The elementary radiator of a planar array for next generation millimeter-wave (mm-wave) 5G base stations is described. The antenna is designed for high density interconnect (HDI) manufacturing for yielding a compact, densely-interconnected, and highly-integrable stacked structure. The layout of the single element is determined by directly optimizing key radiation features of the whole planar arrangement according to specific application-driven requirements. In addition, thanks to the exploitation of a spline-shaped modelling of the radiator, suitable performance in terms of impedance matching, realized gain, half-power beamwidth (HPBW), polarization purity, and inter-element isolation are achieved within the 28-GHz pass-band. Moreover, integrated out-of-band filtering capabilities are obtained in selected and wide non-contiguous stop-bands without additional circuitry.