## 1 Introduction
A beam of the second type, illustrated as the checkboard area (Zone 2) in Figure 2, is formed due to reversal of propagation direction along the depth. In principal, the second type is not experienced unless either a surface reflection takes place, or the propagation path experiences a LEP. Hence, for a receiver in an overlapping zone, multiple transmissions from the same sender are received which either result in wasting the transmitter's energy or increasing the probability of collision. Therefore, the selection of transmission angles is critical for avoiding these problems. Figure 1: Different types of underwater ray configurations based on their propagation path. Part (**a**) illustrates the simulation results of Bellhop ray tracing algorithm for transmitted signals at small angles in the extreme SSP gradients shown on the left, while part (**b**) shows (i) a direct ray (Ray 1), (ii) rays with single Local Extremum Point (LEP) (Rays 2 and 3), (iii) reflected rays (Rays 4 and 5), and (iv) multi LEP rays (Ray 6). Summary of Contribution: To tackle the challenges presented above, this paper proposes a beam selection mechanism for deep-water setups that aids node in utilizing the directional transmission capability and avoiding generation of both overlapping beams and shadow zones in a three-Dimensional (3D) environment. Essentially, we leverage a geodesic grid to define a hypothetical 3D structure around the node and then utilize it to determine transmission angles that minimize beam overlapping while avoiding shadow zones. Moreover, since most of the ray tracing algorithms are designed to work in two-dimensional subspace (2D), we propose a projection scheme that maps the 3D underwater environment into an equivalent 2D where the SSP structure along the depth is retained, i.e., preserve the inhomogeneous effect of the environment on the traversing acoustic rays. Moreover, since most legacy systems have limited computational capabilities, such 2D mapping can be used to lower the computational burden on nodes while ensuring accuracy. Since knowing the last location of a drifted neighbor is not enough to determine the best angle to reestablish communication, we propose a beam classification technique that aids nodes in determining the most suitable angles to cover different geographical regions. Specifically, we utilize the 2D environment and the known SSP of the water column to categorize rays into three distinct types, namely direct rays, reflected rays and refracted rays experiencing LEPs. Then based on the expected coverage area of each ray type, we divide the underwater environment into four distinct geographical regions. We then use the boundaries of these regions to suggest ray types that increases the chances of reestablishing communication with drifted nodes. The paper is organized as follows. The related work is summarized in Section 2. Section 3 discusses the system model and covers basic concepts regarding the used transducer, the layering and SSP estimation mechanism, surface-caused signal reflection and ray tracing. Section 4 goes over the steps of the proposed algorithm in detail where the angle discretization and selection, node orientation, neighbor discovery and ray classification techniques are discussed. Section 5 reports on the performance of the ray classification techniques. Finally, Section 6 concludes the paper. Figure 2: Illustration of shadow and overlapping regions where a transmitter is placed at depth of 500 m while the seabed is at 850 m. The left figure shows the sound speed profile while the right one shows the ray propagation path where the inhomogeneity of the medium complicates the spreading pattern of waves. Nodes laying in the shadow zones will not detect the transmitted waves while node in the overlapping regions receive multiple transmissions.