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233
Cognitive Radio: BrainEmpowered Wireless Communications
 IEEE J. Selected Areas in Comm
, 2005
"... Abstract—Cognitive radio is viewed as a novel approach for improving the utilization of a precious natural resource: the radio electromagnetic spectrum. The cognitive radio, built on a softwaredefined radio, is defined as an intelligent wireless communication system that is aware of its environment ..."
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Cited by 543 (0 self)
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Abstract—Cognitive radio is viewed as a novel approach for improving the utilization of a precious natural resource: the radio electromagnetic spectrum. The cognitive radio, built on a softwaredefined radio, is defined as an intelligent wireless communication system that is aware of its environment and uses the methodology of understandingbybuilding to learn from the environment and adapt to statistical variations in the input stimuli, with two primary objectives in mind: • highly reliable communication whenever and wherever needed; • efficient utilization of the radio spectrum. Following the discussion of interference temperature as a new metric for the quantification and management of interference, the paper addresses three fundamental cognitive tasks. 1) Radioscene analysis. 2) Channelstate estimation and predictive modeling. 3) Transmitpower control and dynamic spectrum management. This paper also discusses the emergent behavior of cognitive radio. Index Terms—Awareness, channelstate estimation and predictive modeling, cognition, competition and cooperation, emergent behavior, interference temperature, machine learning, radioscene analysis, rate feedback, spectrum analysis, spectrum holes, spectrum management, stochastic games, transmitpower control, water filling.
Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions
, 2004
"... In this paper, we develop a robust uncertainty principle for finite signals in C N which states that for nearly all choices T, Ω ⊂ {0,..., N − 1} such that T  + Ω  ≍ (log N) −1/2 · N, there is no signal f supported on T whose discrete Fourier transform ˆ f is supported on Ω. In fact, we can mak ..."
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Cited by 119 (12 self)
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In this paper, we develop a robust uncertainty principle for finite signals in C N which states that for nearly all choices T, Ω ⊂ {0,..., N − 1} such that T  + Ω  ≍ (log N) −1/2 · N, there is no signal f supported on T whose discrete Fourier transform ˆ f is supported on Ω. In fact, we can make the above uncertainty principle quantitative in the sense that if f is supported on T, then only a small percentage of the energy (less than half, say) of ˆ f is concentrated on Ω. As an application of this robust uncertainty principle (QRUP), we consider the problem of decomposing a signal into a sparse superposition of spikes and complex sinusoids f(s) = � α1(t)δ(s − t) + � α2(ω)e i2πωs/N / √ N. t∈T We show that if a generic signal f has a decomposition (α1, α2) using spike and frequency locations in T and Ω respectively, and obeying ω∈Ω T  + Ω  ≤ Const · (log N) −1/2 · N, then (α1, α2) is the unique sparsest possible decomposition (all other decompositions have more nonzero terms). In addition, if T  + Ω  ≤ Const · (log N) −1 · N, then the sparsest (α1, α2) can be found by solving a convex optimization problem. Underlying our results is a new probabilistic approach which insists on finding the correct uncertainty relation or the optimally sparse solution for nearly all subsets but not necessarily all of them, and allows to considerably sharpen previously known results [9, 10]. In fact, we show that the fraction of sets (T, Ω) for which the above properties do not hold can be upper bounded by quantities like N −α for large values of α. The QRUP (and the application to finding sparse representations) can be extended to general pairs of orthogonal bases Φ1, Φ2 of C N. For nearly all choices Γ1, Γ2 ⊂ {0,..., N − 1} obeying Γ1  + Γ2  ≍ µ(Φ1, Φ2) −2 · (log N) −m, where m ≤ 6, there is no signal f such that Φ1f is supported on Γ1 and Φ2f is supported on Γ2 where µ(Φ1, Φ2) is the mutual coherence between Φ1 and Φ2.
Advanced Spectral Methods for Climatic Time Series
, 2001
"... The analysis of uni or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical eld of ..."
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Cited by 96 (30 self)
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The analysis of uni or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical eld of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory.
Selection of a convolution function for Fourier inversion using gridding [computerised tomography application
 IEEE Trans. Medical Imaging
, 1991
"... AbstractIn fields ranging from radio astronomy to magnetic resonance imaging, Fourier inversion of data not falling on a Cartesian grid has been a prbblem. As a result, multiple algorithms have been created for reconstructing images from nonuniform frequency samples. In the technique known as gridd ..."
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Cited by 84 (1 self)
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AbstractIn fields ranging from radio astronomy to magnetic resonance imaging, Fourier inversion of data not falling on a Cartesian grid has been a prbblem. As a result, multiple algorithms have been created for reconstructing images from nonuniform frequency samples. In the technique known as gridding, the data samples are weighted for sampling density and convolved with a finite kernel, then resampled on a grid preparatory to a fast Fourier transform. This paper compares the utility of several convolution functions, including one that outperforms the “optimal ” prolate spheroidal wave function in some situations. I.
Diffusion Wavelets
, 2004
"... We present a multiresolution construction for efficiently computing, compressing and applying large powers of operators that have high powers with low numerical rank. This allows the fast computation of functions of the operator, notably the associated Green’s function, in compressed form, and their ..."
