Results 1  10
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29
LowDimensional Models for Dimensionality Reduction and Signal Recovery: A Geometric Perspective
, 2009
"... We compare and contrast from a geometric perspective a number of lowdimensional signal models that support stable informationpreserving dimensionality reduction. We consider sparse and compressible signal models for deterministic and random signals, structured sparse and compressible signal model ..."
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Cited by 47 (12 self)
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We compare and contrast from a geometric perspective a number of lowdimensional signal models that support stable informationpreserving dimensionality reduction. We consider sparse and compressible signal models for deterministic and random signals, structured sparse and compressible signal models, point clouds, and manifold signal models. Each model has a particular geometrical structure that enables signal information in to be stably preserved via a simple linear and nonadaptive projection to a much lower dimensional space whose dimension either is independent of the ambient dimension at best or grows logarithmically with it at worst. As a bonus, we point out a common misconception related to probabilistic compressible signal models, that is, that the generalized Gaussian and Laplacian random models do not support stable linear dimensionality reduction.
Space division multiple access with a sum feedback rate constraint
 IEEE Trans. Signal Processing
, 2007
"... Abstract—On a multiantenna broadcast channel, simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput, which grows double logarithmically with the number of users. The sum rate for channel state information (CSI) feedback, however, incr ..."
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Cited by 33 (7 self)
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Abstract—On a multiantenna broadcast channel, simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput, which grows double logarithmically with the number of users. The sum rate for channel state information (CSI) feedback, however, increases linearly with the number of users, reducing the effective uplink capacity. To address this problem, a novel space division multiple access (SDMA) design is proposed, where the sum feedback rate is upper bounded by a constant. This design consists of algorithms for CSI quantization, thresholdbased CSI feedback, and joint beamforming and scheduling. The key feature of the proposed approach is the use of feedback thresholds to select feedback users with large channel gains and small CSI quantization errors such that the sum feedback rate constraint is satisfied. Despite this constraint, the proposed SDMA design is shown to achieve a sum capacity growth rate close to the optimal one. Moreover, the feedback overflow probability for this design is found to decrease exponentially with the difference between the allowable and the average sum feedback rates. Numerical results show that the proposed SDMA design is capable of attaining higher sum capacities than existing ones, even though the sum feedback rate is bounded. Index Terms—Broadcast channels, feedback communication, multiuser channels, space division multiplexing. I.
The Incomplete Gamma Functions Since Tricomi
 In Tricomi's Ideas and Contemporary Applied Mathematics, Atti dei Convegni Lincei, n. 147, Accademia Nazionale dei Lincei
, 1998
"... The theory of the incomplete gamma functions, as part of the theory of conuent hypergeometric functions, has received its rst systematic exposition by Tricomi in the early 1950s. His own contributions, as well as further advances made thereafter, are surveyed here with particular emphasis on asy ..."
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Cited by 27 (1 self)
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The theory of the incomplete gamma functions, as part of the theory of conuent hypergeometric functions, has received its rst systematic exposition by Tricomi in the early 1950s. His own contributions, as well as further advances made thereafter, are surveyed here with particular emphasis on asymptotic expansions, zeros, inequalities, computational methods, and applications.
Exponential diversity achieving spatiotemporal power allocation scheme for fading channels
 IEEE Trans. Inf. Theory
, 2008
"... Abstract — We analyze optimum (space–time) adaptive power transmission policies for Rayleigh fading MIMO channels when CSIT and CSIR are available. We show that our power allocation policy provides exponential diversity gain 2 (BER ≤ αe −f(nt,nr),whereα>0 is a constant, and f>0 is an increasin ..."
