Multiple Phase Screen Calculation of Wide Bandwidth Propagation Dennis L. Knepp L. J. Nickisch NorthWest Research Associates 28 URSI General Assembly Chicago, August 28
Outline Summary of MPS technique Examples of scattering by a large cloud of structured ionization Comparison of a calculation of the average generalized power spectrum using the MPS technique and Nickisch s phase-screen diffraction method (PDM)
Introduction Multiple phase screen (MPS) calculations have long been useful for calculation of ionospheric scintillation Study the effects of turbulence on EM propagation Help understand ionospheric sensor measurements and how they relate to ionospheric physical properties Provide realizations of received signals for receiver design We utilize an updated version of an MPS code first written in the 198s New code has better handling of time domain results Several useful animations of transfer function and impulse response function
MPS Solution Technique Parabolic Wave Equation for E-field v U ( r ) 2 v 2 v v 2ik = U ( r ) + k ε1( r ) U ( r ) x Diffraction term Source term Solution Method: Collapse ionospheric structure into multiple thin phasechanging screens with free-space between At phase screen, neglect diffraction term Between screens, the parabolic wave equation is source free, solve by Fourier Transform method Perform MPS calculation for all frequency components in the signal bandwidth
MPS Propagation Geometry Structure extends infinitely into the figure Propagation Distance Incident Plane Wave Layer Thickness MPS Grid Length
Scattering From a Strong Gaussian Defocusing Lens Propagation distance Defocusing lens is a Gaussian with 5 m scale size 2 19 = 524,288288 points along MPS grid, no small scale structure t
Strong Gaussian Defocusing Lens Amplitude and Phase vs Propagation Distance
plitude (d db) Am Phase (ra adians) 1-1 Strong Gaussian Defocusing Lens After Propagating 1 km MPSEFieldCase: 56 PropDistKm: 1-2 15 2 25 3 35 Distance (km) 1 5-5 15 2 25 3 35 Distance (km) Close up of last frame of previous movie
Time Domain Calculation Triangular time domain waveform: Fourier transform: MPS calculation: T c = 1 nsec Bandwidth = 2 MHz No of frequency components = 64 Carrier frequency = 1 MHz
Geometry of Ionized Cloud Plane wave Single phase screen Ionized cloud Propagating Triangular Pulse Barium Cloud Propagation distance Observation Plane MPS grid Diffraction and multipath predominate Signal delay due to large-scale phase perturbation Dis stance along
g 7 Time Domain Signal After Propagating 1 km Past the Strong Gaussian Lens p 6 5 Ampli itude 4 3 2 1.5 1 1.5 2 Delay (μ sec)
Single Phase-Screen Representation of a Large Structured Ionized Cloud 2 15 Phase (ra adians) 1 5-5 1 2 3 4 5 Distance (km) Cloud is a large smooth Gaussian with structure added Structure has a q -3 power-law power spectral density Outer scale = 39 m, Inner scale = 1 m, 2 19 points Phase standard deviation = 4 radians
Amplitude and Phase at the Carrier Frequency after Propagating 1 km Stuctured Cloud mplitude (db) A 1-1 -2-3 1 2 3 4 5 Distance (km) Phase (r radians) 3 2 1-1 1 2 3 4 5 Distance (km) Propagation distance = 1 km Transmission frequency = 1 MHz
Scattering from the Large Gaussian Cloud With No Structure Signal experiences delay, focusing, and dispersion after propagating a distance of 1 km past the screen LargeLensMsec Case: 554 PropDistKm: 1 GridExtentKm: 5 7 6 No scattering on edges 5 plitude Am 4 3 2 1 Pulse spreading 1 points taken from 524,288 -.5.5 1 1.5 2 Delay (μ sec)
