Analysis of Energy Detector in Cooperative Relay Networks for Cognitive Radios

In this paper, performance of the energy detector is analyzed in blind cooperative relay networks operating over independent and identically distributed (IID) Rayleigh fading channels. First, utilizing the closed-form expression of the probability density function (PDF) of the dual-hop relay link along with an alternative series form representation of the generalized marcum-Q function, exact average detection probability expression is obtained for the dual-hop blind relay link. After that, a closed-form PDF expression is derived for the total received signal-to-noise ratio (SNR) of the combined received signal, received via the relay path and direct path, at the destination, which is assumed to be equipped with selection combiner (SC) and energy detector. Finally, within the same analytical framework, as established for the analysis of the relay link, an exact average detection probability expression for the cooperative system is derived. Since the obtained expressions are in the form of infinite summation series, therefore, respective series truncation error bounds are also calculated, which can be used to compute the number of terms required to achieve a given figure of accuracy. In the end, analytical expressions are validated with the help of computer simulations. It is expected that these analysis will be helpful in quantifying the future communication networks such as cognitive radio networks.

[1]  Geoffrey Ye Li,et al.  Cooperative Spectrum Sensing in Cognitive Radio, Part II: Multiuser Networks , 2007, IEEE Transactions on Wireless Communications.

[2]  I. Miller.  Probability, Random Variables, and Stochastic Processes , 1966 .

[3]  Geoffrey Ye Li,et al.  Cooperative Spectrum Sensing in Cognitive Radio, Part I: Two User Networks , 2007, IEEE Transactions on Wireless Communications.

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

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

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

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

[8]  Mazen O. Hasna,et al.  A performance study of dual-hop transmissions with fixed gain relays , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[9]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[10]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[11]  Carlo S. Regazzoni,et al.  Distributed cognitive radio architecture with automatic frequency switching , 2012, 2012 Complexity in Engineering (COMPENG). Proceedings.

[12]  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.

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

[14]  Adeel Razi,et al.  Tight upper bounds on average detection probability in cooperative relay networks with selection combiner , 2015, Trans. Emerg. Telecommun. Technol..

[15]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

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

[17]  R C Robertson,et al.  Digital Communications Over Fading Channels , 2004 .

[18]  D. Owen.  Handbook of Mathematical Functions with Formulas , 1965 .

[19]  Junrong Gu,et al.  Detection probability analysis for AF assisted cooperative spectrum sensing in cognitive radio networks , 2011, ICTC 2011.

[20]  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).