Digital signal processing (DSP) is widely used in many applications spanning the spectrum from audio processing to image and video processing to radar and sonar processing. At the core of digital signal processing applications is the digital filter which are implemented in two ways, using either finite impulse response (FIR) filters or infinite impulse response (IIR) filters. The primary difference between FIR and IIR is that for FIR filters, the output is dependent only on the inputs, while for IIR filters the output is dependent on the inputs and the previous outputs. FIR filters also do not sur from stability issues stemming from the feedback of the output to the input that aect IIR filters. In this thesis, an architecture for FIR filtering based on distributed arithmetic is presented. The proposed architecture has the ability to implement large FIR filters using minimal hardware and at the same time is able to complete the FIR filtering operation in minimal amount of time and delay when compared to typical FIR filter implementations. The proposed architecture is then used to implement the fast affine projection adaptive algorithm, an algorithm that is typically used with large filter sizes. The fast affine projection algorithm has a high computational burden that limits the throughput, which in turn restricts the number of applications. However, using the proposed FIR filtering architecture, the limitations on throughput are removed. The implementation of the fast affine projection adaptive algorithm using distributed arithmetic is unique to this thesis. The constructed adaptive filter shares all the benefits of the proposed FIR filter: low hardware requirements, high speed, and minimal delay.

Adaptive filtering techniques are used in a wide range of applications, including echo cancellation, adaptive equalization, adaptive noise cancellation, and adaptive beamforming. The performance of an adaptive filtering algorithm is evaluated based on its convergence rate, misadjustment, computational requirements, and numerical robustness. We attempt to improve the performance by developing new adaptation algorithms and by using "unconventional" structures for adaptive filters. Part I of this dissertation presents a new adaptation algorithm, which we have termed the Normalized LMS algorithm with Orthogonal Correction Factors (NLMS-OCF). The NLMS-OCF algorithm updates the adaptive filter coefficients (weights) on the basis of multiple input signal vectors, while NLMS updates the weights on the basis of a single input vector. The well-known Affine Projection Algorithm (APA) is a special case of our NLMS-OCF algorithm. We derive convergence and tracking properties of NLMS-OCF using a simple model for the input vector. Our analysis shows that the convergence rate of NLMS-OCF (and also APA) is exponential and that it improves with an increase in the number of input signal vectors used for adaptation. While we show that, in theory, the misadjustment of the APA class is independent of the number of vectors used for adaptation, simulation results show a weak dependence. For white input the mean squared error drops by 20 dB in about 5N/(M+1) iterations, where N is the number of taps in the adaptive filter and (M+1) is the number of vectors used for adaptation. The dependence of the steady-state error and of the tracking properties on the three user-selectable parameters, namely step size, number of vectors used for adaptation (M+1), and input vector delay D used for adaptation, is discussed. While the lag error depends on all of the above parameters, the fluctuation error depends only on step size. Increasing D results in a linear increase in the lag error and hence the total steady-state mean-squared error. The optimum choices for step size and M are derived. Simulation results are provided to corroborate our analytical results. We also derive a fast version of our NLMS-OCF algorithm that has a complexity of O(NM). The fast version of the algorithm performs orthogonalization using a forward-backward prediction lattice. We demonstrate the advantages of using NLMS-OCF in a practical application, namely stereophonic acoustic echo cancellation. We find that NLMS-OCF can provide faster convergence, as well as better echo rejection, than the widely used APA. While the first part of this dissertation attempts to improve adaptive filter performance by refining the adaptation algorithm, the second part of this work looks at improving the convergence rate by using different structures. From an abstract viewpoint, the parameterization we decide to use has no special significance, other than serving as a vehicle to arrive at a good input-output description of the system. However, from a practical viewpoint, the parameterization decides how easy it is to numerically minimize the cost function that the adaptive filter is attempting to minimize. A balanced realization is known to minimize the parameter sensitivity as well as the condition number for Grammians. Furthermore, a balanced realization is useful in model order reduction. These properties of the balanced realization make it an attractive candidate as a structure for adaptive filtering. We propose an adaptive filtering algorithm based on balanced realizations. The third part of this dissertation proposes a unit-norm-constrained equation-error based adaptive IIR filtering algorithm. Minimizing the equation error subject to the unit-norm constraint yields an unbiased estimate for the parameters of a system, if the measurement noise is white. The proposed algorithm uses the hyper-spherical transformation to convert this constrained optimization problem into an unconstrained optimization problem. It is shown that the hyper-spherical transformation does not introduce any new minima in the equation error surface. Hence, simple gradient-based algorithms converge to the global minimum. Simulation results indicate that the proposed algorithm provides an unbiased estimate of the system parameters. / Ph. D.

