Multipath_propagation

# Multipath propagation **Multipath propagation** is the arrival of a single radio transmission at a receiving antenna by two or more distinct paths, each of a different length, produced whenever the transmitted wave is reflected, diffracted or refracted on its way from transmitter to receiver. A path may be a single reflection off the ground, a body of water or a building, a longer detour through several such reflections, or a bend imposed by a change in the refractive index of the air or the ionosphere the wave passes through. Because the paths differ in length, the copies of the signal that reach the antenna differ in delay and in phase, and the receiver sees not the transmitted signal alone but the sum of every copy that arrives close enough in time to combine with it. That sum can help the link or hurt it. Where the copies arrive close to in phase they add constructively and the received signal is briefly stronger than any one path alone would give; where they arrive close to out of phase they cancel, and the received signal weakens or disappears for as long as the geometry holds that relationship. This destructive case is what gives multipath its practical importance: the resulting drop in received strength is called [[Fading|fading]], and because the geometry of a link changes whenever the receiver, the transmitter or a reflecting object moves, a multipath-dominated channel fades and recovers continuously rather than settling at one fixed level. One simple instance of this pattern, a direct ray adding to and cancelling against a single ground-reflected ray as a receiver moves, is rendered in depth by a three.js companion sketch elsewhere on this page. How a channel's fading behaves statistically depends on how many of its paths matter and how they are distributed. A great many paths of comparable strength and effectively random phase, with no one path standing out, produce an envelope whose amplitude follows a [[Rayleigh_fading|Rayleigh distribution]]; one strong path, typically a direct line-of-sight component, alongside many weaker scattered ones instead gives a Rician distribution; and a scene with exactly two comparable dominant paths plus a diffuse background is described by a two-wave-with-diffuse-power model that contains the other two as limiting cases.[^twdp-cn] Multipath is not confined to any one radio service: it shapes ionospheric skywave links at high frequency, ground and building reflections at [[Ultra_high_frequency|UHF]] and above, and any [[Radio_propagation|propagation]] path that departs from a single, unobstructed [[Line-of-sight_propagation|line of sight]]. ## Interference Two copies of the same signal interfere according to the difference in the distance they travelled, converted to a phase difference through the carrier's wavelength: a path-length difference of half a wavelength puts the copies out of phase, and a whole wavelength brings them back into phase, so a receiver moving through the field passes through peaks and nulls spaced roughly half a wavelength apart. With only two significant paths the pattern is simple and periodic in space, the case the three.js companion on this page renders directly. With many paths of comparable strength arriving from many directions, the peaks and nulls become irregular, and the receiver's motion through that irregular pattern is what produces the random-looking fading described under Rayleigh fading below. Because the relevant distances scale with wavelength rather than with the physical size of the reflecting objects, the same interference mechanism produces a slow, large-scale pattern at long wavelengths and a rapid, fine-grained one at short wavelengths for reflectors of a given size, which is one reason multipath is treated so differently across the radio spectrum. Interference between paths is a strictly linear phenomenon: no path modifies any other, only the sum at the receiver's location changes, so the same transmitter, antenna and signal can be strong in one spot and unusable a few tens of centimetres away with nothing about the transmission itself having changed. ## Examples Multipath shows up wherever a receiver has more than one way to hear the same transmitter. Analogue over-the-air television was long troubled by a fainter, time-delayed copy of the picture, a "ghost" offset from the main image, produced by a single strong reflection from a hill, a building or a passing aircraft.[^ghost-cn] FM broadcast reception in a moving car shows the same effect turned into sound: as the car passes through the standing pattern of direct and reflected signals, the audio breaks up in short bursts sometimes called picket-fencing, closely spaced in distance because FM broadcast wavelengths are only a few metres long. High-frequency [[Skywave|skywave]] communication is multipath by design rather than by accident, since a signal reaching the ionosphere can return to earth after one hop or several, or by more than one ionospheric layer at once, and the several arrivals, each a genuinely different path length and therefore a different delay, interfere and fade in ways a single ground-wave link never does. Satellite-navigation receivers face a subtler version of the same problem: a reflection off a nearby building or the ground arrives only slightly after the direct signal and biases the measured range by an amount that depends on the reflector's geometry rather than on the receiver's own error budget. Indoor and urban cellular and Wi-Fi links live inside rooms and streets whose walls, floors and vehicles supply so many reflected paths that a receiver rarely has a clean line of sight to work with at all, which is why systems built for those environments are designed around multipath rather than merely tolerant of it. ## In wired media Multipath is not only a phenomenon of the open air. In a wired transmission line, a signal reflects wherever the line's characteristic impedance changes abruptly, at a connector, a splice, a bridged tap, or a far end that is not perfectly terminated, and the reflected copy travels back down the line to interfere with whatever is transmitted after it, exactly as an over-the-air echo interferes with a later part of the same