In this paper we look at the characterization of the far field regions of antennas located over a ground plane. For antennas radiating in free space the far field starts at a distance 2L2/λ, where L is the effective size of the antenna and λ is the wavelength. The question now is if this same radiating antenna is placed over a height H over a ground plane, then where does the far field of that antenna starts. One of the goal of this paper is to demonstrate that for antennas radiating with either polarizations located over a ground plane, the far field starts at a distance 2H2/λ (here H≫ L). We illustrate the validity of some rules of thumb through numerical simulations and by using the definition of the far field where the radial component of the field is negligible as compared to the other components and for regions where the electric and the magnetic field ratio is characterized by , the characteristic impedance of free space. We also look at the validity of this rule of thumb when antennas are located over an imperfect ground plane. Finally, we examine the phenomenon of height-gain in wireless cellular communication, and illustrate that under the current operating scenarios where the base station antennas are deployed over a tall tower, the field strength actually decreases with the height of the antenna over a realistic ground and there is no height gain. Therefore, to obtain a scientifically meaningful operational environment the vertically polarized base station antennas should be deployed closer to the ground. When deploying antennas over tall towers it may be more advantageous to use horizontally polarized antennas than vertically polarized for communication in cellular environments. Numerical examples are presented to illustrate these cases. Finally we make some observations regarding the variation of the field strength and channel capacity with the height of the transmitting and receiving antenna.