Statistical properties of the capacity of double Nakagami-m channels

In this article, we have presented an extensive statistical analysis of the capacity of double1 Nakagami-m channels. The double Nakagami-m channel model has applications in keyhole channels and amplify-and-forward relay based dualhop communication systems in cooperative networks. We have derived exact analytical expressions for the probability density function (PDF), the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average duration of fades (ADF) of the capacity of double Nakagami-m channels. Moreover, the influence of severity of fading on the statistical properties of the channel capacity has been studied. It is observed that an increase in the severity of fading in one or both links in dualhop communication systems decreases the mean channel capacity, while it results in an increase in the ADF of the channel capacity. Moreover, this effect decreases the LCR of the channel capacity at lower signal levels. The results presented in this paper also reveal that an increase in the maximum Doppler frequencies of the wireless nodes in a dualhop communication system increases the LCR of the channel capacity, while it has an opposite influence on the ADF of the channel capacity. The results presented in this article are useful for mobile communication system engineers for the design and optimization of dualhop communication systems.

[1]  P. Vainikainen,et al.  Impact of double-Rayleigh fading on system performance , 2006, 2006 1st International Symposium on Wireless Pervasive Computing.

[2]  Liviu Iftode,et al.  Adaptive Traffic Lights Using Car-to-Car Communication , 2007, 2007 IEEE 65th Vehicular Technology Conference - VTC2007-Spring.

[3]  Matthias Pätzold,et al.  Two new sum-of-sinusoids-based methods for the efficient generation of multiple uncorrelated rayleigh fading waveforms , 2009, IEEE Transactions on Wireless Communications.

[4]  Gordon L. Stüber,et al.  Statistical properties of amplify and forward relay fading channels , 2006, IEEE Transactions on Vehicular Technology.

[5]  Reinaldo A. Valenzuela,et al.  Keyholes, correlations, and capacities of multielement transmit and receive antennas , 2002, IEEE Trans. Wirel. Commun..

[6]  George K. Karagiannidis,et al.  On the second order statistics of the multihop rayleigh fading channel , 2009, IEEE Transactions on Communications.

[7]  Jørgen Bach Andersen.  Stastistical distributions in mobile communications using multiple scattering , 2002 .

[8]  I. Miller.  Probability, Random Variables, and Stochastic Processes , 1966 .

[9]  Matthias Pätzold,et al.  Capacity studies of MIMO channel models based on the geometrical one-ring scattering model , 2004, 2004 IEEE 15th International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE Cat. No.04TH8754).

[10]  George K. Karagiannidis,et al.  Level crossing rate and average fade duration of the double Nakagami-m random process and application in MIMO keyhole fading channels , 2008, IEEE Communications Letters.

[11]  Elza Erkip,et al.  User cooperation diversity. Part I. System description , 2003, IEEE Trans. Commun..

[12]  Hyundong Shin,et al.  Performance analysis of space-time block codes over keyhole Nakagami-m fading channels , 2004, IEEE Transactions on Vehicular Technology.

[13]  Matthias Patzold,et al.  Mobile Fading Channels , 2003 .

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

[15]  Patrick Claus F. Eggers,et al.  Investigations of outdoor-to-indoor mobile-to-mobile radio communication channels , 2002, Proceedings IEEE 56th Vehicular Technology Conference.

[16]  M. Patzold,et al.  On the statistical properties of the capacity of amplify-and-forward channels under LOS conditions , 2008, 2008 11th IEEE Singapore International Conference on Communication Systems.

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

[18]  Andrea Giorgetti,et al.  MIMO capacity, level crossing rates and fades: The impact of spatial/temporal channel correlation , 2003, Journal of Communications and Networks.

[19]  Victor Adamchik,et al.  The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system , 1990, ISSAC '90.

[20]  Helmut Bölcskei,et al.  Outdoor MIMO wireless channels: models and performance prediction , 2002, IEEE Trans. Commun..

[21]  Jonathan Ling,et al.  Comparisons of a Computer-Based Propagation Prediction Tool with Experimental Data Collected in Urban Microcelluar Environments , 1997, IEEE J. Sel. Areas Commun..

[22]  M. Nakagami.  The m-Distribution—A General Formula of Intensity Distribution of Rapid Fading , 1960 .

[23]  M. Yacoub,et al.  On higher order statistics of the Nakagami-m distribution , 1999 .

[24]  George K. Karagiannidis,et al.  $N{\ast}$Nakagami: A Novel Stochastic Model for Cascaded Fading Channels , 2007, IEEE Transactions on Communications.

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

[26]  Matthias Pätzold,et al.  Exact Closed-Form Expressions for the Distribution, Level-Crossing Rate, and Average Duration of Fades of the Capacity of MIMO Channels , 2007, 2007 IEEE 65th Vehicular Technology Conference - VTC2007-Spring.