The objectives of the proposed work are to (i) study frequency selective, fading communications channels and develop appropriate models to describe the channel's time variations, (ii) derive novel blind and decision feedback algorithms which explicitly take into account the time varying nature of the channel and (iii) develop the analytical tools to assess the applicability of different models under different conditions. Each time-varying tap coefficient of a frequency selective, fading channel is typically modeled as a random processes with low-pass power spectra. However, traditional adaptive techniques typically do not exploit this information. In the proposed work, Kalman filtering methods are derived to track the channel by employing a multichannel autoregressive description of the time-varying taps in a decision-feedback equalization framework. Fitting a model to the variations of the channel's taps is a challenging task because the tap coefficients are not observed directly. A linear method is proposed to estimate the channel's spectral characteristics from input/output data, and consistency is shown. A different emerging framework will also be studied, where each time-varying tap coefficient is described (with respect to time) as a linear combination of a finite number of basis functions. Examples of such channels include periodically varying ones, where each multipath component exhibits a different Doppler shift or channels locally modeled by a truncated Taylor Series. It is shown that the estimation of the expansion parameters is equivalent to estimating the parameters of an FIR Single-Input-Many-Output (SIMO) system. By exploiting this equivalence, a number of different blind subspace methods are applicable, which h ave been originally developed in the context of time-invariant SIMO systems. Identifiability and performance issues will be investigated, as well as the effects of diversity combining, when multiple receiving antennas are available.
