In this paper, we study the performance of all optical AND gates based on the four-wave-mixing (FWM) process, for\ud application in the receivers of the spectral phase encoded optical code division multiple access (SPE-OCDMA) systems. For the\ud performance analysis, the spectral domain auto-correlation function of the multiple access interference signal at the output of the\ud optical AND gate is derived and then mean and variance of the photo-detector current are calculated. For solving the Fourier\ud transform of FWM non-linear Schrodinger equations, spectral domain Volterra series are used and the solution of these\ud coupled equations is approximated with the first three terms of the Volterra expansion. Finally, the performance of AND\ud gating receivers in SPE-OCDMA systems is analysed and the bit error rate in terms of the pump power and the number of\ud active users is depicted. In addition, a compression between the performance of the time-gating receivers, base on FWM in\ud synchronous mode and other non-linear receivers such as second harmonic generation and self-phase modulation is made.Postprint (published version

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