Fading - Wikiparency

# Fading **Fading** is the variation over time, frequency or position of how much a wireless signal is attenuated on its way from transmitter to receiver, usually described statistically rather than predicted exactly, since its immediate causes are themselves effectively random. Three distinct mechanisms are grouped under the name: interference among the several delayed copies a signal takes through [[Multipath_propagation|multipath propagation]], attenuation from weather, chiefly rain, and the blocking or partial blocking of the path by a building, a hill or foliage, usually called shadowing. A communication channel that shows this behaviour is called a fading channel, and keeping a link working through one, rather than only when conditions are ideal, is a large part of what separates a practical radio system from a laboratory demonstration. Fading is conventionally split by how quickly it moves. Shadowing and rain attenuation change slowly, over tens or hundreds of metres or over the minutes a storm takes to pass; multipath-induced fading can change over a fraction of a wavelength, a distance a moving vehicle covers in well under a second. One instance of the fast kind, received power rising and falling with distance along a two-path channel together with a running readout of how deep each fade cuts below the average level, is rendered by a three.js companion sketch elsewhere on this page. The deepest and most closely studied case is the one in which many scattered paths of similar strength combine with no dominant line of sight, giving an envelope whose amplitude follows a Rayleigh distribution and that is treated in its own article on [[Rayleigh_fading|Rayleigh fading]]; where one path dominates, the statistics shift toward a Rician distribution instead. Combating fading, whether through diversity, coding, equalisation or simply a wider power margin, is one of the central design problems of any wireless system whose link is not always in the clear. ## Key concepts Three variables can drive the variation: time, since a channel that is fine now may fade a moment later as the geometry among transmitter, receiver and any reflectors changes; frequency, since a channel's attenuation is rarely flat across an entire band and one part of a signal's spectrum may fade while another does not; and position, since two receivers only a short distance apart can see very different attenuation from the same transmitter. Because none of these can be predicted exactly outside a controlled laboratory link, fading is modelled statistically: a designer asks not how deep the next fade will be but how deep a fade the link must survive some acceptable fraction of the time, and budgets a fading margin, extra [[Signal-to-noise_ratio|signal-to-noise ratio]] held in reserve above what a fade-free link would need, to answer that question. Fading is conventionally separated into a slow, large-scale component, dominated by shadowing and by the general fall of power with distance, and a faster, small-scale component layered on top of it and dominated by [[Multipath_propagation|multipath]]; the two are usually modelled separately and then combined, since the physical mechanisms and the timescales involved are so different. A channel's coherence time and coherence bandwidth, the span over time and over frequency across which its response stays roughly constant, set which of the two components a given signal experiences most strongly, and organise the classification of fading types given next. ## Types ### Slow versus fast fading A channel is classed as slow-fading or fast-fading by comparing its coherence time with the duration of one transmitted symbol. If the coherence time is long compared with a symbol, the channel looks essentially fixed for the length of that symbol and changes only from one transmission to the next, which is slow fading; if the coherence time is short compared with a symbol, the channel changes appreciably within a single symbol, which is fast fading and distorts the symbol itself rather than merely scaling it. Coherence time shortens as the receiver moves faster, tracking the same Doppler relationship described in the [[Doppler_effect|Doppler effect]] article: a receiver in a fast-moving vehicle can turn a channel that would be slow-fading for a pedestrian into a fast-fading one at the same carrier frequency. ### Block fading A convenient simplification, block fading, treats the channel as constant for a fixed block of symbols and then lets it change to a new, independent value for the next block, rather than evolving continuously. The approximation suits systems that already organise their transmissions into frames, and it is close enough to how a slowly varying channel actually behaves that coding and interleaving schemes designed against it also perform well on real, continuously varying channels. ### Selective fading Fading is called selective when it does not affect every frequency in a signal's band equally, the small-scale counterpart of the frequency dependence introduced under Key concepts above. It arises directly from [[Multipath_propagation|multipath propagation]]: when the spread of delays among a channel's paths is large enough that the coherence bandwidth it implies is narrower than the transmitted signal's own bandwidth, different parts of the spectrum add up the delayed copies with different phase relationships and fade independently of one another. A signal narrow enough to fit inside the coherence bandwidth instead sees roughly the same attenuation everywhere in its band, a condition usually called flat fading. ### Upfade An upfade is the opposite excursion: a brief rise of received power above its average level rather than a drop below it, produced by the same shifting interference pattern whenever paths happen to combine unusually constructively instead of unusually destructively. Upfades matter less to link reliability than fades do, since a receiver designed to tolerate the expected deep fades is rarely troubled by an occasional strong burst, but they are the same statistical process seen from its other side. ## Models Small-scale fading is described by the statistical distribution its envelope follows. Where a great many scattered paths of comparable strength combine with no dominant line of sight, the central-limit theorem makes the received envelope [[Rayleigh_fading|Rayleigh]]-distributed, treated at length in its own article; where one path, typically a direct line of sight, dominates the others, the envelope instead follows a Rician distribution, which reduces to the Rayleigh case as that dominant path's strength falls toward the level of the scattered background. A further generalisation, the Nakagami-m distribution, fits a wider range of measured channels by treating the severity of fading as a continuous parameter rather than choosing between two named shapes.