Blind channel approximation: Effective channel order determination

A common assumption of blind channel identification methods is that the ord er of the true channel is known. This information is not available in pract ice, and we are obliged to estimate the channel order by applying a rank de tection procedure to an "overmodeled" data covariance matrix. Information t heoretic criteria have been widely suggested approaches for this tack. We c heck the quality of their estimates in the contest of order estimation of m easured microwave radio channels and confirm that they are very sensitive t o variations in the SNR and the number of data samples. This fact has prohi bited their successful application for channel order estimation and has cre ated some confusion concerning the classification into under- and over-mode led cases. Recently, it has been shown that blind channel approximation met hods should attempt to model only the significant part of the channel compo sed of the "large" impulse response terms because efforts toward modeling " small" leading and/or trailing terms lead to effective overmodeling, which is generically ill-conditioned and, thus, should be avoided. This can be ac hieved by applying blind identification methods with model order equal to t he order of the significant part of the true Channel called the effective c hannel order. Toward developing an efficient approach for the detection of the effective channel order, we use numerical analysis arguments. The deriv ed criterion provides a "maximally stable" decomposition of the range space of an "overmodeled" data covariance matrix into signal and noise subspaces . It is shown to be robust to variations in the SNR and the number of data samples. Furthermore, it provides useful effective channel order estimates, leading to sufficiently good blind approximation/equalization of measured real-world microwave radio channels.