# Misalignment-Resilient Propagation Model for Underwater Optical Wireless Links +
## 1 Introduction
For example, this model assumes absolute alignment between the transmitter and receiver (which clearly does not match the scenario depicted in Figure 1, as it is challenging to maintain the AUV's position due to the presence of currents and tides) and also does not account for the photons that undergo scattering but are still detected by the receiver (which greatly underestimates the detected power, especially in turbid waters). Contrarily, an accurate model for simulating underwater environments is the radiative transfer equation (RTE) [10]. Yet, as this involves nonlinear integro-differential equations (such as the scattering phase function), it is very difficult to solve analytically, and thus numerical procedures such as Monte Carlo simulations are preferred. In our previous work [11; 12], the RTE was numerically solved through a Monte Carlo simulation which accurately predicted the detected power and performed an estimation of the channel bandwidth for four water types and different beam divergences. In this work, our primary focus is to design a model that can account and compensate for a misalignment between the transmitter and receiver. To increase the misalignment tolerance, we simulated a multi-sensor-lens pair scheme in a model based on a Monte Carlo simulation of photon propagation underwater. This system, which additionally models the photon refraction at the lenses' interface, allowed us to obtain novel results for angular misalignments and different sensor configurations based on the circle packing in a circle algorithm. It is pertinent to understand how lateral or angular offsets will impact the signal strength, which needs to be foreseen in an actual system design. The maximum deviation in the Rx or Tx position to avoid misalignment can be assessed by calculation of the maximum allowed lateral offset (MALO). The MALO of the emitter or sensor has been previously analyzed in the literature [4; 5; 13; 14], as the maximum offset complies with a minimum required received optical power. Here, we obtain the MALO even when the transmitter or receiver may be angularly misaligned. These works considered emitter beams with divergence, treating the sensor as a simple aperture. However, to the best of the authors' knowledge, Monte Carlo-based simulation for accurate treatment of lens behavior does not appear in the literature. Moreover, we consider each sensor as a lens and sensor pair located at the lens focal distance from each other to improve the light collected by the sensor. We present several sensor architectures with a variable number of sensor-lens pairs and evaluate the performance in terms of position and rotation misalignment of the sensor with the emitter beam. Moreover, based on this multiple-sensor configuration and specifically the light power distribution at the receiver, defined by the power at each lens-sensor pair, we propose a random forest machine learning method to predict the lateral offset and angle of the AUV in relation to a fixed sensor configuration. The remainder of this paper is organized as follows. Section 2 presents the implemented Monte Carlo simulation model, with a thorough description of the features added and the photon propagation conditions leading to the ulterior validation of the algorithm based on experimental results from the literature. Moreover, several sensor architectures are studied, and proper treatment of the lens behavior is developed, leading to identification of the optimal sensor scheme, and the parameters considered in the simulations are shown. The simulation results for different sensor schemes, water types, propagation distances, and angular misalignment, which are described in Section 3, where several communication scenarios are assessed, and some analysis of the system limitations that permit communications engineers to build their systems more efficiently are shown. Section 4 addresses the live misalignment offset prediction system based on the random forest machine learning technique. The final conclusions and remarks are given in Section 5.