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Spectrum Sensing Algorithms Based on Second-Order Statistics
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
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: urn:nbn:se:liu:diva-78948ISBN: 978-91-7519-876-7 (print)OAI: oai:DiVA.org:liu-78948DiVA: diva2:537182
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
List of papers
1. Optimal and Sub-Optimal Spectrum Sensing of OFDM Signals in Known and Unknown Noise Variance
Open this publication in new window or tab >>Optimal and Sub-Optimal Spectrum Sensing of OFDM Signals in Known and Unknown Noise Variance
2011 (English)In: IEEE Journal on Selected Areas in Communications, ISSN 0733-8716, E-ISSN 1558-0008, Vol. 29, no 2, 290-304 p.Article in journal (Refereed) Published
Abstract [en]

We consider spectrum sensing of OFDM signals in an AWGN 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. The optimal detector exploits the inherent correlation  of the OFDM signal incurred by the repetition of data in the cyclic  prefix, using knowledge of the length of the cyclic prefix and the  length of the OFDM symbol. We compare the optimal detector to the energy  detector numerically. We show that the energy detector is  near-optimal (within 1 dB SNR) when the noise variance is  known. Thus, when the noise power is known, no substantial gain can  be achieved by using any other detector than the energy detector.

For the case of completely unknown noise and signal powers, we  derive a generalized likelihood ratio test (GLRT) based onempirical 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 power or the signal power. The  GLRT detector is compared to state-of-the-art OFDM signal detectors,  and shown to improve the detection performance with 5 dB SNR in  relevant cases.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2011
Keyword
spectrum sensing, signal detection, OFDM, cyclic prefix, subspace detection, second-order statistics
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-58515 (URN)10.1109/JSAC.2011.110203 (DOI)000286676500003 ()
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, Optimal and Sub-Optimal Spectrum Sensing of OFDM Signals in Known and Unknown Noise Variance, 2011, IEEE Journal on Selected Areas in Communications, (29), 2, 290-304. http://dx.doi.org/10.1109/JSAC.2011.110203

The previous status of this article was Manuskript.

Available from: 2010-08-12 Created: 2010-08-12 Last updated: 2017-12-12Bibliographically approved
2. A Unified Framework for GLRT-Based Spectrum Sensing of Signals with Covariance Matrices with Known Eigenvalue Multiplicities
Open this publication in new window or tab >>A Unified Framework for GLRT-Based Spectrum Sensing of Signals with Covariance Matrices with Known Eigenvalue Multiplicities
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
Series
IEEE International Conference on Acoustics, Speech and SignalProcessing, ISSN 1520-6149
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-64320 (URN)10.1109/ICASSP.2011.5946277 (DOI)000296062403092 ()
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
3. Multiantenna Spectrum Sensing of a Second-Order Cyclostationary Signal
Open this publication in new window or tab >>Multiantenna Spectrum Sensing of a Second-Order Cyclostationary Signal
2011 (English)In: Proceedings of the 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP'11), 2011, 329-332 p.Conference paper, Published paper (Refereed)
Abstract [en]

We consider spectrum sensing of a second-order cyclostationary signal receivedat multiple antennas. The proposed detector exploits both the spatial andthe temporal correlation of the received signal, from knowledge of thefundamental period of the cyclostationary signal and the eigenvaluemultiplicities of the temporal covariance matrix. All other parameters, suchas the channel gains or the noise power, are assumed to be unknown. The proposeddetector is shown numerically to outperform state-of-the-art detectors forspectrum sensing of anOFDM signal, both when using a single antenna and with multiple antennas.

Keyword
spectrum sensing, multiple antennas, cyclostationarity, GLRT
National Category
Communication Systems Signal Processing
Identifiers
urn:nbn:se:liu:diva-70858 (URN)10.1109/CAMSAP.2011.6136017 (DOI)978-1-4577-2103-8 (ISBN)
Conference
4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), December 13-16 2011, San Juan, Puerto Rico (USA)
Funder
eLLIIT - The Linköping‐Lund Initiative on IT and Mobile CommunicationsSwedish Research Council
Available from: 2011-09-20 Created: 2011-09-20 Last updated: 2016-08-31Bibliographically approved
4. Spectrum Sensing of Orthogonal Space-Time Block Coded Signals with Multiple Receive Antennas
Open this publication in new window or tab >>Spectrum Sensing of Orthogonal Space-Time Block Coded Signals with Multiple Receive Antennas
2010 (English)In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Institute of Electrical and Electronics Engineers (IEEE), 2010, 3110-3113 p.Conference paper, Published paper (Other academic)
Abstract [en]

