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Book•

Fundamentals Of Statistical Signal Processing

16 Mar 2001-
About: The article was published on 2001-03-16 and is currently open access. It has received 7058 citations till now. The article focuses on the topics: Statistical signal processing.
Citations
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Dissertation•
24 Apr 2002
TL;DR: Results show that remarkable energy and spectral efficiencies are achievable by combining concepts drawn from space-time coding, multiuser detection, array processing and iterative decoding.
Abstract: Space-time codes (STC) are a class of signaling techniques, offering coding and diversity gains along with improved spectral efficiency. These codes exploit both the spatial and the temporal diversity of the wireless link by combining the design of the error correction code, modulation scheme and array processing. STC are well suited for improving the downlink performance, which is the bottleneck in asymmetric applications such as downstream Internet. Three original contributions to the area of STC are presented in this dissertation. First, the development of analytic tools that determine the fundamental limits on the performance of STC in a variety of channel conditions. For trellis-type STC, transfer function based techniques are applied to derive performance bounds over Rayleigh, Rician and correlated fading environments. For block-type STC, an analytic framework that supports various complex orthogonal designs with arbitrary signal cardinalities and array configurations is developed. In the second part of the dissertation, the Virginia Tech Space-Time Advanced Radio (VT-STAR) is designed, introducing a multi-antenna hardware laboratory test bed, which facilitates characterization of the multiple-input multiple-output (MIMO) channel and validation of various space-time approaches. In the third part of the dissertation, two novel space-time architectures paired with iterative processing principles are proposed. The first scheme extends the suitability of STC to outdoor wireless communications by employing iterative equalization/decoding for time dispersive channels and the second scheme employs iterative interference cancellation/decoding to solve the error propagation problem of Bell-Labs Layered Space-Time Architecture (BLAST). Results show that remarkable energy and spectral efficiencies are achievable by combining concepts drawn from space-time coding, multiuser detection, array processing and iterative decoding.

2,286 citations

Journal Article•DOI•
TL;DR: This work focuses on detection algorithms that assume multivariate normal distribution models for HSI data and presents some results which illustrate the performance of some detection algorithms using real hyperspectral imaging (HSI) data.
Abstract: We introduce key concepts and issues including the effects of atmospheric propagation upon the data, spectral variability, mixed pixels, and the distinction between classification and detection algorithms. Detection algorithms for full pixel targets are developed using the likelihood ratio approach. Subpixel target detection, which is more challenging due to background interference, is pursued using both statistical and subspace models for the description of spectral variability. Finally, we provide some results which illustrate the performance of some detection algorithms using real hyperspectral imaging (HSI) data. Furthermore, we illustrate the potential deviation of HSI data from normality and point to some distributions that may serve in the development of algorithms with better or more robust performance. We therefore focus on detection algorithms that assume multivariate normal distribution models for HSI data.

1,170 citations

Journal Article•DOI•
26 Apr 2010
TL;DR: In this article, the authors formalize the notion of multipath sparsity and present a new approach to estimate sparse (or effectively sparse) multipath channels that is based on some of the recent advances in the theory of compressed sensing.
Abstract: High-rate data communication over a multipath wireless channel often requires that the channel response be known at the receiver. Training-based methods, which probe the channel in time, frequency, and space with known signals and reconstruct the channel response from the output signals, are most commonly used to accomplish this task. Traditional training-based channel estimation methods, typically comprising linear reconstruction techniques, are known to be optimal for rich multipath channels. However, physical arguments and growing experimental evidence suggest that many wireless channels encountered in practice tend to exhibit a sparse multipath structure that gets pronounced as the signal space dimension gets large (e.g., due to large bandwidth or large number of antennas). In this paper, we formalize the notion of multipath sparsity and present a new approach to estimating sparse (or effectively sparse) multipath channels that is based on some of the recent advances in the theory of compressed sensing. In particular, it is shown in the paper that the proposed approach, which is termed as compressed channel sensing (CCS), can potentially achieve a target reconstruction error using far less energy and, in many instances, latency and bandwidth than that dictated by the traditional least-squares-based training methods.

1,066 citations

Posted Content•
TL;DR: In this article, the eigenvalues of the covariance matrix of signals received at the secondary users are used for signal detection in cognitive radio systems, and the proposed methods overcome the noise uncertainty problem, and can even perform better than the ideal energy detection when the signals to be detected are highly correlated.
Abstract: Spectrum sensing is a fundamental component is a cognitive radio. In this paper, we propose new sensing methods based on the eigenvalues of the covariance matrix of signals received at the secondary users. In particular, two sensing algorithms are suggested, one is based on the ratio of the maximum eigenvalue to minimum eigenvalue; the other is based on the ratio of the average eigenvalue to minimum eigenvalue. Using some latest random matrix theories (RMT), we quantify the distributions of these ratios and derive the probabilities of false alarm and probabilities of detection for the proposed algorithms. We also find the thresholds of the methods for a given probability of false alarm. The proposed methods overcome the noise uncertainty problem, and can even perform better than the ideal energy detection when the signals to be detected are highly correlated. The methods can be used for various signal detection applications without requiring the knowledge of signal, channel and noise power. Simulations based on randomly generated signals, wireless microphone signals and captured ATSC DTV signals are presented to verify the effectiveness of the proposed methods.

