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Inradio communication,multipath is thepropagation phenomenon that results inradio signals reaching the receivingantenna by two or more paths. Causes of multipath includeatmospheric ducting,ionospheric reflection andrefraction, andreflection from water bodies and terrestrial objects such as mountains and buildings. When the same signal is received over more than one path, it can createinterference andphase shifting of the signal. Destructive interference causesfading; this may cause a radio signal to become too weak in certain areas to be received adequately. For this reason, this effect is also known asmultipath interference ormultipath distortion.

Where the magnitudes of the signals arriving by the various paths have a distribution known as theRayleigh distribution, this is known asRayleigh fading. Where one component (often, but not necessarily, aline of sight component) dominates, aRician distribution provides a more accurate model, and this is known asRician fading. Where two components dominate, the behavior is best modeled with thetwo-wave with diffuse power (TWDP) distribution. All of these descriptions are commonly used and accepted and lead to results. However, they are generic and abstract/hide/approximate the underlying physics.

Multipath interference is a phenomenon in the physics ofwaves whereby a wave from a source travels to a detector via two or more paths and the two (or more) components of the wave interfere constructively or destructively. Multipath interference is a common cause of "ghosting" in analog television broadcasts and of fading ofradio waves.

The condition necessary is that the components of the wave remaincoherent throughout the whole extent of their travel.

The interference will arise owing to the two (or more) components of the wave having, in general, travelled a different length (as measured byoptical path length – geometric length and refraction (differing optical speed)), and thus arriving at the detector out of phase with each other.

The signal due to indirect paths interferes with the required signal in amplitude as well as phase which is called multipath fading.

In analogfacsimile andtelevisiontransmission, multipath causesjitter and ghosting, seen as a faded duplicate image to the right of the main image. Ghosts occur when transmissions bounce off a mountain or other large object, while also arriving at the antenna by a shorter, direct route, with the receiver picking up two signals separated by a delay.

Inradar processing, multipath causes ghost targets to appear, deceiving the radarreceiver. These ghosts are particularly bothersome since they move and behave like the normal targets (which they echo), and so the receiver has difficulty in isolating the correct target echo. These problems can be minimized by incorporating a ground map of the radar's surroundings and eliminating all echoes which appear to originate below the ground or above a certain height (altitude).

In digital radio communications (such asGSM) multipath can cause errors and affect the quality of communications. The errors are due tointersymbol interference (ISI).Equalizers are often used to correct the ISI. Alternatively, techniques such asorthogonal frequency division modulation andrake receivers may be used.

In aGlobal Positioning System receiver, multipath effects can cause a stationary receiver's output to indicate as if it were randomly jumping about or creeping. When the unit is moving the jumping or creeping may be hidden, but it still degrades the displayed accuracy of location and speed.

Multipath propagation is similar inpower line communication and in telephonelocal loops. In either case,impedance mismatch causessignal reflection.

High-speed power line communication systems usually employ multi-carrier modulations (such asOFDM orwavelet OFDM) to avoid theintersymbol interference that multipath propagation would cause. TheITU-TG.hn standard provides a way to create a high-speed (up to 1 gigabit per second)local area network using existing home wiring (power lines, phone lines, andcoaxial cables). G.hn uses OFDM with acyclic prefix to avoid ISI. Because multipath propagation behaves differently in each kind of wire, G.hn uses different OFDM parameters (OFDM symbol duration, guard interval duration) for each media.

DSL modems also use orthogonal frequency-division multiplexing to communicate with theirDSLAM despite multipath. In this case the reflections may be caused by mixedwire gauges, but those frombridge taps are usually more intense and complex. Where OFDM training is unsatisfactory, bridge taps may be removed.

The mathematical model of the multipath can be presented using the method of theimpulse response used for studyinglinear systems.

Suppose you want to transmit a single, idealDirac pulse ofelectromagnetic power at time 0, i.e.

${\displaystyle x(t)=\delta (t)}$

At the receiver, due to the presence of the multiple electromagnetic paths, more than one pulse will be received, and each one of them will arrive at different times. In fact, since the electromagnetic signals travel at thespeed of light, and since every path has a geometrical length possibly different from that of the other ones, there are different air travelling times (consider that, infree space, the light takes 3 μs to cross a 1 km span). Thus, the received signal will be expressed by

${\displaystyle y(t)=h(t)=\sum _{n=0}^{N-1}{\rho }_n{e}^{j{\varphi }_n}\delta (t-{\tau }_n)}$

where${\displaystyle N}$ is the number of received impulses (equivalent to the number of electromagnetic paths, and possibly very large),${\displaystyle {\tau }_n}$ is the time delay of the generic${\displaystyle n^{th}}$ impulse, and${\displaystyle {\rho }_n{e}^{j{\varphi }_n}}$ represent thecomplex amplitude (i.e., magnitude and phase) of the generic received pulse. As a consequence,${\displaystyle y(t)}$ also represents the impulse response function${\displaystyle h(t)}$ of the equivalent multipath model.

More in general, in presence of time variation of the geometrical reflection conditions, this impulse response is time varying, and as such we have

${\displaystyle {\tau }_n={\tau }_n(t)}$

${\displaystyle {\rho }_n={\rho }_n(t)}$

${\displaystyle {\varphi }_n={\varphi }_n(t)}$

Very often, just one parameter is used to denote the severity of multipath conditions: it is called themultipath time,${\displaystyle T_M}$, and it is defined as the time delay existing between the first and the last received impulses

${\displaystyle T_M={\tau }_{N-1}-{\tau }_0}$

In practical conditions and measurement, the multipath time is computed by considering as last impulse the first one which allows receiving a determined amount of the total transmitted power (scaled by the atmospheric and propagation losses), e.g. 99%.

Keeping our aim at linear, time invariant systems, we can also characterize the multipath phenomenon by the channel transfer function${\displaystyle H(f)}$, which is defined as the continuous timeFourier transform of the impulse response${\displaystyle h(t)}$

${\displaystyle H(f)=\mathfrak{F}(h(t))={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}h(t)e^{-j2\pi ft}dt=\sum _{n=0}^{N-1}{\rho }_n{e}^{j{\varphi }_n}{e}^{-j2\pi f{\tau }_n}}$

where the last right-hand term of the previous equation is easily obtained by remembering that the Fourier transform of a Dirac pulse is a complex exponential function, aneigenfunction of every linear system.

The obtained channel transfer characteristic has a typical appearance of a sequence of peaks and valleys (also callednotches); it can be shown that, on average, the distance (in Hz) between two consecutive valleys (or two consecutive peaks), is roughly inversely proportional to the multipath time. The so-calledcoherence bandwidth is thus defined as

${\displaystyle B_C\approx \frac{1}{T_M}}$

For example, with a multipath time of 3 μs (corresponding to a 1 km of added on-air travel for the last received impulse), there is a coherence bandwidth of about 330 kHz.

• Choke ring antenna, a design that can reject extraneous reflection signals
• Diversity schemes
• Doppler spread
• Fading
• Lloyd's mirror
• Olivia MFSK
• Orthogonal frequency-division multiplexing
• Rician fading
• Signal flow
• Two-ray ground-reflection model
• Ultra wide-band
• Rake receiver

• MIL-STD-188
• Federal Standard 1037C

Look upmultipath ormultipathing in Wiktionary, the free dictionary.

 This article incorporatespublic domain material fromFederal Standard 1037C.General Services Administration. Archived fromthe original on 2022-01-22.

• Broadcast engineering
• Radio frequency propagation

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