The globally introduced 5G mobile networks enable a variety of broadband applications from massive machine type communications (mMTC) to ultra-reliable low latency communications (URLLC). Within this context, optical technologies such as radio over fiber (RoF), radio over free space optics (RoFSO) and optical satellite networks are designated to provide excellent backhaul services. In this paper, the power optimization problem is investigated for a fully optical hybrid satellite network. Specifically, the dual hop decode-and-forward optical downlink is considered with a geostationary satellite source, an optical ground gateway and an optical user equipment. The power allocation problem is formatted as a convex optimization problem under separate total and peak power constraints and then a methodology is proposed for the maximization of system's capacity. Moreover, the proposed methodology takes into account the atmospheric attenuation, the optical channel correlation and turbulence effects and its performance is evaluated through numerical simulations and comparisons with other power allocation implementations. Results regarding the spectral efficiency are presented and commented proving the proposed methodology's superiority.
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