An Analytic Way to Optimize the Detector of a Post-Correlation FFT Acquisition Algorithm

H. Mathis, P. Flammant, A. Thiel

Abstract:	The satellite acquisition task in a GPS receiver has been shown to greatly benefit in terms of speed from using postcorrelation FFT methods. Using a finite grid of FFT bins brings about the need for a detection strategy that does not compromise detection sensitivity and false-alarm rate. The problem is treated as a classic Neyman-Pearson Test, which maximizes the probability of detection, constraint to some maximal false-alarm probability. The end goal is to compare different methods against each other by adjusting their parameters such that the false-alarm probability reaches a certain value and compare their respective detection rates. A method is suggested that allows a quick comparison and optimization in the case where several detector parameters have to be twiddled simultaneously. Transformations of loss effects described as pdfs as a function of linear variables can be transformed into a function of logarithmic-scale variables using Jacobi determinants. Examples of the resulting distributions are illustrated. With such distribution models the detection rates can be evaluated by numerical approximations of the tail distributions rather than by computationally infeasible Monte-Carlo simulations. Based on this model expressions for detection and false alarm rates for different detector architectures are given. The trade-off between hardware complexity and quality of the detector can be quickly optimized. Sample structures and the respective modeling results are presented. The different structures are compared in terms of detection probability for a constant false-alarm rate, and an optimal detection strategy is given. All the simulations and calculations are confirmed using measurements on an FPGA implementation.
Published in:	Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/GNSS 2003) September 9 - 12, 2003 Oregon Convention Center Portland, OR
Pages:	689 - 699
Cite this article:	Mathis, H., Flammant, P., Thiel, A., "An Analytic Way to Optimize the Detector of a Post-Correlation FFT Acquisition Algorithm," Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/GNSS 2003), Portland, OR, September 2003, pp. 689-699.
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