The statistical analysis of the fading End to End channel gain of the amplify and forward relaying protocol, however, is well known as extremely complex, and research work to date have only studied the asymptotic behaviour of the outage probability of the network at either very low or very high Signal Noise Ratios. Most current works circumvent the analytical complexity by first ignoring the effect of Additive White Gaussian noise then by using the simple approximated upper bound for the Signal Noise Ratio. The new approximated upper bound proposed in this paper, is far better bound than the previous results for the entire Signal Noise Ratio, which allows us to derive exact analytical expressions to study the effect of Additive White Gaussian noise on the network performance.