1. Presentation Title Pierre-Richard Cornely, Ph.D.,
June 24, 2018
A Complete Amplitude and Phase Characterization of Ionospheric Scintillation
Pierre-Richard Cornely, Ph.D.,
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2. Background - Motivation
Presentation Title
June 24, 2018
Background - Motivation
Patchy Clouds
Foliage
Target &
Target
Complexes
Rain - Hail
Coastal
Input
Waveform
Environment
System
System
Under Inquiry
Inquiring
System
Take Away: The radar signals amplitude and phase are affected by the propagation environment
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3. Background - Motivation
Presentation Title
June 24, 2018
Background - Motivation
At present, we model radar channel fluctuations as follows:
Single Pulse, Constant Amplitude, Known Phase (Rayleigh PDF)
Single Pulse, Constant Amplitude, Uniform Phase (Ricean PDF)
Multiple Pulse,Constant Amplitude, Uniform Phase (Chi-Square PDF with 4 degrees of Freedom)
Multiple Pulse, Swerling Target, Uniform Phase (Chi-Square PDF with 4 degrees of Freedom)
All of the above models do not include severe fluctuations due to the environment
In particular, these models do not include target fluctuations due to Ionospheric Scintillations.
Ionospheric Scintillation is the Rapid Fluctuation in Signal Amplitude of the Radar Echo from a Target due to Interaction with Free Electrons in the Ionosphere
Measurements of Radar Cross Section are Directly Proportional to Signal Amplitude
In Highly Scintillated Ionosphere, even Spherical Targets (e.g., satellite 5398 which normally have constant RCS) exhibit large Fluctuations in RCS
Amplitude Target fluctuations due to ionospheric scintillations are Nakagami-m.
All of the above models approximate the Nakagami-m but for special cases only
The original Nakagami-m amplitude model assumes no correlation within a pulse
In addition, no implicit Phase information was included in the model
Take Away: There is a need to model target fluctuations due to ionospheric scintillations
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4. Background - Motivation
Presentation Title
June 24, 2018
Background - Motivation
Swerling-0 Target
1-m2 RCS, 0-dBsm
~20 dB
RCS (dBsm)
Fluctuations up to 20 dB due to scintillations
The S4 index is the ratio of standard deviation and mean
RCS S4 Index
Take Away: The environment can both benefit and affect radar detection, tracking and discrimination
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5. Background - Previous Work
Presentation Title
June 24, 2018
Background - Previous Work
Uncorrelated Amplitude Nakagami-m
Available in the literature and straight forward to implement [1]
Both Phase and higher order statistics are not well defined in original work
Correlated Amplitude Nakagami-m
Available in the literature but more difficult to implement numerically [2]
Correlation does not satisfy any Predefined Correlation Model
Correlated Amplitude and Phase Nakagami-m
Some work available on Correlated Nakagami-m with correct Phase Property [3],[4]
Joint Nakagami-m PDF being used is only valid for integer values of m [4]
Correlated Amplitude and Phase Nakagami-m /Predefined Autocorrelation
Some work available on Correlated Nakagami-m with correct Phase Property and Predefined Autocorrelation [3], [4]
The joint Nakagami-m PDF being used is only valid for integer values of m [4]
Take Away: Correlated Nakagami-m with the Correct Phase satisfying Predefined Correlation Model are Open Problems
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6. Presentation Title
June 24, 2018
Proposed Approach
The class of signals of interest are usually complex (I & Q)
A complete model of the signal fluctuations must consider both I & Q
x(n) = I(n) + jQ(n)
To include both the real and imaginary parts of the signal x(n) in the fluctuation model
We must be able to describe either the second order statistics of (I,Q), i.e., the joint PDF or the autocorrelation function of x(n)
We must also be able to describe the statistics of the phase of x(n)
Our approach proposes the following:
1. Creation of independent mappings of the real and imaginary parts of x(n) to Nagakami-m sequences, starting with Gaussian sequences
2. Simulation of complex Nakagami-m sequences which satisfy a pre-specified Autocorrelation Model
3. Simulation of complex Nakagami-m sequences which satisfy the theoretical Nakagami-m Phase
Take Away: A Nakagami-m model and simulator that includes both amplitude and phase fluctuations
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7. Background – The Nakagami-m Model
Presentation Title
June 24, 2018
Background – The Nakagami-m Model
Beacon Satellite Or
Radio Star
Target
Noise from the environment
One-Way Scintillation
Amplitude follows
the Nakagami-m Model
1-WAY SCINTILLATION
Amplitude
Intensity
2-WAY SCINTILLATION
Amplitude
Intensity
Receiver
Radar
Take Away: Ionospheric Scintillations modify the received signal Intensity, Phase and Polarization
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8. Background – The Nakagami-m Model
