Asymptotic Analysis of Mimo System Estimates by the Use of Orthonormal Bases

This paper provides asymptotic bias and variance analysis for MIMO system estimates obtained by using generalizations of FIR model structures and least squares techniques. The generalizations are such that prior approximate knowledge of the system poles may be incorporated. The obtained variance expressions provide extensions to well known results that have previously been derived only for FIR model structures. Namely, the asymptotic covariance of the transfer matrix estimate is shown to be proportional not only to the noise-to-signal ratio, but also to a frequency dependent term that depends on the basis functions chosen. By examining a similar expression for the bias error it is shown that it is not possible to minimise the bias error at a particular frequency without increasing the variance error, and vice-versa.