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.

翻译：本文推导了两种渐近情况下指向误差模型的若干精确且计算高效的结果。采用归一化均方误差（NMSE）性能指标来量化不同模型的精度。针对波束宽度相对大于检测孔径的情况，我们提出了三种形如 $c_1\exp(-c_2r^2) $的模型。结果表明，修正强度均匀模型不仅与最优线性化模型具有相当的精度，而且相较于传统的Farid模型，其数学表达更为优美。这表明在考虑指向误差影响的自由空间光（FSO）系统性能分析中，修正强度均匀模型更为可取。通过将波束宽度小于检测孔径的情况类比为光斑可视为点，指向误差模型的求解转化为一个光滑函数逼近问题，并且我们发现，在某些场景下，所提出的点逼近模型相较于源于Vasylyev模型的模型能实现更精确的逼近。