[^nakagami-cn] Large-scale shadowing is instead usually modelled as log-normal: the attenuation in decibels, rather than the attenuation itself, is treated as normally distributed around the value a simple distance-based path-loss law would predict, matching how measured shadowing losses actually scatter around that prediction.[^shadow-cn] Whichever small-scale model applies, it has a direct, measured consequence for how well a link performs: averaged over a Rayleigh-faded channel, a receiver's bit-error rate falls off only in proportion to the inverse of the signal-to-noise ratio, far more slowly than the exponential improvement the same modulation would show on a channel with no fading at all.[^ray-ber] That single fact, more than any other, is why the mitigation techniques described next exist. ## Mitigation Because a deep fade in one place, one frequency or one instant rarely coincides with a deep fade in another, the most direct defence against fading is diversity: sending or receiving the same information over several sufficiently independent paths and combining them, so that all of them fading together becomes far less likely than any one of them fading alone. Diversity can be gathered in space, using two or more antennas separated by enough distance or polarisation to fade independently, an approach carried furthest in [[MIMO|MIMO]] systems that use multiple antennas at both ends of a link; in frequency, by spreading a signal or repeating it across a band wider than the channel's coherence bandwidth; or in time, by repeating a transmission far enough apart that the channel has had time to change in between. Interleaving scrambles the order in which coded bits are sent so that a burst of errors from one deep fade is spread thinly across many codewords rather than concentrated in one, letting an error-correcting code do the job it was designed for; combined with coding, interleaving against Rayleigh fading is reported to recover five to ten decibels of the margin fading would otherwise cost.[^interleave] Adaptive techniques, lowering the data rate or the modulation order when the channel is briefly poor and raising it again once the [[Signal-to-noise_ratio|signal-to-noise ratio]] recovers, trade throughput for reliability moment by moment rather than budgeting one fixed, worst-case margin for every symbol regardless of the channel's actual state. Rake receivers, which resolve and separately combine several multipath components rather than treating them as unwanted interference, turn the same [[Multipath_propagation|multipath propagation]] responsible for fading into an additional, exploitable source of diversity. ## Microsims This article carries no p5.js sketch of its own. A three.js companion instead renders received power against distance along the same two-path geometry as the companion on the [[Multipath_propagation]] page, adding a running readout of fade depth as the receiver crosses each null. *Try:* in the [[Doppler_effect]] sketch, raise the source speed and compare the two observer markers' frequency readouts: the same Doppler shift that widens with speed there is what shortens a channel's coherence time and turns slow fading into fast fading, as described under Types above. *Try:* in the [[Radar]] sketch, watch a target's echo brighten and fade as the rotating beam sweeps past it: the same rise and fall that a fading channel's received power traces out continuously over time is compressed here into one turn of the antenna. *Try:* in the [[Sonar]] sketch, move a target farther out and watch the sonar-equation readout SE fall toward zero as transmission loss grows: the same margin between a wanted signal and a detection threshold that a fading channel's margin must also cover, only measured here in a different medium and different units. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Fading) : [Wikitube](https://en.wikitube.io/wiki/Fading) Skeleton mirrored at revision 1307790196. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Multipath_propagation]] - [[Rayleigh_fading]] - [[Doppler_effect]] - [[MIMO]] - [[Signal-to-noise_ratio]] - [[Radar]] - [[Sonar]] ## References Standard channel-modelling concepts used above, including large-scale versus small-scale fading, coherence time and coherence bandwidth, block fading, and diversity combining, are textbook material used throughout wireless-system engineering and are not separately footnoted here, per the Wikitube style guide's §6.1. Page numbers below are PDF pages of the open editions linked in Literature. [^ray-ber]: Ellingson, S. *Radio Systems Engineering, Revised First Edition*. 2023, pp. 163-164 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^interleave]: Ellingson, S. *Radio Systems Engineering, Revised First Edition*. 2023, pp. 165-166 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^nakagami-cn]: Citation needed: M. Nakagami's original formulation of the m-distribution for rapid fading would fix the exact venue, year and page. [^shadow-cn]: Citation needed: a primary measurement study establishing the log-normal model for shadow fading would fix its precise empirical basis and earliest statement. ## Literature - Steven Ellingson. *Radio Systems Engineering, Revised First Edition*. 2023. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. - Christian Tiberius; Max Mulder. *Engineering Signal Analysis: From Fourier to filtering: Theory*. 2026. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/engineering-signal-analysis-from-fourier-to-filtering-theory . CC BY. - Don Johnson. *Fundamentals of Electrical Engineering I*. 2014. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1 . CC BY. - Michael Stiber; Bilin Stiber; Eric Larson. *Signal Computing: Digital Signals in the Software Domain*. 2020. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/signal-computing-digital-signals-in-the-software-domain . CC BY-SA. - Allen Downey. *Think DSP: Digital Signal Processing in Python*. 2012. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/think-dsp-digital-signal-processing-in-python . CC BY-NC. - John Dyer; Chad Davis. *Measurement and Instrumentation: An Introduction to Concepts and Methods, 1st Edition*. 2020. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/measurement-and-instrumentation-an-introduction-to-concepts-and-methods . CC BY-NC-SA. ## External links This article carries no p5.js or three.js sketch of its own with a published external URL; the interactive sketches referenced above are external-linked from their own articles.