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Time-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture the changes in these types of signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years, decomposition based analysis methods were developed by different researchers to deal with non-linear and non-stationary signals. These methods share the feature that a signal is decomposed into finite number of components on which the time-frequency analysis can be applied. Differences lie in the strategies to extract these components: by iteration or by optimization. However, considering the requirements of being local, adaptive and stable, neither of these decompositions are perfectly satisfactory. Motivated to find a local, adaptive and stable decomposition of a signal, this thesis presents Adaptive Local Iterative Filtering (ALIF) algorithm. The adaptivity is obtained having the filter lengths being determined by the signal itself. The locality is ensured by the filter we designed based on a PDE model. The stability of this algorithm is shown and the convergence is proved. Moreover, we also propose a local definition for the instantaneous frequency in order to achieve a completely local analysis for non-linear and non-stationary signals. Examples show that this decomposition really helps in both simulated data analysis and real world application.

This thesis is an investigation of the sequence of functions defined by fl (x) -xand fn+1 (x) -x , where the power is the principal value.In the case where the sequence is restricted to positive real this sequence of functions over thecomplex plane, we attack real numbers, the problem yields to the methods of analysis and we prove the behavior of the sequence.The more general problem of describing the behavior of both analytically and numerically. Though no full rigorous solution is given, the results presented suggest the behavior of the sequence over the complex plane is very interesting. / Department of Mathematical Sciences

Panel data analysis has become an important tool in applied econometrics and the respective statistical techniques are well described in several recent textbooks. However, for an analyst using these methods there remains the task of choosing a reasonable model for the behavior of the panel data. Of special importance is the choice between so-called fixed and random coefficient models. This choice can have a crucial effect on the interpretation of the analyzed phenomenon, which is demonstrated by an application on research and development spillover. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

In this thesis we have presented an implementation of soft Multi Input Multi Output (MIMO) detection, single tree search algorithm on Graphics Processing Units (GPUs). We have compared its performance on different GPUs and a Central Processing Unit (CPU). We have also done a performance study of iterative decoding algorithms. We have shown that by increasing the number of outer iterations error rate performance can be further improved. GPUs are specialized devices specially designed to accelerate graphics processing. They are massively parallel devices which can run thousands of threads simultaneously. Because of their tremendous processing power there is an increasing interest in using them for scientific and general purpose computations. Hence companies like Nvidia, Advanced Micro Devices (AMD) etc. have started their support for General Purpose GPU (GPGPU) applications. Nvidia came up with Compute Unified Device Architecture (CUDA) to program its GPUs. Efforts are made to come up with a standard language for parallel computing that can be used across platforms. OpenCL is the first such language which is supported by all major GPU and CPU vendors. MIMO detector has a high computational complexity. We have implemented a soft MIMO detector on GPUs and studied its throughput and latency performance. We have shown that a GPU can give throughput of up to 4Mbps for a soft detection algorithm which is more than sufficient for most general purpose tasks like voice communication etc. Compare to CPU a throughput increase of ~7x is achieved. We also compared the performances of two GPUs one with low computational power and one with high computational power. These comparisons show effect of thread serialization on algorithms with the lower end GPU's execution time curve shows a slope of 1/2. To further improve error rate performance iterative decoding techniques are employed where a feedback path is employed between detector and decoder. With an eye towards GPU implementation we have explored these algorithms. Better error rate performance however, comes at a price of higher power dissipation and more latency. By simulations we have shown that one can predict based on the Signal to Noise Ratio (SNR) values how many iterations need to be done before getting an acceptable Bit Error Rate (BER) and Frame Error Rate (FER) performance. Iterative decoding technique shows that a SNR gain of ~1:5dB is achieved when number of outer iterations is increased from zero. To reduce the complexity one can adjust number of possible candidates the algorithm can generate. We showed that where a candidate list of 128 is not sufficient for acceptable error rate performance for a 4x4 MIMO system using 16-QAM modulation scheme, performances are comparable with the list size of 512 and 1024 respectively.

