Abstract
Prior analysis on coprime sampled arrays (CSAs) made the assumption of spatiallywhite, or uncorrelated Gaussian noise. This thesis predicts the performances ofCSAs in spatially colored, or correlated Gaussian noise, modeled as a first-order auto-regressive process to introduce inter-sensor noise correlation that decays exponentially with length. The analysis on the CSA geometry considers both the subarray product processor (CSAₚₚ) [Vaidyanathan & Pal, 2011] and the conventionally beamformed (CBF) CSA (CSAcbf). Coarray processing allows for comparing the two CSA processors to the baseline of the densely populated CBF uniform line array (ULA). In terms of detection performance, the array gains are derived through the deflection statistic [Cox, 1973]. The deflection is generalized for processors that are either incoherent or involve non-linear processing of the array measurements. This statistic quantifies the noise variance reduction achieved at the beamformer output by utilizing the moments of the binary hypothesis test (BHT) probability distribution functions (PDFs). These PDFs are used to evaluate the receiver operating characteristics of each processor to analyze and compare the beamformer detection sensitivities. In terms of estimation performance, the implicit Fourier relations with coarray processing and power spectral density (PSD) estimation shows the estimate produced at the beamformer output is biased. The processing of the measurements inherently smears the "true" spatial characteristics of a random acoustic field. For the same measurements, the CSAₚₚ and CSAcbf will smear the true PSD differently. This thesis considers both aspects of performance metrics to analyze and compare the two CSA processors against the baseline of the ULA in spatially correlated noise.