The document discusses Rayleigh fading channels in mobile digital communication systems. It describes how multipath propagation can cause multipath fading or scintillation. It distinguishes between large-scale fading and small-scale fading. Large-scale fading refers to mean signal attenuation over large areas and variations around the mean due to shadowing. Small-scale fading is also called Rayleigh fading and refers to time spreading of signals and time variance of channels due to small changes in position.

1. Rayleigh Fading Channel in Mobile Digital Communication System Part I: Characterization Oum Saokosal Cambodian Graduate Student March 2009

2. Rayleigh Fading Channel We starts from additive white Gaussian noise (AWGN), with statistically independent Guassian noise sample corrupting data samples free of intersymbol interference (ISI). Causes to degradation: Thermal noise at the receiver External interference received by the antenna Signal attenuation vs. distance

3. Rayleigh Fading Channel Path loss or free space loss: L s (d) = ( 4  d ) 2 where L s (d): path loss d: distance between transmitter and receiver  : wavelength of the propagation signal For this case of idealized propagation, received signal power is very predictable. 

4. Rayleigh Fading Channel In wireless sys, a signal can travels over multiple reflective paths, which is referred to as multipath propagation . It causes to multipath fading or scintillation . Scintillation described the multipath fading caused by physical changes in the propagation medium.

5. Mobile Radio Propagation: Large-Scale and Small-Scale Fading Large Scale Fading at Fig. 1: Large scale fading due to motion over large areas Mean signal attenuation vs. distance Variation about the mean These above fadings are affected by prominent terrain contours. It is as being “ shadowing ”. It described in terms of a mean-path loss ( n th-power law) & log-normally distribution variation .

6. Mobile Radio Propagation: Large-Scale and Small-Scale Fading Small Scale Fading at Fig. 1: Small-scale fading due to small changes in position Time spreading of the signal Time variance of the channel Small scale fading manifests itself in: Time-spreading of the signal (or signal dispersion) Time-variant bahavior of the channel Small scale fading is also called Rayleigh fading

7. Mobile Radio Propagation: Large-Scale and Small-Scale Fading There are 3 basic mechanism impacting Signal Propagation in Mobile Com. Sys.: Reflection : a propagation electromagnetic wave impinges on a smooth face. Diffraction : radio path is obstructed by a dense body. It is often termed “shadowing.” Scattering : radio wave impinges on a large rough surface causing the reflected energy to scatter.

8. Mobile Radio Propagation: Large-Scale and Small-Scale Fading (Fig.2)When estimating path loss for a link budget analysis in a cellular application: Mean path loss as a function of distance due to large-scale fading Near-worse-case variation (6-10 dB) Near-worse-case Rayleigh (20-30 dB)

9. Mobile Radio Propagation: Large-Scale and Small-Scale Fading Generally: r(t) = s(t) * h c (t) , where: * : convolution r(t): receive signal s(t): transmitted signal h c (t): the impulse response of the channel

10. Mobile Radio Propagation: Large-Scale and Small-Scale Fading In case of mobile radios: r(t) = m(t) x r 0 (t) , where: m(t): large-scale-fading component or local mean or log-normal fading. r 0 (t): Small-scale-fading component or multipath or Rayleigh fading.