New exponential lower bounds on the Gaussian Q-function via Jensen's inequality

Abstract

Using the convexity property of the exponential function, we obtain a family of exponential lower bounds on the Gaussian Q-function using the Jensen's inequality. The tightness of the bounds can be improved by increasing the number of exponential terms. The coefficients of the exponentials are constants, allowing easy averaging over the fading distribution using the moment generating function method. This method is also applied to the symbol error probability of M-ary phase shift keying and M-ary differential phase shift keying over additive white Gaussian noise and fading channels. The tightness of the bounds is demonstrated. © 2011 IEEE.