Also known as: Rayleigh fading, Rayleigh channel
Rayleigh fading is a statistical model for the rapid amplitude variation of a radio signal that arrives entirely by scattered and reflected paths, with no dominant direct component.1 When many equal-strength multipath copies add with random phases, the resulting envelope follows a Rayleigh probability distribution — hence the name. It is the worst-case small-scale fading model for a mobile receiver deep inside urban clutter or dense foliage, and it underpins how engineers size a fade margin.
How it works
Model the received signal as a sum of many independent scattered rays. By the central
limit theorem, the in-phase (I) and quadrature (Q) components each become
zero-mean Gaussian random variables. The envelope, r = √(I² + Q²), then follows
the Rayleigh distribution:
- Probability density:
p(r) = (r/σ²)·exp(−r²/2σ²)forr ≥ 0. - The average power is
2σ²; the phase is uniform over 0–2π. - Because there is no steady dominant term, the envelope can occasionally cancel almost completely, producing deep fades tens of decibels below the mean.
The fading is called flat when the channel’s coherence bandwidth exceeds the signal bandwidth (all frequencies fade together) and frequency-selective otherwise, when different parts of the spectrum fade independently and cause intersymbol interference. How fast the envelope moves is set by the Doppler shift: a faster mobile crosses the standing-wave pattern more quickly, giving a higher fade rate.
Relevance to SDR
Rayleigh fading dominates the land-mobile channels that trunking scanners listen to. A pedestrian or vehicle in a city receives P25, DMR, TETRA, and NXDN signals with no clean line of sight, so the instantaneous level swings by tens of dB over fractions of a wavelength. This is why a talkgroup can be perfectly readable one moment and drop into a burst of errors the next, even with a strong average signal — a deep fade briefly pushed the carrier below the demodulator’s usable signal-to-noise ratio.
Cellular and broadcast systems fight Rayleigh fading with antenna diversity, interleaving, and forward error correction so that a fade that kills one branch or one symbol span does not kill the whole message. GopherTrunk is a receiver: it does not implement diversity combining, but its decode chain relies on the FEC and interleaving already built into the on-air protocols to ride through the short fades, and it exposes per-frame error-vector-magnitude and SNR estimates that reveal fading directly.
In practice
The single most useful consequence is the fade margin: because deep fades are inevitable, a link must be budgeted with headroom above the bare minimum SNR. For a Rayleigh channel, achieving a given outage probability requires many decibels of margin, which is why mobile systems close their link budget conservatively. When a line-of-sight component is present, the channel is better described by Rician fading, of which Rayleigh is the limiting case (K-factor = 0).
Sources
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Rayleigh fading — Wikipedia, on the no-line-of-sight multipath model and its Rayleigh-distributed envelope. ↩