Small scale fading types and factors

Small-scale fading (or simply fading) is the rapid change of received signal amplitude and phase over a short distance (a few wavelengths) or short time, due to the constructive and destructive addition of multipath waves. Large-scale path loss is almost constant over such a distance.

Its effects are: rapid changes in signal strength, random frequency modulation due to Doppler shifts on different paths, and time dispersion (echoes) caused by multipath delays.

Types of small-scale fading

A. Based on multipath delay spread

1. Flat fading: Bs ≪ Bc, Ts ≫ στ. All frequencies fade together, no ISI, amplitude is Rayleigh distributed.
2. Frequency selective fading: Bs > Bc, Ts < στ. Parts of the spectrum fade differently, causing ISI and distortion; equalization is needed.

B. Based on Doppler spread 3. Fast fading: Ts > Tc, Bs < BD. Channel impulse response changes within a symbol; causes time-selective distortion. 4. Slow fading: Ts ≪ Tc, Bs ≫ BD. Channel is static over many symbols.

          Small-scale fading
         /                  \
  Delay spread          Doppler spread
   /        \             /        \
 Flat   Freq.-selective  Fast      Slow

Factors influencing small-scale fading

1. Multipath propagation: reflecting and scattering objects (buildings, trees, vehicles) create many waves with different amplitudes, phases and delays. Their vector sum fluctuates, and the spread of delays causes time dispersion and ISI.
2. Speed of the mobile: relative motion between BS and mobile gives each multipath wave a different Doppler shift fd = (v/λ)cos θ, producing random frequency modulation.
3. Speed of surrounding objects: moving vehicles and people change the channel with time. If they move faster than the mobile, they dominate the fading; otherwise their effect can be ignored and only the mobile's speed counts.
4. Transmission bandwidth of the signal: if the signal bandwidth is greater than the channel's coherence bandwidth, the signal is distorted (frequency selective); if much smaller, the amplitude fades but the signal is not distorted (flat).

Example: at 900 MHz (λ = 0.333 m) a car at 72 km/h (20 m/s) has maximum Doppler shift fm = 20/0.333 = 60 Hz, so the fading rate is in the tens of hertz.