Digital Self-Interference Cancellation in Full-Duplex Radios: A Fundamental Limit Perspective

Digital self-interference cancellation (D-SIC) plays a crucial role in in-band full-duplex radios. Unfortunately, its fundamental limit remains unclear. In this paper, we aim to address this problem by exploring the performance limit of the parallel Hammerstein (PH) canceller for D-SIC, which is most commonly used in practice. First, a comprehensive analysis of the power of the residual self-interference (RSI) after the PH canceller with the least squares (LS) estimator is provided, which takes into account the truncation error, reconstruction error and transmitter noise. Specifically, the analysis is greatly simplified by equivalently expanding the PH canceller via generalized Laguerre polynomials (GLP), which enjoys the desirable property of mutual orthogonality among the basis functions. As a by-product of this orthogonal expansion, we establish that the LS estimator for the weights of the GLP canceller is asymptotically \textit{unbiased}, if the pilot sequence is Gaussian distributed. Second, in order to minimize the reconstruction error of the PH canceller, we propose a succinct criterion for optimizing the pilot sequence, which essentially seeks for small eigenvalue spread and large minimum eigenvalue of the Gram matrix corresponding to the pilot sequence. Specifically, the criterion is to minimize the product of the Shannon rank, an effective rank of a positive semidefinite matrix and the minimum eigenvalue of the Gram matrix. Simulation results demonstrate that with the optimized pilot sequence of a single OFDM symbol, over 10 dB gain can be achieved compared to the conventional pilot sequence (HE-LTF) for the PH canceller, and the corresponding RSI can be as low as -87.6 dBm.