This paper introduces a 2D angle-of-arrival (AoA) estimator, which has a 6–18 GHz 7-element nonuniformly spaced array (NSA) and a Direct Data Domain- (D3-) based AoA algorithm for a 2D isotropic-element planar array (IEPA). A 2D calibration and data-transformation method is developed to convert the NSA data to the output of the IEPA, so that the NSA-measured data can be used in the D3 algorithm. Using the steering vector (SV) of the IEPA and the results derived from the D3 method, a new 2D AoA searching method is also developed, which offers frequency-independent performance defined by the probability of AoA estimation, when the required estimation accuracy and signal-to-noise ratio (SNR) are given. For the applications of electronic support measures, this paper also presents the use of precalculated SV and data-transformation matrix databases built on preselected frequency points and a 2D-angle grid that is close to uniformly distributed directions. The simulation results show that with good SNR (≥15 dB), the estimator can have 50% probability of AoA estimation with root mean square error (RMSE) less than or equal to 1° using just a few samples from the NSA. Moreover, the study focuses on the applications with low SNR by using more samples from the NSA. Results show that the estimator has 52% and 80% probabilities of AoA estimation with RMSE ≤1° and 5°, respectively, for phase- or frequency-modulated radar pulses, when the SNR is within [−10, 0] dB. The study also shows that the estimator prefers a circular-shaped planar array with a triangular interelement pattern, since it presents more symmetrical characteristics from different azimuth angles.

中文翻译：

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具有直接数据域方法的非均匀间隔阵列，用于6至18 GHz电子支持测量中的二维到达角测量

本文介绍了一种二维到达角（AoA）估计器，该估计器具有6-18 GHz 7元素非均匀间隔阵列（NSA）和基于直接数据域（D3-）的用于2D各向同性元素的AoA算法平面阵列（IEPA）。开发了一种2D校准和数据转换方法，将NSA数据转换为IEPA的输出，以便将NSA测量的数据用于D3算法。利用IEPA的导引向量（SV）和D3方法得出的结果，还开发了一种新的2D AoA搜索方法，当所需的估计精度和信号达到要求时，该方法可提供由AoA估计概​​率定义的与频率无关的性能给出了信噪比（SNR）。对于电子支持措施的应用，本文还介绍了基于预先选择的频率点和接近均匀分布方向的二维角网格构建的预先计算的SV和数据转换矩阵数据库的使用。仿真结果表明，在信噪比（≥15 dB）良好的情况下，仅使用少量NSA样本，估计器即可进行AoA估计的概率为50％，均方根误差（RMSE）小于或等于1°。此外，通过使用来自NSA的更多样本，该研究集中于低信噪比的应用。结果表明，当SNR在[-10，0] dB之内时，对于相位或频率调制雷达脉冲，估计器分别具有52％和80％的AoA估计概​​率，RMSE≤1°和5°。研究还表明，估算器更喜欢带有三角形元素图案的圆形平面阵列，