In
radio communication
Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmit ...
, multipath is the
propagation
Propagation can refer to:
* Chain propagation in a chemical reaction mechanism
*Crack propagation, the growth of a crack during the fracture of materials
* Propaganda, non-objective information used to further an agenda
* Reproduction, and other fo ...
phenomenon that results in
radio
Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmit ...
signals
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
reaching the receiving
antenna
Antenna ( antennas or antennae) may refer to:
Science and engineering
* Antenna (radio), also known as an aerial, a transducer designed to transmit or receive electromagnetic (e.g., TV or radio) waves
* Antennae Galaxies, the name of two collid ...
by two or more paths. Causes of multipath include
atmospheric ducting
In telecommunications, an atmospheric duct is a horizontal layer in the lower atmosphere in which the vertical refractive index gradients are such that radio signals (and light rays) are guided or ducted, tend to follow the curvature of the Eart ...
,
ionospheric reflection
In radio communication, skywave or skip refers to the propagation of radio waves reflected or refracted back toward Earth from the ionosphere, an electrically charged layer of the upper atmosphere. Since it is not limited by the curvature ...
and
refraction
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
, and
reflection Reflection or reflexion may refer to:
Science and technology
* Reflection (physics), a common wave phenomenon
** Specular reflection, reflection from a smooth surface
*** Mirror image, a reflection in a mirror or in water
** Signal reflection, in ...
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
Interference is the act of interfering, invading, or poaching. Interference may also refer to:
Communications
* Interference (communication), anything which alters, modifies, or disrupts a message
* Adjacent-channel interference, caused by extr ...
and
phase shifting
In physics and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it v ...
of the signal. Destructive interference causes
fading
In wireless communications, fading is variation of the attenuation of a signal with various variables. These variables include time, geographical position, and radio frequency. Fading is often modeled as a random process. A fading channel is a ...
; 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
In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to rescaling, it coincides with the chi distribution with two degrees of freedom.
The distribut ...
, this is known as
Rayleigh fading Rayleigh fading is a statistical model for the effect of a propagation environment on a radio signal, such as that used by wireless devices.
Rayleigh fading models assume that the magnitude of a signal that has passed through such a transmission me ...
. Where one component (often, but not necessarily, a
line of sight
The line of sight, also known as visual axis or sightline (also sight line), is an imaginary line between a viewer/observer/spectator's eye(s) and a subject of interest, or their relative direction. The subject may be any definable object taken ...
component) dominates, a
Rician distribution provides a more accurate model, and this is known as
Rician fading Rician fading or Ricean fading is a stochastic model for radio Wave propagation, propagation anomaly caused by partial cancellation of a radio Signalling (telecommunication), signal by itself — the signal arrives at the receiver by several dif ...
. Where two components dominate, the behavior is best modeled with the
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
![Phase shift](https://upload.wikimedia.org/wikipedia/commons/5/55/Phase_shift.svg)
Multipath interference is a phenomenon in the physics of
wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...
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" in analog television broadcasts and of fading of
radio wave
Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz (GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (short ...
s.
The condition necessary is that the components of the wave remain
coherent
Coherence, coherency, or coherent may refer to the following:
Physics
* Coherence (physics), an ideal property of waves that enables stationary (i.e. temporally and spatially constant) interference
* Coherence (units of measurement), a deri ...
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 In optics, optical path length (OPL, denoted ''Λ'' in equations), also known as optical length or optical distance, is the product of the geometric length of the optical path followed by light and the refractive index of homogeneous medium through ...
– 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
facsimile
A facsimile (from Latin ''fac simile'', "to make alike") is a copy or reproduction of an old book, manuscript, map, Old master print, art print, or other item of historical value that is as true to the original source as possible. It differs from ...
and (analog)
television
Television, sometimes shortened to TV, is a telecommunication medium for transmitting moving images and sound. The term can refer to a television set, or the medium of television transmission. Television is a mass medium for advertisin ...
transmission
Transmission may refer to:
Medicine, science and technology
* Power transmission
** Electric power transmission
** Propulsion transmission, technology allowing controlled application of power
*** Automatic transmission
*** Manual transmission
*** ...
, multipath causes
jitter
In electronics and telecommunications, jitter is the deviation from true periodicity of a presumably periodic signal, often in relation to a reference clock signal. In clock recovery applications it is called timing jitter. Jitter is a significa ...
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.
![Multipath propagation diagram en](https://upload.wikimedia.org/wikipedia/commons/f/f2/Multipath_propagation_diagram_en.svg)
In
radar
Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...
processing, multipath causes ghost targets to appear, deceiving the radar
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
The Global System for Mobile Communications (GSM) is a standard developed by the European Telecommunications Standards Institute (ETSI) to describe the protocols for second-generation ( 2G) digital cellular networks used by mobile devices such ...
