Adaptive minimum-BER decision feedback equalisers for binary signalling

The problem of constructing adaptive minimum bit error rate (MBER) decision feedback equalisers (DFEs) for binary signalling is considered. Gradient and Gauss}Newton algorithms are considered for both conventional and state (orspace) translation forms of the DFE. The Hessian matrix for the Gauss}Newton algorithm is introduced for the first time. Kernel density estimation is demonstrated to provide a convenient mechanism for approximating the BER as a smooth function of the available data. This leads to the development of a number of block and serial adaptive algorithms. Computer simulation is used to assess the performance of these algorithms