Spatial time division multiple access for visible light communication networks

Visible light communication (VLC) technology has recently emerged as a new complementarity approach to radio frequency (RF) methods as it allows transmission data rates of significantly high orders of magnitude [3], [6]. Since power transmission in a VLC network is directly affected by the quality of the channel between the emitter and receiver, it is highly necessary to find minimum slot schedules with minimum power cost while ensuring the whole connectivity of the network. Spatial Time Division Multiple Access (STDMA) protocol achieves full connectivity in wireless networks by allowing simultaneous data rate transmission of multiple nodes within each time slot [10]. In this paper, we propose a weighted mixed integer linear programming (MIP) model to minimize the total number of slots and power consumption in a VLC network. First, we solve the optimization problem assuming that the number of slots can be as large as the number of edges in the network. Then, as second strategy we further propose a greedy algorithm that allows to obtain a reduced slot feasible schedule required to establish communication for every node in the network. The number of slots found by the greedy algorithm is used as input to solve the optimization problem as well. We consider disk graph instances with different densities, radial transmission ranges for direct Line of Sight (LOS) communication and generate power data using VLC formulas. Our preliminary numerical results indicate that the greedy algorithm reduces significantly the CPU time and number of variables of the proposed MIP model leading to optimal solutions with more efficiency.