In this thesis channel capacity of a special type of multiple-input multiple-output (MIMO) Rayleigh fading channels is studied, where the transmitters are subject to a finite phase-shift keying (PSK) input alphabet. The constraint on the input alphabet makes an analytical solution for the capacity beyond reach. However we are able to simplify the final expression, which requires a single expectation and thus can be evaluated easily through simulation. To facilitate simulations, analytical expressions are derived for the eigenvalues and eigenvectors of a covariance matrix involved in the simplified capacity expression. The simplified expression is used to provide some good approximations to the capacity at low signal-to-noise ratios (SNRs). Involved in derivation of the capacity is the capacity-achieving input distribution. It is proved that a uniform prior distribution is capacity achieving. We also show that it is the only capacity-achieving distribution for our channel model. On top of that we generalize the uniqueness case for an input distribution to a broader range of channels.

To satisfy the growing demands of the mobile and personal broadband communications, recently, many innovative technologies have been devised and extensively used for wireless transmission and reception. In the wireless communication systems, even though the performance would be degraded due to channel characteristics, such as multipath fading and background noise, those impacts can be eliminated dramatically through the utilization of diversity and combining. However, some different kinds of interfering sources, including the significant structure interference due to their operation as multiple access in the cellular communication systems, referred to as the multiple access interference (MAI), and inevitable jammers appeared in the overlapped frequency band for common utility, are still existing and now become the main difficulties to collapse the reception performance and system capacity. To suppress the interferences, some advanced signal processing methods, e.g., smart antenna (SA), multiuser detection, interference cancellation, adaptive optimization, and frequency/ frame synchronization, have been suggested to not only alleviate the effects fundamentally but also enhance the signal quality. Orthogonal frequency division multiplexing (OFDM) is a significant multicarrier (MC) technology, and has been widely employed in some commercial communications, such as digital broadcasting and wireless local area network (WLAN). It is considered to be the one of the most promising techniques to combat multipath fading and MAI for the downlinks transmission of the broadband systems. Moreover, spatial processing exploits the diversity provided by SA or intelligent antenna arrays, in which the adaptive beamformer is utilized, and it is an alternative approach to increase the efficiency of wireless system capacity and performance without allocating additional frequency spectrum. It allows the system to make full use of spatial diversity due to multiple antennas. In this dissertation, the wireless communications based on the OFDM technique and the applications of SA are considered. Also, an adaptive linearly constrained (LC) approach via inverse QR-decomposition (IQRD) recursive least-squares (RLS) algorithm is emphasized. The proposed LC-IQRD-RLS algorithm has the merits, such as numerical stability, fast convergence rate, and implementation efficiency, over the conventional adaptive algorithms. Furthermore, by incorporating with derivative constraint, the narrowband array could improve the robustness against to the wideband and coherent jammers. Here, the iterative quadratic maximum likelihood (IQML) algorithm with norm constraint set is utilized to estimate the jammer subspace. Computer simulations verify that the use of narrowband beamformer with an appropriate algorithm, e.g., LC-IQRD-RLS or IQML, could achieve the desired performance for jammer suppression. Next, their applications to the MC-CDMA system with frequency combining process will be fully addressed. In fact, the frequency diversity is achieved through the optimization approach, based on constrained minimum output energy (CMOE) criterion. Unfortunately, it is very sensitive to the signal mismatch due to channel estimation error. To deal with the mismatch problem, the invariant-property provided by constant modulus (CM) criterion along with the LC-IQRD-RLS algorithm is developed. Simulation results show that the frequency combiner with the robust LCCM IQRD-RLS algorithm could be used to recover the transmitted signal without channel mismatch or distortion, and mitigate the MAI efficiently even in the significant near-far effect environment. To further enhance the detection performance and increase system capacity, the space-time MC-CDMA receiver is proposed by combining the advantages of SA and multicarrier transmission technique. This direct fully space-time MC-CDMA receiver can be implemented via a mathematical operator, i.e., kronecker product. For further investigation, a theoretical analysis could be evaluated under certain assumptions to obtain a closed-form expression of bit error rate (BER). This will help us look more inside the impacts due to the numbers of subcarriers and array sensors. In the last chapter, the familiar problem of carrier frequency offset (CFO) is investigated following the standard of IEEE 802.11 a/g OFDM-based WLAN. The overall frequency synchronization scheme consists of three parts, viz., the coarse and fine automatic frequency control (AFC) circuits, and phase locked loop (PLL). With the proposed frequency synchronization scheme, it reserves 2dB power consumption compared with the current specification even some timing issues presented.