Presentation Title
June 24, 2018
Background – The Nakagami-m Model
The Nakagami-m distribution for one-way scintillation amplitude
m: Shape Parameter,
Ω: Scaling Parameter
(Ω =1 in Fig)
Scintillation
Increases as m decreases
Relationship between one way intensity Sm and two way intensity S4
Take Away: Amplitude Scintillations are well modeled
by Nakagami-m Amplitude PDF
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9. The Phase & Autocorrelation Models
Presentation Title
June 24, 2018
The Phase & Autocorrelation Models
The theoretical Nakagami-m Phase
The Nakagami-m phase is a function of m as well as the angle of arrival
Caveat: The Nakagami-m phase is not uniform for m1
The Theoretical Autocorrelation model (“Jake’s Model”)
Chosen correlation model is a function of signal bandwidth
Take Away: Accepted Theoretical Nakagami-m phase and Autocorrelation can be used to anchor our results
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10. Proposed Methodology Block Diagram Walk Through
Presentation Title
June 24, 2018
Proposed Methodology
Block Diagram Walk Through
Start with Gaussian sequences G(0,1) and create [G(0,1)]2
Map [G(0,1)]2 to Chi-Square (2) sequences with N degrees of freedom
Map each (2) sequence to a Gamma sequence with parameter m/2
Map the Gamma sequences to Nakagami-m sequences
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11. Simulator Input/Output Realizations
Presentation Title
June 24, 2018
Simulator Input/Output Realizations
Take Away: Gaussian to Nakagami-m Mapping
works even for the worse case m=0.5
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12. Simulator PDF vs. Theory
Presentation Title
June 24, 2018
Simulator PDF vs. Theory
Take Away: Both the real part and the magnitude of the simulated sequence are consistent with the Nakagami-m model
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13. Simulator Autocorrelation vs. Theory
Presentation Title
June 24, 2018
Simulator Autocorrelation vs. Theory 10 20 30 40 50 60 70 80 90
100
110
120
-0.4
-0.2
0.2
0.4
0.6
0.8 1
Theoretical, Jakes model
Simulated m = 0.5 y
Normalized correlation R
Lags
Take Away: The correlation of the Nakagami-m sequence agrees with the Predefined Correlation Model
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14. Simulator Input/Output Realizations
Presentation Title
June 24, 2018
Simulator Input/Output Realizations
Take Away: Rayleigh to Nakagami-m Mapping
works even for the worse case m=0.5
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15. Simulator Autocorrelation vs. Theory
Presentation Title
June 24, 2018
Simulator Autocorrelation vs. Theory
Take Away: The correlation of the Nakagami-m sequence from the Rayleigh model agrees with the Predefined Correlation Model
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16. Simulator Phase vs. Theory
Presentation Title
June 24, 2018
Simulator Phase vs. Theory
Take Away: The simulated phase agrees with theory for m=1.0,2.0,3.0,4.0
For m=1.0, it is uniform, as predicted by research in the available literature
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17. Presentation Title
June 24, 2018
Summary
An Accurate and systematic radar channel simulation technique is critical for performance evaluation of our radar systems.
Our current models do not include severe target fluctuations due to environment
Amplitude Target fluctuations due to ionospheric scintillations are Nakagami-m.
No Phase or correlation information was included in the original model
In this presentation, we introduced a Nakagami-m model with the following properties:
It satisfies an arbitrary pre-specified Autocorrelation function (open problem)
It satisfies a Nakagami-m Phase consistent with the pre-specified Autocorrelation function (open problem)
It allows means for mapping a Rayleigh model to the Nakagami-m model
Our results show that the proposed Nakagami-m model satisfies:
The theoretical properties of Nakagami-m amplitude
The theoretical properties of Nakagami-m phase
An arbitrary pre-specified Autocorrelation model
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18. Literature Cited and References
Presentation Title
June 24, 2018
Literature Cited and References
M. Nakagami, “The m-distribution, a general formula of intensity distribution of rapid fading,” in Statistical Methods in Radio Wave Propagation, W. G. Hoffman, Ed., Oxford, U.K., Pergamon, 1960.
A. Papoulis, “Probability, Random Variables, and Stochastic Processes,” 3rd ed. New York: McGraw-Hill, 1995.
N. Beaulieu, C. Cheng, “Efficient Nakagami-m Fading Channel Simulation”, IEEE Transactions on Vehicular Technology, Vol. 54, No2, March 2005.
M. D. Yacoub, G. Fraidenraich and J.C.S, Filho, “Nakagami-m Phase-envelope joint distribution”, Electronics Letters 3rd ed, Vol. 41, No. 5, March 2005
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19. QUESTIONS?? Final Comments Presentation Title June 24, 2018
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