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Consider a speaker and a microphone are placed in a multi-path environment and the audio signal to be transmitted is LFM(chirp) signal, the time of arrival of the audio signal is computed by cross-correlation at the receiver side. My question is:

If there are severe reflection, reverberation phenomenons but the direct-path propagation acoustic signal is also received. When doing cross-correlation, will the first correlation peak (which is supposed to belong to direct path propagation signal) shift due to reflections & reverberations?

thank you very much

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I assume by "shift" you mean "shift in time".

No, the first correlation peak should not be shifted in time, you should just get multiple peaks, assuming the time difference of arrival is not much shorter than the chirp length. If it is shorter then you will get "blurring" of the cross-correlation peak. Having said that, there are a couple of other possible issues:

1) Fading. If you happen to get a null in the frequency range of your chirp due to the multi-path, then that will obviously cause you problems.

2) Doppler. If there is no movement of the speaker or the microphone then this isn't a problem, but if there is you will need to deal with the Doppler. Due to the speed of sound being so slow, Doppler is brutal in audio applications.

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  • $\begingroup$ thx, for my case I will study more in NLoS identification which causes ToA/TDoA estimation errors. As for 'blur', my chirp signal's frequency change is relatively large which leads to a very narrow xcorr peak(just 1~2 sampling pts), so even close xcorr peaks may not 'blur' the true xcorr peak $\endgroup$ – WSL Oct 14 '18 at 16:00
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Depending on the circumstances, you can also have other than air borne propagation like through a concrete floor and the support structures of your projector and sensors. the fastest path isn’t necessarily going to be the direct air path.

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  • $\begingroup$ thank you, but I don't think sound is "strong" enough to go through floors or walls $\endgroup$ – WSL Oct 14 '18 at 1:13
  • $\begingroup$ Sound is vibration. It is produced and coupled and propagated. you might explain why you don’t think a hydrophone is immune to structure borne vibration. $\endgroup$ – Stanley Pawlukiewicz Oct 14 '18 at 1:26

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