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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 (R) 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 complexvalued 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 nonstationarity of the environment. Performance analysis are given in terms of the MSE for both synthetic and realistic channels obtained from underwater acoustic recorded signals.

In this paper we consider the theoretical characterization of the ionospheric transmission. More accurately, we derive a closed form expression of the average capacity for Mid-latitude High Frequency (HF) ionospheric channels. Heretofore, this problem has been studied for Rayleigh channels when each tap of the impulse response has a Rayleigh distribution without characterizing the variance of this distribution. In this paper, we extend these works to HF ionospheric channels by evaluating the variance of the amplitude attenuation versus the Doppler spread and then the channel capacity. For a multipath HF ionospheric channel, we model the Doppler phenomenon as a Gaussian profile which is suggested for HF environments. Finally, we derive a closed form expression of the average channel capacity using the probability density function (pdf) of the instantaneous impulse response. Numerical results on both simulated and real measured data are derived at the end of the paper.