On the least squares performance of a novel efficient center estimation method for clustering-based MLSE equalization

Recently, a novel Maximum Likelihood Sequence Estimation (MLSE) equalizer was reported, that avoids the explicit estimation of the channel impulse response. Instead, the centers of the clusters which are formed by the received samples are estimated, in a computationally efficient manner, that exploits the channel linearity and the symmetries underlying the transmitted signal constellation. This paper investigates the relationship of the center estimation (CE) part of the proposed equalizer with the Least Squares (LS) method, demonstrating that it can attain LS performance at a substantially lower computational cost. The importance of CE is thus confirmed, as a methodology that combines high performance, simplicity and low computational cost, as required in a practical equalization task. The results of this paper provide also an alternative, algebraic viewpoint on the CE method, while at the same time leading to a new interpretation of the LS, in terms of averaging for cluster center estimation.