Adaptive Equalisation for Impulsive Noise Environments

This thesis addresses the problem of adaptive channel equalisation in environments where the interfering noise exhibits non–Gaussian behaviour due to impulsive phenomena. The family of alpha-stable distributions has proved to be a suitable and flexible tool for the modelling of signals with impulsive nature. However,non–Gaussian alpha–stable signals have infinite variance, and signal processing techniques based on second order moments are meaningless in such environments. In order to exploit the flexibility of the stable family and still take advantage of the existing signal processing tools, a novel framework for the integration of the stable model in a communications context is proposed, based on a finite dynamic range receiver. The performance of traditional signal processing algorithms designed under the Gaussian assumption may degrade seriously in impulsive environments. When this degradation cannot be tolerated, the traditional signal processing methods must be revisited and redesigned taking into account the non–Gaussian noise statistics. In this direction, the optimum feed–forward and decision feedback Bayesian symbol–by–symbol equalisers for stable noise environments are derived. Then, new analytical tools for the evaluation of systems in infinite variance environments are presented. For the centers estimation of the proposed Bayesian equaliser, a unified framework for a family of robust recursive linear estimation techniques is presented and the underlying relationships between them are identified. Furthermore, the direct clustering technique is studied and robust variants of the existing algorithms are proposed. A novel clustering algorithm is also derived based on robust location estimation. The problem of estimating the stable parameters has been addressed in the literature and a variety of algorithms can be found. Some of these algorithms are assessed in terms of efficiency, simplicity and performance and the most suitable is chosen for the equalisation problem. All the building components of an adaptive Bayesian equaliser are then put together and the performance of the equaliser is evaluated experimentally. The simulation results suggest that the proposed adaptive equaliser offers a significant performance benefit compared with a traditional equaliser, designed under the Gaussian assumption. The implementation of the proposed Bayesian equaliser is simple but the computational complexity can be unaffordable. However, this thesis proposes certain approximations which enable the computationally efficient implementation of the optimum equaliser with negligible loss in performance