Re: Covariance matrix for MUSIC

On 1 Aug, 05:34, "krish_dsp" <nmkr...@xxxxxxxxx> wrote:
hi guys..
I am in the process of doing a project on implementation of MUSIC
algorithm for beamforming.
I want to know as to how to create a covariance matrix.
For example if we have 3 antennas and we are taking 5 snapshots of the
incident signal, then how do we get the covariance matrix of the input
data.
I know the formula to find covariance of two signals.
My confusion is for two sequences of length M, the covariance/correlation
has values for 0 lag, 1st lag, 2nd lag......up M-1 lag.
In the example above, we have 3 antennas each with a length of 5 values.
Does the covariance matrix needs to be calculated for 0 lag....4th lag.

Yes.

I mean do we have 5 covariance matrices??

Yes.

I am kinda stuck here and I am not able to get any sources to clear this
doubt. If anyone can give me an explanation, it will be very helpful.Even a
simple 3x3 matrix example will help me a long way in clearing this doubt.

You are confusing time domain and spatial domain. The MUSIC DoA
estimator
uses the spatial covariance matrix, while you probably have read a
recipe
for the temporal MUSIC algorithm.

Your data will be organized as

x[n,m] = [x_1[n], x_2[n],...,x_M[n]]

where x_m[n] is the time series from the m'th sensor (I am used to
use n as the temporal index and m as the spatial index). The trick
is to fix n and compute the *spatial* covariance

Rxx[k]=Rxx[m,m+k]

for each lag n.

Rune
.

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