Microsoft Word - marzetta_tom.DOC

The Capon-MVDR (Minimum Variance Distortionless Response) method of frequency-wavenumber spectral estimation requires an invertible spatial covariance estimate. Increasingly, however, one must deal with a singular covariance matrix. The ubiquity of inexpensive sensors implies that the dimension of the covariance matrix is ever-increasing, but coherence times have not changed, so the number of vector measurements (snapshots) is typically less than their dimension. The traditional remedy for singularity is diagonal loading the addition of a small identity matrix to make the covariance matrix invertible. Instead we reduce the dimensionality of the covariance matrix, to be less than or equal to the number of snapshots, through constrained random unitary transformations. For each such transformation we compute a Capon-MVDR power estimate without diagonal loading. We then average the powers with respect to the random unitary transformation to obtain the final power estimate. This new spectral estimator shows considerable promise in handling singular covariance matrices while avoiding diagonal loading.