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# Propagation Measurements and Models for Wireless Communications Channels

Jorgen Bach Anderson, Theodore S. Rappaport, and Susumu Yoshida

One-line summary: Complex interactions between geometry, radio propagation effects, and mobility make prediction of coverage and path loss a practically intractable problem; rudimentary models have been developed, but empirical or heuristic methods nearly inevitably fare better.

## Overview/Main Points

• Propagation mechanisms: wave propagation is physically explained by three phenomena - reflection (reflective object >> wavelength), diffraction (obstructive object >= wavelength), and scattering (obstructive object < wavelength).
• Raleigh fading: the field detected at the receiver is the sum of many random contributions of different phase and directions, due to multipath effects deriving from the 3 propagation mechanisms. Raleigh fading implies rapid fluctuation - "small scale fades". Raleigh fading occurs typically for non-line-of-sight (NLOS) environments. In LOS environments, smaller delay spreads (Ricean distribution) dominates.
• Path loss: path loss at some distance d from a transmitter, PL(d), is a local average measurement of received signal strength. The empirical path loss relationship is
PL(d) = PL(do) + 10nlog(d/do) + Xsigma,
where PL(do) is some reference distance, n is a power law parameter known as the "power-delay index", and Xsigma is a Gaussian random fudge factor. n=3-4 is typical of NLOS Raleigh fading, and n=2 is typical of Ricean fading or free space. A more complex indoor propagation formula is in Randy's notes.
• Delay spread: multipath effects create time dispersion, a smearing or spreading out of the signal. Urban delay spreads of around 3 microseconds are commonplace, but much higher values such as 10-100 usec have been observed. Important characteristics are the maximum excess delay (MED), the MED at X db monotonically less than the maximum, the mean excess delay (first moment of power delay profile), and RMS delay spread.
• Path loss models: All models of path loss are empirical in nature, and quite inaccurate. Macrocells in particular suffer from extreme variations in path loss, while the lower power and coverage of microcells makes the propagation characteristics "milder", enabling broadband techniques.
• Indoor propagation: Signal characteristics are much less predictable indoors. Building materials, physical layout, and the number and position of receivers all greatly affect coverage. The motion of people within the building causes Ricean fading in LOS paths, while Raleigh fading still dominates OBS paths. CAD-like tools can be used to aid prediction, although their accuracy is low.

## Relevance

The physics of radio propagation dictate wireless networks' physical layer characteristics, which in turn affect the design and performance limitations of all higher level network layers. Knowledge of radio propagation characteristics may give insight into wireless systems design.

## Flaws

• Radio propagation characteristic models are inaccurate and highly heuristic. This is a fault of the science in general, not this paper.
• The paper is a bombardment of factoids; it is hard to weed through them to find the truly valuable insights.

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