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This contribution focuses on the performance analysis of the serial search pseudo-noise (PN) code acquisition based on a matched filter (MF) correlator. In this work, we present for the widely considered case of two cells per chip. In such a case, no convergent infinite series have been found in the open literature expressing the probability of false alarm and detection. We provide a closed form to analytically express the error probabilities in terms of the modified Gamma functions, already exploited to model the case of overlapped antenna beams in MIMO systems using smart antennas and suited for the radio access of 3G mobile communications. We show the performance of the system in terms of mean acquisition time for signal-to-noise ratios (SNRs) of practical interest, taking into account the effects of cell correlations.