We consider a frequency division duplex (FDD) scheme in which two wireless communication devices simultaneously transmit and receive on adjacent channels. Inevitable out-of-band (OOB) emissions caused by the transmission on one channel induce self-interference on the adjacent channel. As a result, receiver sensitivity severely degrades by self-interference from the transmitter of the same device. Therefore, we propose a novel self-interference cancellation (SIC) method, that has a lower complexity compared to existing approaches. It comprises digital linear SIC in frequency domain and power amplifier backoff adaption to mitigate both linear and nonlinear components. We further present and evaluate an OOB emission model of a transmitter which is subsequently used to analyze the performance of the proposed SIC method. Our simulation results highlight capabilities and limitations of the proposed SIC method in different scenarios. It turns out that the proposed method can significantly reduce the error vector magnitude of a received signal in FDD operation. Prerequisites of the cancellation method and impact to protocol design are thoroughly discussed.