Stochastic gradient minimum-BER decision feedback equalisers

The problem of constructing adaptive minimum bit error rate (MBER) decision feedback equalisers (DFEs) for binary signaling is considered. Gradient algorithms are developed for both conventional and state (or space) translation forms of the DFE. 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 adaptive algorithms. Computer simulation is used to assess the performance of these algorithms.