Blind DFE based on NLMS algorithm with generalized normalized gradient descent regularization

This paper presents robust unsupervised decision feedback equalizer (DFE) for acoustic underwater communications. The proposed equalizer consists of the cascade of four devices whose main components are recursive (7?.) and transverse (T) filters. The feature of the given equalizer is the ability to deal with severe quickly time varying channels by allowing the adjustment of both, its structure and its adaptation according to a mean square error (MSE) criterion. In the existing solution, the recursive and transverse filters are updated by decision directed least-mean-square (LMS) algorithms. However, the weakness of the LMS like algorithms against the time varying environments pushes us to improve the adaptation by the use of other robust solutions. In this paper, we propose the employ of normalized LMS algorithms with self step-size regularization based on complex-valued generalized normalized gradient descent (GNGD) method instead of simple LMS algorithms. Compared to the existent unsupervised DFE, the proposed solution gives the best performance in channel tracking despite the irregularities and the non-stationarity of the environment. Performance analysis are given in terms of the MSE for both synthetic and realistic channels obtained from underwater acoustic recorded signals.