Eigenbeam-space transformation based steerable differential beamforming for linear arrays

Abstract

Since linear differential arrays with small apertures can obtain high directivity and frequency-independent spatial response, much attention has been paid to the design of differential beamformers steered to the endfire direction. Although some works focus on the design of steerable differential beamformers with linear arrays, the synthesis of steerable frequency-invariant beampatterns by linear arrays still needs to be investigated. In this paper, an eigenbeam-space transformation based steerable differential beamforming is proposed for linear arrays. The major contributions are as follows. (1) For the beamformer steered away from the endfire direction, an interference suppression constraint might be imposed to ensure a valid beampattern in the situation where the interference from the endfire direction is very strong, which is not considered in the state-of-the-art approaches of the literature. (2) The synthesis of steerable differential beamformers is formulated as an optimization problem in the eigenbeam-space domain and the optimization problem is solved in a closed form. By experimentally determining the best pair of integers mt and N′, the proposed hybrid least-squares-error solution obtained in the eigenbeam-space domain has shown some advantages over the null constrained method and the weighted least-squares method implemented in the element-space domain.