Improved exponential bounds and approximation for the Q-function with application to average error probability computation

We present new exponential bounds for the Gaussian Q-function or, equivalently, of the complementary error function er f c(.). More precisely, the new bound is in the form of the sum of exponential functions that, in the limit, approaches the exact value. Then, a quite accurate and simple approximated expression given by the sum of two exponential functions is reported. Moreover, some new simple bounds for the inverse er f c(.) are derived. The results are applied to the general problem of evaluating the average error probability in fading channels. An example of application to the computation of the pairwise error probability of space-time codes is also presented.