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This section is on modeling and measuring the propagation of RF and light though different material media. For more examples of projects that used such modeling to mitigate the channels effect, see also Channel Mitigation


Fog scatters an optical link, causing attenuation and "multipath". Mitigated by pulsed laser, pulse width equal to time from coherent arrival to first significant scattered incoherent arrival.

Paper on fog propagation, and a corresponding slide set

MIE modeling of fog water droplets. Far-field scattering coefficients {a,b}n, from which total and scattering cross-sections can be computed for incidence plane waves:

Atmospheric attenuation modeling

Each molecule has quantum resonances, and various line broadening mechanisms.

Extinction analysis, based on std atmosphere, to 400 THz

Interstellar gas interaction with microwaves

Measured using the James Clerk Maxwell telescope on Mauna Kea

In external galaxies: rotational radiation of carbon monoxide molecules, with frequency shifts due to galactic rotation doppler.

CO(3->2) Mapping in M82

Terrestrial radio multipath

Analysis of NTIA propagation experiment data, for evaluation of MMDS channel.
Experimental setup:
  • Transmitter relocatable, 50W linear polarized wideband sounding waveform (PN sequence 10MHz chip, repeats 50us)
  • Mobile receiver, two vertical antennas 15 wavelengths apart, recorded raw complex samples (4x oversampled)
  • Tested over large areas near front range, CO
Data then allows complex impulse response of channel (delay profile)
The example record below shows line-of-sight reception at ~30dB above noise floor, large diffuse multipath with delay 10-20us and 15-20dB down per delay bin, and specular multipath at 4us and 28us:

 Versus time, this data can be visualized in the form of the waterfall diagram below. Macroscopic time follows the vertical axis downward (span 2 minutes), while delay time is read horizontally. The receive power follows the color code legend on the left. Individual multipath sources can be seen by their persistence and geometry trajectories through the time/delay plot:

As an example of the dependence of delay on multipath location, the following figure shows 4 multipath sources (locations in cartoon inset). These dependences can be used to determine multipath location sources from the raw data and its corresponding vehicle GPS locations.

For more information on these channel sounding/characterization techniques, please see this Paper

Channel sounding with passive RFID tags

For complete understanding of the channel propagation environment, it's important at times to fully sound a channel: that is, to measure received signal strength and polarization (and sometimes phase) in a volume.
Passive RFID tags provide an excellent mechanism for these measurements. An array of tags attached to an approximately RF transparent board (for instance, dry cardboard), some of which can be at cross polarization orientations, is moved through the volume. The position/orientation of the board is most easily recorded via a scanning lidar that detects 2 masts projecting above the board. Each mast gives a position, and the two together give board orientation.
Since the RFID interrogator's position is known, the free space path loss to/from the tag can be computed from the tags known (dynamic) position. The received power can then be compared to the expected free space quantity, and and a channel fade/surge can be computed. The following image shows all tag interrogation values while the board was moved over many meters of travel. The tags were also being swept across the 50 RFID frequency channels, to record frequency-selective information in this volume.

These points can be visualized in 3D in the following video:

Channel Sounding 3D visualization

Material RF propagation

Although RF propagation analysis is used to quantify its nuisance and need for mitigation, propagation can also be used to determine material characteristics.
In agriculture, the moisture content of organic products determines when it should be harvested or is safe to store.
For John Deere, several experiments were performed to determine the feasibility of using microwaves as a moisture sensor. These used techniques of attentuation correlation, as well as group delay through a material bulk. These were used as a basis for product development of moisture sensors for grain, cotton, and hay.

Optics extended to general relativity: Gravitational Lenses

General relativity causes effective index-of-refraction changes near a gravity well, and Fermat's theorem can be used to determine gravity well lensing phenomenon. For instance, this diagram shows the relative image shift of a background object caused by a massive object.

Path integrals also allow computation of relative image brightness. For more info, see this paper fragment.

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