A co-prime sensor array (CSA) is a nonuniform line array formed by interleaving two undersampled uniform line arrays (ULAs). The CSA requires fewer sensors to span the same aperture as a densely sampled ULA. Consequently, the CSA matches the resolution of the ULA for direction of arrival estimation for narrowband planewaves. However, each CSA subarray array suffers from aliasing, or grating lobes, due to the spatial undersampling. Vaidyanathan and Pal (2011) proved that if the undersampling factors for the uniform subarrays are co-prime, sharing no common factors greater than one, the aliasing can be resolved by multiplying the spatial spectra of the subarrays. This product spatial spectra is the spatial cross-spectral density between the arrays, and is an estimate of the spatial power spectral density (PSD). In this talk, we extend the classic results of Jenkins and Watts (1968) on the periodogram PSD estimator for Gaussian processes to obtain results the bias, variance and covariance for the CSA product spectra. Additionally, we demonstrate that the CSA's product PSD estimate is not necessarily positive definite. Consequently, the CSA product spectrum may fail to detect weak signals in the presence of strong interferers. We propose an alternative approach for resolving the aliasing ambiguity: choosing the minimum of the two subarray periodograms at each bearing. The resulting nonlinear spectral estimator performs better than the product estimator at detecting weak signals in the presence of loud interferers (Liu & Buck, 2015), and guarantees a positive definite power spectrum.
These results in this talk are the fruit of collaborations with Ms. Kaushallya Adhikari and Mr. Yang Liu. (Work supported by ONR Basic Research Challenge Program)
John R. Buck received his Ph.D. from the MIT/WHOI Joint Program in Oceanographic and Electrical Engineering in 1996. He joined the faculty of UMass Dartmouth later that year, and is presently a Professor in the ECE Dept. He is a past recipient of the IEEE Education Society's Mac Van Valkenburg Early Career Teaching Award (2005), the UMass Dartmouth Faculty Federation Leo M. Sullivan Teacher of the Year Award (2008), the ONR Young Investigator Award (2000) and the NSF CAREER award (1998). He is a Fellow of the Acoustical Society of America, three time chair of the IEEE Underwater Acoustic Signal Processing Workshop, and a former Associate Editor for the IEEE Journal of Oceanic Engineering. He spent 2003-2004 at the Australian Defense Science and Technology Organisation and Sydney University as a Fulbright Senior Scholar, and has also held visiting appointments at the University of New South Wales, George Mason University, Brown University and the Woods Hole Oceanographic Institution. His research interests include array processing, underwater acoustics, animal bioacoustics and engineering pedagogy.