Swanson D C, Culver R L
The Applied Research Laboratory, The Pennsylvania State University, P.O. Box 30, State College, Pennsylvania 16804, USA.
J Acoust Soc Am. 2017 Oct;142(4):2030. doi: 10.1121/1.5006910.
Small aperture arrays (size less than a wavelength) can be used for passive angle of arrival (AOA) estimation of both broadband and narrowband signals in the frequency domain. Phase differences across the array are measured in the frequency domain and can be spectrally averaged if desired for stationary source AOA and frequencies. The array is capable of measuring multiple target AOAs so long as each target produces unique frequencies or radiates in unique frequency bandwidths. Broadband and narrowband signals from targets can be collected from the fast Fourier transform (FFT) bins and summed by arrival angle in elevation and azimuth using a bearing histogram where the amplitude is displayed in dB. This provides a very useful and intuitive display of received signal levels. The Cramer-Rao lower bound (CRLB) for bearing accuracy is presented as a function of frequency, aperture, and signal-to-noise ratio (SNR). The small aperture background noise includes any other coherent or incoherent signal other than the source of interest. Analysis of phase calibration requirements, nonstationary frequencies, and channel cross-talk are also presented, as well as a technique for generating broadband source signals with the fractional delays needed to simulate the correct AOA.
小孔径阵列（尺寸小于一个波长）可用于在频域中对宽带和窄带信号进行被动到达角（AOA）估计。在频域中测量阵列上的相位差，如果需要对静止源的AOA和频率进行测量，可对其进行频谱平均。只要每个目标产生独特的频率或以独特的频率带宽辐射，该阵列就能测量多个目标的AOA。来自目标的宽带和窄带信号可从快速傅里叶变换（FFT）频段中收集，并使用方位直方图按仰角和方位角的到达角进行求和，其中幅度以dB显示。这提供了一种非常有用且直观的接收信号电平显示。给出了方位精度的克拉美 - 罗下界（CRLB）作为频率、孔径和信噪比（SNR）的函数。小孔径背景噪声包括除感兴趣源之外的任何其他相干或非相干信号。还介绍了相位校准要求、非平稳频率和信道串扰的分析，以及一种生成具有模拟正确AOA所需分数延迟的宽带源信号的技术。
