RF Analog Impairments Modeling for Communication Systems Simulation: Application to OFDM-based Transceivers

4.3 SFO Estimation and Correction

4.3.1 SFO Estimation Principle

We have seen in Section 2.6 that SFO, as for CFO, has a twofold effect with a phase rotation and an amplitude reduction for all the subcarriers, and ICI. However, there is a fundamental difference, because the phase rotation and amplitude reduction are not common for all the subcarriers but instead depend on the subcarrier index. The phase rotation introduced by SFO is given by

4.20

where k is the subcarrier index, i is the symbol index from 1, δ is the relative SFO, and N_s = N_g + N is the number of points of a single OFDM symbol including the guard interval.

The phase rotation due to SFO varies both as a function of the subcarrier index:

4.21

and as a function of the OFDM symbol index by

4.22

Equations 4.21 and 4.22 are plotted in Figures 4.9 and 4.10, respectively. Figure 4.9 illustrates that the phase rotation due to SFO increases linearly versus the subcarrier index, with a slope dependent on the symbol index, as demonstrated in Equations 4.20 and 4.21. Consequently, it is difficult to estimate the SFO without knowing the phase shift and symbol position relative to those of a perfect OFDM symbol timing reference. ...