Antenna optimization studies for radiofrequency coupling to the Alfven waves is carried out by using a self-consistent, three-dimensional, fully analytic, Faraday shielded, periodic loop antenna model. The antenna characteristics (the loading resistance R, the reactance X, the quality factor Q, and the efficiency ηA) are investigated over a wide range of parameters using the ASDEX UPGRADE parameters as reference. With proper care, it is possible to obtain an experimentally acceptable loading of R ∼ 1 Ω with an attendant, Q ∼ 20 under optimal conditions. The required conditions consist of (i) locating the singular Alfvén layer at about two-thirds the plasma radius, and (ii) the adjacent antenna separation along the toroidal direction is of the order of the plasma radius. This implies using a toroidal wave number n ∼ 8, for the ASDEX UPGRADE case. The extensive results presented here should facilitate the antenna design for Alfvén wave heating in most existing as well as projected machines. By scaling the linear dimensions of the ASDEX UPGRADE, it is shown that the Alfvén wave heating continues to be an attractive alternative even for plasmas of thermonuclear dimensions. Because of the changing plasma conditions during the radiofrequency heating phase, dynamic impedance tracking may become necessary. Methods are suggested for maintaining an efficient coupling under these conditions through the phase control of a dense cluster array antenna, resembling the lower hybrid grill coupler.