In-Band Full-duplex Residual Self-interference Approximation in Multi-tap Delay Fading Channels

Residual self-interference (SI) is primarily a key challenge when designing In-Band Full-duplex (IBFDX) wireless systems. Channel estimation errors are one of the major causes of the residual SI. The SI channel is composed by multiple fading taps which makes the characterization of the residual SI more challenging as multiple copies of the transmitted signal, with variable delays and gains, are eventually aggregated at the receiver. In this paper, we derive an approximation for the distribution of the residual SI power in multi-tap delay fading channels. In particular, we show that under specific conditions the multi-tap fading channel can be represented by a summation of non-identical independent gamma distributions. In a further step, we approximate the summation of the gamma distributions using the Welch-Satterthwaite equation, obtaining a closed form expression for the distribution of the residual SI power. The accuracy of the theoretical approach is evaluated through simulation results. The similarity comparison between simulated data and the proposed model indicates a high accuracy of the adopted approximation when considering low fading uncertainty associated to the taps and low estimation errors. On the other hand, the accuracy of the approximation slightly decreases for higher uncertainty fading scenarios and for higher estimation errors. However, as a final remark, we highlight that the results computed with the model are close to the simulated ones and for most of the applications the model's error can be negligible.