Software Defined Phase Locked Loops

In my previous blog entry I presented a paper describing a frequency hypothesis tracker (FHT), which is functionally similar to a classical phase-locked loop (PLL).  Because of the well-known advantage of the PLL in terms of efficiency and performance, it is natural to ask what advantage FHT might have to justify the significant computation burden increase.  I believed the answer is that FHT tracking can work effectively a 0 dB or even negative SNRs.  It also provides a more oscillator-like phase noise characteristics.  The PLL operation for comparative purposes is described in the attached note, which may be of general interest for software defined PLLs SoftwarePLL.

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Digital Beacon Receiver Signal Processing

Chapters 1 through 4 of my book “The Theory of Scintillation with Applications to Remote Sensing” established an analytic and computational framework for understanding radio waves propagating through structure media, primarily the earth’s ionosphere.  From the time the book was published in February 2011 corrections, clarifications, and new results have evolved.  The most important new result has been the development of new analytic methods for the computation of intensity scintillation under strong scatter conditions by Charles Carrano.  These results have yet to be fully reported.

This post presents new results for processing data from software-defined digital beacon receivers, which are replacing the analog receivers in continuous use since the launch of Sputnik in the late 1950s.  Chapter 5 introduced the ramifications of ever present noise and multiple time scales that must be considered for propagation diagnostics and remote sensing.  Chapter 5 also introduced signal processing procedures based on frequency tracking, as distinct from phase tracking, for digital processing.  The procedure is viable but incomplete as demonstrated in Chapter 5.

A tested and complete version of the processing algorithm is presented in the paper DigitalSignalProcessingPaper, which has been submitted to Radio Science for publication.

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2014 AGU Poster and Supplemental Material

A new version of a configuration space ionospheric structure model is described.  Previous versions of the model used a random distribution of striation scale sizes.  While in principle this scheme should work, it proved to be difficult to manipulate the size distribution parameters to generate a range of power-law indices.  A new approach based on successive bifurcation solved the problem. The details are described in the following report ConfigurationSpaceModels.   AGU2014Poster

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Application of Wavelet Based Analysis to C/NOFS Ionospheric Density Measurements

In a previous post a wavelet-based analysis procedure was described and demonstrated with simulated inverse-power-law data  The analysis procedure has been applied to a large number of C/NOFS high-resolution equatorial measurements during periods of strong ESF.  The data are particularly well suited to wavelet-based analysis because large extent of the data sets (>1000 km) and the structure scale range.  The analysis and results are described in a paper accepted for publication in Radio Science. URSIPaper2014.

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Wavelet Based Analysis of Ionospheric Data

Ionospheric diagnostics come from in-situ probes carried by rockets or satellites, forward propagation, and radar backscatter.  This blog entry addresses in situ measurements and remote sensing via forward radio propagation from satellite to ground propagation paths.  In situ measurements are time series generated the probe trajectory through the three-dimensional ionospheric structure.  Propagation measurements are one-dimensional scans of a diffraction field that responds to the cumulative structure along the propagation path from the source to the receiver.  The one-dimensional measurements are highly non-stationary with a very large range of contributing scale sizes.  The unpublished manuscript PowerLawModelsMethodsREV1 reviews current stochastic models and presents a wavelet-based analysis procedure for identifying data segments that can be characterized by a generalized power-law structure model.  A classifier finds a two-component power-law fit with a goodness-0f-fit measure using wavelet scale spectra.

As discussed in detail, wavelet scale spectra are particularly well suited for analyzing the class of non-stationary fractional Brownian motion (fBm) processes introduced by Benoit Mandlebrot.   FBm processes have a self-scaling property akin to fractals that is often invoked to characterize the structure cascade associated with convective instabilities.  The paper establishes a framework for data analysis and, ultimately, structure model improvement.  This material updates and replaces earlier blogs that addressed the same material.

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AGU 2013 Poster and Supplemental Material

Tomographic reconstruction of ionospheric electron density profiles from GPS satellite measurement is being used extensively for global ionospheric monitoring.  For the most part, the reconstruction process is a constrained iterative process.  The results are sensitive to errors and initial conditions.  To study these limitations and the possibility of high-resolution reconstruction two-dimensional simulations have been used.  The simulation and analysis procedures are described in IntermediateScaleTomography, with the accompanying poster RinoPosterSA21B-2019(2).

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Phase Screen Models for Numerical Computation

To the extent that propagation disturbances can be approximated by an equivalent phase-screen, there are analytic models that allow computation of the power-spectrum of the intensity of the field as it propagates away from the phase screen.  The analysis involves an integration to characterize the structure initiation as a phase perturbation and a second integration to propagate the structure to the observation plane.   In real-world applications the integrations are two dimensional.  However, the field-aligned structure in the ionosphere can be exploited to reduce the computations to one-dimensional integrations.

This motivated a revisit of early computations based on two-dimensional and one-dimensional phase screens.  To test the numerical computations, which were performed by Charlie Carrano at the Boston College Institute for Scientific Research, analytic results for unconstrained inverse power-law spectra were used.  Disparities between the computations and the analytic results motivated a careful look at the analytic results derived from complicated limiting operations.  Some errors were found that clarified some long standing disparities between results by Victor Rumsey for isotropic structures and my own two-dimensional results, which should agree with the isotropic results if isotropy was assumed.  The new results are summarized in PowerLawPhaseScreenHighlights, with computational details presented in a separate note. PowerLawPhaseScreenReview,

An updated book errata sheet can be found ScintTheoryErrata

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Beacon Satellite Symposium 2013 Keynote Talk

The following attachment is the keynote talk presented at the Beacon Satellite Symposium, Bath England, July 8, 2013 KeynoteTalk

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2013 Cedar Workshop

The following attachment was presented at the CEDAR workshop Friday 29 June at Boulder Colorado. CEDAR-Talk-Rino

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Workshop on GNSS Data Applications to Low Latitude Ionospheric Research May 2013

The following attachment was presented at the International Center for Theoretical Physics, Tereste Italy, on May 14, 2013 GNSS_Rino

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