A note on optimum MMSE/ZF multichannel equalization delay

The reconstruction delay has been, for long time, recognized a significant impact on the performance of an equalizer. Still, no proofs were given that sustain the experimental observations. In this note, we develop a formal analysis that shows that optimum equalization performance is met at a delay larger than the channel memory and smaller than the equalizer order. While it is expected that the optimum delay is larger than the channel memory, we demonstrate, here, the less intuitive fact that increasing the delay beyond the channel memory affects equalization MMSE only slightly.