Comparison of generalized Q-function algorithms
IEEE Transactions on Information Theory
Convex Optimization
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IEEE Transactions on Communications
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IEEE Transactions on Communications
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New bounds for the generalized Marcum Q-function
IEEE Transactions on Information Theory
On the monotonicity of the generalized Marcum and Nuttall Q-functions
IEEE Transactions on Information Theory
CCNC'09 Proceedings of the 6th IEEE Conference on Consumer Communications and Networking Conference
IEEE Transactions on Wireless Communications
New bounds for the Marcum Q-function
IEEE Transactions on Information Theory
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IEEE Transactions on Information Theory
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IEEE Journal on Selected Areas in Communications
| Hi-index | 754.84 |
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 b → ∞. 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.