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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$G_{\mathrm{{bdr}}}$</tex-math></inline-formula> on the boundary of a specified beam region is maximized, even though the technique of parameter scanning is employed. This paper introduces a beam broadening method based on the convex quadratic programming (CQP) that maximizes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$G_{\mathrm{{bdr}}}$</tex-math></inline-formula>. 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 (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula>) in the ULA that maximizes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$G_{\mathrm{{bdr}}}$</tex-math></inline-formula> is derived. Once <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> has been determined, we will be able to calculate the half-power beamwidth (HPBW) 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 seconds for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$32\times 32$</tex-math></inline-formula> 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.