On the robustness of the fractionally-spaced constant modulus criterion to channel order undermodeling. I

This paper studies the robustness properties of the constant modulus (CM) criterion specifically when the fractionally-spaced equalizer time span is less than that of the channel. Hence, there necessarily exists an error in the equalized signal. Noiseless, binary signalling is considered. The change in CM cost from a perfect equalization setting is derived for two cases: (i) perturbations to the channel outside the time span of the equalizer, and (ii) equalizer truncation. This CM cost is related to the mean squared error (MSE) cost and a design guideline for length selection is proposed. This guideline is shown by example to be robust when noisy, multi-level complex signalling is considered.