On the convergence of the multichannel maximum likelihood point spectrum estimator

In 1948, Geronimus discovered that the inverse of the sum of the (modulus squared) orthogonal polynomials corresponding to a Toeplitz matrix converges to the point spectrum as the matrix order goes to infinity. In 1969, Capon independently generalized part of Geronimus´ result to the random field setting as a fixed-order point spectrum estimator. Within signal processing, this Geronimus-Capon result is known as the maximum likelihood spectral estimator or alternatively, the minimum variance estimator. A simple proof that the Geronimus-Capon spectra estimator converges to the point spectrum in the multichannel setting is presented