Error Rates in Generalized Shadowed Fading Channels

Most of the existing models to describe the shadowed fading channels use either the Suzuki or Nakagami-lognormal probability density function (pdf), both based on lognormal shadowing. However, these two density functions do not lead to closed form solutions for the received signal power, making the computations of error rates and outages very cumbersome. A generalized or compound fading model which takes into account both fading and shadowing in wireless systems, is presented here. Starting with the Nakagami model for fading, shadowing is incorporated using a gamma distribution for the average power in the Nakagami fading model. This compound pdf developed here based on a gamma-gamma distribution is analytically simpler than the two pdfs based on lognormal shadowing and is general enough to incorporate most of the fading and shadowing observed in wireless channels. The performance of coherent BPSK is evaluated using this compound fading model.

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

[2]  John G. Proakis,et al.  Digital Communications , 1983 .

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

[4]  Ramjee Prasad,et al.  Effects of Rician faded and log-normal shadowed signals on spectrum efficiency in microcellular radio , 1993 .

[5]  Tjeng Thiang Tjhung,et al.  Fade statistics in Nakagami-lognormal channels , 1999, IEEE Trans. Commun..

[6]  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).

[7]  F.I. Meno,et al.  Mobile fading—Rayleigh and lognormal superimposed , 1977, IEEE Transactions on Vehicular Technology.

[8]  Luciano Tomba.  Outage Probability in Full Spectrum Reuse Cellular Systems with Discontinuous Transmission , 1997, Wirel. Pers. Commun..

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

[10]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[11]  EMAD K. AL-HUSSAINI,et al.  Composite Macroscopic and Microscopic Diversity of Sectorized Macrocellular and Microcellular Mobile Radio Systems Employing RAKE Receiver over Nakagami Fading Plus Lognormal Shadowing Channel , 2002, Wirel. Pers. Commun..

[12]  Suzanne T. McDaniel,et al.  Seafloor reverberation fluctuations , 1990 .

[13]  Hirofumi Suzwi,et al.  A Statistical Model for Urban Radio Propagation , 1977 .

[14]  H. Suzuki,et al.  A Statistical Model for Urban Radio Propogation , 1977, IEEE Trans. Commun..

[15]  D. Lewinski.  Nonstationary probabilistic target and clutter scattering models , 1983 .

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

[17]  P. M. Shankar,et al.  Introduction to Wireless Systems , 2001 .

[18]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[19]  A.A. Abu-Dayya,et al.  Performance of micro- and macro-diversity on shadowed Nakagami fading channels , 1991, IEEE Global Telecommunications Conference GLOBECOM '91: Countdown to the New Millennium. Conference Record.

[20]  G. Lampropoulos,et al.  High resolution radar clutter statistics , 1999 .