# Achievable Rate Region of the Zero-Forcing Precoder in a 2 X 2 MU-MISO Broadcast VLC Channel with Per-LED Peak Power Constraint and Dimming Control

## TL;DR

This paper analyzes the achievable rate region of a 2x2 MU-MISO VLC channel with zero-forcing precoding under power and dimming constraints, proposing a Pareto-optimal boundary and a simplified transceiver architecture.

## Contribution

It introduces an analytical characterization of the rate region boundary and a novel transceiver design for VLC with dimming control, enhancing understanding and practical implementation.

## Key findings

- Maximum rate region occurs at half of the peak power.
- Achievable rates are sensitive to LED and PD placement.
- Coverage zones can be defined with acceptable rate reduction.

## Abstract

In this paper, we consider the 2 X 2 multi-user multiple-input-single-output (MU-MISO) broadcast visible light communication (VLC) channel with two light emitting diodes (LEDs) at the transmitter and a single photo diode (PD) at each of the two users. We propose an achievable rate region of the Zero-Forcing (ZF) precoder in this 2 X 2 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 5 m X 5 m X 3 m 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.