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Developing a Physically Based Model for Multipath Fading

This research focuses on creating a deterministic fading-channel model based on the geometry of reflectors for wireless communication systems. Multipath fading, a critical factor in mobile communications, occurs when transmitted signals reach the receiver via multiple paths, leading to interference patterns. By analyzing the asymptotic behavior of signal strength in relation to multiple reflectors, we aim to improve existing statistical models. The study explores Bessel functions and their role in field strength densities, with future work considering spatial correlation and non-circular reflector geometries.

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Developing a Physically Based Model for Multipath Fading

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  1. Developing a Physically Based Model for Multipath Fading Dwight Hutchenson Clemson University Advisor: Dr. Daniel Noneaker 2003 SURE Program

  2. Basic Wireless Communication System • TX and RX • In general, LOS and reflected signal components • Often no LOS component in mobile communications • Transmitted Signal: s(t) • Received Signal: r(t) = A1s(t - d1/c) + A2s(t – d2/c) + . . .

  3. Multipath Fading • Interference pattern results from radio waves reaching the receiver by two or more paths

  4. Motivation • Statistical model of fading channel often used in communication system analysis • e.g. , Clarke-Jakes model • Our goal: develop deterministic fading-channel model based on geometry of reflectors • Focus on asymptotic behavior • TX dist >> reflector dist • Reflector dist >> RX variation

  5. Signal at O through Pn: Signal at O through P0: (reference signal) (baseband-equivalent complex representation) Signal at the Origin due to Single Reflector

  6. Signal at the Origin due to Single Reflector (cont.)

  7. Signal at S through Pn : Signal at the Receiver due to Single Reflector

  8. Signal at the Receiver due to Multiple Reflectors • Consider circular array of reflectors at distance r from O • Find the signal at S for N total reflectors:

  9. Signal at the Receiver due to Multiple Reflectors (cont.) • Signal strength per reflected component must be normalized, to consider what happens as N approaches infinity • As N approaches infinity: • Bessel Function of the first kind of zero order:

  10. Evaluating Signal Equation with the Bessel Function • Inserting Result into Signal Equation:

  11. Density of Field Strengths • Empirical density of field strengths for fixed path through origin

  12. Densities of Field Strengths (cont.) • Investigate possible relationship to density of sin function Density of sin(x)

  13. Future Work • Spatial Correlation of Field Strengths • Corresponds to temporal correlation for receiver in motion • Non-circular reflector geometries

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