A Fast Number‐theoretic Transform Approach to a GPS Receiver

This paper describes the application of the Fast Number-theoretic Transform (FNT) to the processing of GNSS signals. This FNT is an alternative to Fast Fourier Transform (FFT) techniques and efficiently provides bit-for-bit identical results to a traditional time-domain correlator without the need for word-length growth or the quantization of irrational complex roots of unity. We document a prototype single channel GPS C/A code receiver with a continuously operating correlator that computes hundreds of lags. The design is implemented with an inexpensive Field Programmable Gate Array (FPGA) programmed to implement the FNT. As an initial application, we present a multipath investigation using this receiver in which we were able to localize and then identify the source of the multipath signal.

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