An extended compound gamma model and application to composite fading channels
AbstractWireless communication systems are subject to short and long-term fading channels. In this paper, an extended form of a statistical model for the composite fading channels is derived from the maximum entropy principle. Subsequently, the composite fading channel is derived by replacing the conditional density by entropy-maximizing distribution (Mathai's pathway model). This pathway model is versatile enough to represent short-term fading as well as the shadowing. The new wireless channel model generalizes the commonly used models for multipath fading and shadowing. In particular, using the G-function, we derive the density function, distribution function and moments of the new model in closed form. These derived results are a suitable device to analyze the performance of composite fading systems such as density function of the Signal Noise to Ratio (SNR), Amount of Fading (AF), and Outage Probability (OP) etc. The results will be shown graphically for different signal and fading parameter values.
M. K. Simon, and M. S. Alouini, Digital Communication Over Fading Channels, second edition, John Wiely and sons, 2006.
M. H. Ismail, and M. M. Matalgah, Performance of dual maximal ratio combining diversity in non-identical correlated Weibull fading channels using Padé approximation, IEEE Transactions on Communications, vol. 54, pp. 397–402, 2006.
Tjeng T. Tjhung, Fade Statistics in Nakagami-Lognormal Channels, IEEE Transactions on Communications, vol. 47, pp. 1769–1772, 1999.
H. Suzuki, A statistical model for urban radio propagation, IEEE Transactions on Communications, vol. 25, pp. 673-680, 1977.
P. Bithas, Weibull-Gamma composite distribution: An alternative multipath/shadowing fading model, Electronics Letters, vol. 45, pp. 749-751, 2009.
A. Abdi, and M. Kaveh, Comparison of DPSK and MSK bit error rates for K and Rayleigh-lognormal fading distributions, IEEE Communications Letters, vol. 4, pp.122–124, 2000.
P. M. Shankar, Error rates in generalized shadowed fading channels, Wireless Personal Communications, vol. 28, pp. 233-238, 2004.
S. Nadarajah, and S. Kotz, Compound statistical models for shadowing fading channels, International Journal of Electronics and Communications, vol. 62, pp. 138–142, 2008.
S. Atapattu, C. Tellambura, and H. Jiang, A mixture gamma distribution to model the SNR of wireless channels, IEEE transactions on wireless communications, vol. 10, pp. 4193–4203, 2011.
P. M. Shankar, Outage analysis in wireless channels with multiple interferers subject to shadowing and fading using a compound pdf model, International Journal of Electronics and Communications, vol. 61, pp. 255–261, 2007.
E. T. Jaynes, Probability Theory: The Logic of Science, Cambridge University Press, 2003.
M. Debbah, and R. R. Müller, MIMO channel modelling and the prinicple of maximum entropy, IEEE Transations on Information Theory, vol. 15, pp. 1667–1690, 2005.
M. Guillaud, M. Debbah and A. U. Moustakas, A maximum entropy characterization of spatially correlated MIMO wirelesss channels, IEEE Wireless communications and Networking Conference, Hong Kong, 2007.
A. M. Mathai, and H. J. Haubold, Pathway model, superstatistics Tsallis statistics and a generalized measure of entropy, Physica A, vol. 375, pp. 110–122, 2007.
A. M. Mathai, A pathway to matrix - variate gamma and normal densities, Linear Algebra and Its Applications, vol. 396, pp. 317–328, 2005.
C. Beck, Stretched exponentials from superstatistics, Physica A, vol. 365, pp. 96–101, 2006.
C. Beck, and E. G. D. Cohen, Superstatistcs, Physica A, vol. 322, pp. 267–275, 2003.
C. Tsallis, What should a statistical mechanics satisfy to reflect nature? Physica D, vol. 193, pp. 3–34, 2004.
A. M. Mathai, A Handbook of Generalized Special Functions for Statistical and Physical Sciences, Clarendon Press, Oxford, 1993.
A. M. Mathai, R. K. Saxena, and H. J. Haubold, The H-function: Theory and Applications, Springer, New York, 2010.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).