Efficient algorithms for optimal and suboptimal unconditional ML estimation of DOA

This paper presents efficient algorithms for optimal and suboptimal unconditional maximum likelihood (UML) directions-of-arrival (DOA) finding. In the conventional UML formulation an important condition is missing. That is the non-negative definiteness of the covariance matrix of signal components. Because of the lack of the important condition, inadequate global solution appears in the solution space and global search fails to find adequate solution. Although the exact UML formulation solves this problem, it requires huge computational load because of eigenvalues required in each step of searching DOA. According to the investigation on the local solutions of the previous UML estimation, the exact solution is found in the local solutions in the case of good estimation condition, such as large snapshots and high SNR. This leads to the fact that local search for the previous UML criterion has a good chance to find the exact solution UML estimation. Although no exact solution could not be found in the local solutions of the previous UML estimation in the threshold region, such as small snapshots or low SNR, the local search has a chance to find suboptimum solutions of the exact UML estimation. This paper proposes two kind of efficient algorithms for the conventional UML to find the optimal or exact solutions and suboptimal solutions for exact UML estimation of DOA.