Achievable Rate Region of the Zero-Forcing Precoder in a $2\times 2$ MU-MISO Broadcast VLC Channel With Per-LED Peak Power Constraint and Dimming Control

In this paper, we consider the <inline-formula><tex-math notation="LaTeX">$2\times 2$</tex-math></inline-formula> multiuser multiple-input-single-output (MU-MISO) broadcast visible light communication (VLC) channel with two light emitting diodes (LEDs) at the transmitter and a single photodiode (PD) at each of the two users. We propose an achievable rate region of the zero-forcing precoder in this <inline-formula><tex-math notation="LaTeX">$2\times 2$ </tex-math></inline-formula> MU-MISO VLC channel under a per-LED peak and average power constraint, where the average optical power emitted from each LED is fixed for constant lighting, but is controllable (referred to as dimming control in IEEE 802.15.7 standard on VLC). We analytically characterize the proposed rate region boundary and show that it is Pareto-optimal. Further analysis reveals that the largest rate region is achieved when the fixed per-LED average optical power is half of the allowed per-LED peak optical power. We also propose a novel transceiver architecture where the channel encoder and dimming control are separated, which greatly simplifies the complexity of the transceiver. A case study of an indoor VLC channel with the proposed transceiver reveals that the achievable information rates are sensitive to the placement of the LEDs and the PDs. An interesting observation is that for a given placement of LEDs in a <inline-formula><tex-math notation="LaTeX">$\text{5}\ \text{m}\times \text{5}\ \text{m}\times \text{3}\ \text{m}$</tex-math></inline-formula> room, even with a substantial displacement of the users from their optimum placement, reduction in the achievable rates is not significant. This observation could therefore be used to define “coverage zones” within a room where the reduction in the information rates to the two users is within an acceptable tolerance limit.