Robustness of least-squares and subspace methods for blind channel identification equalization with respect to effective channel undermodeling overmodeling

The least-squares and the subspace methods are two well-known approaches fo r blind channel identification/ equalization, When the order of the channel is known, the algorithms are able to identify the channel, under the so-ca lled length and zero conditions. Furthermore, in the noiseless case, the ch annel can be perfectly equalized. Less is known about the performance of th ese algorithms in the practically inevitable cases in which the channel pos sesses long tails of "small" impulse response terms, We study the performan ce of the mth-order least-squares and subspace methods using a perturbation analysis approach. We partition the true impulse response into the mth-ord er significant part and the tails. We show that the mth-order least-squares or subspace methods estimate an impulse response that is "close" to the mt h-order significant part. The closeness depends on the diversity of the mth -order significant part and the size of the tails. Furthermore, we show tha t if we try to model not only the "large" terms but also some "small" ones, then the quality of our estimate may degrade dramatically; thus, we should avoid modeling "small" terms. Finally, we present simulations using measur ed microwave radio channels, highlighting potential advantages and shortcom ings of the least-squares and subspace methods.