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In this paper, we tackle the problem of theoretical evaluation for the multistage parallel interference cancellation (PIC) scheme in a direct-sequence code division multiple access (DS-CDMA) system with orthogonal modulation and long scrambling codes. The studied system operates on the reverse link in a time varying multipath Rayleigh fading channel. By applying the Central Limit Theorem and some other approximations to multiple access interference (MAI) and intersymbol interference (ISI), as well as assuming identically distributed chips from a single interferer, the bit error rate (BER) performance of the PIC scheme at any stage can be recursively computed from the signal-to-noise ratio, number of users, the number of path per user, processing gain of the CDMA system, and the average received power of each path. For completeness, the BER expression is derived for chip synchronous and chip asynchronous systems over both equal and unequal power multipath channels. The proposed analysis is validated by the Monte Carlo simulations and proved to be reasonably accurate, and it gives insight into the performance and capacity one can expect from PIC-based receivers under different situations. For instance, the analytical results can be used to examine the convergence property, multipath diversity gains, and near-far resistance of the PIC scheme.