Performance Characterization of Ultrahigh SpeedOptically Amplified Spectral-Phase EncodedOCDMA Systems with Second-Harmonic-Generation Effect in Thin and Thick Crystal Receiver Structures

In this paper we study and evaluate the performance of a spectral-phase encoded optical CDMA (SPE-OCDMA) system using advanced receiver structures based on second harmonic generation (SHG) effect imposed in a Thick or Thin crystal. This receiver structure is employed as the nonlinear pre-processor prior to the conventional low-speed photodetector. In our performance evaluation amplified spontaneous emission (ASE) of the optical amplifiers, receiver front end thermal noise and photodetector shot noise which are effective in low power conditions, and multiple access interference (MAI) noise which is the dominant source of noise in high power conditions in any coherent OCDMA communications system have been considered. We begin by studying the statistical behavior of Thick crystals in an optically amplified digital lightwave communication system in the context of a SPE-OCDMA communication system. The error probability for Thick crystal receiver structure is evaluated using Saddle-Point approximation. Furthermore, we obtain a closed form approximation for the probability density function (pdf) of the decision variable in SPE-OCDMA systems with Thin crystal SHG receiver. In this analysis, to obtain approximate probability density function, we employ Gram-Charlier expansion based on the corresponding first order moments of the decision variable. The first three moments are obtained in a closed form approximation and consequently a closed form expression for the error probability is obtained by integrating the approximated pdf of the decision variables for transmitting bit "1" and "0" in Thin crystal receiver structure. The precision of the approximation is verified by the Monte-Carlo simulation. Finally the performance of SPE-OCDMA network for both Thin and Thick SHG crystals are analytically evaluated and discussed for different number of interfering users and different code-lengths and different speed of the conventional photodetectors. We deduce that the performance of Thin SHG crystal receiver is more sensitive to the transmitted power level especially in low power conditions. It is concluded that in low power conditions where ASE, thermal and shot noises are the dominant noise sources, Thick SHG crystal receiver outperforms the Thin crystal receiver. However, in high power conditions where MAI noise is the most effective noise term, Thin SHG crystal receiver structure outperforms the Thick crystal receiver.