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In this work, we propose a joint MAP channel estimation and data detection technique based on the expectation maximization (EM) method with parallel interference cancelation (PIC) for downlink multi-carrier (MC) code division multiple access (CDMA) systems in the presence of frequency selective channels. The EM algorithm derived estimates the complex channel parameters of each subcarriers iteratively and generates the soft information representing the data a posterior probabilities. The soft information is then employed in a PIC module to detect the symbols efficiently. Moreover, the MAP-EM approach considers the channel variations as random processes and applies the Karhunen-Loeve (KL) orthogonal series expansion. The performance of the proposed approach are studied in terms of bit-error rate (BER) and mean square error (MSE). Throughout the simulations, extensive comparisons with previous works in literature are performed, showing that the new scheme can offer superior performance.