Recent wireless testbed implementations have proven that full-duplex communication is in fact possible and can outperform half-duplex systems. Many of these implementations modify existing half-duplex systems to operate in full-duplex. To realize the full potential of full-duplex, radios need to be designed with self-interference in mind. In our work, we use an experimental setup with a patch antenna prototype to characterize the self-interference channel between two radios. In doing so, we form an analytical model to design analog baseband cancellation techniques. We show that our cancellation scheme can provide up to 10 dB improved signal strength, 2.5 bps/Hz increase in rate, and a 10,000 improvement in BER as compared to the RF only cancellation provided by the patch antenna.