A unified performance analysis of digital communication with dual selective combining diversity over correlated Rayleigh and Nakagami-m fading channels

Using a simple finite integral representation for the bivariate Rayleigh (1889) cumulative distribution function previously discovered by the authors, we present expressions for the outage probability and average error probability performances of a dual selective diversity system with correlated slow Rayleigh fading either in closed form (in particular for binary differential phase-shift keying) or in terms of a single integral with finite limits and an integrand composed of elementary (exponential and trigonometric) functions. Because of their simple form, these expressions readily allow numerical evaluation for cases of practical interest. The results are also extended to the case of slow Nakagami-m fading using an alternate representation of the generalized Marcum (1950) Q-function.

[1]  H. Staras.  Diversity Reception with Correlated Signals , 1956 .

[2]  K. A. Karpov,et al.  TABLE OF FUNCTIONS , 1961 .

[3]  W. C. Jakes,et al.  Microwave Mobile Communications , 1974 .

[4]  Mohamed-Slim Alouini,et al.  A unified approach to the performance analysis of digital communication over generalized fading channels , 1998, Proc. IEEE.

[5]  Marvin K. Simon,et al.  A new twist on the Marcum Q-function and its application , 1998, IEEE Communications Letters.

[6]  Lord Rayleigh F.R.S..  XII. On the resultant of a large number of vibrations of the same pitch and of arbitrary phase , 1880 .

[7]  M. Schwartz,et al.  Communication Systems and Techniques , 1996, IEEE Communications Magazine.

[8]  Carl W. Helstrom,et al.  Elements of signal detection and estimation , 1994 .

[9]  F. Adachi,et al.  Postdetection selection diversity reception with correlated, unequal average power Rayleigh fading signals for pi /4-shift QDPSK mobile radio , 1992 .

[10]  Mohamed-Slim Alouini,et al.  A simple single integral representation of the bivariate Rayleigh distribution , 1998, IEEE Communications Letters.

[11]  Norman C. Beaulieu,et al.  Infinite series representations of the bivariate Rayleigh and Nakagami-m distributions , 1997, IEEE Trans. Commun..

[12]  M. Tanda,et al.  Dual diversity reception of M-ary DPSK signals over Nakagami fading channels , 1995, Proceedings of 6th International Symposium on Personal, Indoor and Mobile Radio Communications.

[13]  A. Goldsmith,et al.  A unified approach for calculating error rates of linearly modulated signals over generalized fading channels , 1998, ICC '98. 1998 IEEE International Conference on Communications. Conference Record. Affiliated with SUPERCOMM'98 (Cat. No.98CH36220).

[14]  D. Owen.  Handbook of Mathematical Functions with Formulas , 1965 .

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

[16]  Yongbing Wan,et al.  Fading distribution of diversity techniques with correlated channels , 1995, Proceedings of 6th International Symposium on Personal, Indoor and Mobile Radio Communications.

[17]  Mohamed-Slim Alouini,et al.  A unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels , 1998, IEEE Trans. Commun..

[18]  Rayleigh Lord,et al.  LIII. On the character of the complete radiation at a given temperature , 1889 .

[19]  Sandeep Chennakeshu,et al.  Error rates for Rayleigh fading multichannel reception of MPSK signals , 1995, IEEE Trans. Commun..

[20]  S. Rice,et al.  Distribution of the Phase Angle Between Two Vectors Perturbed by Gaussian Noise , 1982, IEEE Trans. Commun..

[21]  S. Okui.  Probability of co-channel interference for selection diversity reception in the Nakagami m-fading channel , 1992 .

[22]  Dariush Divsalar,et al.  Some new twists to problems involving the Gaussian probability integral , 1998, IEEE Trans. Commun..

[23]  M. Abramowitz,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

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

[25]  J. Craig.  A new, simple and exact result for calculating the probability of error for two-dimensional signal constellations , 1991, MILCOM 91 - Conference record.