Results 1  10
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11
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 18 (10 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 18 (3 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 15 (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.
Inequalities Involving Gamma and Psi Functions
"... We prove that certain functions involving the gamma and qgamma function are monotone. We also prove that (x m /(x)) (m+1) is completely monotonic. We conjecture that (x m / (m\Gamma1 (x)) (m) is completely monotonic for m 2, we prove it, with help from Maple, for 2 m 16. We give a ve ..."
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Cited by 6 (0 self)
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We prove that certain functions involving the gamma and qgamma function are monotone. We also prove that (x m /(x)) (m+1) is completely monotonic. We conjecture that (x m / (m\Gamma1 (x)) (m) is completely monotonic for m 2, we prove it, with help from Maple, for 2 m 16. We give a very useful Maple proceedure to verify this for higher values of m. A stronger result is also formulated where we conjecture that the power series coefficients of a certain function are all positive. Running Title: Gamma Function Inequalities Mathematics Subject Classification. Primary 33B15. Secondary 26D07, 26D10. Key words and phrases. gamma function, digamma function, inequalities, complete monotonicity. 1. Introduction. Inequalities of functions involving gamma functions have been of interest since the 1950's when inequalities by Gautchi, Erber and Kershaw were established. For references and generalizations we refer the interested reader to [5], [13], [14], [15], [16], and to Alzer's p...
Finding NEMO: nearorthogonal sets for multiplexing and opportunistic scheduling in MIMO broadcast
 in MIMO broadcast. In: International Conference on Wireless Networks, Communications and Mobile Computing, Maui
, 2004
"... Abstract — We define a nearorthogonal set of channel vectors as one that meets certain SIR and SNR guarantees. The probability of finding a nearorthogonal set in a pool of n users is characterized. We identify a phase transition phenomenon in channel geometry whereby the probability transitions fr ..."
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Cited by 2 (0 self)
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Abstract — We define a nearorthogonal set of channel vectors as one that meets certain SIR and SNR guarantees. The probability of finding a nearorthogonal set in a pool of n users is characterized. We identify a phase transition phenomenon in channel geometry whereby the probability transitions from 0 to 1 quite sharply. In particular, it is shown that the probability of failing to find such a set as a function of the number of users k that have been examined passes through a sharp threshold at k ∼ Θ(1), after which it behaves like Θ(k −m). The rate at which SNR and SIR can be scaled while we remain above this threshold is also characterized. The existence results we provide are not specific to the MIMO scheduling problem, but apply to the more general setting of finding a nearorthogonal set in a random collection of isotropic vectors. The proofs make use of new tight bounds we develop to bound the surface content of spherical caps in arbitrary dimensions. Broader implications of these results are discussed. Specifically, in the case of zeroforcing the rate increases at a rate on the order of log log n. I.
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 2 (1 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.
Uniform bounds for the complementary incomplete gamma function, Preprint at http://locutus.cs.dal.ca:8088/archive/00000335
"... Abstract. We prove upper and lower bounds for the complementary incomplete gamma function Γ(a, z) with complex parameters a and z. Our bounds are refined within the circular hyperboloid of one sheet {(a, z) : z > ca − 1} with a real and z complex. Our results show that within the hyperboloid, Γ ..."
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Cited by 1 (1 self)
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Abstract. We prove upper and lower bounds for the complementary incomplete gamma function Γ(a, z) with complex parameters a and z. Our bounds are refined within the circular hyperboloid of one sheet {(a, z) : z > ca − 1} with a real and z complex. Our results show that within the hyperboloid, Γ(a, z)  is of order z  a−1 e − Re(z) , and extends an upper estimate of Natalini and Palumbo to complex values of z.
Bangalore 560 012Exponential Diversity Achieving SpatioTemporal Power Allocation Scheme for Fading Channels
, 2004
"... In this paper, we analyze optimum (in space and time) adaptive power transmission policies for fading channels when the channel state information (CSI) at the transmitter (CSIT) and receiver (CSIR) is available. The transmitter has a longterm (time) average power constraint. There can be multiple a ..."
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In this paper, we analyze optimum (in space and time) adaptive power transmission policies for fading channels when the channel state information (CSI) at the transmitter (CSIT) and receiver (CSIR) is available. The transmitter has a longterm (time) average power constraint. There can be multiple antennas at the transmitter and receiver. The channel experiences Rayleigh fading. We consider beamforming and spacetime coded systems with perfect/imperfect CSIT and CSIR. We also consider an inner convolutional code (with beamforming or an outer spacetime code). The performance measure is the bit error rate (BER). We show that in both coded and uncoded systems, our power allocation policy provides exponential diversity gain if perfect CSIT is available. We also show that, if the quality of CSIT degrades then the exponential diversity is retained only in the low SNR region but we get only polynomial diversity in the high SNR region.