Further study on the RCB-like steering vector estimation method: closed-form solution derivation via accurate Lagrange multiplier calculation

Obtaining the signal steering vector (SV) in array perturbation scenarios is vital for an adaptive beamformer. Recently, a robust Capon beamformer (RCB)-like SV estimation (RCB-SVE) method has been given to optimize the SV by maximizing the signal of interest spectrum with an uncertainty set constraint. However, the SV solution to this method cannot be acquired in a closed form and therefore, leading to difficult applications. To address this issue, in this paper, we propose a closed-form expression of the RCB-SVE, which is based upon the Lagrange multiplier method. In particular, to accurately calculate the Lagrange multiplier, we take advantage of a high-order polynomial rooting scheme to get the unique Lagrange multiplier by using its positive feature. The aforesaid steps are free of any approximation or iteration processing. Typical experiments have verified that the proposed beamformer is more effectively implemented than the RCB-SVE and enjoys satisfactory SV estimation results in general array perturbation scenarios.