Blind channel approximation: Effective channel order determination

A common assumption of blind channel identification methods is that the order of the true channel is known. This information is not available in practice, and we are obliged to estimate the channel order by applying a rank detection procedure to an "overmodeled" data covariance matrix. Information theoretic criteria have been widely suggested approaches for this tack. We check the quality of their estimates in the contest of order estimation of measured microwave radio channels and confirm that they are very sensitive to variations in the SNR and the number of data samples. This fact has prohibited their successful application for channel order estimation and has created some confusion concerning the classification into under- and over-modeled cases. Recently, it has been shown that blind channel approximation methods should attempt to model only the significant part of the channel composed 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 achieved by applying blind identification methods with model order equal to the order of the significant part of the true Channel called the effective channel order. Toward developing an efficient approach for the detection of the effective channel order, we use numerical analysis arguments. The derived 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.