Editing Multipath propagation

{{Short description|Concept in radio communication}}
{{About|the electromagnetic propagation phenomenon|usage in computing|Multipath (disambiguation)}}
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{{nofootnotes|date=November 2009}}
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In [[radio communication]], '''multipath''' is the [[radio propagation|propagation]] phenomenon that results in [[radio signal]]s reaching the receiving [[antenna (electronics)|antenna]] by two or more paths. Causes of multipath include [[atmospheric ducting]], [[ionospheric reflection]] and [[refraction]], and [[reflection (physics)|reflection]] from water bodies and terrestrial objects such as mountains and buildings. When the same signal is received over more than one path, it can create [[Interference (wave propagation)|interference]] and [[phase (waves)|phase shifting]] of the signal. Destructive interference causes [[fading]]; 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 as '''multipath interference''' or '''multipath distortion'''.

Where the magnitudes of the signals arriving by the various paths have a distribution known as the [[Rayleigh distribution]], this is known as [[Rayleigh fading]]. Where one component (often, but not necessarily, a [[line of sight (telecommunications)|line of sight]] component) dominates, a [[Rice distribution|Rician distribution]] provides a more accurate model, and this is known as [[Rician fading]]. Where two components dominate, the behavior is best modeled with the [[Two-wave with diffuse power fading|two-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. 

==Interference==
{{main|Wave interference}}

[[File:Phase shift.svg|thumb|Coherent waves that travel along two different paths will arrive with [[phase shift]], hence interfering with each other.]]
Multipath interference is a phenomenon in the physics of [[wave]]s 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 (television)|ghosting]]" in analog television broadcasts and of fading of [[radio wave]]s.

[[Image:IdealTVpathnoghost.png|thumb|right|250px|A diagram of the ideal situation for TV signals moving through space: The signal leaves the [[transmitter]] (TX) and travels through one path to the receiver (the TV set, which is labeled RX)]]
[[Image:MultipathTVghost.png|thumb|right|250px|In this illustration, an object (in this case an aircraft) pollutes the system by adding a second path. The signal arrives at receiver (RX) by means 
of two different paths which have different lengths. The main path is the direct path, while the second is due to a reflection from the plane.]]

The condition necessary is that the components of the wave remain [[Coherence (physics)|coherent]] 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 by [[optical 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.

==Examples==

In analog [[fax|facsimile]] and [[television]] [[transmission (telecommunications)|transmission]], multipath causes [[jitter]] 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.

[[File:Multipath propagation diagram en.svg|thumb|Radar multipath echoes from an actual target cause ghosts to appear.]]

In [[radar]] processing, multipath causes ghost targets to appear, deceiving the radar [[receiver (radio)|receiver]]. 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 as [[GSM]]) multipath can cause errors and affect the quality of communications. The errors are due to [[intersymbol interference]] (ISI). [[Equalization (communications)|Equalizers]] are often used to correct the ISI. Alternatively, techniques such as [[orthogonal frequency division modulation]] and [[rake receiver]]s may be used.

[[File:Gps-multipath-efect.png|thumb|left|GPS error due to multipath]]
In a [[Global 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.

==In wired media==
Multipath propagation is similar in [[power line communication]] and in telephone [[local loop]]s. In either case, [[Impedance matching|impedance mismatch]] causes [[signal reflection]]. 

High-speed power line communication systems usually employ multi-carrier modulations (such as [[OFDM]] or [[wavelet]] OFDM) to avoid the [[intersymbol interference]] that multipath propagation would cause. The [[ITU-T]] [[G.hn]] standard provides a way to create a high-speed (up to 1 gigabit per second) [[local area network]] using existing home wiring ([[power line communication|power lines]], phone lines, and [[ethernet over coax|coaxial cables]]). G.hn uses OFDM with a [[cyclic 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 modem]]s also use orthogonal frequency-division multiplexing to communicate with their [[DSLAM]] despite multipath. In this case the reflections may be caused by mixed [[wire gauge]]s, but those from [[bridge tap]]s are usually more intense and complex. Where OFDM training is unsatisfactory, bridge taps may be removed.

==Mathematical modeling==
[[File:Multipath impulse response.png|thumb|right|320px|Mathematical model of the multipath impulse response.]]
The mathematical model of the multipath can be presented using the method of the [[impulse response]] used for studying [[linear system]]s.

Suppose you want to transmit a single, ideal [[Dirac delta function|Dirac pulse]] of [[electromagnetism|electromagnetic]] power at time 0, i.e.

:<math>x(t)=\delta(t)</math>

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 the [[speed 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, in [[free space]], the light takes 3&nbsp;μs to cross a 1&nbsp;km span). Thus, the received signal will be expressed by

:<math>y(t)=h(t)=\sum_{n=0}^{N-1}{\rho_n e^{j\phi_n} \delta(t-\tau_n)}</math>

where <math>N</math> is the number of received impulses (equivalent to the number of electromagnetic paths, and possibly very large), <math>\tau_n</math> is the time delay of the generic <math>n^{th}</math> impulse, and <math>\rho_n e^{j\phi_n}</math> represent the [[complex amplitude]] (i.e., magnitude and phase) of the generic received pulse. As a consequence, <math>y(t)</math> also represents the impulse response function <math>h(t)</math> 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

:<math>\tau_n=\tau_n(t)</math>

:<math>\rho_n=\rho_n(t)</math>

:<math>\phi_n=\phi_n(t)</math>

Very often, just one parameter is used to denote the severity of multipath conditions: it is called the '''[[multipath time]]''', <math>T_M</math>, and it is defined as the time delay existing between the first and the last received impulses

:<math>T_M=\tau_{N-1}-\tau_0</math>

[[File:Multipath transfer function.png|thumb|320px|Mathematical model of the multipath channel transfer function.]]
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 <math>H(f)</math>, which is defined as the continuous time [[Fourier transform]] of the impulse response <math>h(t)</math>

:<math>H(f)=\mathfrak{F}(h(t))=\int_{-\infty}^{+\infty}{h(t)e^{-j 2\pi f t} d t}=\sum_{n=0}^{N-1}{\rho_n e^{j\phi_n} e^{-j2 \pi f \tau_n}}</math>

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, an [[eigenfunction]] of every linear system.

The obtained channel transfer characteristic has a typical appearance of a sequence of peaks and valleys (also called ''notches''); 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-called [[coherence bandwidth]] is thus defined as

:<math>B_C \approx \frac{1}{T_M}</math>

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

== See also ==
* [[Choke ring antenna]], a design that can reject extraneous reflection signals
* [[Diversity scheme]]s
* [[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]]

==References==
* [[MIL-STD-188]]
* [[Federal Standard 1037C]]

{{Wiktionary|multipath|multipathing}}

{{FS1037C}}

{{Audio broadcasting}}
{{Telecommunications}}

[[Category:Broadcast engineering]]
[[Category:Radio frequency propagation]]