In this letter, we propose a generalized version of the window-based pseudonoise (PN) acquisition scheme verifying one or more best hypotheses rather than the best one per search window. The false alarm probability, detection probability, and mean acquisition time (MAT) of the proposed scheme are derived by using the well-known flow graph approach in additive white Gaussian noise (AWGN) and fading channels. Numerical results demonstrate that the acquisition performances are improved through the proposed generalization, particularly when the pilot energy to total received energy ratio (pilot Ec/Io) is low.