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Optimal and Sub-Optimal Spectrum Sensing of OFDM Signals in Known and Unknown Noise Variance
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: 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. Vol. 29, no 2, 290-304 p.
Keyword [en]
spectrum sensing, signal detection, OFDM, cyclic prefix, subspace detection, second-order statistics
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-58515DOI: 10.1109/JSAC.2011.110203ISI: 000286676500003OAI: oai:DiVA.org:liu-58515DiVA: diva2:343116
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
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
2. Topics in Spectrum Sensing for Cognitive Radio
Open this publication in new window or tab >>Topics in Spectrum Sensing for Cognitive Radio
2009 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Cognitive radio is a new concept of reusing licensed spectrum in an unlicensed manner. Cognitive radio is motivated by recent measurements of spectrum utilization, showing unused resources in frequency, time and space. The spectrum must be sensed to detect primary user signals, in order to allow cognitive radios in a primary system. In this thesis we study some topics in spectrum sensing for cognitive radio.

The fundamental problem of spectrum sensing is to discriminate samples that contain only noise from samples that contain a very weak signal embedded in noise. We derive detectors that exploit known structures of the signal, for the cases of an OFDM modulated signal and an orthogonal space-time block coded signal. We derive optimal detectors, in the Neyman-Pearson sense, for a few different cases when all parameters are known. Moreover we study detection when the parameters, such as noise variance, are unknown. We propose solutions the problem of unknown parameters.

We also study system aspects of cognitive radio. More specifically, we investigate spectrum reuse of geographical spectrum holes in a frequency planned primary network. System performance is measured in terms of the achievable rate for the cognitive radio system. Simulation results show that a substantial sum-rate could be achieved if the cognitive radios communicate over small distances. However, the spectrum hole gets saturated quite fast, due to interference caused by the cognitive radios.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2009. 21 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1417
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-51748 (URN)978-91-7393-523-4 (ISBN)
Presentation
2009-12-21, Glashuset, Campus Valla, Linköpings universitet, Linköping, 13:15 (English)
Opponent
Supervisors
Available from: 2009-11-20 Created: 2009-11-17 Last updated: 2017-01-13Bibliographically approved

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