New results for the multivariate Nakagami-m fading model with arbitrary correlation matrix and applications

Authors:
George C. Alexandropoulos;Nikos C. Sagias;Fotis I. Lazarakis;Kostas Berberidis
Affiliations:
Dept. of Comp. Eng. and Informatics, Univ. of Patras, Patras and Wireless Communications Lab., Inst. of Informatics and Telecommunications, Nat. Centre for Scientific Research–“Demokri ...;Dept. of Telecommunications Sci. and Technology, Univ. of Peloponnese, Tripolis and Wireless Communications Lab., Inst. of Inf. and Telecommunications, Nat. Centre for Scientific Research-“D ...;Wireless Communications Laboratory, Institute of Informatics and Telecommunications, National Centre for Scientific Research-“Demokritos,” Athens, Greece;Dept. of Computer Eng. and Inf., Univ of Patras, Patras and Wireless Communications Lab., Inst. of Informatics and Telecommunications, Nat. Centre for Scientific Research–“Demokritos,& ...
Venue:
IEEE Transactions on Wireless Communications
Year:
2009

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Abstract

New results for the multichannel Nakagami-m fading model with an arbitrary correlation matrix are presented in this paper. By using an efficient tridiagonalization method based on Householder matrices, the inverse of the Gaussian correlation matrix is transformed to tridiagonal, managing to derive a closed-form union upper bound for the joint Nakagami-m probability density function and an exact analytical expression for the moment generating function of the sum of identically distributed gamma random variables. Our analysis considers an arbitrary correlation structure, which includes as special cases the exponential, constant, circular, and linear correlation ones. Based on the proposed mathematical analysis, we obtain a tight union upper bound for the outage probability of multibranch selection diversity receivers as well as exact analytical expressions for the outage and the average error probability of multibranch maximal-ratio diversity receivers. Our analysis is verified by comparing numerically evaluated with extensive computer simulation performance evaluation results, showing the usefulness of the proposed approach.