Multipath propagation
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In
Where the magnitudes of the signals arriving by the various paths have a distribution known as the
Interference
Multipath interference is a phenomenon in the physics of waves 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 waves.
The condition necessary is that the components of the wave remain 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
In
In digital radio communications (such as
In a
In wired media
Multipath propagation is similar in
High-speed power line communication systems usually employ multi-carrier modulations (such as
DSL modems also use orthogonal frequency-division multiplexing to communicate with their DSLAM despite multipath. In this case the reflections may be caused by mixed wire gauges, but those from bridge taps are usually more intense and complex. Where OFDM training is unsatisfactory, bridge taps may be removed.
Mathematical modeling
The mathematical model of the multipath can be presented using the method of the impulse response used for studying linear systems.
Suppose you want to transmit a single, ideal Dirac pulse of electromagnetic 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
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
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, , and it is defined as the time delay existing between the first and the last received impulses
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 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 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 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
References
This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22.