Gregory D. Durgin, originally published on WaveRacer.com
1 January 2002
Rather than present the standard fare, let’s shake things up a bit and switch frequency bands. We will discuss propagation in the optical frequency bands by outlining an experiment that you can do in the comforts of your own home or office. The goal: to understand the concept of shape factors and why they are important in multipath radio (and even optical) wave propagation.
Overview
Ever since the Maxwellian synthesis, engineers have understood optical frequency radiation to follow the same physical laws as radio frequency radiation. The primary difference is that our eyes have sensory experience of optical radiation, while we have only indirect experience of radio wave propagation.
(Perhaps now would be a good time to give thanks that the FCC still considers the TeraHertz bands an “unlicensed” spectrum.)
This sensory experience of light waves, however, gives us a chance to draw analogies to radio wave propagation, both constructive and sometimes misleading. The one big drawback is that most of our experience with optical propagation is with incandescent light, while radio communications is almost always performed with a coherent carrier. If you really want to make experiments or draw analogies, always user laser beams — the most common source of coherent light.
This article is a discussion of how a laser beam can illustrate some very important concepts in radio wave propagation for wireless communications. First, though, we will make a brief discussion of multipath shape factors.
Shape Factors
Typical radio environments are rife with scatterers, making it extremely difficult to characterize all of the multipath power impinging upon any operating receiver. Shape factors were originally invented as a way to circumvent this difficulty. In theory, complicated multipath angle-of-arrival information can be boiled down to just 3 meaningful parameters that have both geometrical and physical significance.
Calculated from the incoming azimuth spectrum of multipath power, the three important shape factors are angular spread, angular constriction, and the direction of maximum fading. To get the technical description of these parameters, download the article IEEE Transactions on Antennas and Propagation, “Theory of Multipath Shape Factors for Small-Scale Fading Wireless Channels“. If you want the digested summary, see the table below for the definition of each shape factor.
| Shape Factor | Geometrical Meaning | Physical Meaning |
| Angular Spread | Measures how concentrated multipath power is about onedirection. Minimum value is 0, corresponding to perfect concentration, Maximum value is 1, corresponding to no clear spatial bias in incoming power. | The average fading rate in space (how often constructive and destructive signal interference occurs) is directly proportional to the angular spread. |
| Angular Constriction | Measures how concentrated multipath power is about two directions. Minimum value is 0, corresponding to no clear concentration in two directions, Maximum value is 1, corresponding to perfect concentration in two directions. | Angular constriction captures directional dependence of fading through space. Constriction of 0 experiences similar fading in any direction of space. Constriction of 1 results in heavy fading in some directions and virtually no fading in others. |
| Direction of Maximum Fading | This is the direction in space corresponding to the most rapid constructive and destructive interference in signal strength. | A receiver that moves along this direction experiences maximum fading rate. Transverse to this direction, it experiences minimum fading rate. |
An Experiment with a Laser
To demonstrate what a shape factor is using optics, get a cheap laser pointer device and shine it on a semi-smooth surface (like a piece of paper or a desk top). Although the surface may be smooth to the touch, the wavelength of laser light is extremely small. Most surfaces appear “electromagnetically” rough to a laser beam, so that diffuse scattering results at the interface of the smooth surface. This diffuse scattering produces the familiar speckle pattern seen on the illuminated area of the semi-smooth surface. The scenario is illustrated below:
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| Layout of the laser beam experiment: a beam strikes a semi-smooth surface and creates a speckle pattern. |
The speckle pattern results from the constructive and destructive interference of multipath waves in space. The human retina, with its dense arrangement of light-sensing rod and cone cells, is like an array of receiver antennas. The semi-smooth surface scatters the coherent laser light so that many tiny multipath waves are traveling in different directions. In a way, the laser speckle pattern is the closest analogy to how a wireless receiver views a radio signal in space: bright areas of operation sprinkled with deep, dark fades.
Normally, the wavelength of light (in the nanometers) is much too small for the human eye to make out the fading in a speckle pattern. However, the illuminated area on the semi-smooth surface only takes up a tiny area in the optical field-of-view. In other words, it has an extremely small angular spread, so the fading pattern is slow enough in space for a human eye to discern it.
A sliver of multipath power like the illuminated speckle also has a large angular constriction that asymptotically approaches 1. The direction of maximum fading is transverse to such a sliver. Thus, fading along the transverse direction of space should be quite rapid, while fading along the parallel direction of space should be much slower. This is characteristic of all constricted channels.
To verify this characteristic, look directly at the illuminated area on the semi-smooth surface. Slowly rock your head to the right and to the left in the transverse direction. You should see the speckle pattern change dramatically since you are moving in the direction of maximum fading. Now change the motion to slowly rock your head forwards and backwards in the parallel direction. You should notice a much slower change in the speckle pattern. The bright spots and dark spots do not undulate nearly as fast compared to the transverse movement.
Analogies to Wireless Communications
If you experience the laser experiment, you will have a near-perfect understanding of what shape factors are and how they are important to wireless communications. There are numerous analogies to draw from the laser beam experiment.
The most immediate analogy is fading at the base station antennas of a cellular network. Base stations are usually placed at the edge of a sector and experience multipath radio waves from the mobile users that arrive over a very small sector of the horizon (less than 5-10 degrees). This small angular spread causes deep fades to occupy large regions of space, on average 10-20 wavelengths of radiation (about 10-20 feet/3-6 meters at analog cellular frequencies). The two diversity antennas used by cellular base stations must be placed very far apart in order to avoid sumultaneous fades.
Furthermore, the spacing of the diversity antennas is always transverse to the cellular area serviced by the tower. Placing the antennas in the parallel direction would be radio propagation suicide, since this is the direction of minimum fading. Such a case would guarantee that the constricted radio propagation as seen by the cellular base station would create simultaneous signal fades on each element.