In wireless communications, channel estimation is necessary for coherent symbol detection. This thesis considers a network which consists of two transceivers communicating with the help of a relay applying the amplify-and-forward (AF) relaying scheme. The training based channel estimation technique is applied to the proposed network where the numbers of the training sequence transmitted by the two transceivers, are different. All three terminals are equipped with a single antenna for signal transmission and reception. Communication between the transceivers is carried out in two phases. In the first phase, each transceiver sends a transmission block of data embedded with known training symbols to the relay. In the second phase, the relay retransmits an amplified version of the received signal to both transceivers. Estimates of the channel coefficients are obtained using the Maximum Likelihood (ML) estimator. The performance analysis of the derived estimates are carried out in terms of the mean squared error (MSE) and we determine conditions required to increase the estimation accuracy. / UOIT

A linear periodically time-varying (LPTV) system is a linear time-varying system with the coefficients changing periodically, which is widely used in control, communications, signal processing, and even circuit modeling. This thesis concentrates on identification of LPTV systems. To this end, the representations of LPTV systems are thoroughly reviewed. Identification methods are developed accordingly. The usefulness of the proposed identification methods is verified by the simulation results.<p> A periodic input signal is applied to a finite impulse response (FIR)-LPTV system and measure the noise-contaminated output. Using such periodic inputs, we show that we can formulate the problem of identification of LPTV systems in the frequency domain. With the help of the discrete Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. A sufficient condition for the identifiability of LPTV systems is given, which can be used to find appropriate inputs for the purpose of identification.<p> In the frequency domain, we show that the input and the output can be related by using the discrete Fourier transform (DFT) and a least-squares method can be used to identify the alias components. A lower bound on the mean square error (MSE) of the estimated alias components is given for FIR-LPTV systems. The optimal training signal achieving this lower MSE bound is designed subsequently. The algorithm is extended to the identification of infinite impulse response (IIR)-LPTV systems as well. Simulation results show the accuracy of the estimation and the efficiency of the optimal training signal design.

Idrottsparken roundabout in Norrkoping is located in the more dense part of the city.Congestion occurs in peak hours causing queue and extended travel time. This thesis aims to provide alternative model to reduce queue and travel time. Types ofobservation data are flow, length of queue, and travel time that are observed during peakhours in the morning and afternoon. Calibration process is done by minimising root meansquare error of queue, travel time, and combination both of them between observation andcalibrated model. SUMO version 0.14.0 is used to perform the microsimulation. There are two proposed alternatives, namely Scenario 1: the additional lane for right turnfrom East leg to North and from North leg to West and Scenario 2: restriction of heavy goodsvehicles passing Kungsgatan which is located in Northern leg of Idrottsparken roundaboutduring peak hours. For Scenario 1, the results from SUMO will be compared with AIMSUNin terms of queue and travel time. The result of microsimulation shows that parameters that have big influence in the calibrationprocess for SUMO are driver imperfection and driver’s reaction time, while for AIMSUN isdriver’s reaction time and maximum acceleration. From analysis found that the model of thecurrent situation at Idrottsparken can be represented by model simulation which usingcombination between root mean square error of queue and travel time in calibration andvalidation process. Moreover, scenario 2 is the best alternative for SUMO because itproduces the decrease of queue and travel time almost in all legs at morning and afternoonpeak hour without accompanied by increase significant value of them in the other legs. Thecomparison between SUMO and AIMSUN shows that, in general, the AIMSUN has higherchanges value in terms of queue and travel time due to the limited precision in SUMO forroundabout modelling.

A linear periodically time-varying (LPTV) system is a linear time-varying system with the coefficients changing periodically, which is widely used in control, communications, signal processing, and even circuit modeling. This thesis concentrates on identification of LPTV systems. To this end, the representations of LPTV systems are thoroughly reviewed. Identification methods are developed accordingly. The usefulness of the proposed identification methods is verified by the simulation results.<p> A periodic input signal is applied to a finite impulse response (FIR)-LPTV system and measure the noise-contaminated output. Using such periodic inputs, we show that we can formulate the problem of identification of LPTV systems in the frequency domain. With the help of the discrete Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. A sufficient condition for the identifiability of LPTV systems is given, which can be used to find appropriate inputs for the purpose of identification.<p> In the frequency domain, we show that the input and the output can be related by using the discrete Fourier transform (DFT) and a least-squares method can be used to identify the alias components. A lower bound on the mean square error (MSE) of the estimated alias components is given for FIR-LPTV systems. The optimal training signal achieving this lower MSE bound is designed subsequently. The algorithm is extended to the identification of infinite impulse response (IIR)-LPTV systems as well. Simulation results show the accuracy of the estimation and the efficiency of the optimal training signal design.

The binary response experiments are often used in many areas. In many investigations, different kinds of optimal designs are discussed under an assumed model. There are also some discussions on optimal designs for discriminating models. The main goal in this work is to find an optimal design with two support points which minimizes the maximal probability differences between possible models from two types of symmetric location and scale families. It is called the minimum bias two-points design, or the $mB_2$ design in short here. D- and A-efficiencies of the $mB_2$ design obtained here are evaluated under an assumed model. Furthermore, when the assumed model is incorrect, the biases and the mean square errors in evaluating the true probabilities are computed and compared with that by using the D- and A-optimal designs for the incorrectly assumed model.

