Thesis (M.App.Sc.) - Carleton University, 2007. / Includes bibliographical references (p. 81-85). Also available in electronic format on the Internet.

No description available.

Master of Science

No description available.

We describe an adaptive filter system that is able to switch between adaptive filter algorithms in order to produce fast convergence and low mean Square error (MSE). The switching system employs two adaptive filters for two different tasks; one is intended to yield fast convergence, and logically called the "fast convergence structure", while the other is intended to give small MSE, and called the "low MSE structure". The switching from one algorithm to the other is determined by the state of the system. For example, switching from the "fast convergence structure” to the “low MSE structure” happens if the former has reached its steady state according to some pre-defined criterion, while switching from the “low MSE structure" to the "fast convergence structure” happens if the former starts diverging according to some pre-defined criterion. We define here that an algorithm has reached its steady state if the average of the square of its output error is small and approximately constant for several iterations. After an algorithm has reached its steady state, not much additional error reduction can be obtained from it, so that there is no payoff using "the fast convergence structure”, which is usually more computation intensive than the "low MSE structure”. In this situation it would be better to use the Least Mean Squares (LMS) algorithm as the “low MSE structure" because of its simplicity and its numerical robustness. Experiments using the recursive-least-squares-lattice (RLSL) algorithm together with the LMS algorithm, the fast-transversal-filter (FTF) algorithm together with the LMS algorithm, and the gradient-adaptive-lattice (GAL) algorithm together with the LMS algorithm for a system identification application, in particular for echo cancellation, show the expected result of providing faster convergence and lower mean square error than would be possible with a single algorithm. The switching system demonstrates other important results: it can avoid the numerical instability of some algorithms, such as the RLSL and FTF algorithms, without adding any additional computations; it is able to handle a change in the unknown system, as long as it settles, without suffering a slow convergence rate caused by an incorrect initial condition; it is able to handle a change of the observation noise without facing a divergence problem; and it is able to produce an optimum result even for i/l-conditioned input signals, i.e. the ratio of the maximum and minimum eigenvalue of the auto-correlation of the signal is high. When switching to the “low MSE structure" we also apply a computationally reduced order technique, in which only the values of the impulse response that are greater than some threshold are used for computation. This technique is applied to the switching structure of the recursive-least-squareslattice algorithm together with the LMS algorithm and exhibits fast convergence and low MSE even for ill-conditioned input signals. For the white Gaussian noise input, on the other hand, this technique yields a somewhat larger mean square error. / Master of Science

ITC/USA 2009 Conference Proceedings / The Forty-Fifth Annual International Telemetering Conference and Technical Exhibition / October 26-29, 2009 / Riviera Hotel & Convention Center, Las Vegas, Nevada / Frequency selective multipath is a key performance limiter for aeronautical telemetry applications. Our research explores multipath mitigation techniques with ARTM Tier-1 waveforms using linear adaptive filters, multiple receive antennas and error-based best source selection. Single antenna adaptive equalization alone is unable to substantially improve performance under certain channel conditions. Analytical investigations demonstrate that nonlinear channel phase response is the principal cause of performance loss. In this adverse environment, spatial diversity with multiple receive antennas along with error-based best source selection are capable of improving bit error rate performance by 5dB for each additional antenna.

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.

