On the Capacity of Bandlimited Optical Intensity Channels With Gaussian Noise

We determine the lower and upper bounds on the capacity of bandlimited optical intensity channels (BLOIC) with white Gaussian noise. Three types of input power constraints are considered: 1) only an average power constraint; 2) only a peak power constraint; and 3) an average and a peak power constraint. Capacity lower bounds are derived by a two-step process including: 1) for each type of constraint, designing admissible pulse amplitude modulated input waveform ensembles and 2) lower bounding the maximum achievable information rates of the designed input ensembles. Capacity upper bounds are derived by exercising constraint relaxations and utilizing known results on discrete-time optical intensity channels. We obtain degrees-of-freedom-optimal (DOF-optimal) lower bounds which have the same pre-log factor as the upper bounds, thereby characterizing the high SNR capacity of BLOIC to within a finite gap. We further derive intersymbol-interference-free (ISI-free) signaling-based lower bounds, which perform well for all practical SNR values. In particular, the ISI-free signaling-based lower bounds outperform the DOF-optimal lower bound when the SNR is below 10 dB.

I. Introduction

Intensity modulation and direct detection (IM/DD) is widely used in optical communications. In IM/DD, information is conveyed by the varying intensity of transmitted optical signal, and the receiver detects the intensity of the received signal. There have been extensive studies on design and realization of IM/DD based optical wireless communication systems (see [1], [2] and references therein). This paper focuses on a simplified IM/DD channel model, known as the optical intensity channel with Gaussian noise. This model is suitable for some kinds of IM/DD systems, e.g., indoor free space optical communications [1], [3]. In optical intensity channels, typically the average and/or peak optical power is constrained due to safety reasons and practical considerations. Therefore the optical intensity channel we considered has two fundamental differences with electrical channel models like the classical AWGN channel: 1) a nonnegativity constraint on the input signal, 2) a different input cost metric. It is clear that typical signaling methods for electrical channels cannot be applied directly in optical intensity channels because of these differences.¹

Since the optical intensity is the optical power transferred per unit area, a constraint on optical power is also a constraint on intensity. In this paper we use ‘power’ to refer to the optical power unless otherwise specified.