Design of multilevel decision feedback equalizers

Multilevel decision feedback equalization scheme (MDFE) is an efficient and simple realization of the fixed-delay tree search with decision feedback (FDTS/DF) for channels using RLL(1,k) codes. In MDFE, the entire tree-search is replaced with a 2-tap transversal filter and a binary comparator with negligible loss in performance. This 2-tap filter can be combined with the forward and feedback equalizers resulting in a structure that is physically identical to DFE but requires very different equalizer settings. This paper focuses on equalizer design for MDFE. It is first shown that the MDFE scheme can also be derived without using the principle of tree-search by exploiting the run-length constraints imposed by the RLL(1,k) code in conjunction with the maximization of an appropriately defined signal-to-noise ratio (SNR). Recognizing that a multilevel eye Is formed at the comparator, we define this SNR as the eye-opening divided by noise plus intersymbol interference. This formulation directly leads to a novel adaptive scheme based on the well known LMS algorithm. The relationship between this work and the earlier derivation of MDFE is then clarified. We also develop a noniterative analytical approach for the optimum equalizer design. Because of the economy of implementation, there is particular interest in the design of continuous-time forward equalizers. A noniterative analytic design approach, which does not suffer from local minima problems, is developed for such equalizers. Computer simulation results are presented for comparing the different design approaches.