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

The least-squares and the subspace methods are well known approaches for blind channel identification/equalization. When the order of the channel is known, the algorithms are able to identify the channel, under the so-called length and zero conditions. Furthermore, in the noiseless case, the channel can be perfectly equalized. Less is known about the performance of these algorithms in the cases in which the channel order is underestimated. We partition the true impulse response into the significant part and the tails. We show that the m-th order least-squares or subspace method-s estimate an impulse response which is "close" to the m-th order significant part of the true impulse response. The closeness depends on the diversity of the m-th order significant part and the size of the "unmodeled" part.