Symmetric small-aperture arrays for three-dimensional bearing estimation

Abstract

Small aperture arrays (size less than a wavelength) can be used for passive direction of arrival (DOA) 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 for stationary DOA and frequencies if desired. Data windowing will bias the DOA measurement toward the center of the FFT data buffer and is useful to prevent spectral leakage from strong target signals overshadowing weak target signals. The array is capable of measuring multiple target DOAs so long as each target produces unique frequencies. Broadband signals from targets can be collected from the FFT bins and grouped by arrival angle using a bearing histogram. The Cramer-Rao lower bound (CRLB) for bearing accuracy is presented as a function of frequency, aperture, and signal-to-noise ratio (SNR). The reduction in DOA accuracy due to a small aperture can be overcome if the SNR is sufficiently high. Using symmetry in 2D and 3D array geometries, we show how the azimuth and elevation angles can be separately measured. Examples are given for several single and multiple targets and different array shapes.