Chernoff-Type Bounds for the Gaussian Error Function
- 29 July 2011
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Communications
- Vol. 59 (11) , 2939-2944
Abstract
We study single-term exponential-type bounds (also known as Chernoff-type bounds) on the Gaussian error function. This type of bound is analytically the simplest such that the performance metrics in most fading channel models can be expressed in a concise closed form. We derive the conditions for a general single-term exponential function to be an upper or lower bound on the Gaussian error function. We prove that there exists no tighter single-term exponential upper bound beyond the Chernoff bound employing a factor of one-half. Regarding the lower bound, we prove that the single-term exponential lower bound of this letter outperforms previous work. Numerical results show that the tightness of our lower bound is comparable to that of previous work employing eight exponential terms.Keywords
This publication has 17 references indexed in Scilit:
- Performance of Distributed Diversity Systems With a Single Amplify-and-Forward RelayIEEE Transactions on Vehicular Technology, 2008
- An Analytically Tractable Approximation for the Gaussian Q-FunctionIEEE Communications Letters, 2008
- Performance of Space–Time Codes: Gallager Bounds and Weight EnumerationIEEE Transactions on Information Theory, 2008
- An accurate closed-form approximation of the average probability of error over a log-normal fading channelIEEE Transactions on Wireless Communications, 2008
- Receive Antenna Selection Based on Union-Bound Minimization Using Convex OptimizationIEEE Signal Processing Letters, 2007
- New exponential bounds and approximations for the computation of error probability in fading channelsIEEE Transactions on Wireless Communications, 2003
- Exponential-type bounds on the generalized Marcum Q-function with application to error probability analysis over fading channelsIEEE Transactions on Communications, 2000
- A new twist on the Marcum Q-function and its applicationIEEE Communications Letters, 1998
- Simple Approximations of the Error Function Q(x) for Communications ApplicationsIEEE Transactions on Communications, 1979
- Probability-of-error bounds for binary transmission on the slowly fading Rician channelIEEE Transactions on Information Theory, 1966