Asymptotic Outage Probability Analysis for General Fixed-Gain Amplify-and-Forward Multihop Relay Systems

In this paper, we present an analysis of the outage probability for fixed-gain amplify-and-forward (AF) multihop relay links operating in the high SNR regime. Our analysis exploits properties of Mellin transforms to derive an asymptotic approximation that is accurate even when the per-hop channel gains adhere to completely different fading models. The main result contained in the paper is a general expression for the outage probability, which is a functional of the Mellin transforms of the per-hop channel gains. Furthermore, we explicitly calculate the asymptotic outage probability for four different systems, whereby in each system the per-hop channels adhere to either a Nakagami-m, Weibull, Rician, or Hoyt fading profile, but where the distributional parameters may differ from hop to hop. This analysis leads to our second main result, which is a semi-general closed-form formula for the outage probability of general fixed-gain AF multihop systems. We exploit this formula to analyze an example scenario for a four-hop system where the per-hop channels follow the four aforementioned fading models, i.e., the first channel is Nakagami-m fading, the second is Weibull fading, and so on. Finally, we provide simulation results to corroborate our analysis.

[1]  George K. Karagiannidis,et al.  Performance analysis of the dual-hop asymmetric fading channel , 2009, IEEE Transactions on Wireless Communications.

[2]  Mazen O. Hasna,et al.  Outage probability of multihop transmission over Nakagami fading channels , 2003, IEEE Communications Letters.

[3]  Mounir Ghogho,et al.  Performance Analysis of Multi-User, Multi-Hop Cooperative Relay Networks over Nakagami-m Fading Channels , 2011, IEEE Communications Letters.

[4]  Norman C. Beaulieu,et al.  A General Framework for Symbol Error Probability Analysis of Wireless Systems and Its Application in Amplify-and-Forward Multihop Relaying , 2010, IEEE Transactions on Vehicular Technology.

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

[6]  S. Lang.  Complex Analysis , 1977 .

[7]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[8]  F. Mainardi,et al.  Fox H functions in fractional diffusion , 2005 .

[9]  L. Debnath.  Tables of Integral Transforms , 2012 .

[10]  Fortunato Santucci,et al.  A comprehensive framework for performance analysis of dual-hop cooperative wireless systems with fixed-gain relays over generalized fading channels , 2009, IEEE Transactions on Wireless Communications.

[11]  A. Erdélyi,et al.  Tables of integral transforms , 1955 .

[12]  George K. Karagiannidis,et al.  Performance bounds of multihop wireless communications with blind relays over generalized fading channels , 2006, IEEE Transactions on Wireless Communications.

[13]  Helmut Bölcskei,et al.  Fading relay channels: performance limits and space-time signal design , 2004, IEEE Journal on Selected Areas in Communications.

[14]  George K. Karagiannidis,et al.  Two hop amplify-and-forward transmission in mixed rayleigh and rician fading channels , 2009, IEEE Communications Letters.

[15]  Joseph Lipka,et al.  A Table of Integrals , 2010 .

[16]  Ronald F. Boisvert,et al.  NIST Handbook of Mathematical Functions , 2010 .

[17]  B. Braaksma,et al.  Asymptotic expansions and analytic continuations for a class of Barnes-integrals , 1964 .

[18]  Norman C. Beaulieu,et al.  On the performance of amplify-and-forward cooperative systems with fixed gain relays , 2008, IEEE Transactions on Wireless Communications.

[19]  Chengwen Xing,et al.  Exact Performance Analysis of Dual-Hop Semi-Blind AF Relaying over Arbitrary Nakagami-m Fading Channels , 2011, IEEE Transactions on Wireless Communications.

[20]  Masoud Ardakani,et al.  Asymptotically-Exact Performance Bounds of AF Multi-Hop Relaying over Nakagami Fading , 2011, IEEE Transactions on Communications.