Maximum partial likelihood framework for channel equalization by distribution learning

We present the general formulation for adaptive equalization by distribution learning in which conditional probability mass function (pmf) of the transmitted signal given the received is parametrized by a general neural network structure. The parameters of the pmf are computed by minimization of the accumulated relative entropy (ARE) cost function. The equivalence of ARE minimization to maximum partial log-likelihood (MPLL) estimation is established under certain regularity conditions which enables us to bypass the requirement that the true conditionals be known. The large sample properties of MPLL estimator are obtained under further regularity conditions, and the binary case with sigmoidal perceptron as the conditional pmf model is shown to be a special case of the new framework. Results are presented which show that the multilayer perceptron (MLP) equalizer based on ARE minimization can always recover from convergence at the wrong extreme whereas the mean square error (MSE) based MLP can not.