Please use this identifier to cite or link to this item: https://doi.org/10.1109/ISIT.2006.261952
Title: Computing and bounding the generalized Marcum Q-function via a geometric approach
Authors: Li, R. 
Kam, P.Y. 
Issue Date: 2006
Source: Li, R., Kam, P.Y. (2006). Computing and bounding the generalized Marcum Q-function via a geometric approach. IEEE International Symposium on Information Theory - Proceedings : 1090-1094. ScholarBank@NUS Repository. https://doi.org/10.1109/ISIT.2006.261952
Abstract: The generalized Marcum Q-function, Qm(a,b), is here explained geometrically as the probability of a 2m-dimensional, real, Gaussian random vector, whose mean vector has a Frobenius norm of a, lying outside of a hypersphere of 2m dimensions, with radius b, and centered at the origin. Based on this new geometric interpretation, a new closed-form representation for Qm (a, b) is derived for the case where m is an odd multiple of 0.5. This representation involves only the exponential and the erfc functions, and thus is easy to handle, both numerically and analytically. For the case where m is an even multiple of 0.5, Qm+0.5(a,b) and Qm-0.5(a,b), which can be evaluated using our new representation mentioned above, are shown to be tight upper and lower bounds on Qm(a,b), respectively. They are shown in most cases to be much tighter than the existing bounds in the literature, and are valid for the entire ranges of a and b concerned. Their average is also a good approximation to Qm(a,b). ©2006 IEEE.
Source Title: IEEE International Symposium on Information Theory - Proceedings
URI: http://scholarbank.nus.edu.sg/handle/10635/83573
ISBN: 1424405041
ISSN: 21578101
DOI: 10.1109/ISIT.2006.261952
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