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Wireless communication systems are limited in performance and capacity by the major impairments of multipath fading and co-channel interference. Smart antenna can combat the impairments, thereby enhancing the system capacity and alleviating the problem of bandwidth limitation. In general, there are two main types of smart antennas; these are switched beam systems and adaptive array systems. An antenna array, which consists of a group of several antenna elements and digital signal processing units, can form several independent beams in different angles. Smart antennas aim the main beam in the direction of the target mobile user and locate the nulls in the direction of the interfering signals from other mobile users to enhance the signal-to-interference power ratio and system capacity. One of the most important parts in adaptive array antenna systems is the adaptive algorithm to adjust the weights of an array. These algorithms include unconstrained as well as constrained LMS, normalized LMS, structured gradient, RLS, CMA, and conjugate gradient method. In this thesis, we propose a new algorithm based on weight-partition RLS method to reduce the computational complexity. The major concept of our algorithm is decreasing the dimension size of data matrix. Performance and complexity of the proposed algorithm is evaluated and compared with traditional WRLS algorithm.

The literature on bounded rationality and learning in macroeconomics has often used recursive algorithms to depict the evolution of agents' beliefs over time. In this thesis we assess this practice from an applied perspective, focusing on the use of such algorithms for the computation of forecasts of macroeconomic variables. Our analysis develops around three issues we find to have been previously neglected in the literature: (i) the initialization of the learning algorithms; (ii) the determination and calibration of the learning gains, which are key parameters of the algorithms' specifications; and, (iii) the choice of a representative learning mechanism. In order to approach these issues we establish an estimation framework under which we unify the two main algorithms considered in this literature, namely the least squares and the stochastic gradient algorithms. We then propose an evaluation framework that mimics the real-time process of expectation formation through learning-to-forecast exercises. To analyze the quality of the forecasts associated to the learning approach, we evaluate their forecasting accuracy and resemblance to surveys, these latter taken as proxy for agents' expectations. In spite of taking these two criteria as mutually desirable, it is not clear whether they are compatible with each other: whilst forecasting accuracy represents the goal of optimizing agents, resemblance to surveys is indicative of actual agents behavior. We carry out these exercises using real-time quarterly data on US inflation and output growth covering a broad post-WWII period of time. Our main contribution is to show that a proper assessment of the adaptive learning approach requires going beyond the previous views in the literature about these issues. For the initialization of the learning algorithms we argue that such initial estimates need to be coherent with the ongoing learning process that was already in place at the beginning of our sample of data. We find that the previous initialization methods in the literature are vulnerable to this requirement, and propose a new smoothing-based method that is not prone to this critic. Regarding the learning gains, we distinguish between two possible rationales to its determination: as a choice of agents; or, as a primitive parameter of agents learning-to-forecast behavior. Our results provide strong evidence in favor of the gain as a primitive approach, hence favoring the use of surveys data for their calibration. In the third issue, about the choice of a representative algorithm, we challenge the view that learning should be represented by only one of the above algorithms; on the basis of our two evaluation criteria, our results suggest that using a single algorithm represents a misspecification. That motivate us to propose the use of hybrid forms of the LS and SG algorithms, for which we find favorable evidence as representatives of how agents learn. Finally, our analysis concludes with an optimistic assessment on the plausibility of adaptive learning, though conditioned to an appropriate treatment of the above issues. We hope our results provide some guidance on that respect.

The increasing demand for high data rate services necessitates the adoption of very wideband waveforms. In this case, the channel is frequency-selective, that is, a large number of resolvable multipaths are present in this environment and fading is not highly correlated across the band. Orthogonal frequency division multiplexing (OFDM) is well-known to be effective against multipath distortion. It is a multicarrier communication scheme, in which the bandwidth of the channel is divided into subcarriers and data symbols are modulated and transmitted on each subcarrier simultaneously. By inserting guard time that is longer than the delay spread of the channel, an OFDM system is able to mitigate intersymbol interference (ISI). Deploying an adaptive antenna array at the receiver can help separate the desired signal from interfering signals which originate from different spatial locations. This enhancement of signal integrity increases system capacity. In this research, we apply adaptive array algorithms to OFDM systems and study their performance in a multipath environment with the presence of interference. A novel adaptive beamforming algorithm based on the minimum mean-squared error (MMSE) criterion, which is referred to as frequency-domain beamforming, is proposed that exploits the characteristics of OFDM signals. The computational complexity of frequency-domain beamforming is also studied. Simulation results show employing an adaptive antenna array with an OFDM system significantly improves system performance when interference is present. Simulations also show that the computational complexity of the algorithm can be reduced by half without significant performance degradation. Adaptive array algorithms based on the maximum signal-to-noise ratio (MSNR) and the maximum signal-to-interference-plus-noise ratio (MSINR) criteria are also applied to adaptive vector OFDM systems (AV-OFDM). Simulation results show that the adaptive algorithm based on the MSNR criterion has superior performance in the multipath environment but performs worse than the one based on the MSINR criterion under the flat fading channel. / Master of Science

