The Theory And Method Of The Pipelined Adaptive Filter Based On Nonlinear Functional Expansion

This thesis mainly focuses on the theory and method of adaptive nonlinar functional expansion filter using the pipelined architecture in the nonlinear signal processing fields, such as channel equalization, system identificaiton and nonstationary signal prediction. It involves the following two aspects:first, based on the analysis of nonlinear adaptive filter (mainly including the neural network based on the functional expansion and pipelined architecture), consider the applicational background of actual nonlinear signal processing, we propose a series of novel low complexity nonlinear adaptive filters;secondly, the corresponding modified adaptive algorithms of novel filters are derived, whose performance is analysed by the theory. The main contributions of this thesis are given as follows:(1) Neural network models based on the nonlinear functional expansion are systemly summarized. Based on the analysis of the neural network based on the nonlinear functional expansion, consider the concurrent characteristic of linear and nonlinear distortions in nonlinear communication channels, we propose a novel combined finite impulse response (FIR) and functional link artificial neural network (FLANN)-based equalizer, and the modified least mean square (LMS) algorithm and its theory analysis are presented. The novel nonlinear equalizer adequately utilizes the fast convergence of the FIR filter and FLANN's characteristic of improving its nonlinear approximating capability by enlarging the input space to further improve the convergence speed, and to reduce steady-state error and bit error rate (BER) performance. Moreover, its computational complexity is lower than that of other equlizers.(2) In virtue of the pipelined architecture, to reduce the computational complexity of the Volterra filter, a novel joint process filter using pipelined feedforward second-order Volterra architecture (JPPSOV) based on the principle of divide and conquer is firstly proposed, and has successfully applied in nonlinear system identification and nonstationary speech signal prediction. This proposed filter which is with the parallel characteristic is a modular structure comprising a number of modules that are interconnected in a chained form. Therefore, these would lead to significantly reduce the computational complexity, and also improve the performance to a certain extent. Furthermore, to improve the performance, we propos the JPPSOV perceptron (JPPSOVP) filter based on the polynomial perceptron using the RTRL algorithm. Theory analysis and simulation results both demonstrate that JPPSOVP outperforms the JPPSOV and direct-form second-order Volterra (SOV).(3) Combining the advantages of Bilinear and recursive second-order Volterra (RSOV) filters with the infinite impulse response (IIR) structure, we can propose two novel pipelined neural networks based on the recurrsive Volterra expansion:a pipelined neural network based on the Bilinear expansion and a pipelined recurrent neural network based on the RSOV expansion. Simulation results show that their filtered performance can be further improved with low computational complexity.(4) To improve the performance of nonlinear filter based on the pipelined architecture, we propose a pipelined Chebyshev functional link artificial recurrent neural network (PCFLARNN) based on the FLANN model, which are sucessfully applied to nonlinear system identification, chaotic time series prediction and nonlinear channel equalization. Theory analysis and simulation results both illustrate that they have low computational complexity. Moreover, they can improve the performance to a certain extent due to the introduced nonlinear functional expansion of each module.(5) According to the pipelined architecture and the characteristics of the decision feedback equalizer in digitial communication system, we propose a novel pipelined decision feedback recurrent neural network-based equalizer (PDFRNE). The novel equalizer utilizes the pipelined architecture to reduce the computational complexity; uses the decision feedback structure of each module to remove the error remaining in the network. Moreover, it can also overcome the unstableness of IIR structure in nature. To process complex-valued signals and channels, the complex-valued pipelined decision feedback recurrent neural network-based equalizer (CPDFRNE) is proposed, and the adaptive complex-valued real-time recurrent learning (RTRL) algorithm is derived.