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Cited by 72 (12 self)
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We present a multiresolution construction for efficiently computing, compressing and applying large powers of operators that have high powers with low numerical rank. This allows the fast computation of functions of the operator, notably the associated Green’s function, in compressed form, and their fast application. Classes of operators satisfying these conditions include diffusionlike operators, in any dimension, on manifolds, graphs, and in nonhomogeneous media. In this case our construction can be viewed as a farreaching generalization of Fast Multipole Methods, achieved through a different point of view, and of the nonstandard wavelet representation of CalderónZygmund and pseudodifferential operators, achieved through a different multiresolution analysis adapted to the operator. We show how the dyadic powers of an operator can be used to induce a multiresolution analysis, as in classical LittlewoodPaley and wavelet theory, and we show how to construct, with fast and stable algorithms, scaling function and wavelet bases associated to this multiresolution analysis, and the corresponding downsampling operators, and use them to compress the corresponding powers of the operator. This allows to extend multiscale signal processing to general spaces (such as manifolds and graphs) in a very natural way, with corresponding fast algorithms.
TimeVariant Channel Estimation Using Discrete Prolate Spheroidal Sequences
 IEEE Trans. Signal Processing
, 2005
"... We propose and analyze a lowcomplexity channel estimator for a multiuser multicarrier code division multiple access (MCCDMA) downlink in a timevariant frequencyselective channel. MCCDMA is based on orthogonal frequency division multiplexing (OFDM). The timevariant channel is estimated individu ..."
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Cited by 62 (21 self)
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We propose and analyze a lowcomplexity channel estimator for a multiuser multicarrier code division multiple access (MCCDMA) downlink in a timevariant frequencyselective channel. MCCDMA is based on orthogonal frequency division multiplexing (OFDM). The timevariant channel is estimated individually for every flatfading subcarrier, assuming small intercarrier interference. The temporal variation of every subcarrier over the duration of a data block is upper bounded by the Doppler bandwidth determined by the maximum velocity of the users. Slepian showed that timelimited snapshots of bandlimited sequences span a lowdimensional subspace. This subspace is also spanned by discrete prolate spheroidal (DPS) sequences. We expand the timevariant subcarrier coefficients in terms of orthogonal DPS sequences we call Slepian basis expansion. This enables a timevariant channel description that avoids the frequency leakage effect of the Fourier basis expansion. The square bias of the Slepian basis expansion per subcarrier is three magnitudes smaller than the square bias of the Fourier basis expansion. We show simulation results for a fully loaded MCCDMA downlink with classic linear minimum mean square error multiuser detection. The users are moving with 19.4 m/s. Using the Slepian basis expansion channel estimator and a pilot ratio of only 2%, we achieve a bit error rate performance as with perfect channel knowledge.
Deconvolution of Images and Spectra
, 1997
"... ngineering, The University of Washington Seattle, Washington I. II. III. IV. V. VI. Introduction 478 Geometrical POCS 478 A. Convex Sets 479 B. Projecting onto a Convex Set 480 c. 482 Convex Sets of Signals 484 A. The Signal Space 484 B. Some Commonly Used Convex Sets of Signals 486 Exampl ..."
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Cited by 36 (0 self)
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ngineering, The University of Washington Seattle, Washington I. II. III. IV. V. VI. Introduction 478 Geometrical POCS 478 A. Convex Sets 479 B. Projecting onto a Convex Set 480 c. 482 Convex Sets of Signals 484 A. The Signal Space 484 B. Some Commonly Used Convex Sets of Signals 486 Examples 490 A. Von Neumann's Alternating Projection Theorem 490 B. The PapoulisGerchberg Algorithm 490 C. Algorithm 494 D. Restoration of Linear Degradation 494 Notes 497 Conclusions 498 References 499 List of Symbols E BE BS sets of vectors or functions the universal set multidimensional vectors vectors in the sets A and B functions of
Autoregressive models for fading channel simulation
 IEEE TRANS. WIRELESS COMMUN
, 2005
"... Autoregressive stochastic models for the computer simulation of correlated Rayleigh fading processes are investigated. The unavoidable numerical difficulties inherent in this method are elucidated and a simple heuristic approach is adopted to enable the synthesis of accurately correlated, bandlimit ..."
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Cited by 36 (2 self)
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Autoregressive stochastic models for the computer simulation of correlated Rayleigh fading processes are investigated. The unavoidable numerical difficulties inherent in this method are elucidated and a simple heuristic approach is adopted to enable the synthesis of accurately correlated, bandlimited Rayleigh variates. Startup procedures are presented, which allow autoregressive simulators to produce stationary channel gain samples from the first output sample. Performance comparisons are then made with popular fading generation techniques to demonstrate the merits of the approach. The general applicability of the method is demonstrated by examples involving the accurate synthesis of nonisotropic fading channel models.
Degrees of freedom in multipleantenna channels: A signal space approach
 IEEE Trans. Inf. Theory
, 2005
"... We consider multipleantenna systems that are limited by the area and geometry of antenna arrays. Given these physical constraints, we determine the limit to the number of spatial degrees of freedom available and find that the commonly used statistical multiinput multioutput model is inadequate. A ..."
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Cited by 34 (4 self)
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We consider multipleantenna systems that are limited by the area and geometry of antenna arrays. Given these physical constraints, we determine the limit to the number of spatial degrees of freedom available and find that the commonly used statistical multiinput multioutput model is inadequate. Antenna theory is applied to take into account the area and geometry constraints, and define the spatial signal space so as to interpret experimental channel measurements in an arrayindependent but manageable description of the physical environment. Based on these modeling strategies, we show that for a spherical array of effective aperture A in a physical environment of angular spread Ω  in solid angle, the number of spatial degrees of freedom is AΩ  for unpolarized antennas and 2AΩ  for polarized antennas. Together with the 2WT degrees of freedom for a system of bandwidth W transmitting in an interval T, the total degrees of freedom of a multipleantenna channel is therefore 4WTAΩ. 1