Channel capacity and power allocation of MIMO visible light communication system

In this paper, the channel capacity of the multiple-input multiple-output (MIMO) visible light communication (VLC) system is investigated under the peak, average optical and electrical power constraints. Finding the channel capacity of MIMO VLC is shown to be a mixed integer programming problem. To address this open problem, we propose an inexact gradient projection method to find the channel capacity-achieving discrete input distribution and the channel capacity of MIMO VLC. Also we derive both upper and lower bounds of the capacity of MIMO VLC with the closed-form expressions. Furthermore, by considering practical discrete constellation inputs, we develop the optimal power allocation scheme to maximize transmission rate of MIMO VLC system. Simulation results show that more discrete points are needed to achieve the channel capacity as SNR increases. Both the upper and lower bounds of channel capacity are tight at low SNR region. In addition, comparing the equal power allocation, the proposed power allocation scheme can significantly increase the rate for the low-order modulation inputs.