Small-Scale Fading Also known by other names such as ‘Fading’; multipath and Rayleigh fading Rayleigh fading is a result of constructive and destructive interference between several versions of the same signal at the receiver, leading to attenuation of signal power or amplitude – Usually over a fraction of the signal wavelength – Attenuation between 20 to 30 dB – multipath fading manifests as time spreading or time variation of the signal (due to motion, foliage, reflections and scattering) Rayleigh Distribution If the impulse response h( , t) of the mobile radio station is time invariant and has zero mean, then the envelope of the impulse response has a Rayleigh distribution given as: r r2 pr 2 exp 2 2 where is the total power in the multipath signal Rice Fading If however the impulse response has a non zero mean then there is a significant component of the direct path (line of sight, specular component) signal and the magnitude of the impulse response has a Ricean distribution Ricean distribution is the combination of Rayleigh signal with the direct line of sight signal. The distribution is: r r 2 s 2 rs pr 2 exp I 2 0 2 2 s2 is the power of the line of sight signal and I0 is a Bessel function of the first kind Characteristics of Small-Scale Fading Small-scale fading occurs as either of 4 types: • frequency selective fading in which the bandwidth of the signal is greater than the coherence bandwidth and the delay spread is greater than the symbol rate; Signals at some frequency components experience more fading than others - (caused by multipath delay spread) • flat fading when the bandwidth of the signal is less than the coherence bandwidth and the delay spread is less than the symbol rate - (caused by multipath delay spread) • fast fading when the Doppler spread is high and the coherence time is less than the symbol period and • slow fading with a low Doppler spread and coherence time is greater than the symbol period - (caused as well by Doppler spread) Summary of Small-scale fading Correct for small-scale fading with • adaptive equalizers • modulation techniques such as spread spectrum Type of fading Frequency Effects Time Effects Effects of Multipath Delay Spread Frequency Selective fading BW of signal > coherence BW Delay spread > symbol period Flat fading BW of signal < coherence BW Delay spread < symbol period Effects of Doppler Spread Slow fading Low Doppler spread Coherence time > symbol period Fast fading High Doppler spread Coherence time < symbol period Propagation of Cellular Communication Signals • Cellular communication is mostly land based. • There are a few applications on ships and airlines using networks in a box and satellites • Propagation considerations are therefore based on – urban, rural, suburban and – in a few cases water and desert terrain – sky or space propagation (satellites) Free Space Propagation Model • Free space propagation Model is used to predict received signal stength when the transmitter and receiver have clear, unobstructed line-of-sight path. • The free space model predicts that received power decays as function of TR separation distance raised to some power. Pr Pt Lp Gt Gr d 7
"Small Scale Fading - Wireless and Mobile Communication"