Carrier Frequency Offset Estimation for Two-Way Relaying: Optimal Preamble and Estimator Design

We consider the problem of carrier frequency offset (CFO) estimation for a two-way relaying system based on the amplify-and-forward (AF) protocol. Our contributions are in designing an optimal preamble, and the corresponding estimator, to closely achieve the minimum Cramer-Rao bound (CRB) for the CFO. This optimality is asserted with respect to a novel class of preambles, referred to as block-rotated preambles (BRPs). This class includes the periodic preamble that is used widely in practice, yet this class provides an additional degree of design freedom via a block rotation angle. We first identify the catastrophic scenario of an arbitrarily large CRB when a conventional periodic preamble is used. We next resolve this problem by using a BRP with a non-zero block rotation angle. This angle creates, in effect, an artificial frequency offset that separates the desired relayed signal from the self-interference that is introduced in the AF protocol. With appropriate optimization, the CRB incurs only marginal loss from one-way relaying under practical channel conditions. To facilitate implementation, a specific low-complexity class of estimators is examined, and conditions for the estimators to achieve the optimized CRB are established. Numerical results corroborate with theoretical findings.