Advanced Replica Transformation & Storage (ARTS) for Fourier Correlation Techniques

Andrew Richardson, Michael Turner, David DeCastro Galan, Michael Batiste

Abstract:	This paper builds on the previously presented MTLL algorithm (M. Turner, 2015) allowing it and related Fourier based techniques to be efficiently implemented and deployed in programmable silicon devices. When implementing a Fourier based tracking (M. Turner, 2015) or acquisition (D.J.R Van Nee, D.J.R Van Nee, A.J.R.M Coenen, 1991) algorithms in an FPGA the instantaneous memory bandwidth and capacity required can very quickly become unacceptably large. To track 100 down links a bandwidth of 266 Gb/s and 1Gb of storage capacity is required for a high performance receiver with sample rate 50MS/s. The objective of this work is to develop a means to address this memory bandwidth and storage bottle neck, to allow the MTLL and other FFT correlation based designs to be realized within commercial programmable silicon. The Advanced Replica Transformation & Storage (ARTS) technique builds on the method explored in the original MTLL paper (M. Turner, 2015) by examining the linear operators that are used to build the time domain correlation function and exploit the commutation relations that are inherent in the equation when it is transformed into the frequency domain. Using the ARTS method it is possible to store the frequency domain replica at the chip rate of the PRN (not the signal sample rate), reduce the bit width required to store it, reduce the number of operations that are required to compute the correlation function and reduce bit width expansion to just before the inverse FFT operation common to all tracking chains. The memory requirement is reduced by the ratio of the sample rate to the PRN chip which crucially allows the frequency domain PRN replicas to be stored in the fast block RAM inside the FPGA negating the need for external memory interfaces. Although this technique has been developed so that the MTLL can be implemented in an FPGA, it clearly has a much wider application. The ARTS technique relies on commutation relations in the frequency domain correlation equation and hence ARTS is equally applicable to any Fourier correlation technique which requires the correlation function to be over sampled. The ARTS technique is currently being deployed in the GERTS receiver project co-funded by Innovate UK and run by Airbus Defence and Space, Portsmouth, UK.
Published in:	Proceedings of the 29th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2016) September 12 - 16, 2016 Oregon Convention Center Portland, Oregon
Pages:	209 - 216
Cite this article:	Richardson, Andrew, Turner, Michael, Galan, David DeCastro, Batiste, Michael, "Advanced Replica Transformation & Storage (ARTS) for Fourier Correlation Techniques," Proceedings of the 29th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2016), Portland, Oregon, September 2016, pp. 209-216. https://doi.org/10.33012/2016.14656
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