Submitted by Geyciane Santos (geyciane_thamires@hotmail.com) on 2015-07-23T12:57:35Z No. of bitstreams: 1 Dissertação - Mauro Lopes de Freitas.pdf: 1646151 bytes, checksum: a4f17991e9db7da2871b0c711b18f484 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2015-07-23T18:44:37Z (GMT) No. of bitstreams: 1 Dissertação - Mauro Lopes de Freitas.pdf: 1646151 bytes, checksum: a4f17991e9db7da2871b0c711b18f484 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2015-07-23T18:47:54Z (GMT) No. of bitstreams: 1 Dissertação - Mauro Lopes de Freitas.pdf: 1646151 bytes, checksum: a4f17991e9db7da2871b0c711b18f484 (MD5) / Made available in DSpace on 2015-07-23T18:47:54Z (GMT). No. of bitstreams: 1 Dissertação - Mauro Lopes de Freitas.pdf: 1646151 bytes, checksum: a4f17991e9db7da2871b0c711b18f484 (MD5) Previous issue date: 2014-09-25 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / systems, mostly due to their welldefined structure and blockwise encoding. Among the main challenges encountered by mobile applications, there is an inherent interblock interference, due to superpositions of delayed signal copies, which is commonly eliminated with the addition of redundancy between adjacent data blocks. In addition to that, channel equalization is also usually employed, in order to further mitigate channel interferences. However, the amount of redundancy may be overestimated, which opens an opportunity for reduced-redundancy superfast transceivers, whose features include high spectral efficiency and low computational cost. Although the superfast approach aims at achieving low complexity, equalizer-coefficient updates are still very complex tasks due to channel variations, and most designs do not employ methodologies for computational-effort reduction. The present work addresses this problem and proposes a new design strategy for block-based transceivers, which provides semiblind equalization with data-selective update, besides the possibility of a generalized approach, based on the fast Fourier transform and diagonal matrices. Simulation results show that our approach updates less than 60% of the equalizer coefficients duringsupervised and blind period and maintain a competitive throughput for single-carrier and multicarrier transmissions. / Atualmente, os transceptores multicanais baseados em blocos são largamente utilizados em sistemas de comunicação sem fio, muito devido a sua estrutura bem definida e ao blockwise encoding. A respeito dos principais problemas encontrados em aplicações móveis, podemos destacar a interferência entre blocos, em decorrência da superposição de cópias atrasadas do sinal, a qual é usualmente eliminada com a adição de uma quantidade de redundância entre blocos de dados adjacentes. Adicionalmente, a equalização é comumente aplicada para mitigar o efeito do canal. Entretanto, a quantidade de redundância pode estar superestimada, abrindo oportunidade para a utilização de transceptores multicanais super-rápidos e com redundância reduzida, que possuem como característica uma alta eficiência espectral e baixa complexidade computacional. Entretanto, a abordagem super-rápida ainda possui uma alta complexidade para atualizar os coeficientes de equalização e a maioria das arquiteturas propostas não utilizam metodologias visando à redução do número de operações. O trabalho atual trata este problema e propõe uma nova arquitetura para tranceptores multicanais com transmissão em blocos, que se utiliza de uma equalização semi-cega com seleção de dados, além da abordagem generalizada, baseadas em transformadas rápidas de Fourier e matrizes diagonais. Os resultados das simulações demonstram que a abordagem permite atualizar menos de 60% dos coeficientes de equalização durante o período supervisionado e não supervisionado de equalização e manter a taxa de saída competitiva para sistemas monoportadora e multiportadora.