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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

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.

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).

Thesis (Ph.D.)--Baylor University, 2008. / Includes bibliographical references (p. 70-74)

Thesis (Ph. D.)--Stanford University, 1987. / "June 1987." "Also numbered Classic-87-03"--Cover. "This research was supported by NASA Ames Consortium Agreement NASA NCA2-150 and Office of Naval Research Contracts N00014-86-K-0565, N00014-82-K-0335, N00014-75-C-1132"--P. vi. Includes bibliographical references (p. 125-129).

Thesis (M.S.)--Florida State University, 2004. / Advisor: Dr. Ashok Srinivasan, Florida State University, College of Arts and Sciences, Dept. of Computer Science. Title and description from dissertation home page (viewed Oct. 27, 2004). Includes bibliographical references.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2002. / Includes bibliographical references (leaves 86-91). Also available in electronic version. Access restricted to campus users.