Sample matrix inversion explained

R

with its estimate. Using

K

N

-dimensional samples

X1,X2,...,XK

, an unbiased estimate of

RX

, the

N x N

correlation matrix of the array signals, may be obtained by means of a simple averaging scheme:

\hat{R}X=

1
K
K
\sum\limits
k=1

Xk

H
X
k,
where

H

is the conjugate transpose. The expression of the theoretically optimal weights requires the inverse of

RX

, and the inverse of the estimates matrix is then used for finding estimated optimal weights.

References

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