Minimizing Communication for Eigenproblems and the Singular Value Decomposition

Algorithms have two costs: arithmetic and communication. The latter represents the cost of moving data, either between levels of a memory hierarchy, or between processors over a network. Communication often dominates arithmetic and represents a rapidly increasing proportion of the total cost, so we seek algorithms that minimize communication. In \cite{BDHS10} lower bounds were presented on the amount of communication required for essentially all $O(n^3)$-like algorithms for linear algebra, including eigenvalue problems and the SVD. Conventional algorithms, including those currently implemented in (Sca)LAPACK, perform asymptotically more communication than these lower bounds require. In this paper we present parallel and sequential eigenvalue algorithms (for pencils, nonsymmetric matrices, and symmetric matrices) and SVD algorithms that do attain these lower bounds, and analyze their convergence and communication costs.Comment: 43 pages, 11 figure

Generic Multiuser Coordinated Beamforming for Underlay Spectrum Sharing

The beamforming techniques have been recently studied as possible enablers for underlay spectrum sharing. The existing beamforming techniques have several common limitations: they are usually system model specific, cannot operate with arbitrary number of transmit/receive antennas, and cannot serve arbitrary number of users. Moreover, the beamforming techniques for underlay spectrum sharing do not consider the interference originating from the incumbent primary system. This work extends the common underlay sharing model by incorporating the interference originating from the incumbent system into generic combined beamforming design that can be applied on interference, broadcast or multiple access channels. The paper proposes two novel multiuser beamforming algorithms for user fairness and sum rate maximization, utilizing newly derived convex optimization problems for transmit and receive beamformers calculation in a recursive optimization. Both beamforming algorithms provide efficient operation for the interference, broadcast and multiple access channels, as well as for arbitrary number of antennas and secondary users in the system. Furthermore, the paper proposes a successive transmit/receive optimization approach that reduces the computational complexity of the proposed recursive algorithms. The results show that the proposed complexity reduction significantly improves the convergence rates and can facilitate their operation in scenarios which require agile beamformers computation.Comment: 30 pages, 5 figure

Self-organising comprehensive handover strategy for multi-tier LTE-advanced heterogeneous networks

Long term evolution (LTE)-advanced was introduced as real fourth generation (4G) with its new features and additional functions, satisfying the growing demands of quality and network coverage for the network operators' subscribers. The term muti-tier has also been recently used with respect to the heterogeneity of the network by applying the various subnetwork cooperative systems and functionalities with self-organising capabilities. Using indoor short-range low-power cellular base stations, for example, femtocells, in cooperation with existing long-range macrocells are considered as the key technical challenge of this multi-tier configuration. Furthermore, shortage of network spectrum is a major concern for network operators which forces them to spend additional attentions to overcome the degradation in performance and quality of services in 4G HetNets. This study investigates handover between the different layers of a heterogeneous LTE-advanced system, as a critical attribute to plan the best way of interactive coordination within the network for the proposed HetNet. The proposed comprehensive handover algorithm takes multiple factors in both handover sensing and decision stages, based on signal power reception, resource availability and handover optimisation, as well as prioritisation among macro and femto stations, to obtain maximum signal quality while avoiding unnecessary handovers

An Imaging Polarimeter(IMPOL) for multi-wavelength observations

Taking advantage of the advances in array detector technology, an imaging polarimeter (IMPOL) has been constructed for measuring linear polarization in the wavelength band from 400-800 nm. It makes use of a Wollaston prism as the analyser to measure simultaneously the two orthogonal polarization components that define a Stoke's parameter. An achromatic half-wave plate is used to rotate the plane of polarization with respect to the axis of the analyser so that the second Stoke's parameter also can be determined. With a field of view correponding to about 30x30 sq. mm for a 1.2 m, f/13 telescope, a sensitive, liquid-nitrogen cooled CCD camera as the detector and a built-in acquisition and guidance unit, the instrument can be used for studying stellar fields or extended objects with an angular resolution close to 2 arcsec. The instrumental polarization is less than 0.05% and the accuracies of measurement are primarily limited by photon noise for typical observations.Comment: 10 pages including 5 embedded figures; submitted to Astronomy and Astrophysics Supplement Series; available on request to A. N. Ramaprakash ([email protected] or [email protected]); quote report n