Robust adaptive beamforming using multi-snapshot direct data domain approach

For the realistic case where there is no secondary snapshot that does not contain the desired signal and exhibits the statistical characteristics similar to the snapshot under test, direct data domain (D³) beamforming approaches have been proposed to estimate a desired signal in the presence of interference. However, the basic idea of the D³ methods is realized by making significant sacrifices with respect to the number of degrees of freedom (DoFs). In this paper, we present a multi-snapshot approach for D³ beamforming. Using the least-squares method with multiple snapshots, we can eliminate the interference without causing a severe reduction in the number of DoFs. In addition, to consider a mismatch between nominal and actual target steering vectors, we propose a D³ approach combined with a probability constraint to prevent the self-nulling effect, and the relationship between the probability constraint and norm constraint is discovered. The simulations verify that the proposed method provides better performance and robustness than the conventional D³ approaches.