Array design for different SLL and null directions with an interior-point optimization method from the generalized-scattering-matrix and spherical modes

This paper presents a pattern synthesis technique for arbitrary planar arrays which can be characterized in terms of a generalized-scattering-matrix (GSM) and whose radiated field can be expressed as a spherical mode expansion (SME). The procedure yields the complex-valued excitations needed to achieve a pattern which fulfils the requirements of different sidelobe levels in different regions and several prescribed field nulls with a maximum directive gain. The formulation is based on matrix-valued functions which are computed from the GSM and the SME, so all interelement coupling effects coming from complex radiating structures used as array elements are inherently taken into account. To solve the resulting nonlinear optimization problem, a primal-dual interior-point filtering method specifically adapted to this formulation is developed. Numerical results are presented for arrays of microstrip patch antennas and dielectric resonator antennas.