First- and Second-Moment Constrained Gaussian Channels

This paper studies the channel capacity of intensity-modulation direct-detection (IM/DD) visible light communication (VLC) systems under both optical and electrical power constraints. Specifically, it derives the asymptotic capacities in the high and low signal-to-noise ratio (SNR) regimes under peak, first-moment, and second-moment constraints. The results show that first- and second-moment constraints are never simultaneously active in the asymptotic low-SNR regime, and only in few cases in the asymptotic high-SNR regime. Moreover, the second-moment constraint is more stringent in the asymptotic low-SNR regime than in the high-SNR regime.