Visibility range distribution modeling for free space optical link design in South Africa: Durban as case study

An investigation of the Visibility Range Distribution (VRD) for Free Space Optical (FSO) applications within South Africa (Durban) is presented in this paper. The behavior of optical signals in the atmospheric channel depends on the magnitude of the visibility which in turn is the most important parameter required to achieve an optimal link performance and optical signal availability at 99%. To obtain the optimal estimation of the observed visibility Probability Distribution Function (PDF), the Triweight Kernel estimator was utilized based on the three years visibility data collected from both the Time and Date Weather Services and South Africa Weather Services (SAWS). The three-parameter Log-Pearson (LP3) and three-parameter Weibull (W3) distributions confirmed their appropriateness in representing the regional visibility data, based on the statistical performance tests. Due to complexities in the computation, the distribution parameters of these two distributions were obtained using the Maximum Likelihood Estimation method. Thus, the nearness of the estimated LP3 and W3 PDFs of the visibility to the observed visibility distribution in Durban, was obtained by applying one of the highest efficiency kernel estimator for non-parametric analysis. As a result, the lowest Integral Square Error (ISE) and Root Mean Square Error (RMSE) values were obtained, and from the investigation, the optimized W3 PDF outperforms the optimized LP3 PDF in terms of the mean ISE and RMSE values for all the weather conditions considered. The mean ISE values of both the LP3 and the W3 distributions are 0.0162 and 0.0059 respectively, and their corresponding mean RMSE values are 0.0514 and 0.0343 respectively. Thus, we obtained the actual coefficients of the LP3 and W3 distributions of the VRD for the city of Durban, which is one of the main focus of this paper. This research has a uniqueness and importance for FSO applications within South Africa and can be extended to regions with similar climatic (sub-tropic) conditions. Also, according to the results, with the best choice of kernel bandwidth this approach for estimating the distribution of visibility which is rarely used for visibility distribution modeling has shown that the kernel estimates yielded a better performance over the optimized PDF approach in terms of the Mean ISE and RMSE evaluations. Finally, the study of the variations and structure of visibility classification is critical and important for FSO link planners and engineers, due to the consequences of the unpredictable nature of visibility on FSO applications.