1. On the Monotonicity, Log-Concavity, and Tight Bounds of the Generalized Marcum and Nuttall Q-Functions.
- Author
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Yin Sun, Baricz, Árpád, and Shidong Zhou
- Subjects
- *
WIRELESS communications , *MOBILE computing , *COMMUNICATION , *DIGITAL communications , *CODE division multiple access , *DATA transmission systems - Abstract
In this paper, we present a comprehensive study of the monotonicity and log-concavity of the generalized Marcum and Nuttall Q -functions. More precisely, a simple probabilistic method is first given to prove the monotonicity of these two functions. Then, the log-concavity of the generalized Marcum Q -function and its deformations is established with respect to each of the three parameters. Since the Nuttall Q -function has similar probabilistic interpretations as the generalized Marcum Q -function, we deduce the log- concavity of the Nuttall Q -function. By exploiting the log-concavity of these two functions, we propose new tight lower and upper bounds for the generalized Marcum and Nuttall Q -functions. Our proposed bounds are much tighter than the existing bounds in the literature in most of the cases. The relative errors of our proposed bounds converge to 0 as 6 → ∞. The numerical results show that the absolute relative errors of the proposed bounds are less than 5% in most of the cases. The proposed bounds can be effectively applied to the outage probability analysis of interference-limited systems such as cognitive radio and wireless sensor network, in the study of error performance of various wireless communication systems operating over fading channels and extracting the log-likelihood ratio for differential phase-shift keying (DPSK) signals. [ABSTRACT FROM AUTHOR]
- Published
- 2010
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