In the description of any Beamforming Technique for microphone array signal processing there is a usage of the co-relation matrix.

What is the use of calculating such a co-relation matrix in such algorithms?

  • $\begingroup$ This could use a little more own research! So, pick a beamforming technique, and figure out what it does. I don't really see how asking this here reduces your workload. $\endgroup$ – Marcus Müller Jun 20 '18 at 7:22

Sometimes you calculate it or sometimes you know it by the assumptions of a particular problem. Most typically you estimate it $$ R=\frac{1}{N} \sum x_k x_k^H $$ where $x_k$ is a vector of outputs at time $k$. This is the “narrow band” case, at a single frequency. The inverse of $R$ is often more important.

$R$ is sometimes called the cross spectral density matrix CSDM and sometimes the cross matrix

The theoretical root of importance $R$ is that it represents the covariance of a Gaussian probability density . $$ w^H R w $$ Is the expected output power the array given $w$ which is the weight vector, A large number of algorithms are based on power and power is related to SNR,

If $R$ is estimated or known , you can calculate the weights of the MVDR beam former. Which is one application.

Another is that you can spatially whiten the output of sensors with the square root of $R$

The eigenvalues of $R$ are important in subspace techniques like MUSIC .

There are more applications but the common assumption is that your data is Gaussian or similar to Gaussian


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