In this talk, we consider the application of random mixtures to the generation of piecewise-continuous pseudo-random functions (hereafter referred to as random processes). Starting with complex-valued correlated Nakgami-m processes, we present a random mixture technique that allows the extension of results holding only for processes with integer and half-integer fading figures to processes with real m. The method relies on the moment determinance of the Nakagami-m joint (envelope and phase) probability density function (pdf) -- which we prove -- and on a formula for the random mixture probabilities to deliver a simple and alternative to the decomposition technique that, to the best of our knowledge, is the state-of-the-art in terms of algorithms to generate Nakagami-m variates with correlation and arbitrary m values. Then, we proceed to demonstrate the application of the random mixture concept to the generation of Tikhonov random variates, which brings in new challenges to the problem. In particular, it is shown how approximate Tikhonov processes can be constructed out of Cauchy and Gaussian processes, with 100% efficiency (in terms of useful versus generated samples). Together, the two examples illustrate how random mixtures can be applied to simplify the generation and modeling of random processes, with further potential implications on the analysis of communications systems over fading and partially coherent channels.

Host: Behnaam Aazhang