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Optical code mutiple access (OCDMA) networks are subject to several limitations, such as multiple access interference (MAI), as well as the noise of the optical components. In this work we propose an interference cancellation technique using the bias mitigation and linear estimators in parallel interference cancellation (PIC) receivers. In order to make the analysis more tractable, the proposed technique is described for a synchronous multiuser communication scenario with multiple access interference in an additive white Gaussian noise (AWGN) channel. Estimates for the error probabilities of the proposed OCDMA detector are derived using the Gaussian approximation for interference terms. Some analytical and numerical results for our system are given and compared with those for other receivers with the same order of complexity.parallel receivers.