Abstract: In this paper the joint probability density function of the envelope and the first time derivative of envelope, and phase and first time derivative of phase for signals in IM-DD optical systems are derived. The level crossing rate and the average fade duration for envelope and phase of sine wave plus narrowband Gaussian noise are given. The envelope of signal and its derivative are independent. The first time derivative of the signals has Gaussian distribution.
Keywords: IM-DD optical system, level crossing rate, average fade duration, Gaussian noise.