Small scale fading and influencing factors

Small scale fading

Small scale fading is the rapid change in the amplitude, phase and multipath delay of a received radio signal over a short distance (a few wavelengths) or a short time (a few seconds). It happens because two or more copies of the transmitted signal (multipath waves) reach the receiver at slightly different times and with different phases, and add constructively or destructively. Large-scale path loss can be treated as constant over such a small distance.

Its three main effects are:

• Rapid changes in signal strength over a small travel distance or time interval.
• Random frequency modulation due to different Doppler shifts on different multipath signals.
• Time dispersion (echoes) caused by multipath propagation delays.

 Power (dB)
   |   /\    /\  /\     /\
   |  /  \/\/  \/  \/\_/  \   <- deep fades
   | /                     \     every ~ λ/2
   +----------------------------> distance

Factors influencing small scale fading

1. Multipath propagation – Reflecting and scattering objects (buildings, vehicles, trees) create many waves with random amplitudes, phases and arrival times. Their vector sum fluctuates strongly, and the spread of arrival times causes time dispersion and ISI.

2. Speed of the mobile – Relative motion between the base station and the mobile gives each multipath component a different Doppler shift, f_d = (v/λ) cos θ. Higher speed means a larger Doppler spread and faster fading (smaller coherence time).

3. Speed of surrounding objects – Moving cars, people and other objects in the radio channel also create time-varying Doppler shifts. If they move faster than the mobile, their effect dominates; otherwise it can be ignored.

4. Transmission bandwidth of the signal – The channel has a coherence bandwidth B_c (inversely related to its delay spread).

   • If signal bandwidth B_s < B_c, all frequency components fade together: flat fading, little distortion.
   • If B_s > B_c, different frequency components fade differently: frequency selective fading, pulse spreading and ISI.

Together, the delay spread (from multipath) and the Doppler spread (from motion) decide whether the channel is flat or frequency selective, and fast or slow fading.