No campo do processamento digital de sinais e em especial da filtragem adaptativa, procura-se continuamente algoritmos que sejam rápidos e simples. Neste contexto, este trabalho apresenta o estudo de novos algoritmos de tempo discreto denominados algoritmos aceleradores (completo, regressivo e progressivo), obtidos a partir da discretização de um algoritmo de tempo contínuo baseado no ajuste da segunda derivada (aceleração) da estimativa dos parâmetros. Destes algoritmos optou-se por estudar mais aprofundadamente os algoritmos aceleradores progressivo e regressivo, devido respectivamente a sua menor complexidade computacional e ao seu desempenho. Para este estudo e análise foram escolhidos como base de comparação os algoritmos LMS e NLMS. Isto porque estes algoritmos estão entre os mais usados e, assim como os algoritmos aceleradores, podem ser obtidos a partir da discretização de algoritmos de tempo contínuo através dos métodos de Euler progressivo e regressivo respectivamente. A análise do algoritmo progressivo mostrou que seu desempenho é inferior ao do algoritmo LMS. Visando diminuir a complexidade computacional do algoritmo acelerador regressivo, foi obtido um novo algoritmo: o versão g. Assim a análise focou-se no algoritmo acelerador regressivo versão g, o qual apresentou um desempenho bom quando comparado no desajuste e no tracking com o algoritmo NLMS, mostrando um melhor compromisso entre velocidade de convergência e variância das estimativas. Este bom desempenho foi comprovado por análises teóricas, por simulações e através da aplicação deste algoritmo na equalização de um canal variante no tempo. / In the digital signal processing field and specially in adaptive filtering, there is a constant search for algorithms both simple and with good performance. This work presents new discrete-time algorithms called accelerating algorithms (APCM and ARg), obtained through the discretization of a continuous-time algorithm that uses the second derivate (acceleration) to adjust the parameter estimates. We provide theoretical analyses for both algorithms, finding expressions for the mean and mean-square errors in the parameter estimates. In addition, we compare the performance of the accelerating algorithms with LMS and NLMS. The analysis of the APCM algorithm showed that its performance is inferior to that of the LMS algorithm. On the other hand, the ARg algorithm presented good performance when compared in terms of misadjustment and tracking with the NLMS algorithm, showing a better compromise between convergence speed and variance of the estimates. This better performance was proven by theoretical analyses, by simulations and through the application of this algorithm to the equalization of a time-variant channel.

No campo do processamento digital de sinais e em especial da filtragem adaptativa, procura-se continuamente algoritmos que sejam rápidos e simples. Neste contexto, este trabalho apresenta o estudo de novos algoritmos de tempo discreto denominados algoritmos aceleradores (completo, regressivo e progressivo), obtidos a partir da discretização de um algoritmo de tempo contínuo baseado no ajuste da segunda derivada (aceleração) da estimativa dos parâmetros. Destes algoritmos optou-se por estudar mais aprofundadamente os algoritmos aceleradores progressivo e regressivo, devido respectivamente a sua menor complexidade computacional e ao seu desempenho. Para este estudo e análise foram escolhidos como base de comparação os algoritmos LMS e NLMS. Isto porque estes algoritmos estão entre os mais usados e, assim como os algoritmos aceleradores, podem ser obtidos a partir da discretização de algoritmos de tempo contínuo através dos métodos de Euler progressivo e regressivo respectivamente. A análise do algoritmo progressivo mostrou que seu desempenho é inferior ao do algoritmo LMS. Visando diminuir a complexidade computacional do algoritmo acelerador regressivo, foi obtido um novo algoritmo: o versão g. Assim a análise focou-se no algoritmo acelerador regressivo versão g, o qual apresentou um desempenho bom quando comparado no desajuste e no tracking com o algoritmo NLMS, mostrando um melhor compromisso entre velocidade de convergência e variância das estimativas. Este bom desempenho foi comprovado por análises teóricas, por simulações e através da aplicação deste algoritmo na equalização de um canal variante no tempo. / In the digital signal processing field and specially in adaptive filtering, there is a constant search for algorithms both simple and with good performance. This work presents new discrete-time algorithms called accelerating algorithms (APCM and ARg), obtained through the discretization of a continuous-time algorithm that uses the second derivate (acceleration) to adjust the parameter estimates. We provide theoretical analyses for both algorithms, finding expressions for the mean and mean-square errors in the parameter estimates. In addition, we compare the performance of the accelerating algorithms with LMS and NLMS. The analysis of the APCM algorithm showed that its performance is inferior to that of the LMS algorithm. On the other hand, the ARg algorithm presented good performance when compared in terms of misadjustment and tracking with the NLMS algorithm, showing a better compromise between convergence speed and variance of the estimates. This better performance was proven by theoretical analyses, by simulations and through the application of this algorithm to the equalization of a time-variant channel.

