical methods to account for the randomness of the propagation environment. However, the ocean bottom is not necessarily flat and most parts of the ocean bottom slope gradually from the shore to the high and deep ocean. This natural feature motivated us to develop a new geometrical model which we call the sloped-ocean-bottom (SOB) model. The objective of this paper is to start from the geometrical SOB model and to develop a general stochastic UWA channel model that accounts for SOB conditions. It is shown that the flat-ocean-bottom (FOB) model, which is widely used in the literature [5], [9]–[13], can be obtained as a special case of the proposed model if the slope angle is zero. In this context, several studies have been conducted to in- vestigate the probability density functions (PDFs) of the UWA channel gains and the corresponding instantaneous capacity [14]–[16]. The study of these statistical characteristics is of great importance as it allows us to gain a deeper insight into the dynamical and temporal behavior of UWA channels. In this paper, we develop a geometry-based UWA chan- nel model assuming ray propagation in shallow-water ocean environments by taking macro-scattering effects, which are caused by specular reflections at the surface and bottom of the ocean, into account. The randomness of the UWA channel as a result of micro-scattering (diffuse scattering) effects will not be discussed in this paper. Starting from the geometrical SOB