The fundamental problem in the design of a full-duplex radio is the cancellation of the self-interference (SI) signal generated by the transmitter.Current techniques for suppressing SI rely on generating a copy of the SI signal and subtracting it partly in the RF (radio frequency) and digital domains. A critical step in replicating the self-interference is the estimation of the multi-path channel through which the transmitted signal propagates to the antenna. Since there is no prior model on the number of multipath reflections, current techniques assume a tap delay line filter (in the RF and digital domain) with a large number of taps, and estimate the taps in the analog and the digital domain. Assuming such a model leads to a large form-factor for the analog and RF circuits and increased complexity in the digital domain. In this paper, using a linearization technique, we show that the self-interference channel in an indoor environment can be effectively modelled as $H(f)=C_0 + C_1f$ in the frequency domain. Thus, the effective self-interference channel can be represented by two parameters $C_0$ and $C_1$, irrespective of the multipath environment. We also provide experimental evidence to verify the above channel model and propose novel low-complexity designs for self-interference cancellation. Linearization not only aids in the practicality of analog cancellation by reducing the form factor, but also results in a simpler SI filter model in the digital domain due to dimensionality reduction of the channel parameters. Therefore this method can enable the widespread adoption of full-duplex techniques to portable devices in addition to infrastructure base-stations.