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I am sending an acoustic signal from a source to a receiver where there are limited number of paths the signal can travel. I want to detect if there has been multipath propagation or not when one path is the dominant line of sight path. Based on this link - Cross-correlation peaks in acoustic multi-path conditions , it seems like cross-correlation and checking for multiple peaks is an option, but it does not work when there is Fading (one dominant signal and others being attenuated).

It seems like this sort of Fading is called Rician Fading - however, I am not sure how to use this to detect if their has been multipath propagation or not. How to use the source and receiver signals to know if multipath propagation happened or not. (Also, I cannot use time of arrival of chirp pulses since the difference between time of arrivals of different paths is less than the chirp width)

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It seems to me that, in the conditions you describe, the most you will see is flat fading. One indication that flat fading is occuring is that a change in the positions of transmitter and receiver, and/or the reflectors causing the multipath, produce a significant change in the received power. Usually the change has to be of the order of $\lambda/2$ meters, so this may be unfeasible in your case.

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  • $\begingroup$ Sorry, could you elaborate on this? Let me make my set up clearer - I have a transmitter and receiver on two sides of a metal block separated by 5cm - so there is a direct path through metal. Now, someone adds a curved wooden tube to connect the transmitter and receiver creating a second path. Looking at the source and receiver signals, is there a way I can tell if the wooden tube is attached or not? $\endgroup$
    – Stat7
    Aug 30, 2019 at 23:59
  • $\begingroup$ This is a related, but different problem. Take a look at xyproblem.info I'll post something later if I come up with any ideas. $\endgroup$
    – MBaz
    Sep 1, 2019 at 2:24
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MLS or sine sweeps are used for estimating the impulse response in acoustic measurements (when the system is approx LTI). Any waveform for which the auto correlation approximates a dirac pulse (in the band of interest) can be used Matched Filter style for solving for the unknown system, but specific details can make one more suitable than the other. You should see any reflections from the IR.

If the system is time variant, things gets more tricky. Sonar applications/radar as well as communication systems «probing» the channel may be starting points.

Edit: Not understanding your physics here, but it sounds like you expect the impulse response to idealized be something like [1, 0, ... alpha]. Ie a two-tap comb filter where the relative gain of the second tap depends on the acoustic properties of that wooden thing? On top of that, expect each tap to be «smeared» by finite bandwidth in transducers, etc.

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