Achieving Channel Capacity of Visible Light Communication

In this article, we propose an efficient inexact gradient descent method to obtain the channel capacity-achieving input distribution of visible light communication (VLC). Under both a peak and an average optical power constraints, finding the channel capacity of VLC is formulated as a mixed continuous-discrete optimization problem without an analytical expression of the objective function. To solve this challenging problem, we first adopt the numerical integration method to approximate the objective function and its gradient. Here, we prove that the gaps between the original functions and the approximations can be arbitrarily small. Then, based on the approximated functions, we describe the method, and theoretically show that the obtained solution sequence converges to the channel capacity-achieving discrete distribution of VLC. We also provide simulation results to verify the effectiveness and optimality of the proposed method. More importantly, the simulations numerically reveal that on-off keying (OOK) modulation achieves the capacity of VLC channel at low signal-to-noise ratio (SNR), while pulse amplitude modulation (PAM) achieves the capacity at high SNR.

I. Introduction

Visible light communication (VLC) has drawn significant attention recently in both academia and industry owing to its vast license-free spectrum, low electromagnetic interference, high security, and high data rates [1]–[5]. Different from the conventional radio frequency (RF) communication, VLC adopts the intensity modulation and direct detection (IM/DD) scheme, where the transmitted information is modulated onto the intensity of light. Thus, the transmitted signal should be real and nonnegative, and the Gaussian distribution that achieves the classic channel capacity of RF cannot be used in VLC channels. To meet the requirements of eye safety and practical illumination, the transmitted signals should be controlled by satisfying both a peak and an average optical power constraints. Under this setup, it has been proved that the capacity-achieving distribution of VLC channels is discrete over a finite set of points [6], [7]. However, it is yet unknown how to efficiently search the capacity-achieving discrete distributions for VLC channels, since the current method is just the exhaustive search at every signal-to-noise ratio (SNR) point [6]. In [7], the authors derived a necessary and sufficient condition for achieving capacity and proposed an exhaustive search algorithm to find the capacity-achieving measure, which is similar to the approach in [6]. The key challenge in finding the capacity of VLC channels is that there is no analytical expression for the mutual information with the discrete input.