Detecting signals buried in noise and clutter is an essential task for many Global Navigation Satellite System (GNSS). This task is performed in the signal detection block of the acquisition stage. In this block a decision about the presence or absence of the desired signal is made by comparing it to a threshold which can be fixed or adaptive. In this work, an adaptive threshold is calculated using two Constant False Alarm Rate (CFAR) detectors. Both SO-CFAR (Smallest of CFAR) and GO-CFAR (Greatest of CFAR) detectors are employed, in Rayleigh fading channels, to estimate the noise power level. The performance of these two detectors is compared with that of the CA-CFAR (Cell Averaging CFAR) detector, used in previous works, through a simulation study. Simulation results demonstrate that the use of the SO-CFAR detector is an effective solution to enhance the detection performance in non-homogeneous environments of the GPS (Global Positioning System).