Achievable Rate With Closed-Form for SISO Channel and Broadcast Channel in Visible Light Communication Networks

In this paper, we study the channel capacity and region for both the single-input-single-output (SISO) channel and broadcast channel (BC) in visible light communication (VLC) systems, under the peak optical power, average optical power, and electrical power constraints. Under the condition that the input signal is continuous, we develop a closed-form lower bound (termed ABG lower bound) and an upper bound for SISO channel using the entropy power inequality and Lagrangian function method. Moreover, a closed-form achievable rate region (termed ABG region) is derived for the VLC BC. Furthermore, for a multi-light-emitting diode and multiuser VLC system, we propose an achievable rate expression for each user, and then investigate a VLC BC beamforming design problem by utilizing the obtained closed-form expression. The beamforming design problem is shown to be NP-hard, and we transform this problem into a convex semidefinite program by using the semidefinite relaxation technique. Finally, numerical results are presented to evaluate the performance of the proposed ABG lower bound/region and the beamforming design.