Sensing of Unknown Signals over Weibull Fading Conditions

Energy detection is a widely used method of spectrum sensing in cognitive radio and Radio Detection And Ranging (RADAR) systems. This paper is devoted to the analytical evaluation of the performance of an energy detector over Weibull fading channels. This is a flexible fading model that has been shown capable of providing accurate characterization of multipath fading in, e.g., typical cellular radio frequency range of 800${/}$900 MHz. A novel analytic expression for the corresponding average probability of detection is derived in a simple algebraic representation which renders it convenient to handle both analytically and numerically. As expected, the performance of the detector is highly dependent upon the severity of fading as even small variation of the fading parameters affect significantly the value of the average probability of detection. This appears to be particularly the case in severe fading conditions. The offered results are useful in evaluating the effect of multipath fading in energy detection-based cognitive radio communication systems and therefore they can be used in quantifying the associated trade-offs between sensing performance and energy efficiency in cognitive radio networks.

[1]  Daniel Benevides da Costa,et al.  Multiuser and Multirelay Cognitive Radio Networks Under Spectrum-Sharing Constraints , 2014, IEEE Transactions on Vehicular Technology.

[2]  A. Ghasemi,et al.  Collaborative spectrum sensing for opportunistic access in fading environments , 2005, First IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, 2005. DySPAN 2005..

[3]  Hai Jiang,et al.  Energy Detection Based Cooperative Spectrum Sensing in Cognitive Radio Networks , 2011, IEEE Transactions on Wireless Communications.

[4]  A. Rabbachin,et al.  UWB Energy Detection in the Presence of Multiple Narrowband Interferers , 2007, 2007 IEEE International Conference on Ultra-Wideband.

[5]  Hai Jiang,et al.  Relay Based Cooperative Spectrum Sensing in Cognitive Radio Networks , 2009, GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference.

[6]  George K. Karagiannidis,et al.  Analytic solutions to a Marcum Q-function-based integral and application in energy detection of unknown signals over multipath fading channels , 2014, 2014 9th International Conference on Cognitive Radio Oriented Wireless Networks and Communications (CROWNCOM).

[7]  Paschalis C. Sofotasios,et al.  The η-μ/gamma composite fading model , 2010, 2010 IEEE International Conference on Wireless Information Technology and Systems.

[8]  David W. Matolak,et al.  Generation of multivariate Weibull random variates , 2008, IET Commun..

[9]  Vijay K. Bhargava,et al.  Cognitive Wireless Communication Networks , 2007 .

[10]  Paschalis C. Sofotasios,et al.  Analytic performance evaluation of underlay relay cognitive networks with channel estimation errors , 2013, 2013 International Conference on Advanced Technologies for Communications (ATC 2013).

[11]  Vladimir I. Kostylev,et al.  Energy detection of a signal with random amplitude , 2002, 2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333).

[12]  Hai Jiang,et al.  Performance of an Energy Detector over Channels with Both Multipath Fading and Shadowing , 2010, IEEE Transactions on Wireless Communications.

[13]  M.C. Stefanovic,et al.  Outage Probability of Sir-Based Dual Selection Diversity over Correlated Weibull Fading Channels , 2007, 2007 8th International Conference on Telecommunications in Modern Satellite, Cable and Broadcasting Services.

[14]  George K. Karagiannidis,et al.  Analytic Expressions and Bounds for Special Functions and Applications in Communication Theory , 2014, IEEE Transactions on Information Theory.

[15]  George K. Karagiannidis,et al.  Channel capacity and second-order statistics in Weibull fading , 2004, IEEE Communications Letters.

[16]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[17]  Paschalis C. Sofotasios,et al.  Analytic results for efficient computation of the Nuttall-Q and incomplete Toronto functions , 2013, 2013 International Conference on Advanced Technologies for Communications (ATC 2013).

[18]  Hai Jiang,et al.  Spectrum Sensing via Energy Detector in Low SNR , 2011, 2011 IEEE International Conference on Communications (ICC).

[19]  D. B. da Costa,et al.  Joint statistics for two correlated Weibull variates , 2005, IEEE Antennas and Wireless Propagation Letters.

[20]  R. M. A. P. Rajatheva,et al.  On the energy detection of unknown deterministic signal over Nakagami channelswith selection combining , 2009, 2009 Canadian Conference on Electrical and Computer Engineering.

[21]  S. Haykin,et al.  Modern Wireless Communications , 1939, Nature.

