Multiple window based minimum variance broadband spatial spectrum estimation

The problem of estimating the power received at an array of sensors as a function of direction for broadband environments is addressed. A multiple-window-based processing scheme is proposed to reduce the variance of the power estimates. The windows are data dependent, and are derived from a linearly constrained minimum variance (LCMV) criterion. Expressions are derived for the bias and variance of the multiple-window-based estimator assuming the array data covariance is estimated by the sample covariance matrix. Comparison of multiple window estimator variance to the single window LCMV estimator variance indicates that variance reduction is guaranteed and is bounded by the number of windows used. Simulations verify the analytical results and show that the multiple window method has about the same bias as the single window LCMV estimator. The variance reduction factor, pf, is observed to be in the range, 1/r⩽pf⩽2/r, where r is the number of windows used