A Novel Equivalent Definition of Modified Bessel Functions for Performance Analysis of Multi-Hop Wireless Communication Systems

A statistical model is derived for the equivalent signal-to-noise ratio of the Source-to-Relay-to-Destination (S-R-D) link for Amplify-and-Forward (AF) relaying systems that are subject to block Rayleigh-fading. The probability density function and the cumulated density function of the S-R-D link SNR involve modified Bessel functions of the second kind. Using fractional-calculus mathematics, a novel approach is introduced to rewrite those Bessel functions (and the statistical model of the S-R-D link SNR) in series form using simple elementary functions. Moreover, a statistical characterization of the total receive-SNR at the destination, corresponding to the S-R-D and the S-D link SNR, is provided for a more general relaying scenario in which the destination receives signals from both the relay and the source and processes them using maximum ratio combining (MRC). Using the novel statistical model for the total receive SNR at the destination, accurate and simple analytical expressions for the outage probability, the bit error probability, and the ergodic capacity are obtained. The analytical results presented in this paper provide a theoretical framework to analyze the performance of the AF cooperative systems with an MRC receiver.

[1]  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.

[2]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[3]  Mehran Abolhasan,et al.  On the Error Exponent of Amplify and Forward Relay Networks , 2011, IEEE Communications Letters.

[4]  R. M. A. P. Rajatheva,et al.  On the Distribution of the Sum of Nakagami-$ m$ Random Variables , 2007, IEEE Transactions on Communications.

[5]  Mazen O. Hasna,et al.  End-to-end performance of transmission systems with relays over Rayleigh-fading channels , 2003, IEEE Trans. Wirel. Commun..

[6]  Chintha Tellambura,et al.  Unified Exact Performance Analysis of Two-Hop Amplify-and-Forward Relaying in Nakagami Fading , 2010, IEEE Transactions on Vehicular Technology.

[7]  Mohamed-Slim Alouini,et al.  Coded Communication over Fading Channels , 2005 .

[8]  John S. Thompson,et al.  Amplify-and-forward with partial relay selection , 2008, IEEE Communications Letters.

[9]  Branka Vucetic,et al.  Performance analysis of beamforming in two hop amplify and forward relay networks with antenna correlation , 2009, IEEE Transactions on Wireless Communications.

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

[11]  Iain B. Collings,et al.  On the Exact and Asymptotic SER of Receive Diversity With Multiple Amplify-and-Forward Relays , 2010, IEEE Transactions on Vehicular Technology.

[12]  Mohamed-Slim Alouini,et al.  Digital Communication Over Fading Channels: A Unified Approach to Performance Analysis , 2000 .

[13]  Siad Daboul,et al.  The Lah Numbers and the nth Derivative of e1/x , 2013 .

[14]  T. Neumann.  Advanced Combinatorics The Art Of Finite And Infinite Expansions , 2016 .

[15]  Behrouz Maham,et al.  Asymptotic performance analysis of amplify-and-forward cooperative networks in a nakagami-m fading environment , 2009, IEEE Communications Letters.

[16]  Chintha Tellambura,et al.  Further results on the Beaulieu series , 2000, IEEE Trans. Commun..

[17]  Norman C. Beaulieu,et al.  On the Ergodic Capacity of Wireless Relaying Systems over Rayleigh Fading Channels , 2008, IEEE Transactions on Wireless Communications.

[18]  Arumugam Nallanathan,et al.  Beamforming in Dual-Hop Fixed Gain Relay Systems with Antenna Correlation , 2010, 2010 IEEE International Conference on Communications.

[19]  Salama Ikki,et al.  Performance Analysis of Generalized Selection Combining for Amplify-and-Forward Cooperative-Diversity Networks , 2009, 2009 IEEE International Conference on Communications.

[20]  Michail Matthaiou,et al.  Capacity Bounds for AF Dual-hop Relaying in ${\cal G}$ Fading Channels , 2012, IEEE Transactions on Vehicular Technology.

[21]  Behrouz Maham,et al.  Distributed GABBA space-time codes in amplify-and-forward relay networks , 2009, IEEE Transactions on Wireless Communications.

[22]  Salama Ikki,et al.  Performance Analysis of Cooperative Diversity Wireless Networks over Nakagami-m Fading Channel , 2007, IEEE Communications Letters.

[23]  D. Rajan.  Probability, Random Variables, and Stochastic Processes , 2017 .

[24]  Gregory W. Wornell,et al.  Cooperative diversity in wireless networks: Efficient protocols and outage behavior , 2004, IEEE Transactions on Information Theory.

[25]  Series Representation of the Modified Bessel Functions , 2001, math-ph/0104018.

[26]  Yik-Chung Wu,et al.  Exact Outage Probability of Dual-Hop CSI-Assisted AF Relaying Over Nakagami-$m$ Fading Channels , 2012, IEEE Transactions on Signal Processing.

[27]  Norman C. Beaulieu,et al.  An infinite series for the computation of the complementary probability distribution function of a sum of independent random variables and its application to the sum of Rayleigh random variables , 1990, IEEE Trans. Commun..

[28]  Norbert Goertz,et al.  Performance analysis of amplify-and-forward relaying using fractional calculus , 2012, 2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR).

[29]  Chintha Tellambura,et al.  Amplify-and-forward partial relay selection with feedback delay , 2011, 2011 IEEE Wireless Communications and Networking Conference.

[30]  Yindi Jing,et al.  Distributed beamforming in wireless relay networks with quantized feedback , 2008, IEEE Journal on Selected Areas in Communications.

[31]  George K. Karagiannidis,et al.  Nonregenerative Dual-Hop Cooperative Links with Selection Diversity , 2006, EURASIP J. Wirel. Commun. Netw..

[32]  Alister G. Burr,et al.  Statistical Analysis of Multiantenna Relay Systems and Power Allocation Algorithms in a Relay With Partial Channel State Information , 2015, IEEE Transactions on Wireless Communications.

[33]  E. Meulen,et al.  Three-terminal communication channels , 1971, Advances in Applied Probability.

[34]  Norbert Goertz,et al.  An Analytical Approach to the Outage Probability of Amplify-and-Forward Relaying with an MRC Receiver , 2013, 2013 IEEE 77th Vehicular Technology Conference (VTC Spring).

[35]  Wei Li,et al.  Exact Closed-Form Expression for Ergodic Capacity of Amplify-and-Forward Relaying in Channel-Noise-Assisted Cooperative Networks with Relay Selection , 2011, IEEE Communications Letters.

[36]  Norman C. Beaulieu,et al.  Ergodic Capacity Analysis of Wireless Relaying Systems In Rayleigh Fading , 2008, 2008 IEEE International Conference on Communications.

[37]  Norbert Goertz,et al.  Amplify and forward relaying; Channel model and outage behaviour , 2012, 2012 International Symposium on Wireless Communication Systems (ISWCS).

[38]  Mostafa Kaveh,et al.  Exact symbol error probability of a Cooperative network in a Rayleigh-fading environment , 2004, IEEE Transactions on Wireless Communications.

[39]  Michail Matthaiou,et al.  Generic Ergodic Capacity Bounds for Fixed-Gain AF Dual-Hop Relaying Systems , 2011, IEEE Transactions on Vehicular Technology.