  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
Broyden-Fletcher-Goldfarb-Shanno (BFGS) 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.
