Low-Complexity Search for Optimal Delay in Linear FIR MMSE Equalization

Abstract—In this letter, an efficient algorithm to determine the optimal delay in linear finite impulse response equalizers based on the minimum mean-square-error criterion is proposed. The algorithm uses the Levinson–Durbin (L–D) recursion as a starting point to find the values of the mean-square error for equalizers with all nontrivial delays. Despite the exhaustive search approach, the complexity of the proposed algorithm is only doubled when compared to the calculation of the equalizer with one prescribed delay. Such increase in complexity may be fully justified in practice because it yields globally optimal equalizer’s design. Index Terms—Equalization, equalization delay, fast algorithm, finite impulse response (FIR) equalization, Levinson–Durbin (L–D) algorithm, minimum mean-square-error (MMSE) equalization, optimal delay, recursive algorithm. I