Fading and Multipath Propagation: Complete Beginner's Guide

Multipath propagation is a signal reaching the receiver along several paths at once: direct, reflected, diffracted and scattered. The copies arrive with different delays and phases, adding constructively at some moments and destructively at others. This rapid random fluctuation of signal strength is fading.

Fading is the dominant impairment in mobile communication: moving a few centimetres can drop a phone into a 20-30 dB fade. Every modern standard, from GSM to 5G and Wi-Fi, is designed around it via OFDM, coding, interleaving and diversity. Understand fading and you understand why wireless standards look as they do.

Key Concepts

• Delay spread: time gap between first and last significant path (microseconds in cities).
• Coherence bandwidth: frequency range over which the channel stays constant; inversely related to delay spread.
• Doppler spread: motion shifts each path's frequency differently; maximum shift f_m = v / lambda.
• Coherence time: time the channel stays constant; inversely related to Doppler spread.
• Flat vs frequency-selective: flat fading hits all frequencies equally; selective fading distorts frequencies differently.
• Slow vs fast: slow means the channel barely changes during one symbol; fast means it changes within a symbol.
• Rayleigh vs Rician: Rayleigh models scattered paths with no line of sight; Rician adds one dominant path (K-factor measures its strength).

Formulas

• Max Doppler: f_m = v / lambda (v in m/s, lambda in m, result in Hz).
• Coherence time (Clarke): T_c = 0.423 / f_m. Symbols much shorter than T_c see slow fading.
• Coherence bandwidth: B_c = 1 / (50 x delay spread). Signal bandwidth well below B_c means flat fading.
• Assumptions: order-of-magnitude relations for rich scattering; not exact laws.

Worked Example

Car at 90 km/h, 900 MHz signal, 5 microsecond delay spread, 200 kHz signal, 3.7 microsecond symbols. Classify the fading:

1. v = 25 m/s; lambda = 3x10^8 / 9x10^8 = 0.333 m.
2. f_m = 25 / 0.333 = 75 Hz; T_c = 0.423 / 75 = 5.64 ms.
3. Symbol (3.7 us) is far shorter than T_c: slow fading.
4. B_c = 1 / (50 x 5x10^-6) = 4 kHz. Signal (200 kHz) is far wider: frequency-selective fading, needing an equalizer or OFDM.

Common Misconceptions

• "Fading just means weak signal." Fading is rapid variation around an average; deep momentary fades corrupt data even when the average is strong.
• "More transmit power fixes fading." Overcoming 30 dB fades needs enormous power; diversity (antennas, paths, time slots) is the practical cure.
• "Rayleigh fits every channel." It assumes no dominant path; with line of sight, Rician models fit better and fading is milder.

Real-World Applications

• OFDM (LTE/5G/Wi-Fi): narrow subcarriers each see flat fading, defeating selectivity.
• Rake receivers: CDMA receivers collect delayed paths and combine them constructively.
• Diversity: multiple antennas or slots make simultaneous fading unlikely.
• Interleaving + coding: spread fade bursts in time so error correction fixes them.

Multipath copies interfere to cause fading. Delay spread sets coherence bandwidth (flat vs selective); Doppler sets coherence time (slow vs fast). Classify with those two numbers, then defeat fading with OFDM, diversity, rake reception and coding.