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Performing direction-of-arrival (DOA) estimation of a detected source target using data collected from an array of sensors is a long-studied problem in signal processing. The emerging framework of signal processing on graphs (SPG) offers the opportunity to look at this problem from a different point of view by adding the concept of a graph underlying the measured data as an extra layer of information that can be incorporated in to the data processing system. While a recent presentation [J. Acoust. Soc. Am. 143, 1852 (2018)] showed how to use the Graph Fourier Transform to estimate DOA on a uniform line array, the purpose of this talk is to show how we can use the smoothness of a graph signal across vertices for the more involved case of a non-uniform line array. The scope of the problem was narrowed to DOA estimation of a single, far-field, and narrowband source signal. An iterative approach was developed that demonstrates the utility of SPG, and the approach was verified and tested through simulation under different signal-to-noise ratios. We also compared the results to conventional delay-and-sum beamforming to gain insight on what differentiates SPG over existing methods.

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Signal processing on graphs (SPG) is an emerging area of research that extends well-established data analysis concepts and tools to support a special type of signal where data samples are defined on the vertices of a graph. Since SPG emerged in 2013, fundamental operations such as filtering, the Fourier transform, and modulation have been formally defined that uniquely consider and take advantage of the underlying complex and irregular relationship between data elements which is captured mathematically by a graph. The purpose of this study is to analyze the applicability of SPG to array signal processing. We show that signals defined on a graph, or graph signals for short, are natural models for data collected over a line array of sensors. We also apply existing SPG processing algorithms to array signal data and investigate and probe whether SPG can help increase array gain.