We recently proposed  that a monocone antenna on a ground plane with an embedded dielectric lens could be designed to have a frequency domain (FD) transfer function that is proportional to Hankel function of the second kind H0(2) (βρ)- Such an antenna would radiate a half-derivative in the time domain (TD). Since an antenna's transient transmit response is the derivative of its receive response, such an antenna would be self-compensating if used as both the transmitter and receiver in a communications link. In this work, the shape of the lens that produces this result is determined, and the effect of the lens on the radiated field is discussed. A full EM numerical model based on the FEM is developed using the PDE toolbox in Matlab. The input impedance and the gain of the modeled antenna are calculated over a wide frequency range. In section IV, fast fourier transform is utilized to observe the radiated field in the TD. We see that the general properties of the self-compensating antenna are in fact observed, namely a channel response that is flat over a broad frequency range. However, the flatness of the response is hurt in the current design due to resonances associated with the finite size of the monocone and the dielectric discontinuity of the lens. Future work will seek to reduce these effects.