This thesis investigates reliable data communication techniques for wireless channels. The problem of data detection at the receiver is considered and several novel detectors and parameter estimators are presented.¶ It is shown that by using a noise-limiting prefilter, with a spectral support at least equal to the signal part of the received signal, and sampling its output at the Nyquist rate, a set of sufficient statistics for maximum likelihood sequence detection (MLSD) is obtained.¶ Observing that the time-variations of the multipaths in a wireless channel are bandlimited, channel taps are closely approximated as polynomials in time. Using this representation, detection techniques for frequency-flat and frequency-selective channels are obtained. The proposed polynomial predictor based sequence detector (PPSD) for frequency-flat channels is similar in structure to the MLSD that employs channel prediction. However, the PPSD uses {\em a priori} known polynomial based predictor taps. It is observed that the PPSD, without any explicit knowledge of the channel autocovariance, performs close to the Innovations based MLSD.¶ New techniques for frequency-selective channel estimation are presented. They are based on a rectangular windowed least squares algorithm, and they employ a polynomial model of the channel taps. A recursive form of the least squares algorithm with orthonormal polynomial basis vectors is developed. Given the appropriate window size and polynomial model order, the proposed method outperforms the conventional least mean squares (LMS) and the exponentially weighted recursive least squares (EW-RLS) algorithms. Novel algorithms are proposed to obtain near optimal window size and polynomial model order.¶ The improved channel estimation techniques developed for frequency-selective channels are incorporated into sliding window and fixed block channel estimators. The sliding window estimator uses received samples over a time window to calculate the channel taps. Every symbol period, the window is moved along another symbol period and a new estimate is calculated. A fixed block estimator uses all received samples to estimate the channel taps throughout a data packet, all at once. In fast fading and at a high signal-to-noise ratio (SNR), both techniques outperform the MLSD receivers which employ the LMS algorithm for channel estimation.¶ An adaptive multiuser detector, optimal in the weighted least squares (WLS) sense, is derived for direct sequence code division multiple access (DS-CDMA) systems. In a multicellular configuration, this detector jointly detects the users within the cell of interest, while suppressing the intercell interferers in a WLS sense. In the absence of intercell interferers, the detector reduces to the well-known multiuser MLSD structure that employs a bank of matched filters. The relationship between the proposed detector and a centralized decision feedback detector is derived. The effects of narrowband interference are investigated and compared with the multiuser MLSD.¶ Since in a fast time-varying channel, the LMS or the EW-RLS algorithms cannot track the channel variations effectively, the receiver structures proposed for single user communications are extended to multiuser DS-CDMA systems. The fractionally-chip-spaced channel taps of the convolution of the chip waveform with the multipath channel are estimated. Linear equalizer, decision feedback equalizer and MLSDs are studied, and under fast fading, as the SNR increases, they are found to outperform the LMS based adaptive minimum mean squared error (MMSE) linear receivers.

