Sum and difference of two squared correlated Nakagami variates in connection with the McKay distribution

General formulas for the probability density function of the sum and the difference of two correlated, not necessarily identically distributed, squared Nakagami variates (or equivalently, gamma variates) are derived. These expressions are shown to be in the form of the McKay "Bessel function" distributions. In addition, formulas for the moments of these distributions, in terms of the Gauss hypergeometric function, are provided. An application of these new results relevant to the calculation of outage probability in the presence of self-interference is discussed.

[1]  M. Win,et al.  Exact error probability expressions for MRC in correlated Nakagami channels with unequal fading parameters and branch powers , 1999, Seamless Interconnection for Universal Services. Global Telecommunications Conference. GLOBECOM'99. (Cat. No.99CH37042).

[2]  P. R. Nelson.  The algebra of random variables , 1979 .

[3]  Norman C. Beaulieu,et al.  Outage probabilities of cellular mobile radio systems with multiple Nakagami interferers , 1991 .

[4]  Karl Pearson,et al.  FURTHER APPLICATIONS IN STATISTICS OF THE Tm (x) BESSEL FUNCTION , 1932 .

[5]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

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

[7]  R. Fisher.  The Advanced Theory of Statistics , 1943, Nature.

[8]  Chintha Tellambura,et al.  Generation of bivariate Rayleigh and Nakagami-m fading envelopes , 2000, IEEE Communications Letters.

[9]  William C. Y. Lee,et al.  Mobile Communications Engineering , 1982 .

[10]  A. Mckay,et al.  A BESSEL FUNCTION DISTRIBUTION , 1932 .

[11]  Cheryl M. Wallgren.  The Distribution of the Product of Two Correlated t Variates , 1980 .

[12]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[13]  Mohamed-Slim Alouini,et al.  Multichannel Reception Of Digital Signals Over Correlated Nakagami Fading Channels , 1998 .

[14]  A. Sheikh,et al.  Investigations into cochannel interference in microcellular mobile radio systems , 1992 .

[15]  Keith Q. T. Zhang.  A decomposition technique for efficient generation of correlated Nakagami fading channels , 2000, IEEE Journal on Selected Areas in Communications.

[16]  Laurence B. Milstein,et al.  Coherent DS-CDMA performance in Nakagami multipath fading , 1995, IEEE Trans. Commun..

[17]  Pierfrancesco Lombardo,et al.  MRC performance for binary signals in Nakagami fading with general branch correlation , 1999, IEEE Trans. Commun..

[18]  Alex ChiChung Kot,et al.  New method of performance analysis for diversity reception with correlated Rayleigh-fading signals , 2000, IEEE Trans. Veh. Technol..

[19]  Asrar U. H. Sheikh,et al.  Indoor mobile radio channel at 946 MHz: Measurements and modeling , 1993, IEEE 43rd Vehicular Technology Conference.

[20]  Agnes Ligeti,et al.  Outage probability in the presence of correlated lognormal useful and interfering components , 2000, IEEE Communications Letters.

[21]  仲上 稔,et al.  The m-Distribution As the General Formula of Intensity Distribution of Rapid Fading , 1957 .

[22]  Valentine A. Aalo,et al.  Performance of maximal-ratio diversity systems in a correlated Nakagami-fading environment , 1995, IEEE Trans. Commun..