Motion estimation is the key issue in video compressing. Several methods for motion estimation based on the center biased strategy and minimum mean square error trend searching have been proposed, such as TSS, FSS, UCBDS and MIBAS, but these methods yield poor estimates or find local minima. Many other methods predict the starting point for the estimation, these can be fast but are inaccurate. This study addresses the causes of wrong estimates, local minima and incorrect predictions in the prior estimation methods. The Multiple Searching Trend (MST) is proposed to overcome the problems of ineffective searches and local minima, and the Adaptive Dilated Searching Field (ADSF) is described to prevent prediction from wrong location. Applying MST and ADSF to the listed estimating methods, such as UCBDS, a fast and accurate can be reached. For this this reason, the method is called CockTail Searching (CTS). In another proposed method, we try to define the new criteria used to determine a referent macro block within the search window in a referent frame, which matches the estimated current macro block in the current frame, in motion estimation process used in MPEG standard. The Prediction Error(PE) in the Pixel Difference(PD) between the referent macro block and the current macro block is defined to be a new criterion which can get better performance in compressed data length than the Mean Square Error(MSE) used by most of motion estimation methods. The other criterion combined PE and MSE is proposed to get better performance than the PE. Two new criteria is applied to a famous motion estimation method, UCBDS, to show the performance of the new criteria. The evaluation results show that using new criteria in UCBDS can get more 40% reduction in compressed data size than the UCBDS with MSE.

This paper is concerned with the problem of finding an experimental design for discrimination between two rival models and for model robustness that minimizing the maximum bias simultaneously in binary response experiments. The criterion for model discrimination is based on the $T$-optimality criterion proposed in Atkinson and Fedorov (1975), which maximizes the sum of squares of deviations between the two rival models while the criterion for model robustness is based on minimizing the maximum probability bias of the two rival models. In this paper we obtain the optimum designs satisfy the above two criteria for some commonly used rival models in binary response experiments such as the probit and logit models etc.

In recent year, tidal gauge has progressed in temporal resolution or measurement accuracy, so that the quality of observational data tends to stable and reliable. However, setting up tidal gauge in the offshore areas restricts may apply due to many factors such as seabed topography, weather, sea state and leveling survey from land to gauge. Good tidal correction is one of key factors to the accuracy of bathymetric survey and to the area where tidal range is large. This study tried to use tide prediction data derived from the Yu(1993)¡¦s tide numerical model and verified with actual observed tide data, and further establishing a tidal zone of Taiwan Strait by tidal characteristic. Using Taichung and Mailiao tide stations as a reference tidal station, the direct tide station correction, tidal zone correction, nearest model grid correction, and virtual station correction methods were applied to evaluate the accuracy of tide calculating value by amplitude ratio and tidal phase difference. The tidal zone correction is not totally depending on the spatial distance from reference tidal station, and it is found that correction result of this approach is one of the best. However, further improvement in tide correction may need to explore due to different spatial resolution applied in different numerical models. In addition, the boundary condition of a harbor for tidal model is very complicated. This is why it is hard to make a numerical model for a harbor. In this study, two additional high accuracy radar tidal gauge were installed in Kaohsiung harbor and first-class leveling survey was performed in order to maintain tidal measurement accuracy, also to avoid the effect of errors propagation. According to the results from experiment, average tidal phase of second entrance of the Kaohsiung harbor is earlier than that of first entrance about 6 minutes, and average difference of tidal height is approximately 2-3cm. For this reason, we should pay attention to decide a proper reference tide station for tidal correction for dredging hydrographic surveying. And any possible tidal observation errors, such as meteorological tide. If two additional tidal gauges of this study are removed in the future, we still can predict tide height from fixed tidal gauge.

In the field of signal processing, one of the underlying enemies in obtaining a good quality signal is noise. The most common examples of signals that can be corrupted by noise are images and audio signals. Since the early 1980's, a time when wavelet transformations became a modernly defined tool, statistical techniques have been incorporated into processes that use wavelets with the goal of maximizing signal-to-noise ratios. We provide a brief history of wavelet theory, going back to Alfréd Haar's 1909 dissertation on orthogonal functions, as well as its important relationship to the earlier work of Joseph Fourier (circa 1801), which brought about that famous mathematical transformation, the Fourier series. We demonstrate how wavelet theory can be used to reconstruct an analyzed function, ergo, that it can be used to analyze and reconstruct images and audio signals as well. Then, in order to ground the understanding of the application of wavelets to the science of denoising, we discuss some important concepts from statistics. From all of these, we introduce the subject of wavelet shrinkage, a technique that combines wavelets and statistics into a "thresholding" scheme that effectively reduces noise without doing too much damage to the desired signal. Subsequently, we discuss how the effectiveness of these techniques are measured, both in the ideal sense and in the expected sense. We then look at an illustrative example in the application of one technique. Finally, we analyze this example more generally, in accordance with the underlying theory, and make some conclusions as to when wavelets are an effective technique in increasing a signal-to-noise ratio.

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