Constant Variance Transversal Filtering for Adaptive Channel Equalization

This paper addresses the problem of channel equalization in communications and channel identification in the context of sonar.In both cases, the study comes from the optimal linear filtering theory, taking out the useful information contained in the received data, that used to be noisy.In this sense, the equalization of a channel in analog or digital communications consists of the characterization of the channel behaviour in such a way that it is possible to correct its frequency response and besides, to reduce the degradating effects of the noise that we are going to consider additive, but not necesarily gaussian.The objective in the problem of channel identification is clearly different.In this case we search for a model of the channel and the desired information remains just in the coefficients of the model.What is really important is that the two refered topics can not be acomplished by the same techniques.For instance, some kind of gradient-based adaptive algorithms performs much better for equalizing than for identifying the channel.that is, the filtering error exhibits a different convergence time than the filter weights.As it is well known, the common strategy for the design of adaptive systems is the minimization of a mean square error function.The gradient-based systems used to be generated from sfhocastic cost functions, and the recursive solutions, usually related to the Kalman filter, as the consecuencie of minimizing deterministic expressions of a mean square error.This paper deals with the second case, generating a solution that is obtained under a maximum likelihood criteria, using the complete set of data that is supplied to the filter.The paper shows that a weighted mean square error cost objective deals and thus, it is necessary to weight the filtering error sequence by a factor that, basically, depends on the probability density function of the error sequence and on its first derivate.As it is well known, this kind of information used to be not available and other proposals must be made.Some kind of data-dependent weighting functions have been refered in the literature, and all them in the context of linear prediction [1] or parametric spectral analysis [8], but never in the context of optimal linear filtering.The paper discusses the design of this weighting factor for including some kind of data-selection mechanism for the final filter weight-vector solution design.'The underlying of the proposal is the search of algorithms achieving better robustness in front of non-gaussianity in the data we are handling, as it happens in a number of actual situations.The main trouble of our proposalis that the ML.objetive leads to a non-linear problem, but under some specific conditions it is possible to give a recursive and linear estruclure to the solution, but as a matter of fact it becomes and open research line with now possible guesses.The main contribution of this paper is an attractive new Newton adaptive algorithm with a clear improvement in the behaviour for narrow band conditions,