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

TL;DR

This paper introduces an optimal preamble design and estimator for carrier frequency offset estimation in two-way AF relaying systems, achieving near-minimum CRB by using block-rotated preambles to mitigate self-interference.

Contribution

It proposes a novel class of block-rotated preambles that enhance CFO estimation accuracy and develops low-complexity estimators that approach the theoretical CRB limit.

Findings

Block-rotated preambles effectively separate signals from self-interference.

Optimized preambles achieve near-minimum CRB under practical conditions.

Low-complexity estimators can attain the CRB with proper design.

Abstract

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 the novel class of preambles, referred to as the block-rotated preambles (BRPs). This class includes the periodic preamble that is used widely in practice, yet it 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 is established. Numerical results are given which corroborate with theoretical findings.