A Fast Number-theoretic Transform Approach to a GPS Receiver

Abstract

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.

A Detailed Analysis of GPS Live-Sky Signals Without a Dish

“…Moreover, we show that the GCAF technique can serve as the basis for transitioning these observations from one‐off efforts into routine practice.…”

“…To do so, we leveraged the High‐Rate Tracking Receiver (HRTR) platform developed at Applied Research Laboratories, the University of Texas at Austin (ARL:UT) and documented more extensively by York, et al . This platform consists of a 2 Gigasample/s direct‐sampling radio‐frequency (RF) front‐end,a digital downconversion FPGA responsible for digitally selecting the desired bands of interest (e.g., L1, L2, and L5 for GPS) ,a baseband processor for generating local replicas, and performing the GCAF processing algorithms in real‐time, anda high‐end commodity PC with 8 terabytes of storage for performing data collection and post‐processing.…”

“…The GCAF computes the cross‐correlation r ( τ ) of the received signal y ( t ) with the locally generated replica of the ideal signal x ( t ) . Thus the GCAF output can loosely be described as …”

“…The HRTR units contain this functionality in a 5.25 in tall, 19 in wide rack‐mount footprint. To facilitate interoperability and reproducibility, internal interfaces and algorithms are extensively documented in open academic literature. HRTRs are currently deployed at a number of the National Geospatial Intelligence Agency's (NGA) GPS Monitor Station Network (MSN) sites around the globe , with deployments to the remaining sites anticipated.…”

“…Notably in these applications, the computational burden can be mitigated by operating the FFT‐based algorithm intermittently or off‐line, perhaps in parallel with a continuously tracking early/prompt/late correlator structure. The GCAF algorithms improve the efficiency of these massive correlation techniques for FPGA implementations, and have allowed many of these algorithms to execute in real‐time on a routine basis for many channels in parallel.…”