Complex-valued nonlinear adaptive filters for noncircular signals

Complex signal has been the backbone of large class of signals encountered in many modern applications as biomedical engineering, power system, radar, communication system, renewable energy and military technologies. However, statistical signal processing in complex domain are suited to only the conventional complex-valued signal processing technique for subset of complex signal known as circular (proper), which is inadequate for the generality of complex signals, as they do not rigorously exploit the statistical information available in the signal. This is because of the under-modelling of the underlying system or due to the inherent blindness of the algorithm (for example, the CNGD algorithm) to capture the full second-order statistical information available in the signal. With the limitation of the CNGD algorithm toward signal generality, an improved CNGD algorithm known as the ACNGD which is derived based on the concept of augmented complex statistic which gives optimal algorithm for the generality of signals in complex domain is introduced. The augmented CNGD has shown low Means Square Error (MSE) capabilities and have optimal performance than the conventional algorithm. To this end, a supervised complex adaptive algorithm convex combination complex nonlinear gradient descent (CC-CNGD) is developed to address the capabilities of processing the generality of complex signals (both circular and non-circular) and systems in either a noisy or a noise-free environment. Their importance in real-world application is showed through case studies. The CC-CNGD algorithm rigorously takes advantage of the fast convergence rate of the CNGD algorithm and as well exploit the low Means Square Error (MSE) of the ACNGD algorithm in order to circumvent the problem of slow convergence rate and high Mean Square Error (MSE) seen in the family of complex signal. The introduced approach is capable of facilitating real-time application, supported by numerous case studies, such as those in renewable energy. This class of algorithm performs well in either noisy or noise-free environments, the introduced approached has achieved a 20% better modelling. Fast convergence and low Mean Square Error (MSE) performance over the conventional and existing methods in the literature review. A rigorous mathematic analysis for the understanding of the proposed algorithm is shown, with ranges of simulations on both synthetic and real-world data; support the approach taken in this thesis.

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