  This paper investigates pilot-aided channel estimation for two-way relay
networks (TWRNs) in the presence of synchronization errors between the two
sources. The unpredictable synchronization error leads to time domain offset
and signal arriving order (SAO) ambiguity when two signals sent from two
sources are superimposed at the relay. A two-step channel estimation algorithm
is first proposed, in which the linear minimum mean-square-error (LMMSE)
estimator is used to obtain initial channel estimates based on pilot symbols
and a linear minimum error probability (LMEP) estimator is then developed to
update these estimates. Optimal training sequences and power allocation at the
relay are designed to further improve the performance for LMMSE based initial
channel estimation. To tackle the SAO ambiguity problem, the generalized
likelihood ratio testing (GLRT) method is applied and an upper bound on the SAO
detection error probability is derived. By using the SAO information, a scaled
LMEP estimation algorithm is proposed to compensate the performance degradation
caused by SAO detection error. Simulation results show that the proposed
estimation algorithms can effectively mitigate the negative effects caused by
asynchronous transmissions in TWRNs, thus significantly outperforming the
existing channel estimation algorithms.
