Sparsity-enforcing sensor selection for DOA estimation

The sensitivity of direction-of-arrival (DOA) estimation to different array geometries motivates the design of optimal sensor constellations. We propose a framework for array geometry design for a linear array with fixed aperture and fixed inter-element spacing, where the array geometry design is formulated as a sensor selection problem. The sensor selection is performed such that it achieves a desired Cramér-Rao bound (CRB) for estimating the DOA of a single source. The nonuniformity of the sensor selection typically results in sidelobes. These sidelobes are suppressed in a specified angular sector again via sensor selection. The aforementioned problems are jointly casted as a semidefinite programming (SDP) problem which can be efficiently solved in polynomial time. Simulations exhibit the trade-offs among the number of selected sensors, sidelobe minimization, and CRB of the DOA estimates.