[22]  R. M. A. P. Rajatheva,et al.  Energy Detection of Unknown Signals in Fading and Diversity Reception , 2011, IEEE Transactions on Communications.

[23]  H. Urkowitz.  Energy detection of unknown deterministic signals , 1967 .

[24]  Kerstin Vogler,et al.  Table Of Integrals Series And Products , 2016 .

[25]  R. Tandra,et al.  Fundamental limits on detection in low SNR under noise uncertainty , 2005, 2005 International Conference on Wireless Networks, Communications and Mobile Computing.

[26]  Mohamed-Slim Alouini,et al.  Digital Communication Over Fading Channels: A Unified Approach to Performance Analysis , 2000 .

[27]  C. Tellambura,et al.  Energy detection of primary signals over η - μ fading channels , 2009, 2009 International Conference on Industrial and Information Systems (ICIIS).

[28]  George K. Karagiannidis,et al.  On the Monotonicity of the Generalized Marcum and Nuttall ${Q}$ -Functions , 2007, IEEE Transactions on Information Theory.

[29]  W. Weibull.  A Statistical Distribution Function of Wide Applicability , 1951 .

[30]  Simon Haykin,et al.  Cognitive radio: brain-empowered wireless communications , 2005, IEEE Journal on Selected Areas in Communications.

[31]  Amir Ghasemi,et al.  Asymptotic performance of collaborative spectrum sensing under correlated log-normal shadowing , 2007, IEEE Communications Letters.

[32]  Rahul Tandra,et al.  Fundamental limits on detection in low SNR , 2005 .

[33]  Hai Jiang,et al.  Performance of Energy Detection: A Complementary AUC Approach , 2010, 2010 IEEE Global Telecommunications Conference GLOBECOM 2010.

[34]  Daniel Benevides da Costa,et al.  On the weibull autocorrelation and power spectrum functions: field trials and validation , 2006, IEEE Communications Letters.

[35]  P. Sofotasios,et al.  A novel representation for the Nuttall Q-function , 2010, 2010 IEEE International Conference on Wireless Information Technology and Systems.

[36]  Amir Ghasemi,et al.  Impact of User Collaboration on the Performance of Sensing-Based Opportunistic Spectrum Access , 2006, IEEE Vehicular Technology Conference.

[37]  Paschalis C. Sofotasios,et al.  Novel expressions for the Marcum and one dimensional Q-functions , 2010, 2010 7th International Symposium on Wireless Communication Systems.

[38]  R. M. A. P. Rajatheva,et al.  Analysis of Equal Gain Combining in Energy Detection for Cognitive Radio over Nakagami Channels , 2008, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference.

[39]  Paschalis C. Sofotasios,et al.  Bit error rate of underlay multi-hop cognitive networks in the presence of multipath fading , 2013, 2013 Fifth International Conference on Ubiquitous and Future Networks (ICUFN).

[40]  Mohamed-Slim Alouini,et al.  On the Energy Detection of Unknown Signals Over Fading Channels , 2007, IEEE Transactions on Communications.

[41]  Norman C. Beaulieu,et al.  Novel Analysis for Performance Evaluation of Energy Detection of Unknown Deterministic Signals Using Dual Diversity , 2011, 2011 IEEE Vehicular Technology Conference (VTC Fall).

[42]  Kalle Ruttik,et al.  Detection of Unknown Signals in a Fading Environment , 2009, IEEE Communications Letters.

[43]  Amir Ghasemi,et al.  Spectrum sensing in cognitive radio networks: requirements, challenges and design trade-offs , 2008, IEEE Communications Magazine.

[44]  Danijela Cabric,et al.  Cognitive radio: Ten years of experimentation and development , 2011, IEEE Communications Magazine.

[45]  Paschalis C. Sofotasios,et al.  On the η-µ/gamma and the λ-µ/gamma multipath/shadowing distributions , 2011, 2011 Australasian Telecommunication Networks and Applications Conference (ATNAC).

[46]  Paschalis C. Sofotasios,et al.  Underlay cooperative cognitive networks with imperfect Nakagami-m fading channel information and strict transmit power constraint: Interference statistics and outage probability analysis , 2014, Journal of Communications and Networks.

[47]  Jess Marcum,et al.  A statistical theory of target detection by pulsed radar , 1948, IRE Trans. Inf. Theory.

[48]  Paschalis C. Sofotasios,et al.  Outage behaviour of cooperative underlay cognitive networks with inaccurate channel estimation , 2013, 2013 Fifth International Conference on Ubiquitous and Future Networks (ICUFN).