On adaptive filter structure and performance

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The design and implementation of a microprocessor controlled adaptive filter

This thesis describes the construction and implementation of a microprocessor controlled recursive adaptive filter applied as a noise canceller. It describes the concept of the adaptive noise canceller, a method of estimating the received signal corrupted with additive interference (noise). This canceller has two inputs, the primary input containing the corrupted signal and the reference input consisting of the additive noise correlated in some unknown way to the primary noise. The reference input is filtered and subtracted from the primary input without degrading the desired components of the signal. This filtering process is adaptive and based on Widrow-Hoff Least-Mean-Square algorithm. Adaptive filters are programmable and have the capability to adjust their own parameters in situations where minimum piori knowledge is available about the inputs. For recursive filters, these parameters include feed-forward (non-recursive) as well as feedback (recursive) coefficients. A new design and implementation of the adaptive filter is suggested which uses a high speed 68000 microprocessor to accomplish the coefficients updating operation. Many practical problems arising in the hardware implementation are investigated. Simulation results illustrate the ability of the adaptive noise canceller to have an acceptable performance when the coefficients updating operation is carried out once every N sampling periods. Both simulation and hardware experimental results are in agreement

Microprocessor based signal processing techniques for system identification and adaptive control of DC-DC converters

PhD ThesisMany industrial and consumer devices rely on switch mode power converters (SMPCs) to provide a reliable, well regulated, DC power supply. A poorly performing power supply can potentially compromise the characteristic behaviour, efficiency, and operating range of the device. To ensure accurate regulation of the SMPC, optimal control of the power converter output is required. However, SMPC uncertainties such as component variations and load changes will affect the performance of the controller. To compensate for these time varying problems, there is increasing interest in employing real-time adaptive control techniques in SMPC applications. It is important to note that many adaptive controllers constantly tune and adjust their parameters based upon on-line system identification. In the area of system identification and adaptive control, Recursive Least Square (RLS) method provide promising results in terms of fast convergence rate, small prediction error, accurate parametric estimation, and simple adaptive structure. Despite being popular, RLS methods often have limited application in low cost systems, such as SMPCs, due to the computationally heavy calculations demanding significant hardware resources which, in turn, may require a high specification microprocessor to successfully implement. For this reason, this thesis presents research into lower complexity adaptive signal processing and filtering techniques for on-line system identification and control of SMPCs systems. The thesis presents the novel application of a Dichotomous Coordinate Descent (DCD) algorithm for the system identification of a dc-dc buck converter. Two unique applications of the DCD algorithm are proposed; system identification and self-compensation of a dc-dc SMPC. Firstly, specific attention is given to the parameter estimation of dc-dc buck SMPC. It is computationally efficient, and uses an infinite impulse response (IIR) adaptive filter as a plant model. Importantly, the proposed method is able to identify the parameters quickly and accurately; thus offering an efficient hardware solution which is well suited to real-time applications. Secondly, new alternative adaptive schemes that do not depend entirely on estimating the plant parameters is embedded with DCD algorithm. The proposed technique is based on a simple adaptive filter method and uses a one-tap finite impulse response (FIR) prediction error filter (PEF). Experimental and simulation results clearly show the DCD technique can be optimised to achieve comparable performance to classic RLS algorithms. However, it is computationally superior; thus making it an ideal candidate technique for low cost microprocessor based applications.Iraq Ministry of Higher Educatio

Maximum-likelihood estimation of delta-domain model parameters from noisy output signals

Fast sampling is desirable to describe signal transmission through wide-bandwidth systems. The delta-operator provides an ideal discrete-time modeling description for such fast-sampled systems. However, the estimation of delta-domain model parameters is usually biased by directly applying the delta-transformations to a sampled signal corrupted by additive measurement noise. This problem is solved here by expectation-maximization, where the delta-transformations of the true signal are estimated and then used to obtain the model parameters. The method is demonstrated on a numerical example to improve on the accuracy of using a shift operator approach when the sample rate is fast

Adaptive estimation and equalisation of the high frequency communications channel

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Channel estimation techniques for filter bank multicarrier based transceivers for next generation of wireless networks

