Two sparse-based methods for off-grid direction-of-arrival estimation

- overcome the grid mismatch limitation inherent in conventional sparse-based techniques.
- Two off-grid direction-of-arrival (DOA) estimation methods are proposed by using a two-step iterative technique.
- The proposed methods are accelerated by deriving the closed-form solution of the optimization problems.
- The proposed algorithm can be extended for other sparse methods to improve their estimation accuracy.
- The root mean square error (RMSE) of the proposed methods can coincide with the cramer-rao lower bound (CRLB).

Recently, many sparse-based methods have been proposed for direction-of-arrival (DOA) estimation. However, these methods often suffer from the grid mismatch problem caused by the discretization of the potential angle space. Most of them employ the iterative grid refinement (IGR) method to alleviate this problem. Nevertheless, IGR requires a high computational load and may not comply with the restricted isometry property (RIP) condition in the compressed sensing (CS) theory. This paper aims to overcome the grid mismatch limitation inherent in conventional sparse-based techniques. In particular, we first introduce an off-grid model by incorporating the bias parameter into the signal model, then propose a two-step iterative method named off-grid ℓ1 Cholesky covariance decomposition (OGL1CCD) to solve the DOA estimation problem. Our method can be accelerated to save computations and the proposed algorithm framework can be extended for any other sparse-based method to improve their estimation accuracy. We then propose another off-grid method named off-grid ℓ1 covariance matrix reconstruction approach (OGL1CMRA) based on the covariance matrix model. Compared to OGL1CCD, OGL1CMRA is more computationally efficient and accurate, but requires sufficient snapshots and uncorrelated sources. Our proposed methods are superior to many other methods in estimation performance, which is verified by extensive numerical simulations.