Efficient DOA estimation based on difference-set table traversal searching for the generalized coprime array

Abstract This paper aims to achieve both high degree-of-freedom (DOF) and high efficiency in direction-of-arrival (DOA) estimation. On one hand, to realize high DOF, this paper optimizes the interelement spacings and the displacement of the generalized coprime sparse array. On the other hand, to achieve high efficiency, a series of approaches are proposed: Firstly, a normalized-coordinate representation is formulated to explore the conversion relationship between the covariance matrix of the physical sparse array and that of the expected virtual Nyquist uniform linear array (ULA); Secondly, a difference-set table traversal searching method is proposed to guide this conversion; Thirdly, the mapping relationship between the element coordinates in the observation covariance matrix and a lag of the Nyquist-ULA is built up, from which the DOAs can be readily estimated through MUSIC decomposition. Deep analysis shows that the proposed estimator saves approximately O ( ( MN + 1 ) 3 ) times of multiplications involved in the spatial smoothing based estimator. Numerical results also confirmed that our proposed estimator does not pay the cost of performance attenuation, which presents vast potentials in radar, communication and sonar systems, etc.