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A Unified Framework for GLRT-Based Spectrum Sensing of Signals with Covariance Matrices with Known Eigenvalue Multiplicities
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7599-4367
2011 (English)In: Proceedings of the IEEE International Conference on Acoustics, Speech and SignalProcessing (ICASSP), IEEE conference proceedings, 2011, 2956-2959 p.Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, we create a unified framework for spectrum sensing of signals which have covariance matrices with known eigenvalue multiplicities. We derive the generalized likelihood-ratio test (GLRT) for this problem, with arbitrary eigenvalue multiplicities under both hypotheses. We also show a number of applications to spectrum sensing for cognitive radio and show that the GLRT for these applications, of which some are already known, are special cases of the general result.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2011. 2956-2959 p.
Series
IEEE International Conference on Acoustics, Speech and SignalProcessing, ISSN 1520-6149
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-64320DOI: 10.1109/ICASSP.2011.5946277ISI: 000296062403092OAI: oai:DiVA.org:liu-64320DiVA: diva2:389318
Note
©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Erik Axell and Erik G. Larsson, A Unified Framework for GLRT-Based Spectrum Sensing of Signals with Covariance Matrices with Known Eigenvalue Multiplicities, 2011, Proceedings of the IEEE International Conference on Acoustics, Speech and SignalProcessing (ICASSP), 2956-2959. http://dx.doi.org/10.1109/ICASSP.2011.5946277 Available from: 2011-01-19 Created: 2011-01-19 Last updated: 2016-08-31
In thesis
1. Spectrum Sensing Algorithms Based on Second-Order Statistics
Open this publication in new window or tab >>Spectrum Sensing Algorithms Based on Second-Order Statistics
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Cognitive radio is a new concept of reusing spectrum in an opportunistic manner. Cognitive radio is motivated by recent measurements of spectrum utilization, showing unused resources in frequency, time and space. Introducing cognitive radios in a primary network inevitably creates increased interference to the primary users. Secondary users must sense the spectrum and detect primary users' signals at very low SNR, to avoid causing too much interference.This dissertation studies this detection problem, known as spectrum sensing.

The fundamental problem of spectrum sensing is to discriminate an observation that contains only noise from an observation that contains a very weak signal embedded in noise. In this work, detectors are derived that exploit known properties of the second-order moments of the signal. In particular, known structures of the signal covariance are exploited to circumvent the problem of unknown parameters, such as noise and signal powers or channel coefficients.

The dissertation is comprised of six papers, all in different ways related to spectrum sensing based on second-order statistics. In the first paper, we considerspectrum sensing of orthogonal frequency-division multiplexed (OFDM) signals in an additive white Gaussian noise channel. For the case of completely known noise and signal powers, we set up a vector-matrix model for an OFDM signal with a cyclic prefix and derive the optimal Neyman-Pearson detector from first principles. For the case of completely unknown noise and signal powers, we derive a generalized likelihood ratio test (GLRT) based on empirical second-order statistics of the received data. The proposed GLRT detector exploits the non-stationary correlation structure of the OFDM signal and does not require any knowledge of the noise or signal powers.

In the second paper, we create a unified framework for spectrum sensing of signals which have covariance matrices with known eigenvalue multiplicities. We derive the GLRT for this problem, with arbitrary eigenvalue multiplicities under both hypotheses. We also show a number of applications to spectrum sensing for cognitive radio.

The general result of the second paper is used as a building block, in the third and fourth papers, for spectrum sensing of second-order cyclostationary signals received at multiple antennas and orthogonal space-time block coded (OSTBC) signals respectively. The proposed detector of the third paper exploits both the spatial and the temporal correlation of the received signal, from knowledge of the fundamental period of the cyclostationary signal and the eigenvalue multiplicities of the temporal covariance matrix.

In the fourth paper, we consider spectrum sensing of signals encoded with an OSTBC. We show how knowledge of the eigenvalue multiplicities of the covariance matrix are inherent owing to the OSTBC, and propose an algorithm that exploits that knowledge for detection. We also derive theoretical bounds on the performance of the proposed detector. In addition, we show that the proposed detector is robust to a carrier frequency offset, and propose another detector that deals with timing synchronization using the detector for the synchronized case as a building block.

A slightly different approach to covariance matrix estmation is taken in the fifth paper. We consider spectrum sensing of Gaussian signals with structured covariance matrices, and propose to estimate the unknown parameters of the covariance matrices using covariance matching estimation techniques (COMET). We also derive the optimal detector based on a Gaussian approximation of the sample covariance matrix, and show that this is closely connected to COMET.

The last paper deals with the problem of discriminating samples that containonly noise from samples that contain a signal embedded in noise, when the variance of the noise is unknown. We derive the optimal soft decision detector using a Bayesian approach. The complexity of this optimal detector grows exponentially with the number of observations and as a remedy, we propose a number of approximations to it. The problem under study is a fundamental one andit has applications in signal denoising, anomaly detection, and spectrum sensing for cognitive radio.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. 37 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1457
National Category
Communication Systems
Identifiers
urn:nbn:se:liu:diva-78948 (URN)978-91-7519-876-7 (ISBN)
Public defence
2012-09-14, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 13:15 (English)
Opponent
Supervisors
Available from: 2012-06-27 Created: 2012-06-26 Last updated: 2017-01-13Bibliographically approved

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Axell, ErikLarsson, Erik G.

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