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Multistage partial parallel interference cancellation (PPIC) is proposed for turbo-encoded DS-CDMA systems where the partial cancellation factors are derived based on the log-likelihood ratios (LLR's) of each user's bit. The LLR is obtained based on an enhanced estimate of the variance of the multiple- access interference (MAI) and residual MAI (RMAI) plus noise. The (R)MAI terms are modeled as conditionally Gaussian with a time-dependent variance that is a function of the user cross-correlations and fading coefficients. Significant performance gains due to the improved LLR's are realized over PPIC schemes using fixed variance estimates in frequency non-selective Rayleigh fading channels. The performance gap is greater when two stages of the improved PPIC are used. Reduced complexity forms of the variance estimates and LLR's are proposed and also shown to give a performance advantage.