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The multiport parasitic array radiator (MuPAR) antenna is a compact low-profile beam-steering antenna, which is composed of two excited inverted-F elements and two parasitic elements with variable reactors. Although the MuPAR antenna seems to have a good potentiality to achieve full azimuthal beam/null steering performance, the detailed controllability of the beam and null has not been clarified yet. This is because the two different types of variables, which are excitation coefficients and reactance values, make the gain optimization problem complex and difficult. Thus, in this paper, we have first developed a generalized model of the inverted-F MuPAR antenna. For the accurate modeling, structural features of inverted-F antennas are taken into account, and also the closed-form gain definition for the MuPAR antenna is derived. The formulation enables us to efficiently obtain both excitation coefficients and reactance values with optimization techniques. Applying the model to both a gradient-based optimization and a particle swarm optimization successfully, the beam/null forming performances of the four-element MuPAR antenna is made clear. Through experiments including numerical calculations and measurements at 2.45 GHz, the validity of our model and precise formulation is confirmed.