On the robustness of the linear prediction method for blind channel identification with respect to effective channel undermodeling/overmodeling

We study the performance of the linear prediction (LP) method for blind channel identification when the true channel is of order M, whereas the channel model is of order m, with m<M. By partitioning the true channel into the mth-order significant part and the unmodeled tails, we show that the LP method furnishes an approximation to the mth-order significant part. The closeness depends on the diversity of the mth-order significant part and the size of the unmodeled tails. Furthermore, we show that two frequently encountered claims concerning the LP method, namely, that (a) the method is robust with respect to channel overmodeling and (b) the performance of the method depends critically on the size of the first impulse response term, are not correct in realistic scenarios