Concatenated Vertical Channel Modeling and Performance Analysis for HAP-Based Optical Networks

In this paper, we look into the modeling of free space optical channel and design of the HAP-based wireless optical networks. For vertical beam propagation, the pressure and temperature gradients alter with height. Microscale variations in refractivity result in uncertainties that depend on elevation. As a result, irradiance fading variance caused by turbulence keeps on changing throughout the propagation path. Also, the eddies' shape transitions from spherical and symmetrical near the ground to highly asymmetrical and anisotropic at heights far away from the ground. In this paper, taking into account these variations concerning height, we propose to break the vertical FSO (VFSO) channel into parallel layers. We develop a VFSO channel model built upon the cascaded structure of fading coefficients. Correlated phase screen simulation method is used to verify the accuracy of the proposed channel model. Next, a closed-form expression for the probability density function is developed for the concatenated channel incorporating a generalized pointing error model. To demonstrate the significance of this newly developed VFSO channel model in HAP-based optical networks, closed-form expressions for bit error rate performance is also derived. Monte Carlo simulations substantiate that the newly formulated analytical expressions offer accurate assessments of the BER performance for HAP-based VFSO links. For HAP-based optical networks facing weak turbulence, the newly developed expressions provide an accuracy of about 2 dB for a BER of $10^{-4}$ as compared to the existing competitive models. This value increases to 4 dB after incorporating pointing errors in HAP-based optical networks. In optical networks facing strong fluctuation regions, the newly developed expressions provide an accuracy of about 8 dB for a BER of $10^{-4}$ as compared to the existing competitive model. Similar observations are made after incorporating pointing errors in HAP-based optical networks facing strong turbulence regions.