Sparse array design for underdetermined DoA estimation exploiting fourth-order non-circularity

A sparse linear array exploiting fourth-order (FO) non-circularity, called the fourth-order nested array (fNA), is proposed for underdetermined direction-of-arrival (DoA) estimation of statistically independent narrowband non-Gaussian signals. The fNA is designed by concatenating three subarrays with distinct structures. The first one is a uniform linear array (ULA) with half-wavelength inter-sensor spacing, while the second and third ones are both sparse ULAs whose inter-sensor spacings are larger than half wavelength. With a joint exploitation of both the standard and the complementary FO cumulant matrices, two equal-size virtual ULAs, associated with the FO difference co-array and the FO sum co-array, respectively, can be synthesized. The processing capacity (the maximum number of FO non-circular signals whose DoAs can be unambiguously determined) of the fNA is thus higher than those of the current FO sparse arrays which make use of the FO difference co-array only, leading to improved DoA estimation performance measured by root mean square error (RMSE). A processing capacity enhanced DoA estimation algorithm is also developed by employing the two virtual ULAs. The performance of fNA and the associated DoA estimation algorithm is illustrated and compared with existing arrays via simulated and real-world data, in terms of processing capacity, DoA estimation accuracy, robustness against sensor position perturbations, reduction in inter-sensor mutual coupling, and practicality.