A Global Navigation Satellite System (GNSS) receiver and associated method capable of acquiring weak GNSS signals from a plurality of GNSS satellites produces a GNSS signal's code time, carrier frequency, and data bit transition parameters for subsequent signal tracking and position fixing. The GNSS receiver includes a baseband signal processor with special functionalities for acquiring weak signals. In a preferred embodiment, the time and frequency uncertainty space is reduced using available information and then special techniques are used to rapidly search the remaining uncertainty space. Successive reversal of short-length correlations within a data bit interval (a block) enables data bit transition detection and data bit sign correction prior to coherent integration. Fast Fourier Transform (FFT) is applied as a bank of bandpass filters to coherently accumulate blocks of short-length correlations over extended coherent integration intervals to boost the signal power while averaging noise out despite unknown data bit transitions.