New asymptotics for performance of energy detector

Performance analysis of the energy detector (ED) in fading channels has received enormous attention recently. However, averaging the generalized Marcum-Q function over fading statistics often results in complicated special functions and/or infinite series based expressions. Motivated by the need for simple expressions without compromising the accuracy, we propose a new representation for the probability density function (PDF) of the fading channel gain. This representation is then used to derive simple, unified expression for asymptotic miss-detection probability in closed-form. The derived expression is evaluated for several fading channels and antenna diversity schemes. Numerical results reveal its high accuracy over a wide range of signal-to-noise-ratio (SNR) (as low as 0 dB) unlike the existing asymptotic expression which is accurate only for high SNR regime (say, SNR ≥ 20 dB).

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

[2]  Hai Jiang,et al.  Analysis of area under the ROC curve of energy detection , 2010, IEEE Transactions on Wireless Communications.

[3]  Umberto Mengali,et al.  UWB Energy Detection Receivers with Partial Channel Knowledge , 2006, 2006 IEEE International Conference on Communications.

[4]  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).

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

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

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

[8]  Georgios B. Giannakis,et al.  A simple and general parameterization quantifying performance in fading channels , 2003, IEEE Trans. Commun..

[9]  Dian-Wu Yue,et al.  A General Parameterization Quantifying Performance in Energy Detection , 2009, IEEE Signal Processing Letters.

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

[11]  M. Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. U.S. Department of Commerce, National Bureau of Standards , 1965 .

[12]  Anke Schmid,et al.  An Introduction To Complex Analysis , 2016 .

[13]  Hai Jiang,et al.  Energy Detection for Spectrum Sensing in Cognitive Radio , 2014, SpringerBriefs in Computer Science.

[14]  R.W. Brodersen,et al.  Implementation issues in spectrum sensing for cognitive radios , 2004, Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004..

[15]  Harry L. Van Trees,et al.  Detection, Estimation, and Modulation Theory: Radar-Sonar Signal Processing and Gaussian Signals in Noise , 1992 .

[16]  Mohamed-Slim Alouini,et al.  Digital Communication over Fading Channels: Simon/Digital Communications 2e , 2004 .

[17]  Zhongding Lei,et al.  IEEE 802.22: The first cognitive radio wireless regional area network standard , 2009, IEEE Communications Magazine.

[18]  Mandy Eberhart,et al.  Digital Communication Over Fading Channels , 2016 .

[19]  J. I. Mararm,et al.  Energy Detection of Unknown Deterministic Signals , 2022 .