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Efficient Approximated Q-Function Form for Error Probability over Rayleigh Fading Channels

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Abstract

Error rate probability is considered as important metric to evaluate the behavior of communication system. Gaussian Q-function is gaining more intention from researchers due to its direct relation in computing the error probability in terms of symbol error rate (SER) or bit error rate. In literature, several approximated functions have been proposed to evaluate and analyze the error rate in fading channel. In this paper, a novel, simple and accurate closed form for Gaussian Q-function is derived. In contrast to previous related approximated functions; it is noticeable that the designed formula improves the accuracy for large range of positive argument. Furthermore, an efficient SER formula is derived for additive white Gaussian noise and for Rayleigh fading channel. Numerical analysis and simulation were conducted to verify and validate the designed approximated functions. The results show that the proposed form can achieve high accuracy compared to that of previous work; and also simplify the evaluation analysis of SER in fading channels.

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Acknowledgments

The authors would like to thank the Univeristi Sains Malaysia for providing RUI Grant entitled Relative Velocity-based Forwarding Strategy For Vehicular Ad hoc Naetworks (1001/PNAV/814233) to fund this research project.

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Authors and Affiliations

  1. National Advanced IPv6 Centre, Universiti Sains Malaysia, Pulau Penang, Malaysia

    Sabri M. Hanshi, Mohammed M. Kadhum & Tat-Chee Wan

  2. Seiyun Community College, Hadhramout, Yemen

    Sabri M. Hanshi

  3. Telecommunication Research Lab, Queen’s University, Kingston, Canada

    Mohammed M. Kadhum

  4. School of Computer Sciences, Universiti Sains Malaysia, Pulau Penang, Malaysia

    Tat-Chee Wan

Authors
  1. Sabri M. Hanshi
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  2. Mohammed M. Kadhum
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  3. Tat-Chee Wan
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Correspondence to Sabri M. Hanshi.

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Hanshi, S.M., Kadhum, M.M. & Wan, TC. Efficient Approximated Q-Function Form for Error Probability over Rayleigh Fading Channels. Wireless Pers Commun 89, 467–478 (2016). https://doi.org/10.1007/s11277-016-3282-0

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  • DOI: https://doi.org/10.1007/s11277-016-3282-0

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