We consider detection of signals encoded with orthogonal space-time block codes (OSTBC), using multiple receive antennas. Such signals contain redundancy and they have a specific structure, that can be exploited for detection. We derive the optimal detector, in the Neyman-Pearson sense, when all parameters are known. We also consider unknown noise variance, signal variance and channel coefficients. We propose a number of GLRT based detectors for the different cases, that exploit the redundancy structure of the OSTBC signal. We also propose an eigenvalue-based detector for the case when all parameters are unknown. The proposed detectors are compared to the energy detector. We show that when only the noise variance is known, there is no gain in exploiting the structure of the OSTBC. However, when the noise variance is unknown there can be a significant gain.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2010
Series
Acoustics Speech and Signal Processing (ICASSP), ISSN 1520-6149 (Print), 2379-190X (online), 1520-6149 (CD)
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-51745 (URN)10.1109/ICASSP.2010.5496088 (DOI)000287096003014 ()9781424442959 (ISBN)9781424442966 (ISBN)
Conference
IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2010, 14-19 March, Dallas, Texas, U.S.A.
Note

©2010 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, Spectrum Sensing of Orthogonal Space-Time Block Coded Signals with Multiple Receive Antennas, 2010, Proceedings of the 35th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'10).

The previous status of this articel was Manuscript.

Available from: 2009-11-17 Created: 2009-11-17 Last updated: 2017-01-13Bibliographically approved
5. Spectrum Sensing of Signals with Structured Covariance Matrices Using Covariance Matching Estimation Techniques
Open this publication in new window or tab >>Spectrum Sensing of Signals with Structured Covariance Matrices Using Covariance Matching Estimation Techniques
2011 (English)In: Proceedings of the IEEE Global Communications Conference (GLOBECOM), 2011, 1-5 p.Conference paper, Published paper (Refereed)
Abstract [en]

In this work, we consider spectrum sensing of Gaussian signals with structured covariance matrices. We show that the optimal detector based on the probability distribution of the sample covariance matrix is equivalent to the optimal detector based on the raw data, if the covariance matrices are known. However, the covariance matrices are unknown in general. Therefore, we propose to estimate the unknown parameters 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.

Keyword
spectrum sensing, sample covariance, COMET
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-69639 (URN)10.1109/GLOCOM.2011.6133506 (DOI)978-1-4244-9267-1 (ISBN)978-1-4244-9266-4 (ISBN)
Conference
IEEE Global Communications Conference (GLOBECOM), 3-7 December, Anaheim, California, USA
Available from: 2011-07-08 Created: 2011-07-08 Last updated: 2016-08-31
6. A Bayesian Approach to Spectrum Sensing, Denoising and Anomaly Detection
Open this publication in new window or tab >>A Bayesian Approach to Spectrum Sensing, Denoising and Anomaly Detection
2009 (English)In: Proceedings of the 34th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'09), 2009, 2333-2336 p.Conference paper, Published paper (Refereed)
Abstract [en]

This paper deals with the problem of discriminating samples that contain only noise from samples that contain a signal embedded in noise. The focus is on the case 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 and it has applications in signal denoising, anomaly detection, and spectrum sensing for cognitive radio. We illustrate the results in the context of the latter.

Series
Acoustics, Speech and Signal Processing, ISSN 1520-6149 ; 2009
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-25592 (URN)10.1109/ICASSP.2009.4960088 (DOI)978-1-4244-2354-5 (ISBN)978-1-4244-2353-8 (ISBN)
Conference
34th IEEE international conference on acoustics, speech and signal processing,19-24 April, Taipei, Taiwan
Note
©2009 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 Bayesian Approach to Spectrum Sensing, Denoising and Anomaly Detection, 2009, Proceedings of the 34th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'09), 2333-2336. http://dx.doi.org/10.1109/ICASSP.2009.4960088Available from: 2009-10-08 Created: 2009-10-08 Last updated: 2016-08-31Bibliographically approved

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