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In this work, exact analysis of the multiple access interference (MAI) for synchronous downlink CDMA systems is carried out for BPSK signals with random signature sequences in both additive white Gaussian (AWGN) noise and different fading environments, namely Nakagami and Rician. Two different scenarios are considered: one with equal transmitted powers while the other considers the case of unequal transmitted power. For both cases, the exact probability density function (pdf) of MAI plus noise is derived. Finally, a number of simulation results are presented to verify our theoretical derivations.