1,022 citations

Journal Article•DOI•
TL;DR: A new paradigm for the design of transmitter space-time coding is introduced that is referred to as linear precoding, which leads to simple closed-form solutions for transmission over frequency-selective multiple-input multiple-output (MIMO) channels, which are scalable with respect to the number of antennas, size of the coding block, and transmit average/peak power.
Abstract: We introduce a new paradigm for the design of transmitter space-time coding that we refer to as linear precoding. It leads to simple closed-form solutions for transmission over frequency-selective multiple-input multiple-output (MIMO) channels, which are scalable with respect to the number of antennas, size of the coding block, and transmit average/peak power. The scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension. The specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses, under average and peak power constraints. The solutions are shown to convert the MIMO channel with memory into a set of parallel flat fading subchannels, regardless of the design criterion, while appropriate power/bits loading on the subchannels is the specific signature of the different designs. The proposed designs are compared in terms of various performance measures such as information rate, BER, and symbol mean square error.

891 citations


Cites background or methods from "Fundamentals Of Statistical Signal ..."

  • ...The that minimizes the whole MSE matrix is the same as the MMSE (Wiener) receiver [15], which is known to minimize the tr MSE and is given by...

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  • ...Such diagonalization decomposes the system in a set of parallel independent AGN subchannels for which symbol-by-symbol decision is optimal [15]....

    [...]

  • ...3 Specifically, if we let denote the symbol vector corresponding to hypothesis , and let denote the decision on the th symbol block, then the ML decision rule is [15]...

    [...]

References
More filters
Book•
01 Jan 1986
TL;DR: In this paper, the authors propose a recursive least square adaptive filter (RLF) based on the Kalman filter, which is used as the unifying base for RLS Filters.
Abstract: Background and Overview. 1. Stochastic Processes and Models. 2. Wiener Filters. 3. Linear Prediction. 4. Method of Steepest Descent. 5. Least-Mean-Square Adaptive Filters. 6. Normalized Least-Mean-Square Adaptive Filters. 7. Transform-Domain and Sub-Band Adaptive Filters. 8. Method of Least Squares. 9. Recursive Least-Square Adaptive Filters. 10. Kalman Filters as the Unifying Bases for RLS Filters. 11. Square-Root Adaptive Filters. 12. Order-Recursive Adaptive Filters. 13. Finite-Precision Effects. 14. Tracking of Time-Varying Systems. 15. Adaptive Filters Using Infinite-Duration Impulse Response Structures. 16. Blind Deconvolution. 17. Back-Propagation Learning. Epilogue. Appendix A. Complex Variables. Appendix B. Differentiation with Respect to a Vector. Appendix C. Method of Lagrange Multipliers. Appendix D. Estimation Theory. Appendix E. Eigenanalysis. Appendix F. Rotations and Reflections. Appendix G. Complex Wishart Distribution. Glossary. Abbreviations. Principal Symbols. Bibliography. Index.

16,062 citations

Journal Article•DOI•
Steven Kay1•
TL;DR: The Fundamentals of Statistical Signal Processing: Estimation Theory as mentioned in this paper is a seminal work in the field of statistical signal processing, and it has been used extensively in many applications.
Abstract: (1995). Fundamentals of Statistical Signal Processing: Estimation Theory. Technometrics: Vol. 37, No. 4, pp. 465-466.

14,342 citations

Book•
01 Jan 1965
TL;DR: This chapter discusses the concept of a Random Variable, the meaning of Probability, and the axioms of probability in terms of Markov Chains and Queueing Theory.
Abstract: Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing Theory

13,886 citations

Book•
01 Jan 2002
TL;DR: In this paper, the meaning of probability and random variables are discussed, as well as the axioms of probability, and the concept of a random variable and repeated trials are discussed.
Abstract: Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing Theory

12,407 citations

Book•
01 Jan 1989
TL;DR: In this paper, the authors provide a thorough treatment of the fundamental theorems and properties of discrete-time linear systems, filtering, sampling, and discrete time Fourier analysis.
Abstract: For senior/graduate-level courses in Discrete-Time Signal Processing. THE definitive, authoritative text on DSP -- ideal for those with an introductory-level knowledge of signals and systems. Written by prominent, DSP pioneers, it provides thorough treatment of the fundamental theorems and properties of discrete-time linear systems, filtering, sampling, and discrete-time Fourier Analysis. By focusing on the general and universal concepts in discrete-time signal processing, it remains vital and relevant to the new challenges arising in the field --without limiting itself to specific technologies with relatively short life spans.

10,388 citations