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 a novel patch antenna prototype in an experimental setup to characterize the self-interference channel between transmit and receive radios. We derive an equivalent analytical baseband model and propose analog baseband cancellation techniques to complement the RF cancellation provided by the patch antenna prototype. Our results show that a wide bandwidth, moderate isolation scheme achieves up to 2.4 bps/Hz higher achievable rate than a narrow bandwidth, high isolation scheme. Furthermore, the analog baseband cancellation yields a 10-10,000 improvement in BER over RF only cancellation.