ABSTRACT
We formulate the adaptive channel equalization as a conditional probability distribution estimation problem. Conditional probability density function of the transmitted signal given the received signal is parametrized by a sigmoidal perceptron. In this setting, the natural choice for a cost function is the relative entropy (Kullback-Leibler discriminant) between the desired probability density function and the perceptron model. Since the desired probabilities are not readily available for a given channel, we use first order stochastic approximations. The validity of such an approach in terms of consistency and asymptotic behavior is shown by linking the scheme to maximum partial likelihood estimation. We use gradient descent on this relative entropy cost function to derive the Least Relative Entropy (LRE) algorithm. The complex LRE algorithm is applied to the equalization of multipath channels, and is shown to outperform the widely used Least Mean Square (LMS) algorithm with a computational complexity comparable to that of LMS.
