On the Mutual Coherence Function for Transionospheric Waves and its Utility for Characterizing Ionospheric Irregularities with a GNSS Scintillation Monitor

Charles S. Carrano, Charles L. Rino, Keith M. Groves, and Patricia H. Doherty

Abstract:	When interpreting GNSS observations of ionospheric scintillation, it is instructive to distinguish between the separate goals of characterizing the GNSS signal fluctuations and characterizing the disturbed ionospheric medium that produces the scintillations. The statistics of GNSS signal fluctuations are of primary interest for GNSS tracking loop analysis and design studies intended to quantify and model the impacts of ionospheric scintillation on navigation accuracy. Conversely, from an ionospheric physics standpoint, of primary interest are the statistical characteristics of the random ionospheric medium itself, and how these relate to the physical processes that structure the plasma. When the scintillation is weak, receiver diagnostics can serve both applications because the spectra of signal fluctuations at the ground are simply related to the spectra of variations in the ionospheric density. On the other hand, when the scintillation is strong refraction and diffraction generate small scale structures in the fluctuating signal which have no counterparts in the ionosphere. Unraveling the characteristics of the ionospheric medium from strong signal fluctuations requires one to remove, or otherwise account for, these unwanted propagation effects. Sophisticated inverse techniques have been developed for this purpose. The Inverse Diffraction Method (Carrano et al., Proc. ION ITM, 2014) employs back-propagation to explicitly remove the unwanted propagation effects so that the statistics of the random ionospheric medium may be characterized directly. Another technique, called Iterative Parameter Estimation (Carrano et al., Int. J. Geophys., 2012), characterizes the random medium indirectly using nonlinear least-squares to fit the observations to numerical solutions of the differential equation governing the 4th moment of the fluctuating field. These techniques are relatively complex and can be quite computationally expensive (particularly the latter). In this paper we explore an alternative approach that leverages the mutual coherence function (MCF) for transionospheric waves measured by a GNSS scintillation monitor to characterize the ionospheric disturbances that cause scintillation. For plane waves traversing a homogeneous random medium, the MCF is invariant to free-space propagation regardless of the scintillation strength. As such, fitting the MCF in the appropriate range of temporal separations can provide estimates for the strength and spectral index of electron density fluctuations that are largely uncorrupted by propagation effects (in essence, the statistics of an equivalent phase changing screen are inferred). This technique is simpler and computationally less demanding than the Inverse Diffraction Method or Iterative Parameter Estimation. We demonstrate that fitting the MCF provides a more accurate description of the irregularities than measurements of T (phase spectral strength) and p (spectral index) provided by a GNSS scintillation monitor, since the latter may be corrupted by unwanted propagation effects. The approach we describe is relatively simple and suitable for implementation in the firmware of future GNSS scintillation monitors to provide improved ionospheric characterization in real time under both weak and strong scintillation conditions.
Published in:	Proceedings of the ION 2015 Pacific PNT Meeting April 20 - 23, 2015 Marriott Waikiki Beach Resort & Spa Honolulu, Hawaii
Pages:	48 - 62
Cite this article:	Carrano, Charles S., Rino, Charles L., Groves, Keith M., Doherty, Patricia H., "On the Mutual Coherence Function for Transionospheric Waves and its Utility for Characterizing Ionospheric Irregularities with a GNSS Scintillation Monitor," Proceedings of the ION 2015 Pacific PNT Meeting, Honolulu, Hawaii, April 2015, pp. 48-62.
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