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13
On Beamforming with Finite Rate Feedback in Multiple Antenna Systems
, 2003
"... In this paper, we study a multiple antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations. Assuming that the transmitter uses the quantized information for beamforming, we derive a universal lower bound on the outage probability for any f ..."
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Cited by 188 (13 self)
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In this paper, we study a multiple antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations. Assuming that the transmitter uses the quantized information for beamforming, we derive a universal lower bound on the outage probability for any finite set of beamformers. The universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel. Using the bound, it is shown that finite information systems approach the perfect information case as (t 1)2 , where B is the number of feedback bits and t is the number of transmit antennas. The geometrical bounding technique, used in the proof of the lower bound, also leads to a design criterion for good beamformers, whose outage performance approaches the lower bound. The design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook, and is equivalent to the problem of designing unitary space time codes under certain conditions. Finally, we show that good beamformers are good packings of 2dimensional subspaces in a 2tdimensional real Grassmannian manifold with chordal distance as the metric.
Global Optimization of Statistical Functions with Simulated Annealing
 Journal of Econometrics
, 1994
"... Many statistical methods rely on numerical optimization to estimate a model’s parameters. Unfortunately, conventional algorithms sometimes fail. Even when they do converge, there is no assurance that they have found the global, rather than a local, optimum. We test a new optimization algorithm, simu ..."
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Cited by 126 (1 self)
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Many statistical methods rely on numerical optimization to estimate a model’s parameters. Unfortunately, conventional algorithms sometimes fail. Even when they do converge, there is no assurance that they have found the global, rather than a local, optimum. We test a new optimization algorithm, simulated annealing, on four econometric problems and compare it to three common conventional algorithms. Not only can simulated annealing find the global optimum, it is also less likely to fail on difficult functions because it is a very robust algorithm. The promise of simulated annealing is demonstrated on the four econometric problems.
Theory of molecular machines. I. Channel capacity of molecular machines
 J. Theor. Biol
, 1991
"... Schneider, T. D. (1991). Theory of molecular machines. I. Channel capacity ..."
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Cited by 18 (10 self)
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Schneider, T. D. (1991). Theory of molecular machines. I. Channel capacity
Remote sensing techniques for mangrove mapping
, 2006
"... on the authority of the Rector Magnificus of Wageningen University, ..."
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Cited by 2 (0 self)
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on the authority of the Rector Magnificus of Wageningen University,
Correlation, Cost Risk, And Geometry
, 1993
"... this paper is to examine key aspects of simulating this case. CORRELATION AND GEOMETRY Correlation is largely perceived to be a statistical phenomena. It is. But it is also a geometric phenomena (Herr, 1980). To see this, we must first view the data in vector form (Halmos, 1974). Let x i be the vect ..."
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Cited by 2 (1 self)
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this paper is to examine key aspects of simulating this case. CORRELATION AND GEOMETRY Correlation is largely perceived to be a statistical phenomena. It is. But it is also a geometric phenomena (Herr, 1980). To see this, we must first view the data in vector form (Halmos, 1974). Let x i be the vector x i =
A Rational Quaternion Spline of Arbitrary Continuity
, 1999
"... Quaternion splines are a classical tool for orientation control in computer animation and robotics. In this paper, we design a rational quaternion spline with many desirable properties: it is a fully general NURBS curve of arbitrary continuity; it has a closed form algebraic description, leading ..."
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Cited by 1 (0 self)
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Quaternion splines are a classical tool for orientation control in computer animation and robotics. In this paper, we design a rational quaternion spline with many desirable properties: it is a fully general NURBS curve of arbitrary continuity; it has a closed form algebraic description, leading to simple derivative computation; its construction is an efficient generalization of classical interpolation techniques in Euclidean space, leading to simple implementation and easy incorporation into existing NURBSbased modelers; it is coordinateframe invariant; and it is of high quality.
Sharp Generalization Error Bounds for Randomlyprojected Classifiers
 30th International Conference on Machine Learning (ICML 2013), JMLR W&CP
, 2013
"... We derive sharp bounds on the generalization error of a generic linear classifier trained by empirical risk minimization on randomlyprojected data. We make no restrictive assumptions (such as sparsity or separability) on the data: Instead we use the fact that, in a classification setting, the questi ..."
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Cited by 1 (1 self)
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We derive sharp bounds on the generalization error of a generic linear classifier trained by empirical risk minimization on randomlyprojected data. We make no restrictive assumptions (such as sparsity or separability) on the data: Instead we use the fact that, in a classification setting, the question of interest is really ‘what is the effect of random projection on the predicted class labels? ’ and we therefore derive the exact probability of ‘label flipping ’ under Gaussian random projection in order to quantify this effect precisely in our bounds. 1.
Optimizing Hydrocarbon Field Development Using a Genetic Algorithm Based Approach
, 1997
"... ... kind of problem encompasses two main entities: the field production system and the geological reservoir. Each of these entities presents a wide set of decision variables and the choice of their values is an optimization problem. In view of the large number of decision variables it is infeasible ..."
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... kind of problem encompasses two main entities: the field production system and the geological reservoir. Each of these entities presents a wide set of decision variables and the choice of their values is an optimization problem. In view of the large number of decision variables it is infeasible to try to enumerate all possible combinations. Analysis tools encoded in computer programs can spend hours or days of processing for a single run, depending on their sophistication and features. Also, it can be costly to prepare the input data if many hypotheses are going to be considered and if it is desirable to allow the parameters to vary. A typical