On the Simulation of Tikhonov Random Processes

Abstract— A novel, simple and efficient method for the generation of Tikhonov (a.k.a. von Mises) random variates is proposed. In the proposed method, circular variates of a prescribed Tikhonov distribution pT(x; α, ξ) are generated via the transformation of numbers selected randomly, on a one-forone basis, from a bank of K distinct Cauchy and Gaussian generators. The mutually exclusive probabilities of sampling from each of the Cauchy or Gaussian generators, as well as the parameters that specify the latter, are derived directly from the Cauchy, Gaussian and Tikhonov circular moments, all of which are either known or given in closed form. The proposed technique is extremely efficient in that it requires a single pair of uniform random numbers to generate one Tikhonov (or von Mises) sample, regardless of the prescribed concentration and centrality parameters, without sample rejection or the repetitive evaluation of computationally demanding functions. Additional attractive feature...

• Type: Conference
• Year: 2007
• Where: ICC
• Authors: Giuseppe Thadeu Freitas de Abreu
• Keywords: Communications, Gaussian Generators, ICC 2007, Tikhonov Variates, Von Mises