A Low-Complexity Chinese Remainder Theorem Based Multi-Carrier Delay Estimation Approach

With the rapid development of cluster systems, such as unmanned aerial vehicle (UAV) networks and satellite constellations, multi-node collaboration has emerged as a critical requirement. Accurate time synchronization, a cornerstone of such collaborative systems, heavily relies on high-precision delay estimation. Traditional multi-carrier delay estimation methods face an inherent trade-off between estimation accuracy and unambiguous range. While the Chinese Remainder Theorem (CRT)-based approach resolves this dilemma by enabling high-precision estimation without sacrificing range, its computational complexity remains prohibitively high for practical implementations. To address this challenge, we propose a novel low-complexity CRT algorithm based on remainder reconstruction (RR-CRT). By introducing an auxiliary phase to reconstruct erroneous remainders, our method reduces the computational complexity from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i>(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>) to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i>(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i>), where K denotes the number of subcarriers. Crucially, this reduction in complexity only marginally impacts the algorithm’s performance, including the phase error tolerance range, the probability of correctly solving phase ambiguity, and the root mean square error (RMSE) of delay estimation. Numerical simulations validate the effectiveness and robustness of the proposed algorithm, demonstrating its superiority in balancing computational efficiency and estimation performance.