A Universal Splitting Estimator for the Performance Evaluation of Wireless Communications Systems

IEEE Transactions on Wireless Communications, vol. 19, pp. 4353–4362

Abstract

We propose a unified rare-event estimator for the performance evaluation of wireless communication systems. The estimator is derived from the well-known multilevel splitting algorithm. In its original form, the splitting algorithm cannot be applied to the simulation and estimation of time-independent problems, because splitting requires an underlying continuous-time Markov process whose trajectories can be split. We tackle this problem by embedding the static problem of interest within a continuous-time Markov process, so that the target time-independent distribution becomes the distribution of the Markov process at a given time instant. The main feature of the proposed multilevel splitting algorithm is its large scope of applicability. For illustration, we show how the same algorithm can be applied to the problem of estimating the cumulative distribution function (CDF) of sums of random variables (RVs), the CDF of partial sums of ordered RVs, the CDF of ratios of RVs, and the CDF of weighted sums of Poisson RVs. We investigate the computational efficiency of the proposed estimator via a number of simulation studies and find that it compares favorably with existing estimators.

Authors 5

1. Nadhir Ben Rached Aachen Chair of Mathematics for Uncertainty Quantification Department of Mathematics

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

   Chair of Mathematics for Uncertainty Quantification, Department of Mathematics, RWTH Aachen University, Aachen, Germany

2. Daniel MacKinlay

   UNSW Sydney

   Affiliation as printed

   School of Mathematics and Statistics, University of New South Wales (UNSW Sydney), Sydney, Australia

   School of Mathematics and Statistics, University of New South Wales (UNSW Sydney), Sydney, NSW, Australia

3. Zdravko I. Botev

   UNSW Sydney

   Affiliation as printed

   School of Mathematics and Statistics, University of New South Wales (UNSW Sydney), Sydney, Australia

   School of Mathematics and Statistics, University of New South Wales (UNSW Sydney), Sydney, NSW, Australia

4. Raul F. Tempone Aachen

   King Abdullah University of Science and Technology · RWTH Aachen University

   Affiliation as printed

   Alexander von Humboldt Professor in Mathematics for Uncertainty Quantification, RWTH Aachen University, Aachen, Germany

   Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia

   Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE)King Abdullah University of Science and Technology (KAUST)Thuwal Saudi Arabia

5. Mohamed‐Slim Alouini

   King Abdullah University of Science and Technology

   Affiliation as printed

   Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia

   Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE)King Abdullah University of Science and Technology (KAUST)Thuwal Saudi Arabia