Design of optimum two-dimensional non-redundant arrays

Recent advancements in array signal processing focus on enhancing source detection and reducing the effects of mutual coupling among array elements. This has been achieved using Direction of Arrival (DOA) estimation via virtual arrays formed by sparse arrays. Non-Redundant Arrays (NRAs) are a very common structure among sparse arrays. Traditionally, one-dimensional NRAs capture either azimuth or elevation angles of sources, but practical scenarios often require both simultaneously. This paper introduces optimized methods for designing two-dimensional (2-D) NRAs to address this need. In addition to the optimized design approach for creating 2-D NRAs with minimum aperture, the optimized design approaches for creating 2-D NRAs with desired aperture, with minimized mutual coupling effect and with hybrid of both are proposed. The designed arrays can be in the form of a rectangle or a regular polygon with the number of sides being a multiple of 4. The proposed array design methods significantly enhance the flexibility in designing NRAs, allowing the creation of various array configurations for any desired number of sensors. Simulation results show that the proposed arrays outperform the existing 2-D arrays in estimating the DOAs of signal sources and show more robustness against the effects of mutual coupling.