Thesis (Ph. D.)--Oklahoma State University, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--Oklahoma State University, 2006. / Vita. Includes bibliographical references.

Thesis (M. S.)--Oklahoma State University, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--Oklahoma State University, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--Oklahoma State University, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--Oklahoma State University, 2006. / Vita. Includes bibliographical references.

This thesis presents techniques that suppress the multiple access interference (MAI) in CDMA wireless systems. MAI is the main factor that influences the communication quality and the capacity in CDMA wireless systems. Hence the suppression of MAI is essential to the performance of a CDMA wireless system. For conventional CDMA systems where matched filters are used as receivers, the only MAI suppression method available is the power control, which allocates each user in the system an appropriate transmitter power level such that the transmitter power is minimized to decrease the MAI, while at the same time each user maintains a given SIR requirement. Another MAI suppression method that has received much attention is the multiuser detection, which employs more complex receivers than the matched filters and uses signal processing techniques to suppress the MAI. These two methods form the basis for MAI suppression in CDMA wireless systems. In this thesis, we first investigate the power control method. A decentralized adaptive power control algorithm which requires only the received signal and the signature sequence of the desired user is discussed. Then the multiuser detection method is discussed. A blind adaptive multiuser detection algorithm that requires the same knowledge as matched filters to demodulate received signals is presented. Both theoretic study and simulation results show the effectiveness of these algorithms. Finally, power control and multiuser detection are combined together within the same system model. A power controlled multiuser detection algorithm is proposed, which preserves the decentralized property and is shown to be effective in simulation studies. Simulation results also show that this algorithm is superior to conventional power control algorithm and multiuser detection algorithm in terms of total transmitter power and more relaxed requirement on the SIR targets of the system.

The Minimum-degree Pole Placement algorithm for Self-tuning Regulator design and the Recursive Least-square method and the projection algorithm for plant estimation are studied first in this thesis. Simulation studies for the estimator and controller algorithms are mainly undertaken after describing how to use MATLAB S-function in detail. Not only do Simulation experiments illustrates how and how well the MDPP and RLS algorithms work, but also show how to write and debug MATLAB codes for S-function programs. The robustness of the adaptive control system is intensively discussed subsequently. By using an estimator resistant to the noise contamination, the adaptive control system can not be destablized by the introduced noise at the input of the plant or the estimator. However, the adaptive control system is subject to the unmodeled dynamics that have a magnitude response like an impulse at the crossover frequency of the system. Simulation results also show that a classic feedback controller has a better performance, compared with the adaptive controller.

The problem of computing linear convolution is a very important one because with linear convolution we can mechanize digital filtering. The linear convolution of two N-point sequences can be computed by the cyclic convolution of the following 2N-point sequences. The original sequence padded with N zeros each. The cyclic convolution of two N-point sequences requires multiplications and additions for its computation. A very efficient way of computing cyclic convolution of two sequences is by using the Polynomial Residue Number System (PRNS) technique. Using this technique the cyclic convolution of two N-point sequences can be computed using only N multiplications instead of N2 multiplications. This can be achieved based on some forward and inverse PRNS transformation mappings. These mappings rely on additions, subtractions and many scaling operations (multiplications by constants). The PRNS technique would lose a lot in value if these many scaling operations were difficultly implemented. In this thesis we will show how to calculate cyclic convolution of two sequences using the PRNS technique based on forward and inverse transformation mapping which rely on complement operations (negations), additions and rotation operations. These rotation operations do not require any computational hardware. Therefore the complicated hardware required for the scaling operations has now been substituted by rotators, which do not require any computational hardware.

The Hamilton-Jacobi equation (HJE) arose early in the last century in the study of the calculus of variation, classical mechanics and Hamiltonian systems. Recently, there has been a renewed interest in HJEs arising in various analysis and synthesis problems in systems theory. The HJE despite providing a necessary and sufficient condition for an optimal control, is very difficult to solve for general nonlinear systems, and therefore its application remained limited to linear systems. Yet, the HJE has been studied extensively in the literature from diverse areas of science and engineering, varying from mathematical physics, to mechanics, control theory, and to partial differential equations. In this dissertation, some analytical approaches for solving the HJEs arising in H_∞, mixed H₂/H_∞ and H₂ control problems for nonlinear systems are developed. Two major approaches are presented. The first approach is essentially an inversion or factorization method, and involves solving the HJE like a scalar quadratic algebraic equation with the gradient of the smooth scalar function as unknown. Since the HJE is a quadratic equation in the gradient of the unknown scalar function, we obtain two parameterized solutions which represent a parameterization of all solutions to the HJE. Thus, the problem is reduced to that of factorization of a scalar algebraic equation which we call the <i>discriminant equation</i> (or inequality). The main difficulties with this approach however are: (i) even after obtaining a solution to the discriminant equation, there is no guarantee that the gradient vector obtained subsequently represents a scalar function (i.e. represents a symmetric solution to the HJE); and (ii) there is no guarantee that the resulting solution is positive-definite. However, these difficulties can still be overcome by some additional constraints to the problem. Computational procedures for determining symmetric elementary solutions are then presented. The second approach involves converting the first-order HJ partial differential equation (PDE) to a second-order PDE. Then using a suitable parameterization, this second-order PDE is converted to a coupled system of higher-order nonlinear PDEs which can be solved using some available SYMBOLIC manipulation packages or by other methods. In general, there are no systematic procedures for solving the resulting system of higher-order PDEs, but various ad-hoc procedures can be used. This presents the most serious limitations of the approach. Both the time-varying and time-invariant systems are considered.