This paper presents a multi-field coupling model for magnetoelectric (ME) antennas, encompassing a ME film, electrode layers, and a substrate featuring a cavity structure. This model accounts for the nonlinear magnetoelastic coupling within the radiation layer and employs a combined DC and AC simulation methodology to capture the antenna's radiation mechanism. Leveraging this multi-field coupling model, performance differences between the ME antenna and an ideal ME composite film are analyzed. By exploring optimization schemes based on multi-physics fields, electrode materials, and structural design, the ME antenna's radiation performance is significantly enhanced. The findings demonstrate that the complete antenna structure, with its increased thickness and cavity design, exhibits a lower resonance frequency and a higher converse ME (CME) coefficient compared to the ideal ME film. The optimal CME effect is achieved under proper external stimuli, leading to a broader 3 dB bandwidth. Expanding the cavity dimensions enhances the CME coefficient by 42% and reduces the resonance frequency due to decreased acoustic wave loss. Adopting electrode materials with higher acoustic impedance elevates the CME coefficient, yet narrows the bandwidth. Conversely, using silver (Ag) electrodes promotes a broader bandwidth. Additionally, ME antenna arrays are designed to broaden the bandwidth by 300%.