Mainlobe/Sidelobe Region Gap Minimization for Shaped-Beam Pattern Synthesis via Antenna Array
Ao Zhang, Shiwen Lei, Wei Yang, Jing Tian, Haoquan Hu, Likang Xiao
Abstract
The letter adaptively minimizes the gap between the mainlobe region and the sidelobe region for the shaped-beam pattern synthesis (SBPS) via antenna array. The gap setting is empirically in the existing SBPS methods, full of uncertainty and flexibility. Therefore, a gap autominimization algorithm is proposed. First, the original SBPS problem is approximated to be a quasi-convex one by relaxing the nonconvex cost function from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathit{l}_{0}$</tex-math></inline-formula> -norm to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathit{l}_{1}$</tex-math></inline-formula> -norm with a penalty constraint. Then, the referenced shaped-beam pattern (SBP) is synthesized with existing approaches. The proposed algorithm iteratively shrinks the mainlobe/sidelobe gap by synthesizing an SBP similar to the referenced one. As a result, the proposed algorithm enables obtaining the minimum gap while obtaining the desired sidelobe level with a narrow mainlobe ripple level. The effectiveness of the proposed algorithm is validated via numerical simulations from different perspectives.