In this work, we studied the effect of multi-user and multipath, on the performance of a serial acquisition search system, using adaptive threshold with constant false alarm rate, in Rayleigh fading channels. Since the received signal levels in mobile communications are unknown and location varying, the acquisition schemes for pseudo-noise (PN) sequences with fixed thresholds may cause too many false alarms and/or low probability of detection. Therefore, adaptively varying threshold schemes are proposed through the use of a constant false alarm rate (CFAR) algorithms. We propose the use of cell-averaging (CA), greatest-of (GO), smallest-of (SO) and order-statistics (OS) CFAR processors for PN code acquisition in DS/CDMA systems. From simulation results, we observe that the CA-CFAR detector gives good performances in this environment, followed by the SO-CFAR detector. The OS-CF AR outperforms the GO-CFAR which gives the worst results. All studied CFAR detectors are sensible to multi-user and multipath effect.