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

TL;DR

This paper introduces a universal multilevel splitting estimator for evaluating the performance of wireless communication systems, capable of handling various static probability estimation problems by embedding them into continuous-time Markov processes.

Contribution

It extends the multilevel splitting algorithm to static problems by embedding them into Markov processes, broadening its applicability to diverse performance metrics.

Findings

Estimator performs favorably compared to existing methods.

Applicable to multiple types of probability distribution estimations.

Demonstrates efficiency through simulation studies.

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.