MGF Approach to the Analysis of Generalized Two-Ray Fading Models

We analyze a class of generalized two-ray (GTR) fading channels that consist of two line-of-sight (LOS) components with random phase plus a diffuse component. We derive a closed-form expression for the moment-generating function of the signal-to-noise ratio (SNR) for this model, which greatly simplifies its analysis. This expression arises from the observation that the GTR fading model can be expressed in terms of a conditional underlying Rician distribution. We illustrate the approach to derive simple expressions for statistics and performance metrics of interest, such as the amount of fading, the level crossing rate, the symbol error rate, and the ergodic capacity in GTR fading channels. We also show that the effect of considering a more general distribution for the phase difference between the LOS components has an impact on the average SNR.

[1]  Kwok Hung Li,et al.  Performance of BPSK Pre-detection MRC Systems over Two-Wave with Diffuse Power Fading Channels , 2007, IEEE Transactions on Wireless Communications.

[2]  A. Goldsmith,et al.  Capacity of Rayleigh fading channels under different adaptive transmission and diversity-combining techniques , 1999, IEEE Transactions on Vehicular Technology.

[3]  T. Rappaport.  Characterization of UHF multipath radio channels in factory buildings , 1989 .

[4]  Jeff Frolik,et al.  A case for considering hyper-Rayleigh fading channels , 2007, IEEE Transactions on Wireless Communications.

[5]  Jeff Frolik.  On appropriate models for characterizing hyper-rayleigh fading , 2008, IEEE Transactions on Wireless Communications.

[6]  Kwok Hung Li,et al.  BER performance of BPSK receivers over two-wave with diffuse power fading channels , 2005, IEEE Transactions on Wireless Communications.

[7]  Theodore S. Rappaport,et al.  New analytical models and probability density functions for fading in wireless communications , 2002, IEEE Trans. Commun..

[8]  S. Rice.  Mathematical analysis of random noise , 1944 .

[9]  M.D. Yacoub,et al.  The κ-μ distribution and the η-μ distribution , 2007, IEEE Antennas and Propagation Magazine.

[10]  Michel Daoud Yacoub,et al.  The κ-μ Extreme Distribution , 2011, IEEE Transactions on Communications.

[11]  Juan Manuel Romero-Jerez,et al.  A New Framework for the Performance Analysis of Wireless Communications Under Hoyt (Nakagami- $q$ ) Fading , 2014, IEEE Transactions on Information Theory.

[12]  Gustavo Gasaneo,et al.  Derivatives of any order of the confluent hypergeometric function F11(a,b,z) with respect to the parameter a or b , 2008 .

[13]  Mohamed-Slim Alouini,et al.  Novel asymptotic results on the high-order statistics of the channel capacity over generalized fading channels , 2012, 2012 IEEE 13th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC).

[14]  Giuseppe Thadeu Freitas de Abreu,et al.  On the generation of Tikhonov variates , 2008, IEEE Trans. Commun..

[15]  Yao Lu,et al.  Outage Probability of Cooperative Relay Networks in Two-Wave with Diffuse Power Fading Channels , 2012, IEEE Transactions on Communications.

[16]  Hari M. Srivastava,et al.  Some expansions of the exponential integral in series of the incomplete Gamma function , 2005, Applied Mathematics Letters.

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

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

[19]  David W. Matolak,et al.  Worse-than-Rayleigh fading: Experimental results and theoretical models , 2011, IEEE Communications Magazine.

[20]  Mohamed-Slim Alouini,et al.  A Unified MGF-Based Capacity Analysis of Diversity Combiners over Generalized Fading Channels , 2010, IEEE Transactions on Communications.

[21]  Jeff Frolik,et al.  Diversity gains in two-ray fading channels , 2009, IEEE Transactions on Wireless Communications.

[22]  P. R. Sahu,et al.  Performance of QAM Signaling over TWDP Fading Channels , 2013, IEEE Transactions on Wireless Communications.

[23]  Lifeng Wang,et al.  Physical Layer Security of Maximal Ratio Combining in Two-Wave With Diffuse Power Fading Channels , 2014, IEEE Transactions on Information Forensics and Security.

[24]  Mandy Eberhart,et al.  Digital Communication Over Fading Channels , 2016 .

[25]  Andrea J. Goldsmith,et al.  Statistics and system performance metrics for the Two Wave with Diffuse Power fading model , 2014, 2014 48th Annual Conference on Information Sciences and Systems (CISS).

[26]  A. Field.  Communications , 1963, The Journal of Asian Studies.

[27]  Kwok Hung Li,et al.  Symbol-error rate of selection combining over two-wave with diffuse power fading , 2011, 2011 5th International Conference on Signal Processing and Communication Systems (ICSPCS).

[28]  Marvin K. Simon.  On the Probability Density Function of the Squared Envelope of a Sum of Random Phase Vectors , 1985, IEEE Trans. Commun..

[29]  E. Gumbel,et al.  The Circular Normal Distribution: Theory and Tables , 1953 .

[30]  Raffaele Esposito,et al.  Statistical properties of two sine waves in Gaussian noise , 1973, IEEE Trans. Inf. Theory.

[31]  Mohamed-Slim Alouini,et al.  MGF approach to the capacity analysis of Generalized Two-Ray fading models , 2015, 2015 IEEE International Conference on Communications (ICC).

[32]  Antonia Maria Tulino,et al.  High-SNR power offset in multiantenna communication , 2005, IEEE Transactions on Information Theory.

[33]  Thorsten Gerber,et al.  Handbook Of Mathematical Functions , 2016 .

[34]  Kerstin Vogler,et al.  Table Of Integrals Series And Products , 2016 .

[35]  I. S. Ansari,et al.  A Unified Performance Analysis of Free-Space Optical Links over Gamma-Gamma Turbulence Channels with Pointing Errors , 2013 .

[36]  Norman C. Beaulieu,et al.  New Expressions for TWDP Fading Statistics , 2013, IEEE Wireless Communications Letters.

[37]  Yao Lu,et al.  Symbol Error Rate of Decode-and-Forward Relaying in Two-Wave with Diffuse Power Fading Channels , 2012, IEEE Transactions on Wireless Communications.

[38]  Abbas Jamalipour,et al.  Wireless communications , 2005, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[39]  Fortunato Santucci,et al.  Channel Capacity Over Generalized Fading Channels: A Novel MGF-Based Approach for Performance Analysis and Design of Wireless Communication Systems , 2010, IEEE Transactions on Vehicular Technology.

[40]  Gregory D. Durgin,et al.  Theory of Stochastic Local Area Channel Modeling for Wireless Communications , 2000 .