A dissertation submitted to Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Master of Science in Engineering (Electrical and Information Engineering), August 2017The fourth generation (4G) of wireless communication system is designed based on the principles of cyclic prefix orthogonal frequency division multiplexing (CP-OFDM) where the cyclic prefix (CP) is used to combat inter-symbol interference (ISI) and inter-carrier interference (ICI) in order to achieve higher data rates in comparison to the previous generations of wireless networks. Various filter bank multicarrier systems have been considered as potential waveforms for the fast emerging next generation (xG) of wireless networks (especially the fifth generation (5G) networks). Some examples of the considered waveforms are orthogonal frequency division multiplexing with offset quadrature amplitude modulation based filter bank, universal filtered multicarrier (UFMC), bi-orthogonal frequency division multiplexing (BFDM) and generalized frequency division multiplexing (GFDM). In perfect reconstruction (PR) or near perfect reconstruction (NPR) filter bank designs, these aforementioned FBMC waveforms adopt the use of well-designed prototype filters (which are used for designing the synthesis and analysis filter banks) so as to either replace or minimize the CP usage of the 4G networks in order to provide higher spectral efficiencies for the overall increment in data rates. The accurate designing of the FIR low-pass prototype filter in NPR filter banks results in minimal signal distortions thus, making the analysis filter bank a time-reversed version of the corresponding synthesis filter bank. However, in non-perfect reconstruction (Non-PR) the analysis filter bank is not directly a time-reversed version of the corresponding synthesis filter bank as the prototype filter impulse response for this system is formulated (in this dissertation) by the introduction of randomly generated errors. Hence, aliasing and amplitude distortions are more prominent for Non-PR. Channel estimation (CE) is used to predict the behaviour of the frequency selective channel and is usually adopted to ensure excellent reconstruction of the transmitted symbols. These techniques can be broadly classified as pilot based, semi-blind and blind channel estimation schemes. In this dissertation, two linear pilot based CE techniques namely the least square (LS) and linear minimum mean square error (LMMSE), and three adaptive channel estimation schemes namely least mean square (LMS), normalized least mean square (NLMS) and recursive least square (RLS) are presented, analyzed and documented. These are implemented while exploiting the near orthogonality properties of offset quadrature amplitude modulation (OQAM) to mitigate the effects of interference for two filter bank waveforms (i.e. OFDM/OQAM and GFDM/OQAM) for the next generation of wireless networks assuming conditions of both NPR and Non-PR in slow and fast frequency selective Rayleigh fading channel. Results obtained from the computer simulations carried out showed that the channel estimation schemes performed better in an NPR filter bank system as compared with Non-PR filter banks. The low performance of Non-PR system is due to the amplitude distortion and aliasing introduced from the random errors generated in the system that is used to design its prototype filters. It can be concluded that RLS, NLMS, LMS, LMMSE and LS channel estimation schemes offered the best normalized mean square error (NMSE) and bit error rate (BER) performances (in decreasing order) for both waveforms assuming both NPR and Non-PR filter banks. Keywords: Channel estimation, Filter bank, OFDM/OQAM, GFDM/OQAM, NPR, Non-PR, 5G, Frequency selective channel.CK201

Structures and Algorithms for Two-Dimensional Adaptive Signal Processing

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryOpe

The Application of Adaptive Linear and N on-Linear Filters to Fringe Order Identification in White-Light Interferometry Systems