) multipath can cause errors and affect the quality of communications. The errors are due to
intersymbol interference
In telecommunication, intersymbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have a similar effect as noise, thus making ...
(ISI).
Equalizers are often used to correct the ISI. Alternatively, techniques such as
orthogonal frequency division modulation
In telecommunications, orthogonal frequency-division multiplexing (OFDM) is a type of digital transmission and a method of encoding digital data on multiple carrier frequencies. OFDM has developed into a popular scheme for wideband digital commun ...
and
rake receiver
A rake receiver is a radio receiver designed to counter the effects of multipath fading. It does this by using several "sub-receivers" called ''fingers'', that is, several correlators each assigned to a different multipath component. Each finger ...
s may be used.
![Gps-multipath-efect](https://upload.wikimedia.org/wikipedia/commons/4/49/Gps-multipath-efect.png)
In a
Global Positioning System receiver
A satellite navigation device (satnav device) is a user equipment that uses one or more of several global navigation satellite systems (GNSS) to calculate the device's geographical position and provide navigational advice.
Depending on the s ...
, 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
Power-line communication (also known as power-line carrier or PLC) carries data on a conductor that is also used simultaneously for AC electric power transmission or electric power distribution to consumers.
A wide range of power-line communicat ...
and in telephone
local loop
In telephony, the local loop (also referred to as the local tail, subscriber line, or in the aggregate as the last mile) is the physical link or circuit that connects from the demarcation point of the customer premises to the edge of the common ...
s. In either case,
impedance mismatch
In electronics, impedance matching is the practice of designing or adjusting the input impedance or output impedance of an electrical device for a desired value. Often, the desired value is selected to maximize power transfer or minimize sign ...
causes
signal reflection
In telecommunications, signal reflection occurs when a signal is transmitted along a transmission medium, such as a copper cable or an optical fiber. Some of the signal power may be reflected back to its origin rather than being carried all the ...
.
High-speed power line communication systems usually employ multi-carrier modulations (such as
OFDM
In telecommunications, orthogonal frequency-division multiplexing (OFDM) is a type of digital transmission and a method of encoding digital data on multiple carrier frequencies. OFDM has developed into a popular scheme for wideband digital commun ...
or
wavelet
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the num ...
OFDM) to avoid the
intersymbol interference
In telecommunication, intersymbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have a similar effect as noise, thus making ...
that multipath propagation would cause. The
ITU-T
The ITU Telecommunication Standardization Sector (ITU-T) is one of the three sectors (divisions or units) of the International Telecommunication Union (ITU). It is responsible for coordinating standards for telecommunications and Information Commu ...
G.hn
G.hn is a specification for home networking with data rates up to 2 Gbit/s and operation over four types of legacy wires: telephone wiring, coaxial cables, power lines and plastic optical fiber. A single G.hn semiconductor device is able to n ...
standard provides a way to create a high-speed (up to 1 gigabit per second)
local area network
A local area network (LAN) is a computer network that interconnects computers within a limited area such as a residence, school, laboratory, university campus or office building. By contrast, a wide area network (WAN) not only covers a larger ...
using existing home wiring (
power lines
Electric power transmission is the bulk movement of electrical energy from a generating site, such as a power plant, to an electrical substation. The interconnected lines that facilitate this movement form a ''transmission network''. This is d ...
, phone lines, and
coaxial cables
Coaxial cable, or coax (pronounced ) is a type of electrical cable consisting of an inner conductor surrounded by a concentric conducting shield, with the two separated by a dielectric ( insulating material); many coaxial cables also have a ...
). G.hn uses OFDM with a
cyclic prefix
In telecommunications, the term cyclic prefix refers to the prefixing of a symbol, with a repetition of the end. The receiver is typically configured to discard the cyclic prefix samples, but the cyclic prefix serves two purposes:
* It provides a ...
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
A digital subscriber line (DSL) modem is a device used to connect a computer or router to a telephone line which provides the digital subscriber line (DSL) service for connection to the Internet, which is often called ''DSL broadband''. The m ...
s also use orthogonal frequency-division multiplexing to communicate with their
DSLAM
A digital subscriber line access multiplexer (DSLAM, often pronounced ''DEE-slam'') is a network device, often located in telephone exchanges, that connects multiple customer digital subscriber line (DSL) interfaces to a high-speed digital co ...
despite multipath. In this case the reflections may be caused by mixed
wire gauge
Wire gauge is a measurement of wire diameter. This determines the amount of electric current the wire can safely carry, as well as its electrical resistance and weight.
Types of wire gauge
Wire gauges may be broadly divided into two groups, th ...
s, but those from
bridge tap
Bridged tap or bridge tap is a long-used method of cabling for telephone lines. One cable pair (of wires) will "appear" in several different terminal locations (poles or pedestals). This allows the telephone company to use or " assign" that pair t ...
s are usually more intense and complex. Where OFDM training is unsatisfactory, bridge taps may be removed.
