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\begin{document}

\title{New Convex Approaches to General MVDR Robust Adaptive Beamforming
Problems}



\author[1]{Yao Zhao}%
\author[1]{Qingsong Liu}%
\author[2]{He Tian}%
\author[3]{Mingfan Luo}%
\author[1]{Bingo Ling}%
\author[4]{Zhe Zhang}%
\affil[1]{Guangdong University of Technology}%
\affil[2]{Science and Technology on Electromagnetic Scattering Laboratory}%
\affil[3]{Surveying and Mapping Institute Lands and Resource Department of Guangdong Province}%
\affil[4]{Aerospace Information Research Institute, Chinese Academy of Sciences}%


\vspace{-1em}



  
  \date{March 14, 2025}


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\begin{abstract}
Consider general minimum variance distortionless response (MVDR) robust
adaptive beamforming problems based on the optimal estimation for both
the desired signal steering vector and the interference-plus-noise
covariance (INC) matrix. The optimal robust adaptive beamformer design
problem is an array output power maximization problem, subject to three
constraints on the steering vector, namely, a (convex or nonconvex)
quadratic constraint ensuring that the direction-of-arrival (DOA) of the
desired signal is separated from the DOA region of all linear
combinations of the interference steering vectors, a double-sided norm
constraint, and a similarity constraint; as well as a ball constraint on
the INC matrix, which is centered at a given data sample covariance
matrix. To tackle the nonconvex problem, a new tightened semidefinite
relaxation (SDR) approach is proposed to output a globally optimal
solution; otherwise, a sequential convex approximation (SCA) method is
established to return a locally optimal solution. The simulation results
show that the MVDR robust adaptive beamformers based on the optimal
estimation for the steering vector and the INC matrix have better
performance (in terms of, e.g., the array output
signal-to-interference-plus-noise ratio) than the existing MVDR robust
adaptive beamformers by the steering vector estimation only.%
\end{abstract}%



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