In this paper, the problem of clock synchronization is analyzed based on the two-way message exchange mechanism. In order to estimate the clock offset and the clock skew with unknown fixed delay, the maximum likelihood estimator (MLE) and a low-complexity estimator are proposed. Furthermore, their corresponding performance limits and complexities are analyzed. It is found that the MLE achieves the best performance with the price of high complexity, while the newly proposed estimator achieves the same performance as the MLE with low complexity.