Optimized FFT Algorithm and its Application to Fast GPS Signal Acquisition

The essence of GPS signal acquisition is a two-dimensional search process for the carrier Doppler and code phase, generally including correlator, signal capture device, and logic control module. The disposal efficiency of correlator would affect the capture speed of the whole acquisition process. Because of the corresponding relation between frequencydomain multiplication and time-domain convolution, the Discrete Fourier Transform (DFT) could be applied to play the role of the correlator, which is suitable to implement for computers (Akopian, 2005) (Van Nee & Coenen, 1991). However, with the performance requirements of GPS receivers increasing, especially in the cold start and the long code acquisition, such as P code, the acquisition time should be furtherly reduced. Therefore, the fast discrete Fourier transform processing approach, that is, Fast Fourier Transform (FFT), is described, including radix-2, radix-4, split-radix algorithm, Winograd Fourier Transform Algorithm (WFTA) which is suitable for a small number of treatment points, and Prime Factor Algorithm (PFA) in which the treatment points should be the product of some prime factors. According to the actual needs of GPS signal acquisition, an optimized FFT algorithm was put forward, which comprehensively utilize the advantages of different FFT algorithms. Applying optimized FFT algorithm to GPS signal acquisition, the results of simulations indicate that the improved processing could reduce the acquisition time significantly and improve the performance of GPS baseband processing.