Preamble design for carrier frequency offset estimation in two-way relays

A two-way relaying OFDM system based on the two-phase, amplify-and-forward protocol is considered. Preambles are designed for each of the sources with the criterion to minimize the Cramer-Rao bound (CRB) of the carrier frequency offset (CFO) estimate. The resulted CRB shows that it is possible for two-way relaying to incur only marginal loss from one-way relaying in CFO estimation under practical channel conditions. In contrast, the CRB is unbounded if conventional periodic preambles are applied. To facilitate implementation, a specific class of estimators, based on linear filtering followed by conventional CFO estimation, is examined. The necessary and sufficient condition for this class to preserve the CRB is established. Numerical results corroborate with theoretical findings.