Symmetric Displaced Coprime Array Configurations for Mixed Near- and Far-Field Source Localization

Conventionally, mixed near-field (NF) and far-field (FF) source localization is performed using a symmetric uniform linear array (ULA). Recently, two symmetric nonuniform linear arrays (NLAs), symmetric nested array (SNA) and compressed SNA (CSNA), have been developed to enhance the positioning performance by their advantages in the degrees of freedom and the array aperture over symmetric ULAs. In this article, we devise a new symmetric NLA, termed symmetric displaced coprime array (SDCA), to locate the NF and FF sources simultaneously. The SDCA configuration consists of three sparse ULAs with a certain displacement, implying there are two displaced coprime arrays with one common subarray. For a given number of sensors, the SDCA configuration is solely determined by a closed-form expression and its consecutive coarray ranges can also be analytically computed. In addition, we derive two optimum SDCA configurations by maximizing the number of the unique and consecutive lags in the difference coarray. Compared with the SNA and the CSNA, the SDCA provides more unique and consecutive virtual sensors, as well as a larger physical array aperture. Numerical experiments are presented to verify the superiorities of the SDCA configuration over the existing symmetric NLAs.