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With single-carrier frequency-domain equalization (SC-FDE), the carrier-frequency offset (CFO) and sampling-frequency offset (SFO) are embedded in the phase rotations of the complex frequency-domain signal components at the output of the fast Fourier transform (FFT). To extract the phase rotations and estimate the CFO and SFO, the frequency-domain signal components need to be known. However, they are, in general, not known to the receiver, since they are a mixture of the data and pilot symbols. To solve this difficulty sub-block processing is proposed, such that joint estimation of the CFO and SFO can be applied. For the joint estimation, both the linear least-squares (LLS) and simple weighted least-squares (SWLS) regressions are considered, where the latter is shown to be robust to the channel frequency-selectivity. Finally, the SC-FDE receiver with proposed closed-loop tracking algorithm is tested on both quasi-static and time-varying multipath fading channels and its effectiveness is demonstrated.