阵列天线实现误差对功率方向图扰动的影响分析

对阵列天线工程实现过程中的阵元位置、激励幅度和相位误差进行了分析，在假定各误差为高斯分布的情况下分析了阵列天线功率方向图的期望，并推导了功率方向图方差的理论公式。利用切比雪夫不等式，推导了在给定概率条件下功率方向图上、下边界的理论结果。使用蒙特卡洛模拟，验证了理论推导的正确性和准确度。利用该结果，可以较为准确地预测实际阵列天线中随机实现误差对阵列功率方向图的影响，对于阵列天线工程实践具有重要的指导意义。

Analysis of Power Pattern Pertubations Due to Implementation Errors in Practical Antenna Arrays

The influence of amplitude, phase and position errors on the performance of an antenna array is analyzed and studied in this paper. On the assumption that each type of these random errors obeys the Gauss distribution, the expectation of the antenna array power pattern is analyzed, and the theoretical formula of variance is derived for the first time. In addition, theoretical upper and lower boundaries on which the power pattern falls on with a given probability are derived by using the Chebyshev's inequality. The effectiveness and accuracy of all the obtained theoretical equations are verified by Monte Carlo simulation. The simulation results show that the influence of the random implementation errors on the power pattern can be accurately predicted by using the proposed technique. Hence, it provides significant guidance for the practical array antenna design.