I'm estimating the ToA using MUSIC algorithm, but I don't know how to decide on which peak represents the desired ToA. Meaning, how to calculate the threshold after which the first peak is the estimated ToA?
Also, in Matlab (http://www.mathworks.com/help/signal/ref/pmusic.html) , they labeled the MUSIC pseudospectrum as a "Power" in their plots. Is it really power? My intuition is that MUSIC pseudospectrum is not a power spectrum (because it is inverse of power).
There is no need for threshold. In power spectrum you have to design an algorithm which can detect number of peaks which correspond to your transmitted signals. The peaks which contain max values would be the transmitted signals.
And your intention is wrong....
Threshold based ranging algorithms compare the received signal samples against a
threshold in order to identify the first arriving MPC.
Dear Mohanad,
If you want to get the maximum value, or the peak, you can easily use the command MAX in matlab. And if you want to get also the index where the maximum occur, the use the second output argument, for example IDX:
[MaxVal IDX] = max(P)
After you get the maximum value, you may want to delete or replace this maximum with zero, and then the second peak now become the peak value, again you can take this second max and index as the second TOA. and so on.
As for thresholding you mention, there is no mathematical rule to get an optimum threshold value.
I would suggest that you do a trial by error for example 10 or 100 trails, and change the threshold values until you get the optimum value that fulfill to your need.
As for MUSIC spectrum. As you see, MUSIC algorithm is using EIGEN VALUE decomposition. And separate its eigen vectors to SIGNAL SUBSPACE and NOISE SUBSPACE.
It is a fact that each Signal Subspace and Noise Subspace is perpendicular to each other. In other word, their dot product is zero.
Therefore, by putting this dot product in inverse form, so that when steering vector is perpendicular to Noise Subspace (in MUSIC spectrum), the value is zero, thus the inverse is very high.
You are right that it is not a pure power spectrum. As it is in fact the inverse of dot product of steering vector and Noise Subspace.
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