Conventional optical interferometry systems driven by highly coherent light sources have a very short unambiguous operating range, a direct consequence of the flatness of the interference fringes visibility profile at the output of the system. The range can be extended by using a white-light interferometer (WU), which is driven by a low-coherence source and produces a Gaussian visibility profile with a unique maximum in correspondence of the central fringe. Due to system and/or measurement noise, however, the position of the maximum (from which an accurate measurement of the measurand - displacement, temperature, pressure, flow, etc. - can be derived) is not easily detectable, and can lead to large measurement errors. This is especially true in a multiplexing scheme, where the source power is distributed evenly among various sensors, with a corresponding drop in the overall signal-to-noise ratio. The inclusion of a signal processing scheme at the receiver end is thus a necessity. As the fringe pattern at the output of a WLI system is basically a noisy sine wave amplitude modulated by a Gaussian envelope, it can be classified as a non-stationary, narrow-band, linear but non-Gaussian signa\. So far, no attempt has been made to apply digital filtering techniques, as understood in the signal processing community, to the output signal of a WLI system. This thesis constitutes a first step in that direction. Since the only measurable information given by the system is contained in the output signal, the system is modelled as a "black box" driven by the system and measurement noise processes and containing an unknown set of parameters. Standard least squares techniques can then be applied to estimate the parameters of the model, as is usually done in the field of system identification when only noisy output measurements are available. It is shown that identification of the model parameters is equivalent to finding a set of coefficients for an inverse filter which takes the WU signal at its input and delivers the unknown noise process at the output. The non-stationarity of the signal is accounted for by allowing for time variations of the model parameters; this justifies the use of adaptive filters with time-varying coefficients. A new central fringe identification scheme is proposed, based on a modification of the standard least mean square (LMS) adaptive filtering algorithm in combination with amplitude thresholding of the fringe pattern. The new scheme is shown to offer considerable improvement in the identification rate when tested against current schemes over comparable operating ranges, while retaining the computational simplicity and operational speed of the standard LMS. Its performance is also shown to be largely independent of the step-size parameter controlling the rate of convergence and tracking in the standard LMS, which is known to be the main obstacle for a successful application of the algorithm in a practical setting. The non-Gaussianity of the signal is explored and an attempt is made to apply higher-order statistics (HOS) algorithms to central fringe identification. The effectiveness of Gaussianity tests on pilot Gaussian data is seen to depend not only on the number and length of records available but, perhaps more importantly, on the bandwidth of the process. Violation of the stationarity assumption is shown to lead to mis-classification of a seemingly non-Gaussian signal into a Gaussian one, as the visibility profile may alter the distribution of the underlying sinusoid making it appear Gaussian, even when beam diffraction and wavefront aberrations combine to produce a nonGaussian profile. HOS-based adaptive algorithms may still be of some benefit, however, if processing is confined to that region of the fringe pattern where sufficient non-Gaussianity is allowed to develop. Non-linear adaptive filters based on the Volterra theories are finally applied to compensate for possible non-linearities introduced by mismatches in optical components, chromatic aberrations, and analogue-to-digital converters. It is shown that although a Volterra filter is able to reproduce the low-amplitude distortions of the fringe pattern better than a linear filter does, the identification rate does not improve. Reasons are given for such behaviour

Tree-Structured Nonlinear Adaptive Signal Processing

In communication systems, nonlinear adaptive filtering has become increasingly popular in a variety of applications such as channel equalization, echo cancellation and speech coding. However, existing nonlinear adaptive filters such as polynomial (truncated Volterra series) filters and multilayer perceptrons suffer from a number of problems. First, although high Order polynomials can approximate complex nonlinearities, they also train very slowly. Second, there is no systematic and efficient way to select their structure. As for multilayer perceptrons, they have a very complicated structure and train extremely slowly Motivated by the success of classification and regression trees on difficult nonlinear and nonparametfic problems, we propose the idea of a tree-structured piecewise linear adaptive filter. In the proposed method each node in a tree is associated with a linear filter restricted to a polygonal domain, and this is done in such a way that each pruned subtree is associated with a piecewise linear filter. A training sequence is used to adaptively update the filter coefficients and domains at each node, and to select the best pruned subtree and the corresponding piecewise linear filter. The tree structured approach offers several advantages. First, it makes use of standard linear adaptive filtering techniques at each node to find the corresponding Conditional linear filter. Second, it allows for efficient selection of the subtree and the corresponding piecewise linear filter of appropriate complexity. Overall, the approach is computationally efficient and conceptually simple. The tree-structured piecewise linear adaptive filter bears some similarity to classification and regression trees. But it is actually quite different from a classification and regression tree. Here the terminal nodes are not just assigned a region and a class label or a regression value, but rather represent: a linear filter with restricted domain, It is also different in that classification and regression trees are determined in a batch mode offline, whereas the tree-structured adaptive filter is determined recursively in real-time. We first develop the specific structure of a tree-structured piecewise linear adaptive filter and derive a stochastic gradient-based training algorithm. We then carry out a rigorous convergence analysis of the proposed training algorithm for the tree-structured filter. Here we show the mean-square convergence of the adaptively trained tree-structured piecewise linear filter to the optimal tree-structured piecewise linear filter. Same new techniques are developed for analyzing stochastic gradient algorithms with fixed gains and (nonstandard) dependent data. Finally, numerical experiments are performed to show the computational and performance advantages of the tree-structured piecewise linear filter over linear and polynomial filters for equalization of high frequency channels with severe intersymbol interference, echo cancellation in telephone networks and predictive coding of speech signals