973 research outputs found

    Employing data fusion & diversity in the applications of adaptive signal processing

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    The paradigm of adaptive signal processing is a simple yet powerful method for the class of system identification problems. The classical approaches consider standard one-dimensional signals whereby the model can be formulated by flat-view matrix/vector framework. Nevertheless, the rapidly increasing availability of large-scale multisensor/multinode measurement technology has render no longer sufficient the traditional way of representing the data. To this end, the author, who from this point onward shall be referred to as `we', `us', and `our' to signify the author myself and other supporting contributors i.e. my supervisor, my colleagues and other overseas academics specializing in the specific pieces of research endeavor throughout this thesis, has applied the adaptive filtering framework to problems that employ the techniques of data diversity and fusion which includes quaternions, tensors and graphs. At the first glance, all these structures share one common important feature: invertible isomorphism. In other words, they are algebraically one-to-one related in real vector space. Furthermore, it is our continual course of research that affords a segue of all these three data types. Firstly, we proposed novel quaternion-valued adaptive algorithms named the n-moment widely linear quaternion least mean squares (WL-QLMS) and c-moment WL-LMS. Both are as fast as the recursive-least-squares method but more numerically robust thanks to the lack of matrix inversion. Secondly, the adaptive filtering method is applied to a more complex task: the online tensor dictionary learning named online multilinear dictionary learning (OMDL). The OMDL is partly inspired by the derivation of the c-moment WL-LMS due to its parsimonious formulae. In addition, the sequential higher-order compressed sensing (HO-CS) is also developed to couple with the OMDL to maximally utilize the learned dictionary for the best possible compression. Lastly, we consider graph random processes which actually are multivariate random processes with spatiotemporal (or vertex-time) relationship. Similar to tensor dictionary, one of the main challenges in graph signal processing is sparsity constraint in the graph topology, a challenging issue for online methods. We introduced a novel splitting gradient projection into this adaptive graph filtering to successfully achieve sparse topology. Extensive experiments were conducted to support the analysis of all the algorithms proposed in this thesis, as well as pointing out potentials, limitations and as-yet-unaddressed issues in these research endeavor.Open Acces

    A Unifying Approach to Quaternion Adaptive Filtering: Addressing the Gradient and Convergence

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    A novel framework for a unifying treatment of quaternion valued adaptive filtering algorithms is introduced. This is achieved based on a rigorous account of quaternion differentiability, the proposed I-gradient, and the use of augmented quaternion statistics to account for real world data with noncircular probability distributions. We first provide an elegant solution for the calculation of the gradient of real functions of quaternion variables (typical cost function), an issue that has so far prevented systematic development of quaternion adaptive filters. This makes it possible to unify the class of existing and proposed quaternion least mean square (QLMS) algorithms, and to illuminate their structural similarity. Next, in order to cater for both circular and noncircular data, the class of widely linear QLMS (WL-QLMS) algorithms is introduced and the subsequent convergence analysis unifies the treatment of strictly linear and widely linear filters, for both proper and improper sources. It is also shown that the proposed class of HR gradients allows us to resolve the uncertainty owing to the noncommutativity of quaternion products, while the involution gradient (I-gradient) provides generic extensions of the corresponding real- and complex-valued adaptive algorithms, at a reduced computational cost. Simulations in both the strictly linear and widely linear setting support the approach

    Channel Prediction Using Ordinary Differential Equations for MIMO systems

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    Channel state information (CSI) estimation is part of the most fundamental problems in 5G wireless communication systems. In mobile scenarios, outdated CSI will have a serious negative impact on various adaptive transmission systems, resulting in system performance degradation. To obtain accurate CSI, it is crucial to predict CSI at future moments. In this paper, we propose an efficient channel prediction method in multiple-input multiple-output (MIMO) systems, which combines genetic programming (GP) with higher-order differential equation (HODE) modeling for prediction, named GPODE. In the first place, the variation of one-dimensional data is depicted by using higher-order differential, and the higher-order differential data is modeled by GP to obtain an explicit model. Then, a definite order condition is given for the modeling of HODE, and an effective prediction interval is given. In order to accommodate to the rapidly changing channel, the proposed method is improved by taking the rough prediction results of Autoregression (AR) model as a priori, i.e., Im-GPODE channel prediction method. Given the effective interval, an online framework is proposed for the prediction. To verify the validity of the proposed methods, We use the data generated by the Cluster Delay Line (CDL) channel model for validation. The results show that the proposed methods has higher accuracy than other traditional prediction methods
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