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In the absence of an efficient power control system, performance of CDMA wireless networks deteriorates significantly due to the effects of imperfect power control on multi-user receivers. In this paper this effect is studied for the partial parallel interference cancellation (PPIC) technique in multipath Rayleigh fading channels. Practical considerations of PPIC implementation, including non-ideal cancellation rations, and imperfect estimation of the users' powers were taken into account. Since perfect power control is not feasible, the results presented in this paper are useful in setting a practical limit on the dynamic range of power variations to maintain a certain level of acceptable performance.