A Comparative Study of Two Shadow Fading Models in Ultrawideband and Other Wireless Systems

The distribution of the local average power at a mobile is usually considered to be lognormal in terrestrial and satellite channels. However, the mathematical form of the lognormal distribution is not convenient for analytic calculations. In this paper, we show the utility of the gamma distribution for shadow fading, in both terrestrial and satellite channels, using empirical data. Furthermore, we show that the application of the gamma model of shadow fading results in closed-form and mathematically-tractable solutions for key system performance measures such as the average symbol error rate of different modulations with a variety of diversity combining techniques.

[1]  E Jakeman,et al.  Scattering by a corrugated random surface with fractal slope , 1982 .

[2]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[3]  H. Crutcher.  A Note on the Possible Misuse of the Kolmogorov-Smirnov Test , 1975 .

[4]  Ali Abdi,et al.  Comparison of the level crossing rate and average fade duration of Rayleigh, Rice and Nakagami fading models with mobile channel data , 2000, Vehicular Technology Conference Fall 2000. IEEE VTS Fall VTC2000. 52nd Vehicular Technology Conference (Cat. No.00CH37152).

[5]  Ali Abdi,et al.  Signal modelling in wireless fading channels using spherically invariant processes , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[6]  Jean-Paul M. G. Linnartz,et al.  Narrowband land-mobile radio networks , 1993 .

[7]  K. B. Oldham,et al.  An Atlas of Functions. , 1988 .

[8]  George P. Efthymoglou,et al.  Performance of generalized selection combining receivers in K fading channels , 2008, IEEE Communications Letters.

[9]  E. Jakeman.  On the statistics of K-distributed noise , 1980 .

[10]  Helmut Bölcskei,et al.  Ultrawideband Channel Modeling on the Basis of Information-Theoretic Criteria , 2005, IEEE Transactions on Wireless Communications.

[11]  Ali Abdi,et al.  Comparison of DPSK and MSK bit error rates for K and Rayleigh-lognormal fading distributions , 2000, IEEE Communications Letters.

[12]  M. Peruggia.  Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (2nd ed.) , 2003 .

[13]  Eugene P. Wigner,et al.  Formulas and Theorems for the Special Functions of Mathematical Physics , 1966 .

[14]  Gordon L. Stuber,et al.  Principles of Mobile Communication , 1996 .

[15]  D. Middleton.  New physical-statistical methods and models for clutter and reverberation: the KA-distribution and related probability structures , 1999 .

[16]  Ali Abdi,et al.  A parametric model for the distribution of the angle of arrival and the associated correlation function and power spectrum at the mobile station , 2002, IEEE Trans. Veh. Technol..

[17]  Chia-Chin Chong,et al.  A Comprehensive Standardized Model for Ultrawideband Propagation Channels , 2006, IEEE Transactions on Antennas and Propagation.

[18]  Peter Albrecht.  A remark on Albrecht's "On the correct use of the chi-square goodness-of-fit test" , 1982 .

[19]  David S. Moore,et al.  The Effect of Dependence on Chi-Squared and Empiric Distribution Tests of Fit , 1983 .

[20]  Daniel Cygan,et al.  The land mobile satellite communication channel-recording, statistics, and channel model , 1991 .

[21]  Franco Mazzenga,et al.  Statistical channel modelling and performance evaluation in satellite personal communications , 1998 .

[22]  S Geisser,et al.  A necessary and sufficient condition for the square of a random variable to be gamma. , 1966, Biometrika.

[23]  Ali Abdi,et al.  K distribution: an appropriate substitute for Rayleigh-lognormal distribution in fading-shadowing wireless channels , 1998 .

[24]  J. D. Parsons,et al.  The Mobile Radio Propagation Channel , 1991 .

[25]  Gordon L. Stuber,et al.  Principles of mobile communication (2nd ed.) , 2001 .

[26]  W. Lee,et al.  On the Estimation of the Second-Order Statistics of Log Normal Fading in Mobile Radio Environment , 1974, IEEE Trans. Commun..

[27]  P. Takis Mathiopoulos,et al.  Diversity reception over generalized-K (KG) fading channels , 2007, IEEE Transactions on Wireless Communications.

[28]  Ali Abdi,et al.  A simple alternative to the lognormal model of shadow fading in terrestrial and satellite channels , 2001, IEEE 54th Vehicular Technology Conference. VTC Fall 2001. Proceedings (Cat. No.01CH37211).

[29]  P. Albrecht,et al.  On the correct use of the chi-square goodness-of-fit test , 1980 .

[30]  V. K. Bhargawa,et al.  Analysis of M-ary phase-shift keying with diversity reception for land-mobile satellite channels , 1997 .

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

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

[33]  C. Baker,et al.  Maritime surveillance radar Part 1 : Radar scattering from the ocean surface , 1990 .

[34]  Ali Abdi,et al.  On the utility of gamma PDF in modeling shadow fading (slow fading) , 1999, 1999 IEEE 49th Vehicular Technology Conference (Cat. No.99CH36363).

[35]  M. Nesenbergs,et al.  Binary Error Probability Due to an Adaptable Fading Model , 1964 .

[36]  H. A. Barger.  Dynamic characteristics of a narrowband land mobile communication channel , 1998 .

[37]  Richard Barakat,et al.  Second-order Statistics of Integrated Intensities and of Detected Photoelectrons , 1987 .

[38]  Daniel Cygan.  Analytical evaluation of average bit error rate for the land mobile satellite channel , 1989 .

[39]  E. Jakeman.  Fresnel scattering by a corrugated random surface with fractal slope , 1982 .

[40]  P. Mohana Shankar.  Performance Analysis of Diversity Combining Algorithms in Shadowed Fading Channels , 2006, Wirel. Pers. Commun..