Performance analysis and comparison of blind to non-blind least squares equalization with respect to effective channel overmodeling

Summarization: The object of this work is the study of a direct blind equalization algorithm which appeared recently in the literature. It is a least-squares (LS) equalization method in the blind context, assuming a linear FIR communication channel and a linear equalizer. If channel order is known, blind LS equalizers can be constructed that entirely suppress intersymbol interference in noiseless signal transmission. In practice, though, channels may be comprised of a few “big” consecutive taps, which we call “significant part”, surrounded by a lot of smaller leading and/or trailing “tail” terms. In such an environment, channel order is harder to define while the value used by the algorithm is critical to its performance. We carry out both theoretical analysis, making use of perturbation theory arguments, and simulations for the cases where channel order determination procedure has yielded an estimate greater than (“effective overmodeling”) or equal to the order of the significant part. Our purpose is to compare the performance of blind LS algorithm with that of its non-blind counterpart. We conclude that (a) when channel does not possess leading tail terms, blind LS is robust to effective overmodeling, meaning that it behaves very much like non-blind LS, and (b) when leading tail terms are present, blind LS will generally not work satisfactorily in the effective overmodeling scenario. In either case, when the order of the significant part is identified correctly and the actual significant parts of subchannels are sufficiently diverse, the algorithm behaves well.Presented on: Signal Processin