264 research outputs found
Random Beamforming with Heterogeneous Users and Selective Feedback: Individual Sum Rate and Individual Scaling Laws
This paper investigates three open problems in random beamforming based
communication systems: the scheduling policy with heterogeneous users, the
closed form sum rate, and the randomness of multiuser diversity with selective
feedback. By employing the cumulative distribution function based scheduling
policy, we guarantee fairness among users as well as obtain multiuser diversity
gain in the heterogeneous scenario. Under this scheduling framework, the
individual sum rate, namely the average rate for a given user multiplied by the
number of users, is of interest and analyzed under different feedback schemes.
Firstly, under the full feedback scheme, we derive the closed form individual
sum rate by employing a decomposition of the probability density function of
the selected user's signal-to-interference-plus-noise ratio. This technique is
employed to further obtain a closed form rate approximation with selective
feedback in the spatial dimension. The analysis is also extended to random
beamforming in a wideband OFDMA system with additional selective feedback in
the spectral dimension wherein only the best beams for the best-L resource
blocks are fed back. We utilize extreme value theory to examine the randomness
of multiuser diversity incurred by selective feedback. Finally, by leveraging
the tail equivalence method, the multiplicative effect of selective feedback
and random observations is observed to establish the individual rate scaling.Comment: Submitted in March 2012. To appear in IEEE Transactions on Wireless
Communications. Part of this paper builds upon the following letter: Y. Huang
and B. D. Rao, "Closed form sum rate of random beamforming", IEEE Commun.
Lett., vol. 16, no. 5, pp. 630-633, May 201
Performance Analysis of Heterogeneous Feedback Design in an OFDMA Downlink with Partial and Imperfect Feedback
Current OFDMA systems group resource blocks into subband to form the basic
feedback unit. Homogeneous feedback design with a common subband size is not
aware of the heterogeneous channel statistics among users. Under a general
correlated channel model, we demonstrate the gain of matching the subband size
to the underlying channel statistics motivating heterogeneous feedback design
with different subband sizes and feedback resources across clusters of users.
Employing the best-M partial feedback strategy, users with smaller subband size
would convey more partial feedback to match the frequency selectivity. In order
to develop an analytical framework to investigate the impact of partial
feedback and potential imperfections, we leverage the multi-cluster subband
fading model. The perfect feedback scenario is thoroughly analyzed, and the
closed form expression for the average sum rate is derived for the
heterogeneous partial feedback system. We proceed to examine the effect of
imperfections due to channel estimation error and feedback delay, which leads
to additional consideration of system outage. Two transmission strategies: the
fix rate and the variable rate, are considered for the outage analysis. We also
investigate how to adapt to the imperfections in order to maximize the average
goodput under heterogeneous partial feedback.Comment: To appear in IEEE Trans. on Signal Processin
An Analytical Framework for Heterogeneous Partial Feedback Design in Heterogeneous Multicell OFDMA Networks
The inherent heterogeneous structure resulting from user densities and large
scale channel effects motivates heterogeneous partial feedback design in
heterogeneous networks. In such emerging networks, a distributed scheduling
policy which enjoys multiuser diversity as well as maintains fairness among
users is favored for individual user rate enhancement and guarantees. For a
system employing the cumulative distribution function based scheduling, which
satisfies the two above mentioned desired features, we develop an analytical
framework to investigate heterogeneous partial feedback in a general
OFDMA-based heterogeneous multicell employing the best-M partial feedback
strategy. Exact sum rate analysis is first carried out and closed form
expressions are obtained by a novel decomposition of the probability density
function of the selected user's signal-to-interference-plus-noise ratio. To
draw further insight, we perform asymptotic analysis using extreme value theory
to examine the effect of partial feedback on the randomness of multiuser
diversity, show the asymptotic optimality of best-1 feedback, and derive an
asymptotic approximation for the sum rate in order to determine the minimum
required partial feedback.Comment: To appear in IEEE Trans. on Signal Processin
Liouville Quantum Gravity on the unit disk
Our purpose is to pursue the rigorous construction of Liouville Quantum Field
Theory on Riemann surfaces initiated by F. David, A. Kupiainen and the last two
authors in the context of the Riemann sphere and inspired by the 1981 seminal
work by Polyakov. In this paper, we investigate the case of simply connected
domains with boundary. We also make precise conjectures about the relationship
of this theory to scaling limits of random planar maps with boundary
conformally embedded onto the disk
On Structure of cluster algebras of geometric type I: In view of sub-seeds and seed homomorphisms
Our motivation is to build a systematic method in order to investigate the
structure of cluster algebras of geometric type.
The method is given through the notion of mixing-type sub-seeds, the theory
of seed homomorphisms and the view-point of gluing of seeds. As an application,
for (rooted) cluster algebras, we completely classify rooted cluster
subalgebras and characterize rooted cluster quotient algebras in detail. Also,
we build the relationship between the categorification of a rooted cluster
algebra and that of its rooted cluster subalgebras.
Note that cluster algebras of geometric type studied here are of the
sign-skew-symmetric case.Comment: 41 page
Another probabilistic construction of Phi(2n)(2)*
This note provides an alternative probabilistic approach to the Phi(2n) theory in dimension 2. The key idea is to study the concentration phenomenon of martingales associated to polynomials of Gaussian variables. This is based on an adaptation of the work of Lacoin-Rhodes-Vargas [3] on the quantum Mabuchi K-energy.Peer reviewe
FrameNet: Learning Local Canonical Frames of 3D Surfaces from a Single RGB Image
In this work, we introduce the novel problem of identifying dense canonical
3D coordinate frames from a single RGB image. We observe that each pixel in an
image corresponds to a surface in the underlying 3D geometry, where a canonical
frame can be identified as represented by three orthogonal axes, one along its
normal direction and two in its tangent plane. We propose an algorithm to
predict these axes from RGB. Our first insight is that canonical frames
computed automatically with recently introduced direction field synthesis
methods can provide training data for the task. Our second insight is that
networks designed for surface normal prediction provide better results when
trained jointly to predict canonical frames, and even better when trained to
also predict 2D projections of canonical frames. We conjecture this is because
projections of canonical tangent directions often align with local gradients in
images, and because those directions are tightly linked to 3D canonical frames
through projective geometry and orthogonality constraints. In our experiments,
we find that our method predicts 3D canonical frames that can be used in
applications ranging from surface normal estimation, feature matching, and
augmented reality
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