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10. Multipath

10. Multipath


Multipath – Video: Register for Course

Multipath – Transcript:

Multipath Disortion

  • The next effect in the wireless channel is called multipath.
  • It comes from the fact that the signal is going through different paths from tx to Rx, where there could be one direct path, (but its not always the truth – and maybe even in most cases it is not) – and there are other paths comign from reflections (from bigger objects (>> wavelength), like buildings, cars) and diffractions (at the edges of objects – like building roofs,e tc.) and scattering (from small objects (small in the means of ~wavelength) e.g. tree leaves) from other objects.
  • So in the end the received signal shows up at the receiver as a set of its copies that rae delayed and attenuated depending on the actual path.
  • So we have a signal (pulse) of amplitudę A0, of length D and transmitted at time t0. This comes to the receiver delayed by a certain time showing up at t1, and attenuated with free space pathloss – to A1. Then we have another signal copy coming a bit later as it comes from the reflection from building and longer path, so coming at additonal delay with bigger attenuation.etc.
  • So the resulting received signal is a summed up version of several copies of these individual copies and looks like this. But in realyti we have an infinete number of those copies, so the signal goes smoother. But its shape and duration is different than the original signal – it is smeered and with modified amplitudę over time

  • The immediate effect of multipath is as mentioned – the signal distortion and „smeering” out changing its shape
  • The more indirect effect is when we take a look on the transmission as a set of consecutive transmitted symbols that carry information
  • So lets assume we transmit 2 consecurtive symbols (e.g. 2 bits of value 1).
  • And both of them experience the same set of paths to reach the receiver
  • So what happens is that the first symbol interferes the second symbol – i.e. its signal power is received together with the second symbol. This is called inter-symbol interference. And the example delay spreads that depend on the environment (e.g. how many significant reflections and signal copies will we get; and how early/late will they show up – e.g. in an office environment they will all show up very soon, while in the mountain area, there will be some very late ones – showing up as an echo due to the distance)
  • This table shows example values
  • In order to decrease the impact of the ISI, we should put a guard time between symbols.

Multipath Fading

  • Multipath effect also results in fast fading – in contrary to slow fading
  • This is due to the fast amplitudę and phase change with time around on the average value and depends on speed and freq
  • We get an average value that is independent on time, set by pathloss and shadowing, and the mutlipath effect with +10 to -30 variations resulting form constructive or destructive additions of signal from different paths
  • Channel coherence time is a measure of how stable the channel is – and one of the formulas is this.
  • When you move faster – the coherence time is shorter
  • When the frequency is higher at the same speed – the cocherence time is also shorter – meaning that the channel values are changing faster
  • Example of wifi freq and walking speed – in this, we have a coherence time of 16ms, in which we can assume that the channel is „stable”

Multipath Frequency Fading

  • There is yet another effect comeing from the constructive or destructive additions of signals over different paths (i.e. from multipath).
  • This happens in the frequency domain
  • The different paths between Tx and Rx, have different lengths as already mention, so the signals from different paths have different delay showing up at the receiver from the original signal transmission time as also already mentioned

Multipath Frequency Fading

  • The signals in each path consist of multiple frequencies (as also already mention)
  • Thus all frequencies travel via the same individual path to reach the receiver

Multipath FSF

  • So when the signal comes to the receiver, all the frequencies are delayed by the same value
  • AND the signals coming from different paths have all frequencies delayed in the same way
  • BUT inbetween those paths we have different delays
  • SO when the different frequencies meet each other at the receiver, the sinewaves could be summed with the maximas on top of each other, while in other frequency the same delay makes the maximum of a sinewave from one path meeting the minimum of the other thus the resulting signal is
  • There are of course other options inbetween thus the signal is changed differently at different freqs- see next slide

Multipath FSF 2