Accurate Approximations to the Sum of Generalized Random Variables and Applications in the Performance Analysis of Diversity Systems

• Published in: IEEE transactions on communications Vol. 57; no. 5; pp. 1271 - 1274
• Main Authors: da Costa, D.B., Yacoub, M.D.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Approximation; Approximation methods; Bit error rate; Communication systems; Detection, estimation, filtering, equalization, prediction; Diversity reception; Diversity systems; Exact sciences and technology; Exact solutions; generalized random variables; Information, signal and communications theory; Jitter; Laboratories; Mathematical analysis; Measurement; Performance analysis; Random variables; Receivers; Signal and communications theory; Signal detection; Signal, noise; Statistical distributions; Sums; sums approximation methods; Telecommunications and information theory; η-κ sums; η-μ sums; Performance evaluation; Approximate method; Bit error rate; Signal estimation; η-μ sums; Exact solution; sums approximation methods; Diversity combining; Level crossing rate; κ-μ sums; Telecommunication system; Metric; generalized random variables; Diversity systems; Random variable; performance analysis
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2009.05.070312

Accurate closed-form approximations to the sum of independent identically distributed eta-mu and kappa-mu random variables are provided. The proposed approximations turn out to be simple, precise, and useful for obtaining important performance metrics of communications systems where sums of variates arise. In particular, average bit error rate and level crossing rate of multibranch equal-gain combining receivers are attained to illustrate the applicability of the approximations. Some sample examples show that the intricate exact solution and the simple approximate expressions yield results that are almost indistinguishable from each other.