Abstract
Multiplicative processors generate spatial spectrum estimates for sparse arrays, such as nested and coprime arrays, by multiplying the beamformed outputs of two interleaved subarrays. Nested and coprime arrays achieve significant sensor savings compared to dense Uniform Linear Arrays (ULAs) since one or both subarrays are undersampled. Chavali et al. show that careful design of the subarrays and proper selection of beamformer weights can guarantee power pattern performance (response to single planewave source) comparable to a conventional ULA processor [JASA (2018)]. The multiplicative processors’ response to multiple sources contains cross terms that appear as erroneous sources in the spectral estimate. The height of cross term peaks in the spectrum depends on the subarray design, beamformer weights, and signal powers. Ksienski and Pedinoff show that averaging the multiplicative processor output over snapshots reduces the power of uncorrelated cross terms [IEEE (1962)], though they do not explore how much averaging is required. This talk derives the statistics of the averaged cross terms assuming complex Gaussian planewave signals and noise. The statistical model is used to predict the number of snapshots required to eliminate uncorrelated cross term peaks from the multiplicative spectra. Analytical predictions show excellent agreement with planewave simulations. [Work supported by ONR.]
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