broadcast. Analogue telephone local loops historically suffered a version of this at the two-to-four-wire hybrid that lets a single pair carry both directions of a call: an imperfectly balanced hybrid returns a delayed sample of the talker's own voice as an audible echo, a problem modern networks solve with adaptive echo cancellers rather than with the original hybrid balance alone. High-speed data links over twisted-pair and [[Coaxial_cable|coaxial cable]] see the same reflections as a source of intersymbol interference, and a [[Transmission_line|transmission line]]'s [[Reflection_coefficient|reflection coefficient]] at any discontinuity, `Gamma = (Z_L - Z0)/(Z_L + Z0)`, is exactly the quantity that predicts how large a given mismatch's reflected copy will be. The same reflected pulse that causes the problem is also put to deliberate use in time-domain reflectometry, where timing a pulse's return from a fault or an open end locates it precisely, on the same delay-to-distance principle used by the pulsed-ranging systems described in the neighbouring [[Radar]] article. ## Mathematical modeling A multipath channel is usually modelled as a linear system whose impulse response is a sum of scaled, delayed copies of an impulse, `h(t) = sum_i a_i * delta(t - tau_i) * exp(j*phi_i)`, one term for each significant path, with amplitude `a_i`, delay `tau_i` and phase `phi_i`. The received signal is then the [[Convolution|convolution]] of the transmitted signal with this response,[^conv100] so the model says nothing more exotic than that every path's contribution is scaled, delayed and added: the complexity of real multipath fading comes entirely from how many terms matter and how their amplitudes, delays and phases are distributed, not from any nonlinearity in the channel itself. When the number of independent paths is large and no one term dominates, the central-limit theorem makes the sum's real and imaginary parts approximately Gaussian, and the envelope of that sum, the quantity a receiver actually measures, follows the Rayleigh distribution discussed in the [[Rayleigh_fading|Rayleigh fading]] article. That statistical picture has a direct, measured consequence: 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, rather than exponentially as it would on a channel with no fading, so every added decibel of transmit power buys far less improvement than the same decibel would on a clear, unfaded link.[^ray-ber] How finely a receiver can separate two paths rather than lump them into one is set by timing resolution: a direct-sequence spread-spectrum system with a 10-megahertz chip rate, for example, can resolve two paths delayed by 100 nanoseconds or more from each other, using exactly the impulse-response model above to decide how many distinct terms a real channel needs.[^dsss-res] ## Microsims This article carries no p5.js sketch of its own. A three.js companion instead renders two rays — one direct, one reflected from the ground — adding and cancelling as the receiver moves along the line joining them, tracing out in three dimensions the same rise and fall in received strength that a real multipath channel produces from many more paths at once. *Try:* in the [[Radar]] sketch, drag a target past the dashed unambiguous-range ring and watch its echo fold back as a ghost at a shorter apparent range — a single, deliberately delayed copy of the kind that a multipath channel produces continuously and at random. *Try:* in the [[Doppler_effect]] sketch, raise the source speed and compare the two observer markers' frequency readouts — a moving receiver Doppler-shifts every multipath component by a different amount, and it is exactly this spread of shifts that turns a fixed interference pattern into the time-varying fading described above. *Try:* in the [[Sonar]] sketch, lengthen the ping until the zoomed pair of close targets merges into one hump, or change the assumed sound speed and watch every measured range slide off its true-range tick — underwater ranging is undone by the same overlapping, mistimed echoes that a radio receiver must sort out on land.  **Microsim — three.js (Wikitube framework), pending deploy:** *Two-ray multipath: direct and reflected paths add and cancel* will play here once `https://wikitube-3d-microsims.netlify.app/radio/Multipath_propagation.html` is live.  *Built from `MICROSIM_GUIDE/specs/sims/Multipath_propagation.json`; part of the [[PORTAL_Radio|Radio]] set.*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Multipath_propagation) : [Wikitube](https://en.wikitube.io/wiki/Multipath_propagation) Skeleton mirrored at revision 1365045733. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Fading]] - [[Rayleigh_fading]] - [[Ultra_high_frequency]] - [[Radio_propagation]] - [[Line-of-sight_propagation]] - [[Radar]] - [[Doppler_effect]] - [[Sonar]] - [[Transmission_line]] - [[Reflection_coefficient]] ## References Standard interference and transmission-line theory — the superposition of delayed copies, the reflection coefficient at an impedance discontinuity, and the channel impulse-response model built from convolution — is textbook material used throughout radio and signal engineering and is not separately footnoted here, per the Wikitube style guide's §6.1. Page numbers below are PDF pages of the open editions linked from the citations. [^ghost-cn]: Citation needed: a broadcast-engineering source describing and dating the characteristic "ghosting" symptom of multipath in analog television reception would fix when the effect was first formally documented. [^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. [^dsss-res]: Ellingson, S. *Radio Systems Engineering, Revised First Edition*. 2023, pp. 179-180 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^conv100]: Tiberius, C.; Mulder, M. *Engineering Signal Analysis: From Fourier to filtering: Theory*. 2026, pp. 88-91 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/engineering-signal-analysis-from-fourier-to-filtering-theory . CC BY. [^twdp-cn]: Citation needed: a primary source establishing the two-wave-with-diffuse-power (TWDP) model's original formulation, and its precise relationship to the Rayleigh and Rician special cases it contains, would fix exact attribution.