A comprehensive mathematical model of Successive Interference Cancellation (SIC) using Direct Sequence (DS) and Spectral Amplitude Coding (SAC), which is employed in incoherent optical CDMA using On-Off Keying (OOK) Pulse Position Modulation (PPM) and On-Off Keying (OOK) considering the presence of Phase-Induced Intensity Noise (PIIN), shot noise and thermal noise is presented in this work. SIC scheme has the potential to suppress Multiple Access Interference (MAI). The concept of SIC is the following: detection is taken place in successive stages where the most reliable symbols are chosen at each stage. Where the interference contributed by the already detected symbols will be removed. It has been found out that, theoretically, the size of M-ary on optical CDMA system limits the MAI effect. Thus, the system performance improves with the increasing of M-ary PPM. Hence, the system using PPM has better performances if compared to the one using OOK, due to a lower average number of interfering optical pulses. In addition, a lot of users can be accommodated with SIC/SAC-optical CDMA based PPM signaling system instead of the SIC/SAC-optical CDMA based OOK one.