Optimal Training for Residual Self-Interference for Full-Duplex One-Way Relays

Channel estimation and optimal training sequence design for full-duplex one-way relays are investigated. We propose a training scheme to estimate the residual self-interference (RSI) channel and the channels between nodes simultaneously. A maximum likelihood estimator is implemented with the Broyden-Fletcher-Goldfarb-Shanno algorithm. In the presence of RSI, the overall source-to-destination channel becomes an inter-symbol-interference (ISI) channel. With the help of estimates of the RSI channel, the destination is able to cancel the ISI through equalization. We derive and analyze the Cramer-Rao bound (CRB) in closed-form by using the asymptotic properties of Toeplitz matrices. The optimal training sequence is obtained by minimizing the CRB. Extensions for the fundamental one-way relay model to the frequency-selective fading channels and the multiple relays case are also considered. For the former, we propose a training scheme to estimate the overall channel, and for the latter the CRB and the optimal number of relays are derived when the distance between the source and the destination is fixed. Simulations using LTE parameters corroborate our theoretical results.

I. Introduction

Due to the growing demands on wiredless bandwidth, the need for high spectral efficiency has become more urgent. In-band full-duplex (FD) relays, which transmit and receive simultaneously in the same frequency band, offer a viable solution since they theoretically have the ability to double the spectral efficiency, compared to half-duplex relays. In practice, however, the relay receives strong self-interference in FD mode, which is challenging to overcome. Recently, self-interference cancellation techniques have been developed with great promise [1]–[3]. With these techniques, the self-interference can be canceled by estimating the self-interference channels [4]–[6] in FD mode, or be suppressed with null-space methods in MIMO systems [7]. However, despite these advances, residual self-interference (RSI) still exists after the self-interference cancellation [3], [7]–[9]. Therefore, accurate channel estimation in the presence of RSI is required at the destination to further improve the system performance by canceling RSI.