Constrained probability distributions of correlation functions

Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation. However, this has been shown to be insufficient. Aims: For the case of Gaussian random fields, we search for an exact probability distribution of correlation functions, which could improve the accuracy of future data analyses. Methods: We use a fully analytic approach, first expanding the random field in its Fourier modes, and then calculating the characteristic function. Finally, we derive the probability distribution function using integration by residues. We use a numerical implementation of the full analytic formula to discuss the behaviour of this function. Results: We derive the univariate and bivariate probability distribution function of the correlation functions of a Gaussian random field, and outline how higher joint distributions could be calculated. We give the results in the form of mode expansions, but in one special case we also find a closed-form expression. We calculate the moments of the distribution and, in the univariate case, we discuss the Edgeworth expansion approximation. We also comment on the difficulties in a fast and exact numerical implementation of our results, and on possible future applications.Comment: 13 pages, 5 figures, updated to match version published in A&A (slightly expanded Sects. 5.3 and 6

Numerische Simulation der Phasengrenzen und Schmelzenströmung bei der Züchtung von Siliziumeinkristallen mit dem Floating-Zone Verfahren

The problem of beamforming and rate estimation in a multi-user downlink multiple-input multiple-output (MIMO) system with limited feedback and statistical channel information at the transmitter is considered. In order to exploit the spatial properties of the channel, the norm of the channel to each receive antenna is computed. We propose to feed back the largest norm to the transmitter and derive the conditional second and fourth order channel moments in order to design the downlink beamforming weights. Similar approaches have previously been presented for multi-user multiple-input single-output (MISO) systems. Herein, these techniques are generalized to MIMO systems, by either antenna selection or receive beamforming at the receiver. Two eigenbeamforming strategies are proposed and shown to outperform opportunistic beamforming, based on similar feedback information.© 2007 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. QC 20110704</p

Resource Allocation in Multi-Antenna Communication Systems with Limited Feedback

The use of multiple transmit antennas is considered a key ingredient to significantly improve the spectral efficiency of wireless communication systems beyond that of currently employed systems. Transmit beamforming schemes have been proposed to exploit the spatial characteristics of multi-antenna radio channels; that is, multiple-input single-output (MISO) channels. In multiuser communication systems, the downlink throughput can be significantly increased by simultaneously transmitting to several users in the same timefrequency slot, by means of spatial-division multi-access (SDMA). Several SDMA beamforming algorithms are available for joint optimal beamforming and power control for the downlink. Such optimal beamforming minimizes the total transmission power, while ensuring an individual target quality of service (QoS) for each user; alternatively the weakest QoS is maximized, subject to a transmit power constraint. In this thesis, both of these formulations are considered and some of the available algorithms are generalized to enable quadratic shaping constraints on the beamformers. By imposing additional constraints, the QoS measure can be extended to take factors other than the customary signal to interference-plus-noise ratio (SINR) into account. Alternatively, other limitations such as interference requirements or physical constraints may be incorporated in the optimization. The proposed beamforming algorithms are also based on a more general SINR expression than previously analyzed in this context. The generalized SINR expression allows for more accurate modeling; for example, non-zero self interference can be modeled in code-division multi-access (CDMA) systems. A major limiting factor for downlink resource allocation is the amount of channel-state information (CSI) available at the base station. In most cases, CSI can be estimated only at the receivers, and then fed back to the base station. This procedure typically constrains the amount of CSI that can be conveyed. In this thesis, a minimum mean squared-error (MMSE) SINR estimation framework is proposed, which combines partial CSI with channel-distribution information (CDI); the CDI varies slowly and is assumed to be known at the transmitter. User selection (scheduling) and beamforming techniques, suitable for the MMSE SINR estimates, are also proposed. Special attention is given to the feedback of a scalar channel-gain information (CGI) parameter. The CSI provided by CGI feedback is studied in depth for correlated Rayleigh and Ricean fading channels. It is shown, using asymptotic analysis, that large realizations of the CGI parameter convey additional spatial CSI at the transmitter; the proposed scheme is thus ideal for multiuser diversity transmission schemes, where resources are allocated only to users experiencing favorable channel conditions. It is shown by numerical simulations that, in wide-area scenarios, feeding back a single scalar CGI parameter per user, provides sufficient information for the proposed downlink resource-allocation algorithms to perform efficient SDMA beamforming and user selectionQC 2010071

Spatial Transmit Processing using Long-Term Channel Statistics and Pilot Signaling on Selected Antennas

Abstract — In wireless high performance systems utilizing smart antenna transmission techniques, increased pilot signaling becomes problematic when more transmit antennas are added. Herein, we propose a scheme where the pilot signaling is restricted to a subset of the transmit antennas, and the total signal strength of these antennas is fed back to the transmitter. This potentially reduces the required pilot signaling and feedback so it becomes comparable to that of single antenna systems. By combining the feedback with channel statistics, known to the transmitter, substantial spatial information is gained. Herein, this information is used to develop elaborate scheduling and beamforming techniques. I

Resource Allocation in Multi-Antenna Communication Systems with Limited Feedback

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Exploiting the spatial information provided by channel statistics and SNR feedback

c ○ 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. KUNGL TEKNISKA HÖGSKOLAN Institutionen fö

Dimensions of Self-Motivated Teacher Collaboration

This qualitative study explores six English teachers’ perceptions regarding teaching collaboration. In open-ended interviews, the teachers responded to questions regarding the extent to which they were able to engage in meaningful collaboration. The study’s focus was to gain insight on the most valuable dimensions of informal and formal collaborative activities. The outcome of the study indicated that although many teachers engage in self-motivated collaborative activities, they wished to build on their experiences in different ways, incorporating more formal activities and professional development opportunities. Peer observations, feedback and discussions were found to be effective means of increasing teachers’ repertoire of teaching skills. The teachers in this study perceived collaboration as a positive and productive dimension of both teaching and learning. A broader implication of the study’s results is that these teachers’ perceptions reflected a bottom-up approach to school development addressing teachers’ actual concerns, rather than a top-down approach as imposed by the school administration

Acquiring Partial CSI for Spatially Selective Transmission by Instantaneous Channel Norm Feedback

In the design of next-generation multiuser communication systems, multiple-antenna transmission is an essential part providing additional spatial degrees of freedom and allowing efficient use of resources. A major limiting factor in the resource allocation is the amount of channel state information (CSI) available at the transmitter, particularly in multiuser systems where the feedback from each user terminal must be limited. Herein, we show that the Euclidean norm of the instantaneous channel, when combined with long-term channel statistics provides sufficient information for the transmitter to efficiently utilize multiuser diversity in time, frequency, and space. We consider the downlink of a communication system where the base station has multiple transmit antennas whereas each user terminal has a single receive antenna. The CSI provided by channel statistics and feedback of the norm of the instantaneous channel vector is studied in depth for correlated Rayleigh and Ricean fading channels, within a minimum mean-square error (MMSE) estimation framework. An asymptotic analysis (high instantaneous SNR) is presented which shows that channel realizations with large channel norm provide additional spatial CSI at the transmitter. This makes the proposed scheme ideal for multiuser diversity transmission schemes, where resources are only allocated to users experiencing favorable channel conditions