Applying concepts and tools from signal processing on graphs (SPG) to problems in array signal processing

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.