Multiple signal classification

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MUltiple SIgnal Classification (MUSIC) is a method of frequency estimation [1]. MUSIC estimates the frequency content of a signal or autocorrelation matrix using an eigenspace method. This method assumes that a signal, x(n), consists of p complex exponentials in the presence of Gaussian white noise. Given an MxM autocorrelation matrix, \mathbf{R}_x, if the eigenvalues are sorted in decreasing order, the p eigenvectors corresponding to the p largest eigenvalues span the signal subspace. Note that for M = p + 1, MUSIC is identical to Pisarenko's method. The general idea is to use averaging to improve the performance of the Pisarenko's estimator.

The frequency estimation function for MUSIC is

\hat P_{MU}(e^{j \omega}) = \frac{1}{\sum_{i=p+1}^{M} |\mathbf{e}^{H} \mathbf{v}_i|^2},

where \mathbf{v}_i are the noise eigenvectors and

e = \begin{bmatrix}1 & e^{j \omega} & e^{j 2 \omega} & \cdots & e^{j (M-1) \omega}\end{bmatrix}^T.

[edit] History

MUSIC was originated by R. O. Schmidt in 1979 as an improvement to Pisarenko's method.

[edit] References

  1. ^ Hayes, Monson H., Statistical Digital Signal Processing and Modeling, John Wiley & Sons, Inc., 1996. ISBN 0-47159-431-8.
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