Channel equalization using simplified least mean-fourth algorithm

The steady flow of new research results and developments in the field of adaptive equalization that was witnessed for at least the last four decades is clearly evidenced by the many footprints of success it left behind and shows no sign of ending. The thrust of research and implementation in this field is mainly powered by the use of the well-known mean-square cost function upon which relies the ubiquitous least-mean square (LMS) algorithm. However, such an algorithm is well-known to lead to sub-optimal solutions in the real world that is largely dominated by non-Gaussian interference signals. The use of a non-mean-square cost function would successfully tackle these types of interference signals but would invariably involve a higher computational cost. To address these important practical issues, this paper proposes a new adaptive equalization technique that combines both the least-mean-fourth (LMF) algorithm, which is governed by a non-mean-square cost function, with a power-of-two quantizer (PTQ) in the coefficient update process, which greatly reduces the computational cost involved and which therefore makes the proposed technique applicable to time-varying environments. This paper not only elaborates on the basic idea behind the proposed technique but also defines the necessary assumptions and provides a thorough statistical performance analysis (including a study of the convergence behavior) of the combined algorithm LMF-PTQ that is at the core of the proposed technique. An extensive simulation work was carried out and showed that the theoretical predictions are very well substantiated.