by Hing-cheung So. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 133-141). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Time Delay Estimation (TDE) and its Applications --- p.1 / Chapter 1.2 --- Goal of the Work --- p.6 / Chapter 1.3 --- Thesis Outline --- p.9 / Chapter 2 --- Adaptive Methods for TDE --- p.10 / Chapter 2.1 --- Problem Description --- p.11 / Chapter 2.2 --- The Least Mean Square Time Delay Estimator (LMSTDE) --- p.11 / Chapter 2.2.1 --- Bias and Variance --- p.14 / Chapter 2.2.2 --- Probability of Occurrence of False Peak Weight --- p.16 / Chapter 2.2.3 --- Some Modifications of the LMSTDE --- p.17 / Chapter 2.3 --- The Adaptive Digital Delay-Lock Discriminator (ADDLD) --- p.18 / Chapter 2.4 --- Summary --- p.20 / Chapter 3 --- The Explicit Time Delay Estimator (ETDE) --- p.22 / Chapter 3.1 --- Derivation and Analysis of the ETDE --- p.23 / Chapter 3.1.1 --- The ETDE system --- p.23 / Chapter 3.1.2 --- Performance Surface --- p.26 / Chapter 3.1.3 --- Static Behaviour --- p.28 / Chapter 3.1.4 --- Dynamic Behaviour --- p.30 / Chapter 3.2 --- Performance Comparisons --- p.32 / Chapter 3.2.1 --- With the LMSTDE --- p.32 / Chapter 3.2.2 --- With the CATDE --- p.34 / Chapter 3.2.3 --- With the CRLB --- p.35 / Chapter 3.3 --- Simulation Results --- p.38 / Chapter 3.3.1 --- Corroboration of the ETDE Performance --- p.38 / Chapter 3.3.2 --- Comparative Studies --- p.44 / Chapter 3.4 --- Summary --- p.48 / Chapter 4 --- An Improvement to the ETDE --- p.49 / Chapter 4.1 --- Delay Modeling Error of the ETDE --- p.49 / Chapter 4.2 --- The Explicit Time Delay and Gain Estimator (ETDGE) --- p.52 / Chapter 4.3 --- Performance Analysis --- p.55 / Chapter 4.4 --- Simulation Results --- p.57 / Chapter 4.5 --- Summary --- p.61 / Chapter 5 --- TDE in the Presence of Multipath Propagation --- p.62 / Chapter 5.1 --- The Multipath TDE problem --- p.63 / Chapter 5.2 --- TDE with Multipath Cancellation (MCTDE) --- p.64 / Chapter 5.2.1 --- Structure and Algorithm --- p.64 / Chapter 5.2.2 --- Convergence Dynamics --- p.67 / Chapter 5.2.3 --- The Generalized Multipath Cancellator --- p.70 / Chapter 5.2.4 --- Effects of Additive Noises --- p.73 / Chapter 5.2.5 --- Simulation Results --- p.74 / Chapter 5.3 --- TDE with Multipath Equalization (METDE) --- p.86 / Chapter 5.3.1 --- The Two-Step Algorithm --- p.86 / Chapter 5.3.2 --- Performance of the METDE --- p.89 / Chapter 5.3.3 --- Simulation Results --- p.93 / Chapter 5.4 --- Summary --- p.101 / Chapter 6 --- Conclusions and Suggestions for Future Research --- p.102 / Chapter 6.1 --- Conclusions --- p.102 / Chapter 6.2 --- Suggestions for Future Research --- p.104 / Appendices --- p.106 / Chapter A --- Derivation of (3.20) --- p.106 / Chapter B --- Derivation of (3.29) --- p.110 / Chapter C --- Derivation of (4.14) --- p.111 / Chapter D --- Derivation of (4.15) --- p.113 / Chapter E --- Derivation of (5.21) --- p.115 / Chapter F --- Proof of unstablity of A°(z) --- p.116 / Chapter G --- Derivation of (5.34)-(5.35) --- p.118 / Chapter H --- Derivation of variance of αs11(k) and Δs11(k) --- p.120 / Chapter I --- Derivation of (5.40) --- p.123 / Chapter J --- Derivation of time constant of αΔ11(k) --- p.124 / Chapter K --- Derivation of (5.63)-(5.66) --- p.125 / Chapter L --- Derivation of (5.68)-(5.72) --- p.129 / References --- p.133

