Higher Transcendental Functions [Volumes I-III]

The work of which this book is the first volume might be described as an up-to-date version of Part II. The Transcendental Functions of Whittaker and Watson's celebrated "Modern Analysis". Bateman (who was a pupil of E. T. Whittaker) planned his "Guide to the Functions" on a gigantic scale. In addition to a detailed account of the properties of the most important functions, the work was to include the historic origin and definition of, the basic formulas relating to, and a bibliography for all special functions ever invented or investigated. These functions were to be catalogued and classified under twelve different headings according to their definition by power series, generating functions, infinite products, repeated differentiations, indefinite integrals, definite integrals, differential equations, difference equations, functional equations, trigonometric series, series of orthogonal functions, or integral equations. Tables of definite integrals representing each function and numerical tables of a few new functions were to form part of the "Guide". An extensive table of definite integrals and a Guide to numerical tables of special functions were planned as companion works

Distributed transmission schemes for wireless communication networks

In this thesis new techniques are presented to achieve performance enhancement in wireless cooperative networks. In particular, techniques to improve transmission rate and maximise end-to-end signal-to-noise ratio are described. An offset transmission scheme with full interference cancellation for a wireless cooperative network with frequency flat links and four relays is introduced. This method can asymptotically, as the size of the symbol block increases, achieve maximum transmission rate together with full cooperative diversity provided the destination node has multiple antennas. A novel full inter-relay interference cancellation method that also achieves asymptotically maximum rate and full cooperative diversity is then designed for which the destination node only requires a single antenna. Two- and four-relay selection schemes for wireless cooperative amplify and forward type networks are then studied in order to overcome the degradation of end-to-end bit error rate performance in single-relay selection networks when there are feedback errors in the relay to destination node links. Outage probability analysis for a four-relay selection scheme without interference is undertaken. Outage probability analysis of a full rate distributed transmission scheme with inter-relay interference is also studied for best single- and two-relay selection networks. The advantage of multi-relay selection when no interference occurs and when adjacent cell interference is present at the relay nodes is then shown theoretically. Simulation results for outage probability analysis are included which support the theoretical expressions. Finally, outage probability analysis of a cognitive amplify and forward type relay network with cooperation between certain secondary users, chosen by best single-, two- and four-relay selection is presented. The cognitive amplify and forward relays are assumed to exploit an underlay approach, which requires adherence to an interference constraint on the primary user. The relay selection scheme is performed either with a max−min strategy or one based on maximising exact end-to-end signal-to-noise ratio. The outage probability analyses are again confirmed by numerical evaluations

Rate enhancement and multi-relay selection schemes for application in wireless cooperative networks

In this thesis new methods are presented to achieve performance enhancement in wireless cooperative networks. In particular, techniques to improve transmission rate, mitigate asynchronous transmission and maximise end-to-end signal-to-noise ratio are described. An offset transmission scheme with full interference cancellation for a two-hop synchronous network with frequency flat links and four relays is introduced. This approach can asymptotically, as the symbol block size increases, achieve maximum transmission rate together with full cooperative diversity provided the destination node has multiple antennas. A novel full inter-relay interference cancellation method that also achieves asymptotically maximum rate and full cooperative diversity is then designed which only requires a single antenna at the destination node. Extension to asynchronous networks is then considered through the use of orthogonal frequency division multiplexing (OFDM) type transmission with a cyclic prefix, and interference cancellation techniques are designed for situations when synchronization errors are present in only the second hop or both the first and second hop. End-to-end bit error rate evaluations, with and without outer coding, are used to assess the performance of the various offset transmission schemes. Multi-relay selection methods for cooperative amplify and forward type networks are then studied in order to overcome the degradation of end-to-end bit error rate performance in single-relay selection networks when there are feedback errors in the destination to relay node links. Outage probability analysis for two and four relay selection is performed to show the advantage of multi-relay selection when no interference occurs and when adjacent cell interference is present both at the relay nodes and the destination node. Simulation studies are included which support the theoretical expressions. Finally, outage probability analysis of a cognitive amplify and forward type relay network with cooperation between certain secondary users, chosen by single and multi-relay (two and four) selection is presented. The cognitive relays are assumed to exploit an underlay approach, which requires adherence to an interference constraint on the primary user. The relay selection is performed either with a max-min strategy or one based on maximising exact end-to-end signal-to-noise ratio. The analyses are again confirmed by numerical evaluations

Contributions to statistical distribution theory

Thesis (D.Sc.)--University of Adelaide, Dept. of Mathematical Sciences, 198