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We consider the problem of far-field sensing by means of a sensor array.Traditional array geometry design techniques are agnostic to prior informationabout the far-field scene. However, in many applications such priors areavailable and may be utilized to design more efficient array topologies. Weformulate the problem of array geometry design with scene prior as one offinding a sampling configuration that enables efficient inference, which turnsout to be a combinatorial optimization problem. While generic combinatorialoptimization problems are NP-hard and resist efficient solvers, we show how forarray design problems the theory of submodular optimization may be utilized toobtain efficient algorithms that are guaranteed to achieve solutions within aconstant approximation factor from the optimum. We leverage the connectionbetween array design problems and submodular optimization and port severalresults of interest. We demonstrate efficient methods for designing arrays withconstraints on the sensing aperture, as well as arrays respecting combinatorialplacement constraints. This novel connection between array design andsubmodularity suggests the possibility for utilizing other insights andtechniques from the growing body of literature on submodular optimization inthe field of array design.

Sensor Array Design Through Submodular Optimization