The authors consider a multi‐hop amplify‐and‐forward full‐duplex relay system. They take a signal flow graph approach for finding the input–output relationship using Mason's gain formula, and use this expression to compute the system outage probability for different equalisers. For sufficiently large target rates, full‐duplex relaying with equalisers has lower outage probability than half‐duplex relaying, despite the higher residual self‐interference (RSI) of the full‐duplex approach. The full‐duplex system with (unequalised) matched filter at the destination is seen to be sensitive to RSI which shows that equalisation at the destination is a feasible approach to combating the RSI for full‐duplex multi‐hop systems.

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.

Training schemes for full duplex two-way relays are investigated. We propose a novel one-block training scheme with a maximum likelihood estimator to estimate the channels between the nodes as well as the residual self-interference (RSI) channel simultaneously. A quasi-Newton algorithm is used to solve the estimator. As a baseline, a multi-block training scheme is also considered. The Cramer-Rao bounds of the one-block and multi-block training schemes are derived. By using the Szegö's theorem about Toeplitz matrices, we analyze how the channel parameters and transmit powers affect the Fisher information. We show analytically that exploiting the structure arising from the RSI channel increases its Fisher information. Numerical results show the benefits of estimating the RSI channel.