There are many novel techniques have been invented to provide high-data rate with high quality communication services for future wireless communications systems. Recently, a novel digital modulation technology for multiple accesses, referred to as the Multi-Carrier Code Division Multiple Access (MC-CDMA), has been proposed to support high data rate transmission; it is based on the combination of CDMA and orthogonal frequency division multiplexing (OFDM). The MC-CDMA has been shown to be an effective technique for combating multipath fading. With MC-CDMA system, a user¡¦s spreading code can be modulated on separate subcarriers, undergo frequency-flat fading channel and offers frequency diversity advantage. But in a multi-user environment, othogonality among spreading codes is severely distorted due to multipath delay spread, such that the system capacity will be limited by the multiple access interferences (MAI). Similar situations exist due to possible narrowband interference (NBI) from other systems. Effective interference reduction will render system capacity to increase, which means interference suppression techniques are vital in improving overall system performance. In this thesis, we propose a new linearly constrained recursive least square algorithm, with diagonal loading approach, referred to as the DL-LC RLS algorithms, to further improve the system performance. The proposed diagonal loading RLS algorithm is different from conventional diagonal loading RLS algorithm, in which the diagonal loading was used to improve the robustness to pointing errors in beamforming problem. However, in this thesis, the diagonal loading approach could be used to alleviate the effect due to multiple access interference (MAI), such that under certain circumstances, better performance could be achieved. Basically, in the proposed algorithm, the power of interference plus noise of received signal will be estimated and subtracted from the diagonal terms of the autocorrelation matrix of received signal. After that instead of using the original autocorrelation matrix, the new correlation matrix, with subtracting power related to the interference plus noise, will be involved during the adaptation processes for updating the weights of the multi-user detector. Finally, computer simulation results, in terms of bit error rate, are used to demonstrate the merits of the proposed scheme compared with the conventional RLS algorithm approach without using the diagonal approaches.

The traveling salesman problem (TSP) is defined as: given a finite number of cities along with the cost of travel between each pair of them, find the cheapest way of visiting all the cities only once and returning to your starting city. Some variants of TSP are proposed to visit cities depending on the profit gained when the visit occurs. In literature, these kind of problems are named TSP with profit. In TSP with profit, there are two conflicting objectives, one to collect profit and the other to decrease traveling cost. In literature, TSP with profit are addressed as single objective, either two objectives are combined linearly or one objective is constrained with a specified bound. In this study, a multiobjective approach is developed by combining &amp / #949 / -constrained method and heuristics from the literature in order to find the efficient frontier for the TSP with profit. The performance of approach is tested on the problems studied in the literature. Also an interactive software is developed based on the multiobjective approach.

The classical multiple knapsack problem selects a set of items and assigns each to one of the knapsacks so as to maximize the total profit. The knapsacks have limited capacities. The cardinality constrained multiple knapsack problem assumes limits on the number of items that are to be put in each knapsack, as well. Despite many efforts on the classical multiple knapsack problem, the research on the cardinality constrained multiple knapsack problem is scarce. In this study we consider the cardinality constrained multiple knapsack problem. We propose heuristic and optimization procedures that rely on the optimal solutions of the linear programming relaxation problem. Our computational results on the large-sized problem instances have shown the satisfactory performances of our algorithms.

In this work, Schr&ouml / dinger and Dirac equations will be examined in geometries that confine the particles to hypersurfaces. For this purpose, two methods will be considered. The first method is the thin layer method which relies on explicit use of geometrical relations and the squeezing of a certain coordinate of space (or spacetime). The second is Dirac&rsquo / s quantization procedure involving the modification of canonical quantization making use of the geometrical constraints. For the Dirac equation, only the first method will be considered. Lastly, the results of the two methods will be compared and some notes on the differences between the results will be included.

