Underdetermined DOA estimation, which means estimating more sources than sensors, is a challenging problem in the array signal processing community. This paper proposes a novel algorithm that extends the underdetermined DOA estimation in a Sparse Circular Array (SCA). We formulate this problem as a matrix completion problem. Meanwhile, we propose an inverse beamspace transformation combined with the Gridless SPICE (GLS) algorithm to complete the covariance matrix sampled by SCA. The DOAs are then obtained by solving a polynomial equation with using the Root-MUSIC algorithm. The proposed algorithm is named GSCA. Monte-Carlo simulations are performed to evaluate the GSCA algorithm, the spatial spectrum plots and RMSE curves demonstrated that the GSCA algorithm can give reasonable results of underdetermined DOA estimation in SCA. Meanwhile, the performance of the algorithm under various configurations of SCA is also evaluated. Numerical results indicated that the GSCA algorithm can provide access to solve the DOA estimation problem in Uniform Circular Array (UCA) when random sensor failures occur.