É investigado o uso de redes neurais aplicadas à equalização de canais de comunicação, sendo consideradas três tipos de redes: MLP (Multilayer Perceptron), RBF (Radial Basis Function) e RNN (Recurrent Neural Network). Os equalizadores não-lineares baseados nestas redes foram comparados com o equalizador linear transversal e com os equalizadores ótimos segundo os critérios de Bayes e da máxima verossimilhança. Nestas comparações foram utilizados um alfabeto binário e um quaternário transmitidos em modelos de canais cuja resposta ao pulso unitário é finita. Além das versões usuais de equalizadores, foram consideradas versões com realimentação de decisões sempre que isso se mostrou adequado. O treinamento desses equalizadores foi feito de forma supervisionada, ou seja, na fase de treinamento a seqüência de símbolos transmitida era conhecida no receptor. Além disso, foi realizado um estudo comparativo dos algoritmos de treinamento das redes. Neste âmbito, foi obtido um algoritmo do tipo acelerador para o treinamento de redes MLP. Com o intuito de se obter uma estrutura não-linear menos complexa e mais flexível, foi proposto ainda um equalizador híbrido constituído de uma combinação do equalizador linear e da rede RNN que faz uso de realimentação de decisões. Resultados de simulações indicam que o seu uso pode ser vantajoso tanto para canais não-lineares como lineares. / Equalization of communication channels using neural networks is investigated by considering three kinds of networks: MLP (Multilayer Perceptron), RBF (Radial Basis Function) and RNN (Recurrent Neural Network). The performance of the nonlinear equalizers based on these networks are compared with the linear transversal equalizer and the optimal equalizers given by the bayesian and maximum likelihood criteria. Binary and quaternary alphabets are used and transmitted over finite pulse response channel models. Decision feedback is considered whenever it is worthwhile. The training of these equalizers is considered in the supervised form and a comparison of some training algorithms has been performed. In this scope, a new algorithm based on parameter acceleration is introduced for the training of MLP networks. Moreover, a hybrid equalizer composed of a linear transversal equalizer and a RNN network is proposed. It is a simple and flexible nonlinear structure making use of decision feedback. imulation results show that it may be advantageously used to equalize linear and nonlinear channels.

Neste trabalho, investigam-se técnicas autodidatas baseadas em estatísticas de ordem superior, aplicadas à equalização de canais de comunicação. Inicialmente, obtém-se um intervalo do passo de adaptação que assegura a convergência do algoritmo do Módulo Constante com o gradiente exato. Algoritmos como o CMA (Constant Modulus Algorithm) e o SWA (Shalvi-Weinstein Algorithm) são revisitados e suas capacidades de tracking analisadas, utilizando-se uma relação de conservação de energia. Além disso, é proposto um algoritmo autodidata denominado AC-CMA (Accelerated Constant Modulus Algorithm) que utiliza a segunda derivada (“aceleração") da estimativa dos coeficientes. Esse algoritmo pode apresentar um compromisso mais favorável entre complexidade computacional e velocidade de convergência que o CMA e o SWA. Esses resultados são estendidos para o caso multiusuário. Através de simulações, os algoritmos são comparados e as análises de convergência e tracking validadas. Considerando o DFE (Decision Feedback Equalizer) no caso monousuário com o critério do módulo constante, é proposto um algoritmo concorrente que evita soluções degeneradas e apresenta um desempenho melhor do que os existentes na literatura. Com o intuito de evitar propagação de erros, é proposta uma estrutura híbrida que utiliza uma rede neural recorrente na malha de realimentação. Resultados de simulações indicam que seu uso pode ser vantajoso para canais lineares e não-lineares. / The equalization of communication channels is addressed by using blind techniques based on higher order statistics. A step-size interval is obtained to ensure the convergence of Steepest-Descent Constant Modulus Algorithm. The Shalvi-Weinstein Algorithm (SWA) and Constant Modulus Algorithm (CMA) are revisited and their tracking capabilities are analyzed by using an energy conservation relation. Moreover, a novel blind algorithm named Accelerated Constant Modulus Algorithm (AC-CMA) is proposed. It adjusts the second derivative (“acceleration") of the coefficient estimates and presents a more favorable compromise between computational complexity and convergence rate than CMA or SWA. These results are extended to the MIMO (Multiple-Input Multiple-Output) case. By means of simulations, the algorithms are compared and the convergence and tracking analysis are validated. The Decision Feedback Equalizer (DFE) is considered in the SISO (Single-Input Single-Output) case with the Constant Modulus criterion and a concurrent algorithm is proposed. It avoids degenerated solutions and shows better behavior than the others presented in the literature. In order to avoid error propagation, a hybrid DFE is also proposed. It includes a recurrent neural network in the feedback filter and may be advantageously used to equalize linear and nonlinear channels.