Tight upper bound on the probability that the sum of L random variables exceeds a threshold

The problem of obtaining the probability that the sum of L random variables exceeds a threshold often occurs in obtaining the error rate performance of digital communication systems. The probability density function of the sum, when the random variables are independent and identically distributed may be obtained by the L-1 dimensional auto-convolution of the probability density function of each random variable. The probability density function must then be integrated to obtain the probability that the sum exceeds a threshold. These operations may be computationally very intensive. An upper bound on the desired probability may be obtained using the Chernoff Bound. However, this upper bound is not extremely tight. A tight analytical upper bound to the probability is presented in this paper. The bound parametrically trades off tightness for computational complexity. A numerical example is given involving signal detection with quantized channel observations.