# An Accurate Sample Rejection Estimator for the Estimation of Outage Probability of EGC Receivers

## TL;DR

This paper introduces a novel importance sampling method based on sample rejection to accurately estimate outage probability in EGC receivers over fading channels, reducing computational cost compared to traditional Monte Carlo simulations.

## Contribution

It proposes a new importance sampling scheme using sample rejection that leverages the closed-form CDF of the sum of channel gains, applicable to various fading models and generalized selection combining.

## Key findings

- The method achieves bounded relative error in outage probability estimation.
- Validated results show high accuracy with fewer samples compared to Monte Carlo.
- Applicable to Rayleigh, correlated Rayleigh, and Rice fading models.

## Abstract

In this work, we evaluate the outage probability (OP) for L-branch equal gain combining (EGC) diversity receivers operating over fading channels, i.e. equivalently the cumulative distribution function (CDF) of the sum of the L channel envelopes. In general, closed form expressions of OP values are unobtainable. The use of Monte Carlo (MC) simulations is not considered a good alternative as it requires a large number of samples for small values of OP, making MC simulations very expensive. In this paper, we use the concept of importance sampling (IS), being known to yield accurate estimates using fewer simulation runs. Our proposed IS scheme is essentially based on sample rejection where the IS probability density function (PDF) is the truncation of the underlying PDF over the L dimensional sphere. It assumes the knowledge of the CDF of the sum of the L channel gains in a closed-form expression. Such an assumption is not restrictive since it holds for various challenging fading models. We apply our approach to the case of independent Rayleigh, correlated Rayleigh, and independent and identically distributed Rice fading models. Next, we extend our approach to the interesting scenario of generalised selection combining receivers combined with EGC under the independent Rayleigh fading environment. For each case, we prove the desired bounded relative error property. Finally, we validate these theoretical results through some selected experiments.