Two-Stage Reconstruction for Co-Array 2D DOA Estimation of Mixed Circular and Noncircular Signals

Two-dimensional (2D) direction-of-arrival (DOA) estimation using sparse arrays shows advantages in reducing hardware costs and enhancing degrees-of-freedom. However, most current studies primarily focus on generating covariance-like matrices associated with higher dimensional difference co-arrays, neglecting the valuable information embedded in pseudo covariance matrices relevant to sum co-arrays when noncircular (NC) components are present in impinging signals. This leads to suboptimal estimation performance. To address this limitation and well leverage both covariance and pseudo covariance matrices, we propose a two-stage reconstruction-based sequential decoupled (TR-SD) approach using both sum and difference co-arrays corresponding to the deployed sparse symmetric planar array (SSPA). This approach enables the estimation of 2D DOAs of impinging signals and NC phases of NC signals simultaneously. The TR pre-procedures are developed to efficiently reconstruct the conjugate augmented covariance matrix corresponding to the uniform counterpart of the SSPA. Subsequently, SD post-procedures are devised with low computational complexity, maintaining high identifiability and the capability to estimate the NC phases. Numerical simulations are conducted to validate the effectiveness of our proposed TR-SD approach in diverse signal scenarios, demonstrating enhanced identifiability, improved detection probability, increased estimation accuracy, and high angular resolution.