7 6 Time Domain Signal After Propagating a Distance of 1 pkm Structured Cloud Am mplitud de 5 4 3 2 1 points taken from 524,288 1 -.5 5 5.5 1 15 1.5 2 Delay (μ sec) Ionization structure adds amplitude and phase scintillation to the previous figure
Close-Up of Center of the Previous Figure LensMsec Case: 551 PropDistKm: 1 GridExtent 7 Amp plitude 6 5 4 3 2 1 points taken from 524,288 1 -.5.5 1 1.5 2 Delay y(μ sec)
7 Close-up of Center of Previous Figure p Amp plitude 6 5 4 3 2 1 points taken from 524,288 1 -.5.5 1 1.5 2 Delay y(μ sec)
First Frame of MPS Animation Transfe er fn (db) 1-1 -2 Movie: 164 MPS Case: 551 Grid DistKm: 15. -3-2 -15-1 -5 5 1 15 2 Frequency (MHz) Distance along the grid Amplitude of transfer function Voltag ge (db) 1-1 -2-3 -.2 2 -.1 1 1.1 2.2 3.3 4.4 5.5 6.6 7.7 Time (Microsec) Amplitude of impulse response function
Variation of Transfer Function and Impulse Response Function Along the MPS Grid
Comparison of Averaged MPS Results to Strong-Scatter Theory
Phase Screen Diffraction Method (PDM) Where ω d, x, y are difference variables 1/z term applies to spherical wave propagation A is the quadratic expansion of the phase structure function PDM is valid for strong scattering Solution employs a split-step Fourier transform to march from phase screen to phase screen
Thick-Layer Propagation Geometry Incident Plane Wave 84 km 42 km Receiver plane L = 1 km Structure has a q -3 power-law power spectral density Outer scale = 5 km, Inner scale = 1 m, 2 17 points Phase standard deviation = 17 radians Carrier = 3 MHz, BW = 4 MHz, 128 discrete freqs Based on unpublished measurements (March 21)
5 4 Log 1 ( Γ(x,f) )(x,f) ) Thick Layer (42 km) 5 4 y -2 DeltaFr requency (MHz) 3 2 1-1 -2-3 DeltaFr requency (MHz) 3 2 1-1 -2-3 -4-6 -8-1 -12-14 -16-4 MPS calculation -5-2 -1 1 2 Separation (Meters) Two-position, two-frequency MCF Average of 5 realizations -4 Strong scatter theory -5-2 -1 1 2 5-2 Separation (Meters) -18
5 4 Log 1 ( Γ(x,f) )(x,f) ) - Single Phase Screen 5 4 y -2 DeltaFr requency (MHz) 3 2 1-1 -2-3 DeltaFre equency (MHz) 3 2 1-1 -2-3 -4-6 -8-1 -12-14 -16-4 MPS calculation -5-2 -1 1 2 Separation (Meters) Two-position, two-frequency MCF Average of 5 realizations -4 Strong scatter theory -5-2 -1 1 2-5 -2 Separation (Meters) -18
Delay-Angle Power Spectrum Layer Thickness = 42 km MPS calculation Strong scatter theory 4 2 2 4 For frozen-in turbulence, this becomes the Delay-Doppler power spectrum
Delay-Angle Power Spectrum Layer Thickness = km MPS calculation Strong scatter theory 4 2 2
Comparison of Thick Layer and Single Thin Phase Screen Layer Thickness = km Layer Thickness = 42 km CASE 547 CASE 548 Delay-angle power spectrum Average of 5 realizations
Conclusions MPS codes are very useful to analyze wide bandwidth signals Include diffraction and scintillation Include the effects of ionospheric dispersion Allow for non-homogeneous media Time delay results are obtained by FFTs Animations i of the combined transfer function and impulse response function are useful to understand wideband scintillation and develop mitigation MPS and PDM agree for our example of a wideband signal
BACKUPS
Foca al Distance Focusing and Defocusing Incident Plane Wave Focusing Gaussian Lens (Glass) Strong Defocusing Lens (Plasma) Gaussian Lens Z X Delayed Signal On-Time Signal Delayed Signal
2 to 3 km LensMsec Case: 551 PropDistKm: 1 GridExtent 7 6 5 Amp plitude 4 3 2 1 -.5.5 1 1.5 2 Delay (μ sec)
Entire 1 km grid LensMsec Case: 548 PropDistKm: 84 GridExtentK 7 6 5 Amp plitude 4 3 2 1-1 1 2 3 4 5 Delay (μ sec)
LargeLensMsec L Case: 554 PropDistKm: 1 GridExtentKm: tk 2 7 6 5 Amp plitude 4 3 2 1 -.5.5 1 1.5 2 Delay (μ sec)