# Difference between revisions of "Radio Wave Propagation"

Nature is seldom kind. This is true for the typical wireless radio channel as well, which is due to the effect of wave propagation and noise resulting in an unpredictable evolution of its characteristic parameters. The resulting complexity of the channel is easy to evaluate but might be hard to predict which is known as the concept of Physical Unclonable Function (PUF)s for cost-efficient, strong security mechanism [1]. In this chapter, we introduce fundamentals of the wireless channel, which are important for later analyses and development of WPLS primitives. In this section, we give an overview of the properties of a wireless radio channel. We refer to literature of Rappaport [2], Goldsmith [3], and Jakes [4] for further details and elaborate here on the issue of building a WPLS system rather than a robust communication system.

Essentials. The wireless radio channel is a complex shape. It is time variant, environment dependent, carrier frequency dependent, and due to motion a time/space uncertainty is introduced. The measurement accuracy is dependent on receiver and transmitter hardware, of the transmitted waveform, as well as of the Analog to Digital Converter (ADC). Nevertheless, it can be measured and characterized by the changes and affections a signal takes by traveling through it. Radio waves sent through a physical medium can be affected by the following channel distortions [5]:

• Attenuation over distance
• Multipath propagation
• Reflections at large obstacles
• Refraction at medium crossing
• Scattering at small obstacles
• Diffraction at edges
• Interference with other transmissions
• Random noise

The channel between two antennas, e.g., of two transceivers, is of interest. In practice, channels are bandwidth limited. This is due to physical limitations of the transceiver’s hardware, e.g., number of antennas, antenna sizes and design, power amplifier, and low-noise amplifier, etc. Additionally, a frequency-selective wireless radio channel can be time-variant. That meant that due to changes in the environment, e.g., temperature variations, motion of scatters, or motion of one or both antennas, the channel also changes. The connection between physical changes of the environment and the resulting channel changes can be extremely complex, e.g., in a rich multipath environment. However, it can also be trivial, e.g., in free-space only the distance between both antennas matters. Summarizing, a wireless radio channel is a shared, bandwidth restricted resource which has a characteristic that can vary in time, spectrum and space/environment. The detailed trace of a channel can be infinitely complex, but it mainly depends on the measurement procedure.

Details. Details of the wireless channel are given in the section about Key Extraction Principles.

### Free Space Propagation and Log-Normal

In the absence of multipath propagation effects, interferences, and noise, the radio wave propa- gation can be simulated using the free space propagation model in Equation (2.1). The power of the received signal at the antenna is:

$\displaystyle P_R[dBm] = P_0 - 20log(\frac{d}{d_0})$



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## References

1. Pim Tuyls, BSkori´ c, Sjoerd Stallinga, Anton HM Akkermans, and Wil Ophey. Information-theoretic security analysis of physical uncloneable functions. In Financial Cryptography and Data Security, pages 141–155. Springer, 2005.
2. Theodore S. Rappaport et al. Wireless communications: principles and practice, volume 2. Prentice Hall PTR New Jersey, 1996.
3. Andrea Goldsmith. Wireless Communications. Cambridge university press, 2005.
4. William C. Jakes. Microwave Mobile Communications. John Wiley and Sons Inc., 1994.
5. Sanja Sain. Modelling and Characterization of Wireless Channels in Harsh Environments. PhD thesis, School of Innocation, Design and Engineering, Mälardalen University, 2011.
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