Mainlobe/Sidelobe Region Gap Minimization for Shaped-Beam Pattern Synthesis via Antenna Array

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
$\mathit{l}_{0}$
-norm to
$\mathit{l}_{1}$
-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.