Optimal Placement of Access Points in Cellular Visible Light Communication Networks: An Adaptive Gradient Projection Method

In this paper, a new approach toward the optimization of Access Point (AP) placement in cellular Visible light Communication (VLC) networks is proposed based on the projected gradient algorithm. The objective of the optimal placement problem is to maximize the average throughput of the network subject to constraints on the minimum illumination level and the minimum rate of the users. This optimization framework gives the enhanced AP deployment in case of users with static, nomadic, or completely mobile behavior. Taking the distribution of users, the receiver's field of view, reflection from walls and interference from neighboring APs into account makes the deployment problem complicated. To solve the arising intricate optimization problem, we derive analytical expressions for gradients of the objective and use them in the gradient ascent algorithm. The proposed adaptive gradient projection method then realizes the constraints. This method relaxes the projection onto a high dimensional space to planar projections, which are implemented using efficient tools from computational geometry. The proposed method eliminates the need for an intractable exhaustive search to find the optimal placement of VLC APs in cellular VLC networks, while it gives either exact optimum or very close approximations to the optimal placement. It is shown, with the aid of properties of convolution of parametric concave functions, that in some practical cases the objective function is unimodal and has no local optimum. Simulation results show a significant improvement in the throughput, SINR and outage probability of the system when the access points are deployed according to their optimized placement, determined by the algorithm. On the other hand, proper constraints on the minimum achievable rate and minimum illumination level improve the worst-case performance of the network to the desired extent.