A minimum mean-squared error interpretation of residual ISI channel shortening for discrete multitone transceivers

P.J.W. Melsa et al. (see IEEE Transactions on Communications, vol.44, p.1662-72, 1996) presented a channel shortening technique for discrete multitone transceivers that reduces intersymbol interference (ISI) by forcing the effective channel´s impulse response to lie within a window of v+1 consecutive samples. G. Arslan et al. (see IEEE International Conference on Acoustic Speech and Signal Processing (ICASSP), p.2965-8, 2000) claim that although this method is intuitive, no previous study has been made on its optimality. They comment on its optimality by simulation. We demonstrate that Melsa´s approach is in fact theoretically equivalent to a minimum mean-squared error (MMSE) solution to the channel-shortening problem. As a corollary to this we are afforded an insight into MMSE channel shortening as originally proposed by D.D. Falconer and F.R. Magee (see Bell Systems Technical Journal, p.1541-62, 1973). Previously, it has not been intuitive as to why the desired impulse response (DIR) should be made adaptive in this approach. Our result demonstrates that allowing DIR adaptation achieves a minimisation of the effective impulse response energy outside the desired window of v samples