by Wan, Kwok Fai. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 138-148). / Chapter Chapter 1. --- Adaptive signal processing and its applications --- p.1 / Chapter 1.1. --- Introduction --- p.1 / Chapter 1.2. --- Applications of adaptive system --- p.3 / Chapter 1.2.1. --- Adaptive noise cancellation --- p.3 / Chapter 1.2.2. --- Adaptive echo cancellation --- p.5 / Chapter 1.2.3. --- Adaptive line enhancement --- p.5 / Chapter 1.2.4. --- Adaptive linear prediction --- p.7 / Chapter 1.2.5. --- Adaptive system identification --- p.8 / Chapter 1.3. --- Algorithms for adaptive systems --- p.10 / Chapter 1.4. --- Transform domain adaptive filtering --- p.12 / Chapter 1.5 --- The motivation and organization of the thesis --- p.13 / Chapter Chapter 2. --- Time domain split-path adaptive filter --- p.16 / Chapter 2.1. --- Adaptive transversal filter and the LMS algorithm --- p.17 / Chapter 2.1.1. --- Wiener-Hopf solution --- p.17 / Chapter 2.1.2. --- The LMS adaptive algorithm --- p.20 / Chapter 2.2. --- Split structure adaptive filtering --- p.23 / Chapter 2.2.1. --- Split structure of an adaptive filter --- p.24 / Chapter 2.2.2. --- Split-path structure for a non-symmetric adaptive filter --- p.25 / Chapter 2.3. --- Split-path adaptive median filtering --- p.29 / Chapter 2.3.1. --- Median filtering and median LMS algorithm --- p.29 / Chapter 2.3.2. --- The split-path median LMS (SPMLMS) algorithm --- p.32 / Chapter 2.3.3. --- Convergence analysis of SPMLMS --- p.36 / Chapter 2.4. --- Computer simulation examples --- p.41 / Chapter 2.5. --- Summary --- p.45 / Chapter Chapter 3. --- Multi-stage split structure adaptive filtering --- p.46 / Chapter 3.1. --- Introduction --- p.46 / Chapter 3.2. --- Split structure for a symmetric or an anti-symmetric adaptive filter --- p.48 / Chapter 3.3. --- Multi-stage split structure for an FIR adaptive filter --- p.56 / Chapter 3.4. --- Properties of the split structure LMS algorithm --- p.59 / Chapter 3.5. --- Full split-path adaptive algorithm for system identification --- p.66 / Chapter 3.6. --- Summary --- p.71 / Chapter Chapter 4. --- Transform domain split-path adaptive algorithms --- p.72 / Chapter 4.1. --- Introduction --- p.73 / Chapter 4.2. --- general description of transforms --- p.74 / Chapter 4.2.1. --- Fast Karhunen-Loeve transform --- p.75 / Chapter 4.2.2. --- Symmetric cosine transform --- p.77 / Chapter 4.2.3. --- Discrete sine transform --- p.77 / Chapter 4.2.4. --- Discrete cosine transform --- p.78 / Chapter 4.2.5. --- Discrete Hartley transform --- p.78 / Chapter 4.2.6. --- Discrete Walsh transform --- p.79 / Chapter 4.3. --- Transform domain adaptive filters --- p.80 / Chapter 4.3.1. --- Structure of transform domain adaptive filters --- p.80 / Chapter 4.3.2. --- Properties of transform domain adaptive filters --- p.83 / Chapter 4.4. --- Transform domain split-path LMS adaptive predictor --- p.84 / Chapter 4.5. --- Performance analysis of the TRSPAF --- p.93 / Chapter 4.5.1. --- Optimum Wiener solution --- p.93 / Chapter 4.5.2. --- Steady state MSE and convergence speed --- p.94 / Chapter 4.6. --- Computer simulation examples --- p.96 / Chapter 4.7. --- Summary --- p.100 / Chapter Chapter 5. --- Tracking optimal convergence factor for transform domain split-path adaptive algorithm --- p.101 / Chapter 5.1. --- Introduction --- p.102 / Chapter 5.2. --- The optimal convergence factors of TRSPAF --- p.104 / Chapter 5.3. --- Tracking optimal convergence factors for TRSPAF --- p.110 / Chapter 5.3.1. --- Tracking optimal convergence factor for gradient-based algorithms --- p.111 / Chapter 5.3.2. --- Tracking optimal convergence factors for LMS algorithm --- p.112 / Chapter 5.4. --- Comparison of optimal convergence factor tracking method with self-orthogonalizing method --- p.114 / Chapter 5.5. --- Computer simulation results --- p.116 / Chapter 5.6. --- Summary --- p.121 / Chapter Chapter 6. --- A unification between split-path adaptive filtering and discrete Walsh transform adaptation --- p.122 / Chapter 6.1. --- Introduction --- p.122 / Chapter 6.2. --- A new ordering of the Walsh functions --- p.124 / Chapter 6.3. --- Relationship between SM-ordered Walsh function and other Walsh functions --- p.126 / Chapter 6.4. --- Computer simulation results --- p.132 / Chapter 6.5. --- Summary --- p.134 / Chapter Chapter 7. --- Conclusion --- p.135 / References --- p.138

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.