Extremely efficient generation of Gamma random variables for \alpha >= 1

The Gamma distribution is well-known and widely used in many signal processing and communications applications. In this letter, a simple and extremely efficient accept/reject algorithm is introduced for the generation of independent random variables from a Gamma distribution with any shape parameter \alpha >= 1. The proposed method uses another Gamma distribution with integer \alpha_p <= \alpha, from which samples can be easily drawn, as proposal function. For this reason, the new technique attains a higher acceptance rate (AR) for \alpha >= 3 than all the methods currently available in the literature, with AR tends to 1 as \alpha\ diverges.