Fear of crime is a phenomenon which affects individuals&#039 / standard of living and influences their everyday behaviors. In this sense, it can be said that if a person has high fear of crime, this will have a negative effect on his or her standard of living. Fear of crime does not always bear resemblance to the crime rate of the society. From this standpoint, residents of a region where crime rate is high do not always have high fear of crime. Similarly, the residents of a region where crime rate is low may have high fear of crime. This situation points out the need of an extensive analysis on fear of crime as a significant variable regarding individuals&#039 / standard of living. This study aims to examine the relationship between perceived risk of victimization and fear of crime. Studies about fear of crime mainly focus on gender differences, social inequalities and physical incivilities. all of this factor are important element to grasp its nature and dimensions of fear of crime. In addition to this factors fear of crime is affected by individuals risk perception of victimization. Our study aims to deal fear of crime concept among students in a multidimensional approach. In this respect, it will evaluate how much the students are afraid of and uncomfortable with being exposed to a crime rather than the assessing merely the possibility of being exposed to a crime. The study will measure the concept of fear of crime over the concept of anticipated fear according to Ferraro&rsquo / s (1995) model. The advantage of this approach is that it allows the measurement of fear of crime the individuals show as a result of contacting other person and environment rather than the instantaneous fears. Our study will evaluate the Metu students&rsquo / fear of crime in terms of specific crimes rather than a general evaluation of crime in line with the approach of risk perception. In this sense, our study seeks to measure the fear of crime over certain crimes such as theft, robbery, simple attack, serious attack and sexual abuse.

Backward stochastic differential equations appear in many areas of research including mathematical finance, nonlinear partial differential equations, financial economics and stochastic control. The first existence and uniqueness result for nonlinear backward stochastic differential equations was given by Pardoux and Peng (Adapted solution of a backward stochastic differential equation. System and Control Letters, 1990). They looked for an adapted pair of processes {x(t) / y(t)} / t is in [0 / 1]} with values in Rd and Rd&times / k respectively, which solves an equation of the form: x(t) + int_t^1 f(s,x(s),y(s))ds + int_t^1 [g(s,x(s)) + y(s)]dWs = X. This dissertation studies this paper in detail and provides all the steps of the proofs that appear in this seminal paper. In addition, we review (Cvitanic and Karatzas, Hedging contingent claims with constrained portfolios. The annals of applied probability, 1993). In this paper, Cvitanic and Karatzas studied the following problem: the hedging of contingent claims with portfolios constrained to take values in a given closed, convex set K. Processes intimately linked to BSDEs naturally appear in the formulation of the constrained hedging problem. The analysis of Cvitanic and Karatzas is based on a dual control problem. One of the contributions of this thesis is an algorithm that numerically solves this control problem in the case of constant volatility. The algorithm is based on discretization of time. The convergence proof is also provided.

The technique of direct sequence spread spectrum (DS/SS) has been widely used in commercial mobile communication systems. The efficiency of DS/SS system is highly dependent on the accurate and fast synchronization between the incoming and locally generated PN (pseudo-noise) codes. The code synchronization is processed in two steps, acquisition (coarse alignment) and tracking (fine alignment), to bring the delay offset between the two codes. Conventionally, for code synchronization, most of techniques were proposed based on the correlation property of PN codes. Recently, the different approach, by using the adaptive LMS filtering scheme, has been proposed to reduce the hardware complexity and to improve the performance of code synchronization, especially for a long PN code. In this thesis, a new coherent adaptive code synchronization scheme is proposed, where the adaptive constrained LMS (CLMS) algorithm with the maximum tap-weight (MTW) test method is devised for code acquisition. The statistics of weight vector of the proposed CLMS scheme are derived to evaluate the performance, in terms of mean acquisition time (MAT). Analytical and simulation results verify that the proposed scheme for code acquisition outperforms the one using the conventional LMS filtering schemes, under the integer and non-integer time delay cases. Moreover, the setting of threshold value is derived for code acquisition, which is independent of the values of signal-to-noise ratio (SNR) and time delay. Next, the CLMS scheme is proposed associated with the direct delay estimation (DDE) formula for code tracking. This approach does achieve a good delay-tracking performance, which is verified via computer simulation. Simultaneously, the hardware complexity can further be reduced due to that a code-tracking loop implemented by the interpolation method is not required.

A spectral element algorithm for solution of the incompressible Navier-Stokes and heat transfer equations is developed, with an emphasis on extending the classical conforming Galerkin formulations to nonconforming spectral elements. The new algorithm employs both the Constrained Approximation Method (CAM), and the Mortar Element Method (MEM) for p-and h-type nonconforming elements. Detailed descriptions, and formulation steps for both methods, as well as the performance comparisons between CAM and MEM, are presented. This study fills an important gap in the literature by providing a detailed explanation for treatment of p-and h-type nonconforming interfaces. A comparative eigenvalue spectrum analysis of diffusion and convection operators is provided for CAM and MEM. Effects of consistency errors due to the nonconforming formulations on the convergence of steady and time dependent problems are studied in detail. Incompressible flow solvers that can utilize these nonconforming formulations on both p- and h-type nonconforming grids are developed and validated. Engineering use of the developed solvers are demonstrated by detailed parametric analyses of oscillatory flow forced convection heat transfer in two-dimensional channels.