Sample matrix inversion

Sample Matrix Inversion (or Direct Matrix Inversion) is an algorithm that estimates weights of an array (adaptive filter) by replacing the correlation matrix Ru with its estimate. Using K samples $x(k),k=1,2,....,K-1$the correlation matrix of the array signals, an unbiased estimate of Rmay be obtained by means of a simple averaging scheme $Ru^{(}k)=1/ksum(x(k)*x^{H}(k))$ The expression of the optimal weights requires the inverse of Ru^. The inverse of Ru^ is then required for finding optimal weights.

References

[1] B.Widrow , P.E Mantey, L.J Griffiths and b.B.Goode. Adaptive Antenne systems. Proceedings of the IEEE, 55(12):2143-2159, december 1967 [2] S.Haykin Adaptive Filter Theory. Prentice hall , pages 165-168, 1996.