Analysis of carrier frequency offset estimation with multiple pilot block sequences

As is well known, dividing the pilot symbols into multiple blocks and separating these blocks at some distances away from each other can significantly improve the frequency estimation accuracy. However, the mean square error (MSE) performance at moderate and low SNR, especially the SNR threshold effect, with multiple pilot block sequences has not been investigated properly. Thus, a numerical calculation method is proposed in this paper to derive the approximate MSE of the ML estimator with multiple pilot block sequences at all SNRs and the proposed calculation method obtains the MSEs coinciding with the simulation results and the calculated approximate MSEs can tell exactly where the SNR thresholds are.