The performance of the conventional beamforming for angle-of-arrival (AOA) estimation algorithm under measurement uncertainty is analyzed. Gaussian random variables are used for modeling measurement noises. Analytic expression of the mean square error (MSE) is obtained via Taylor series expansion. In traditional performance analysis, estimation accuracy in terms of the MSEs is usually obtained from the Monte Carlo simulation, which is computationally intensive especially for large number of repetitions in the Monte Carlo simulation. For reliable MSE in the Monte Carlo simulation, the number of repetitions should be very large. To circumvent this problem, analytic performance analysis which is less computationally intensive than the Monte Carlo simulation-based performance analysis is proposed in this paper. After some approximations, we derive the closed form expression of the mean square error (MSE) for each incident signal. The validity of the derived expressions is shown by comparing an analytic MSE with an empirical MSEs. The Cramer–Rao bound is also used to further validate the derived analytic expression.

中文翻译：

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测量不确定性下传统波束形成算法的到达角估计性能分析

分析了测量不确定度下传统波束形成到达角（AOA）估计算法的性能。高斯随机变量用于对测量噪声进行建模。通过泰勒级数展开获得均方误差（MSE）的解析表达式。在传统的性能分析中，通常从蒙特卡洛模拟获得关于MSE的估计精度，这在计算上非常费力，尤其是对于蒙特卡洛模拟中的大量重复。为了在蒙特卡洛模拟中获得可靠的MSE，重复次数应非常大。为了解决这个问题，本文提出了比基于蒙特卡洛模拟的性能分析计算量少的分析性能分析。经过一些近似，我们导出每个入射信号的均方误差（MSE）的闭式表达式。通过将分析型MSE与经验型MSE进行比较，可以得出派生表达式的有效性。Cramer-Rao界限也用于进一步验证派生的分析表达式。