Gridless DOA estimation for arbitrary array geometries based on maximum likelihood

This paper presents a gridless maximum likelihood (ML) direction-of-arrival (DOA) estimation method for arbitrary array geometries. The approach parameterizes the likelihood function of the received signal covariance matrix and formulates a structured optimization problem to recover a positive semidefinite Hermitian Toeplitz matrix encoding the sources’ azimuth and power information. Gridless DOA estimates are then extracted from this matrix via ESPRIT or Vandermonde decomposition. To solve the resulting nonconvex ML problem, two iterative algorithms are developed: a difference-of-convex programming method with convergence guarantees and a Quasi-Newton scheme that reduces computational complexity while maintaining accuracy. Simulations with an eight-element uniform circular array compare the proposed method with MUSIC, SPICE, SBL, OGSBI, and SPICE-GL, demonstrating effective mitigation of grid-mismatch errors and superior or comparable estimation accuracy under various scenarios.