On the detection probability of parallel code phase search algorithms in GPS receivers

The first stage of the signal processing chain in a Global Positioning System (GPS) receiver is the acquisition, which provides for a desired satellite coarse code phase and Doppler frequency estimates to subsequent stages. Thus, acquisition is a two-dimensional search, implemented as demodulation and non-coherent correlation. For a certain Doppler estimate, software-defined GPS receivers typically compute the correlation for all time lags in parallel. One way to detect the presence of a signal is by comparing the ratio between the largest and the second largest correlation peak against a threshold. For this type of receivers, the detection and false alarm probabilities are derived. Interestingly, the false alarm probability is independent of the noise power spectral density, which allows a fixed threshold setting. The analytic results are verified by a series of simulations.