The ever-increasing demand for higher information-transfer rates in wireless data networks invokes the need to develop more spectrally-efficient communication strategies. Techniques such as MIMO and turbo-coded CDMA are well known and obvious candidates for improving the spectral efficiency of next generation wireless networks, and addressing the limitations of currently implemented technologies. Correspondingly, such methods are finding their way into wireless network standards such as 3GPP and IEEE 802.20. / One measure of the size of a communication system is the number of independent data streams being transmitted simultaneously through a channel, assuming tight constraints on available bandwidth and signal power. Such data streams may originate from different users all wishing to communicate at once. In addition, each user may wish to transmit independent data on more than one antenna simultaneously in order to increase his or her own data rate. Although strategies for such multi-dimensional signalling have seen significant improvements in recent years, most of the techniques proposed in the literature still suffer from either poor performance or prohibitive complexity when the size of the system grows large. / This thesis is concerned primarily with supporting high system spectral-efficiencies in very large systems, while maintaining strong resistance to data errors with manageable complexity. / Iterative decoding, or Bayesian message-passing, is demonstrably able to approach closely the performance of an optical decoder for certain families of single-user error correction codes, with low computational complexity. The topic of this work, iterative list detection, is a technique for jointly decoding many independent data streams from multiple users and/or antennas, using powerful iterative decoding strategies developed for such single-user codes. The receiver strategies presented are based on the premise that iterative Bayesian decoding is capable of achieving performance very close to that of an optimal decoder for a multi-dimensional system, given certain assumptions on the system model. Other than this, iterative list detection makes no assumptions about the statistics of the interfering signals, linearity, or any other simplifying impositions. Rather, the method seeks only to approximate closely the probabilistic quantities dictated by the rules of the iterative decoding paradigm, which is by now well understood. / List detection itself refers to the computationally efficient calculation of signal probabilities conditioned on a noise-and-interference corrupted signal at the receiver, computed for each simultaneously transmitted signal. The calculation is the key step in the implementation of an iterative receiver for such a system. / After introducing the list detection strategy in the context of iterative receivers for multi-user MIMO channels, algorithms for optimal list detection are described. A new optimal list detection algorithm with some superior properties to other implementations in the literature is proposed. While still very computationally complex, performance results for optimal list detection are presented that demonstrate the effectiveness and utility of the paradigm, and provide a performance benchmark for any sub-optimal list detection technique. The performance is also compared with other techniques such as linear filters, providing an appreciation of the benefits of list detection. / An asymptotic large-systems analysis is then undertaken in order to determine the behaviour of a fundamental parameter that determines the complexity of list detection, specifically the number of terms in a certain summation. The minimum number of terms is derived under an accuracy constraint on the signal probabilities. Results demonstrate that the number of terms does not necessarily increase with the size of the system, and the conditions under which this is true are indicated. / The main contribution of the thesis is the development of a number or computationally efficient sub-optimal list detection algorithms. Various strategies are proposed for different system scenarios, resulting in near-optimal performance with complexity that adapts automatically to cope with changing channel conditions and interference. The performance of the new techniques is demonstrated via simulation in channels with various statistics, dimensionality and interference, showing significant improvements in terms of both error resistance and complexity over other proposed methods. / Thesis (PhDTelecommunications)--University of South Australia, 2004.

Doctor of Philosophy(PhD) / In this thesis, we propose and investigate promising approaches for interference mitigation in multiple input multiple output (MIMO) and code division multiple access (CDMA) systems. Future wireless communication systems will have to achieve high spectral efficiencies in order to meet increasing demands for huge data rates in emerging Internet and multimedia services. Multiuser detection and space diversity techniques are the main principles, which enable efficient use of the available spectrum. The main limitation for the applicability of the techniques in these practical systems is the high complexity of the optimal receiver structures. The research emphasis in this thesis is on the design of a low complexity interference suppression/cancellation algorithm. The most important result of our research is the novel design of interference cancellation receivers which are adaptive and iterative and which are of low computational complexity. We propose various adaptive iterative receivers, based on a joint adaptive iterative detection and decoding algorithm. The proposed receiver can effectively suppress and cancel co-channel interference from the adjacent antennas in the MIMO system with a low computation complexity. The proposed adaptive detector, based on the adaptive least mean square (LMS) algorithm, is investigated and compared with the non-adaptive iterative receiver. Since the LMS algorithm has a slow convergence speed, a partially filtered gradient LMS (PFGLMS) algorithm, which has a faster convergence speed, is proposed to improve the convergence speed of the system. The performance and computational complexity of this receiver are also considered. To further reduce the computational complexity, we apply a frequency domain adaptation technique into the adaptive iterative receivers. The system performance and complexity are investigated. It shows that the computational complexity of the frequency domain based receiver is significantly lower than that of the time domain based receiver with the same system performance. We also consider applications of MIMO techniques in CDMA systems, called MIMO-CDMA. In the MIMO-CDMA, the presence of the co-channel interference (CCI) from the adjacent antennas and multiple access interference (MAI) from other users significantly degrades the system performance. We propose an adaptive iterative receiver, which provides the capability to effectively suppress the interference and cancel the CCI from the adjacent antennas and the MAI from other users so as to improve the system performance. The proposed receiver structure is also based on a joint adaptive detection and decoding scheme. The adaptive detection scheme employs an adaptive normalized LMS algorithm operating in the time and frequency domain. We have investigated and compared their system performance and complexity. Moreover, the system performance is evaluated by using a semi-analytical approach and compared with the simulation results. The results show that there is an excellent agreement between the two approaches.

The ever-increasing demand for higher information-transfer rates in wireless data networks invokes the need to develop more spectrally-efficient communication strategies. Techniques such as MIMO and turbo-coded CDMA are well known and obvious candidates for improving the spectral efficiency of next-generation wireless networks, and addressing the limitations of currently implemented technologies. Correspondingly, such methods are finding their way into wireless network standards such as 3GPP and IEEE 802.20. One measure of the size of a communication system is the number of independent data streams being transmitted simultaneously through a channel, assuming tight constraints on available bandwidth and signal power. Such data streams may originate from different users all wishing to communicate at once. In addition, each user may wish to transmit independent data on more than one antenna simultaneously in order to increase his or her own data rate. Although strategies for such multi-dimensional signalling have seen significant improvements in recent years, most of the techniques proposed in the literature still suffer from either poor performance or prohibitive complexity when the size of the system grows large. This thesis is concerned primarily with supporting high systemspectral-efficiencies in very large systems, while maintaining strong resistance to data errors with manageable complexity. / thesis (PhDTelecommunications)--University of South Australia, 2004.

Thesis (Ph.D.)--Ohio University, November, 2007. / Title from PDF t.p. Includes bibliographical references.

Thesis (M.S.)--University of Alabama at Birmingham, 2008. / Description based on contents viewed Feb. 11, 2009; title from PDF t.p. Includes bibliographical references (p. 49-54).