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The hybrid search algorithm, a combination of the maximum-likelihood search and serial search algorithms, is known as one of the most promising techniques that can be used for code acquisition in CDMA forward links. An efficient adaptive hybrid search code acquisition algorithm with embedded CFAR is designed in this paper, which employs two operating modes, i.e., search and verification modes with M-parallel correlators used for maximum-likelihood detection in search mode. An analytical expression for the mean acquisition time is obtained and the exact expressions on the probabilities of detection, miss, and false alarm are derived for slowly varying frequency-selective Rayleigh fading environments. Numerical evaluation shall be performed to investigate the effects of sub-window size, number of post-detection integration, and so on, in the forward link of cellular CDMA networks.