Coprime arrays in the context of compressive sensing

Abstract

Arising naturally from the formalism of coarrays, coprime arrays offer a means of achieving sparsity along an array while maintaining certain measures of performance. This configuration offers benefits over traditional configurations for large aperture towed arrays in the ocean environment, but shallow water propagation complicates the wide sense stationarity assumption that is essential to proper application of coarray concepts. Compressive sensing techniques allow for the reconstruction of generalized signals which are sparse on some known basis. Existing literature has shown the connection between compressive sensing and random arrays, drawing direct parallels between the results and methods that arose independently in both fields. Compressive sensing may offer an alternative understanding of coprime arrays, which is independent of wide sense stationarity, and thus applicable to shallow water environments. Coprime arrays will be considered in the context of compressive sensing. It will be discussed if the measurement matrices that arise from this array geometry might possess properties necessary for compressive sensing reconstruction to function, such as the Restricted Isometry Property. [This research was supported by the Applied Research Laboratory, at the Pennsylvania State University through the Eric Walker Graduate Assistantship Program.]