An Analytical Method to Determine Squaring Loss and Weak Signal Post Correlation SNR for a Broad Class of GNSS Signals

Christopher N. Kurby

Peer Reviewed

Abstract:	In some analysis the output correlation SNR for coherent and non-coherent integration of GPS signals is determined either from the probability density function (pdf) of the signal plus noise or from a direct calculation from the random variable. The normally used coherent integration pdf’s are Rician pdf’s and the non-coherent integrations of squared outputs are chi-squared random variables composed of Bessel functions. The use of the pdf’s to compute the output SNR depends on the application of the pdf’s to the particular Rx input parameter of concern, which in this case is the RF carrier to noise spectral density “C/No”. This paper focuses on the derivation of the output SNR due to a combination of coherent and non-coherent integrations and can be applied to a variety of signal types with no knowledge of the pdf. It presents a simple analytical method to compute the output SNR of coherent and non-coherent integrations and is general, meaning it can easily be applied to more complicated signals like the GPS L5 signal. It is also interesting that the output SNR calculated shows a 3 dB lower SNR loss when the input SNR is used rather than the SNR on the I channel alone. The method developed here represents the input signal plus noise and the reference signal to be correlated with as vectors of length equal to the integration time. The two vectors are then processed through the correlation process of multiply by the conjugate of the reference and integrate, or sum in discrete time, over the vector length. Using properties of the correlation, random signals, vector sums and averages, the vectors are converted to single variables which can be used to simply compute the system and output SNR’s using algebra and voltage and power laws. The output signal to noise ratios are given in terms of different input SNR‘s perspectives to provide easier application to various systems. Also provided is a Monte Carlo simulation of detection probability to output SNR where it is seen output SNR is not a perfect predictor for performance for non-coherent systems as also indicated by others through analytical means. Further squaring loss equations and curves are presented which may further provide some clarity in the use of such equations.
Published in:	Proceedings of the 28th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2015) September 14 - 18, 2015 Tampa Convention Center Tampa, Florida
Pages:	2875 - 2886
Cite this article:	Kurby, Christopher N., "An Analytical Method to Determine Squaring Loss and Weak Signal Post Correlation SNR for a Broad Class of GNSS Signals," Proceedings of the 28th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2015), Tampa, Florida, September 2015, pp. 2875-2886.
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