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Cited by 19 (3 self)
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Abstract — We analyze optimum (space–time) adaptive power transmission policies for Rayleigh fading MIMO channels when CSIT and CSIR are available. We show that our power allocation policy provides exponential diversity gain 2 (BER ≤ αe −f(nt,nr),whereα>0 is a constant, and f>0 is an increasing function of nt & nr) if perfect CSIT is available. Exponential diversity is lost at high SNR if the quality of CSIT degrades. I. Perfect/Imperfect CSIT We consider a single user narrowband (flat fading) communication system employing nt transmit antennas and nr receive antennas. The channel between i th receive antenna and j th transmit antenna, hij is a complex Gaussian random variable (H = [hij] represents the channel). We assume i.i.d. Rayleigh fading from symbol to symbol and on each of the diversity branches. The additive noise, n, is temporally and spatially white with mean zero, i.e., n ∼NC(0,σ 2 Inr). We assume that ˆ H is the transmitter’s estimate of the channel. We assume that ˆ H and H are jointly complex Gaussian with correlation ρ. We assume perfect CSIR. ˆ H is used to get the optimal beamforming transmit weight vector w (the eigenvector of ˆ H H H ˆ corresponding to its largest eigenvalue) and transmit power P (.) for that symbol duration. The output of the matched filter sampled at symbol duration is given by y = √ P (ˆγ) Hwx+n, where x is the transmitted symbol, γ = ‖Hw ‖ 2 Ex  2 /σ 2 is the SNR, P (ˆγ) is the transmit power, and ˆγ ( = ‖ ˆ Hw ‖ 2 Ex  2 /σ 2) is the estimate of γ at the transmitter. The BER performance of the above system for the coherent ( √2γ) BPSK signaling is given by Peγ,ˆγ = Q P(ˆγ). We minimize Pe subject to the average transmit power constraint. For the perfect CSIT case (ˆγ = γ), the optimization problem is
Posterior contraction in sparse Bayesian factor models for massive covariance matrices
, 2012
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DirichletLaplace priors for optimal shrinkage. arXiv preprint arXiv:1401.5398
, 2014
"... Penalized regression methods, such as L1 regularization, are routinely used in highdimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is routinely induced through twocomponent mixture priors having a pro ..."
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Cited by 6 (0 self)
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Penalized regression methods, such as L1 regularization, are routinely used in highdimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is routinely induced through twocomponent mixture priors having a probability mass at zero, but such priors encounter daunting computational problems in high dimensions. This has motivated an amazing variety of continuous shrinkage priors, which can be expressed as globallocal scale mixtures of Gaussians, facilitating computation. In sharp contrast to the frequentist literature, little is known about the properties of such priors and the convergence and concentration of the corresponding posterior distribution. In this article, we propose a new class of Dirichlet– Laplace (DL) priors, which possess optimal posterior concentration and lead to efficient posterior computation exploiting results from normalized random measure theory. Finite sample performance of Dirichlet–Laplace priors relative to alternatives is assessed in simulated and real data examples.
A comprehensive framework for devicetodevice communications in cellular networks,” arXiv preprint arXiv:1305.4219
, 2013
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A PROBABILISTIC CONSTRAINT APPROACH FOR ROBUST TRANSMIT BEAMFORMING WITH IMPERFECT CHANNEL INFORMATION
"... Transmit beamforming is a powerful technique for enhancing performance of wireless communication systems. Most existing transmit beamforming techniques require perfect channel state information at the transmitter (CSIT), which is typically not available in practice. In such situations, the design sh ..."
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Cited by 5 (3 self)
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Transmit beamforming is a powerful technique for enhancing performance of wireless communication systems. Most existing transmit beamforming techniques require perfect channel state information at the transmitter (CSIT), which is typically not available in practice. In such situations, the design should take errors in CSIT into account to avoid performance degradation. Among two popular robust designs, the stochastic approach exploits channel statistics and optimizes the average system performance. The maximin approach considers errors as deterministic and optimizes the worstcase performance. The latter usually leads to conservative results as the extreme (but rare) conditions may occur at a very low probability. In this work, we propose a more flexible approach that maximizes the average signaltonoise ratio (SNR) and takes the extreme conditions into account proportionally. Simulation results show that the proposed beamformer offers higher robustness against channel estimation errors than several popular transmit beamformers. 1.