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I have been studying the Minimum Variance Distortionless Response beamformer, and I've come to find I don't understand the spatial correlation matrix as given.

For clarity, consider the output of a beamformed signal $s(n)$ given as: $$ x(n)=\sqrt{M}v(\phi_s)s(n) $$ where, $\sqrt{M}$ is the normalization factor for the steering vector $v(\phi_s)$. Now the correlation matrix is given as: $$ R_x=E\left\lbrace x(n)x(n)^H \right\rbrace=MA_s^2v(\phi_s)v(\phi_s)^H $$ where, $A_s$ is the deterministic amplitude of the signal and it's square is the power of the signal $s(n)$.

I was hoping for some elaboration on why this is true. I can get to where I have $R_x=Mv(\phi_s)E\left\lbrace s(n)s(n)^H \right\rbrace v(\phi_s)^H$, however I don't see the next step.

For reference I am using Statistical and Adaptive Signal Processing by Manolakis and Ingle, chapter 11. Any help is greatly appreciated.

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migrated from electronics.stackexchange.com Jun 21 '18 at 0:39

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  • $\begingroup$ It helps to explicitly use notation where vectors and scalers are denoted as such. Not all authors develop MVDR the same way. A beam will be Signal and noise and your matrix is only signal. It is hard to tell where your confusion is $\endgroup$ – Stanley Pawlukiewicz Jun 21 '18 at 3:08

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