MULTIPLE WINDOW BASED MINIMUM VARIANCE SPECTRUM ESTIMATION FOR MULTIDIMENSIONAL RANDOM-FIELDS

Spectrum analysis is viewed as the problem of estimating the power of a process contained within narrow bands. This view leads naturally to consideration of filter-based methods for estimating spectra. We consider multiple window based estimators where the power in a band is estimated as the average of the powers estimated at the outputs of multiple filters. The filters are designed using a linearly constrained minimum variance criterion commonly employed in adaptive beamforming. This results in filters that automatically adjust their side-lobes to minimize leakage of energy from outside the band of interest. Expressions for the bias and variance of the power estimates are derived assuming the sample covariance matrix estimate is utilized to estimate the data covariance matrix and that the data is independent and identically Gaussian distributed. These expressions lead to the definition of a performance factor that indicates the degree of variance reduction obtained via multiple window processing. Lastly, we present a technique for obtaining increased suppression of energy leaking through the filter sidelobes at the expense of the response fidelity to energy in the band. Simulations are presented to illustrate the effectiveness of the technique.