It is well-known that low-frequency electromagnetic (EM) signals are heavily attenuated in a medium with dense electron population. All signals below the plasma frequency of the medium get cut off. If we create in this medium, a small population of relatively hot electrons the composite medium then supports low-frequency electrostatic oscillations known as electron acoustic waves (EAW) [e.g., Gary and Tokar, Phys. Fluids 28, 2439]. The dispersion relation of this composite medium shows that it supports EAW in the frequency band where EM signals are cut off. Thus, it is possible, in principle, to employ EAW to transmit signals across an overdense plasma medium. Our primary interest in this paper is to study the radiation characteristics of a source current distribution embedded in a half-space of our composite medium. To enable this, we derive the Green's functions for our problem and, hence, study the radiation characteristics of antennas. When the source signal frequency is below the plasma frequency, only EAW exist in the composite medium, while only EM waves can exist in the free space above. We find that the far-zone radiation fields of any current distribution consist only of θ-polarized waves. Explicit expressions for the radiated fields are obtained for horizontally- and vertically-polarized Hertzian dipoles embedded in our composite medium. We, hence, find that in both cases the radiation patterns are skewed towards the horizon. In particular, we find that the radiation pattern of a horizontal dipole has two lobes as opposed to one in the underdense case.