  In this paper, we derive for the first time the exact Cramer-Rao bounds
(CRBs) on semi-blind channel estimation for amplify-and-forward two-way relay
networks. The bounds cover a wide range of modulation schemes that satisfy a
certain symmetry condition. In particular, the important classes of PSK and
square QAM are covered. For the case square QAM, we also provide simplified
expressions that lend themselves more easily to numerical implementation. The
derived bounds are used to show that the semi-blind approach, which exploits
both the transmitted pilots and the transmitted data symbols, can provide
substantial improvements in estimation accuracy over the training-based
approach which only uses pilot symbols to estimate the channel parameters. We
also derive the more tractable modified CRB which accurately approximates the
exact CRB at high SNR for low modulation orders.
