Reduced degree of freedom minimum variance spectrum estimation

The order-N minimum-variance spectrum estimator has N-1 degrees of freedom. Techniques are applied from partially adaptive beamforming to reduce the degrees of freedom to M where M < N-1. The benefits of reducing degrees of freedom include reduced estimator variance, potential for improved resolution, and in some cases reduced computational complexity. Assuming that multiple observations of independent data vectors are used to estimate the covariance matrix, it is shown that reducing degrees of freedom decreases the bias and variance of the estimator. Given a single data record, reducing degrees of freedom enlarges the maximum permissible estimator order and thus provides potential for improved resolution. It is also shown that the reduced degree-of-freedom estimator offers substantial computational savings if the power at only several frequencies is estimated. Simulations are provided to support the analytical results.