In this paper, we consider an indoor hybrid visible light communication (VLC) and radio frequency (RF) communication scenario with two-hop downlink transmission. The LED carries both data and energy in the first phase, VLC, to an energy harvester relay node, which then uses the harvested energy to re-transmit the decoded information to the RF user in the second phase, RF communication. The direct current (DC) bias and the assigned time duration for VLC transmission are taken into account as design parameters. The optimization problem is formulated to maximize the data rate with the assumption of decode-and-forward relaying for fixed receiver orientation. The non-convex optimization is split into two sub-problems and solved cyclically. It optimizes the data rate by solving two sub-problems: fixing time duration for VLC link to solve DC bias and fixing DC bias to solve time duration. The effect of random receiver orientation on the data rate is also studied, and closed-form expressions for both VLC and RF data rates are derived. The optimization is solved through an exhaustive search, and the results show that a higher data rate can be achieved by solving the joint problem of DC bias and time duration compared to solely optimizing the DC bias.

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