Multipath propagation
Where two components dominate, the behavior is best modeled with the two-wave with diffuse power (TWDP) distribution.
Multipath interference is a common cause of "ghosting" in analog television broadcasts and of fading of radio waves.
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.
Alternatively, techniques such as orthogonal frequency division modulation and rake receivers may be used.
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 in power line communication and in telephone local loops.
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.
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 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 μs to cross a 1 km span).
, 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
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.
