On the second order statistics of the multihop Rayleigh fading channel

  • Authors:

  • Zoran Hadzi-Velkov;Nikola Zlatanov;George K. Karagiannidis

  • Affiliations:

  • Faculty of Electrical Engineering and Information Technologies, Ss. Cyril and Methodius University, Skopje;Faculty of Electrical Engineering and Information Technologies, Ss. Cyril and Methodius University, Skopje;Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki

  • Venue:
  • IEEE Transactions on Communications
  • Year:
  • 2009

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Abstract

Second order statistics provides a dynamic representation of a fading channel and plays an important role in the evaluation and design of the wireless communication systems. In this paper, we present a novel analytical framework for the evaluation of important second order statistical parameters, as the level crossing rate (LCR) and the average fade duration (AFD) of the amplify-and-forward multihop Rayleigh fading channel. More specifically, motivated by the fact that this channel is a cascaded one and can be modeled as the product of N fading amplitudes, we derive novel analytical expressions for the average LCR and the AFD of the product of N Rayleigh fading envelopes (or of the recently so-called N*Rayleigh channel). Furthermore, we derive simple and efficient closed-form approximations to the aforementioned parameters, using the multivariate Laplace approximation theorem. It is shown that our general results reduce to the corresponding ones of the specific dual-hop case, previously published. Numerical and computer simulation examples verify the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations.