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In this study, we propose a least mean square-partial parallel interference cancellation (LMS-PPIC) method named parallel LMS-PPIC (PLMS-PPIC) in which the normalised least mean square (NLMS) adaptive algorithm with optimised chip time-varying step-size is engaged to obtain the cancellation weights. The former LMS-PPIC method is based on fixed not optimised step-size, which causes propagation of error from one stage to the next one and increases the bit error rate (BER). The unit magnitude of the cancellation weights is the principal property in our step-size optimisation. To avoid computational complexity a small set of NLMS algorithms with different step-sizes are executed. In each iteration the parameter estimate of that NLMS algorithm which the elements magnitudes of its cancellation weight estimate have the best match with unit is chosen. Magnificent decrease in BER is achieved by executing the proposed method. Moreover PLMS-PPIC like former LMS-PPIC method comes to practice only when the channel phases are known. When they are unknown, having only their quarters in (0, 2π), we propose modified versions of LMS-PPIC and PLMS-PPIC to find the channel phases and the cancellation weights simultaneously. Simulation scenarios are given to compare the performance of our methods with that of LMS-PPIC in two cases: balanced channel and unbalanced channel. The results show that in both cases the proposed method outperforms LMS-PPIC, especially for high processing gains.