Beam Broadening Design for Large-Scale Antenna Arrays Using Convex Quadratic Programming

Pencil beam broadening for large-scale antenna arrays has many applications in radar and communication systems to achieve better search and coverage performance. Current windowing methods cannot guarantee that the array gain $G_{\mathrm{bdr}}$ on the boundary of a specified beam region is maximized, even though the technique of parameter scanning is employed. This article introduces a beam broadening method based on the convex quadratic programming (CQP) that maximizes $G_{\mathrm{bdr}}$. We first approximate the pattern cut of the broadened beam by a uniform linear array (ULA). Then, an analytical formula for the number of elements ($N$) in the ULA that maximizes $G_{\mathrm{bdr}}$ is derived. Once $N$ has been determined, we will be able to calculate the half-power beamwidth of the broadened beam. Based on this information, the task of beam broadening can be formulated as a quadratic program with few constraints, which can be transformed to a CQP problem using the symmetry of array structure and solved efficiently using the interior point method (within 0.1 s for a $32\times 32$ rectangular array). In addition, we derive a closed-form solution to the CQP problem when the positivity constraints on the weighting coefficients are removed. Array factor analysis and full-wave simulation show that the proposed method obtains a higher beam boundary gain than the conventional windowing methods.