New Results for the Pointing Errors Model in Two Asymptotic Cases

TL;DR

This paper derives precise, computationally efficient pointing error models for two asymptotic cases in free space optical systems, comparing their accuracy using NMSE and proposing a new point approximation model.

Contribution

It introduces new pointing error models for different asymptotic cases and demonstrates their accuracy and mathematical elegance over traditional models.

Findings

Modified intensity uniform model achieves accuracy comparable to the best linearized model.

The proposed point approximation model offers more accurate results than the Vasylyev-based model in certain scenarios.

The models are computationally efficient and suitable for performance analysis of FSO systems.

Abstract

Several precise and computationally efficient results for pointing errors models in two asymptotic cases are derived in this paper. The normalized mean-squared error (NMSE) performance metric is employed to quantify the accuracy of different models. For the case that the beam width is relatively larger than the detection aperture, we propose the three kinds of models that have the form of $c_1\exp(-c_2r^2) $.It is shown that the modified intensity uniform model not only achieves a comparable accuracy with the best linearized model, but also is expressed in an elegant mathematical way when compared to the traditional Farid model. This indicates that the modified intensity uniform model is preferable in the performance analysis of free space optical (FSO) systems considering the effects of the pointing errors. By analogizing the beam spot with a point in the case that beam width is smaller than the detection aperture, the solution of the pointing errors model is transformed to a smooth function approximation problem, and we find that a more accurate approximation can be achieved by the proposed point approximation model when compared to the model that is induced from the Vasylyev model in some scenarios.