Secrecy Capacity Analysis for Indoor Visible Light Communications with Input-Dependent Gaussian Noise

This paper mainly focus on the performance of secrecy capacity in the physical layer security (PLS) for the eavesdropping channel in visible light communication (VLC) system. In this system, due to the effects of thermal and shoot noises, the main interference of the channel is not only from additive white Gaussian noise (AWGN), but also dependent on the input signal. Considering a practical scenery, based on the input-dependent Gaussian noise, the closed-form expression of the upper and lower bounds of secrecy capacity are derived under the constraints of non-negative and average optical intensity. Specifically, since the entropy of the output signal is always greater than the input signal, on this basis, the derivation of lower bound is using the variational method to obtain a better input distribution. The upper bound is derived by the dual expression of channel capacity. We verified the performance of secrecy capacity through numerical results. The results show that the upper and lower bounds are relatively tight when optical intensity is high, which proves validity of the expression. In the low signal-to-noise ratio (SNR) scheme, the result of bounds with more input-dependent noise is better than less noise. And in the high SNR scheme, the result of bounds with less input-dependent noise outperforms that noise is more.