Application of Mixed-radix FFT Algorithms in Multi-band GNSS Signal Acquisition Engines

Due to their fast operation, Fast Fourier Transform (FFT)-based coarse signal synchronization methods are an attractive option for Global Navigation Satellite System (GNSS) receiver baseband signal processing. However, there are several reasons why the utility of FFT-based methods is dependent on understanding the trade-off between synchronization speed and the required processing power. Firstly, the new signals of the GNSS family, for instance Galileo and GPS modernization, employ longer period Pseudo Random Noise (PRN) codes and higher signal bandwidths, which demand FFTs of large transform lengths. Secondly, to gain an advantage in positioning performance, next generation receivers target multiple GNSS signals, and since each signal has its own code length (and hence a minimum sampling frequency), the receiver should accommodate FFT blocks of varying lengths. This paper discusses the requirements of FFT-based algorithms for such a multi-band receiver and analyzes the application of prime-factor and mixed-radix FFT algorithms. A novel way of factorizing different transform lengths into smaller transforms and then combining these smallerpoint FFTs to compute the larger required FFTs is described. It is shown that the use of the proposed architecture reduces the computational load (or processor cycles) and increases the re-usability of the acquisition search engine to process different signals.