Mathematical modeling
![Multipath impulse response](https://upload.wikimedia.org/wikipedia/commons/c/c4/Multipath_impulse_response.png)
The mathematical model of the multipath can be presented using the method of the
impulse response
In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an Dirac delta function, impulse (). More generally, an impulse ...
used for studying
linear system
In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator.
Linear systems typically exhibit features and properties that are much simpler than the nonlinear case.
As a mathematical abstraction o ...
s.
Suppose you want to transmit a signal, ideal
Dirac pulse of
electromagnetic
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
power at time 0, i.e.
:
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
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
, 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
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
, the light takes 3 μs to cross a 1 km span). Thus, the received signal will be expressed by
:
where
is the number of received impulses (equivalent to the number of electromagnetic paths, and possibly very large),
is the time delay of the generic
impulse, and
represent the
complex amplitude
Complex commonly refers to:
* Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe
** Complex system, a system composed of many components which may interact with each ...
(i.e., magnitude and phase) of the generic received pulse. As a consequence,
also represents the impulse response function
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
:
:
:
Very often, just one parameter is used to denote the severity of multipath conditions: it is called the
multipath time
In radio communication, multipath is the propagation phenomenon that results in radio signals reaching the receiving antenna by two or more paths. Causes of multipath include atmospheric ducting, ionospheric reflection and refraction, and reflecti ...
,
, and it is defined as the time delay existing between the first and the last received impulses
:
![Multipath transfer function](https://upload.wikimedia.org/wikipedia/commons/a/a1/Multipath_transfer_function.png)
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
, which is defined as the continuous time
Fourier transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
of the impulse response
:
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
In mathematics, an eigenfunction of a linear operator ''D'' defined on some function space is any non-zero function f in that space that, when acted upon by ''D'', is only multiplied by some scaling factor called an eigenvalue. As an equation, th ...
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
:
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.
See also
*
Choke ring antenna
A choke ring antenna is a particular form of omnidirectional antenna for use at high frequencies ( VHF & UHF). It consists of a number of concentric conductive cylinders around a central antenna.
Due to its intricate construction, it is often en ...
, a design that can reject extraneous reflection signals
*
Diversity scheme
In telecommunications, a diversity scheme refers to a method for improving the reliability of a message signal by using two or more Channel (communications), communication channels with different characteristics. Diversity is mainly used in radio ...
s
*
Doppler spread
In wireless communications, fading is variation of the attenuation of a signal with various variables. These variables include time, geographical position, and radio frequency. Fading is often modeled as a random process. A fading channel is a ...
*
Fading
In wireless communications, fading is variation of the attenuation of a signal with various variables. These variables include time, geographical position, and radio frequency. Fading is often modeled as a random process. A fading channel is a ...
*
Lloyd's mirror Lloyd's mirror is an optics experiment that was first described in 1834 by Humphrey Lloyd in the ''Transactions of the Royal Irish Academy''. Its original goal was to provide further evidence for the wave nature of light, beyond those provided by ...
*
Olivia MFSK
Olivia MFSK is an amateur radioteletype protocol, using multiple frequency-shift keying (MFSK) and designed to work in difficult (low signal-to-noise ratio plus multipath propagation) conditions on shortwave bands. The signal can be accurately re ...
*
Orthogonal frequency-division multiplexing
In telecommunications, orthogonal frequency-division multiplexing (OFDM) is a type of digital transmission and a method of encoding digital data on multiple carrier frequencies. OFDM has developed into a popular scheme for wideband digital commun ...
*
Rician fading Rician fading or Ricean fading is a stochastic model for radio Wave propagation, propagation anomaly caused by partial cancellation of a radio Signalling (telecommunication), signal by itself — the signal arrives at the receiver by several dif ...
*
Signal flow
Audio signal flow is the path an audio signal takes from source to output. The concept of audio signal flow is closely related to the concept of audio gain staging; each component in the signal flow can be thought of as a gain stage.
In typical h ...
*
Two-ray ground-reflection model The two-rays ground-reflection model is a multipath radio propagation model which predicts the path losses between a transmitting antenna and a receiving antenna when they are in line of sight (LOS). Generally, the two antenna each have different ...
*
Ultra wide-band
References
*
MIL-STD-188
MIL-STD-188 is a series of U.S. military standards relating to telecommunications.
Purpose
Faced with "past technical deficiencies in telecommunications systems and equipment and software…that were traced to basic inadequacies in the applicat ...
*
Federal Standard 1037C
Federal Standard 1037C, titled Telecommunications: Glossary of Telecommunication Terms, is a United States Federal Standard issued by the General Services Administration pursuant to the Federal Property and Administrative Services Act of 1949, a ...
{{Telecommunications
Broadcast engineering
Radio frequency propagation