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

4.2 CFO Estimation and Correction

4.2.1 CFO Estimation Principle

We have seen in Section 2.5 that the main issue with CFO is that it introduces two distinct components which degrade the overall system performance. For each subcarrier the two deleterious effects are

• Phase rotation and amplitude reduction common to all the subcarriers.
• ICI caused by the other subcarriers.

In addition, from one OFDM symbol to the next CFO also introduces another deterministic phase increment to the subcarriers depending on the OFDM symbol duration. Taking the first symbol as the reference, i = 1, the phase rotation introduced by CFO for symbol i is

4.1

where i is symbol index, Δ_CFO is the CFO in hertz, Δf is the subcarrier spacing in hertz, N_s = N_g + N is the number of points of a single OFDM symbol including the guard interval, and T_s is the sampling frequency.

Figure 4.1 is a plot of Equation 4.1 showing that the phase shift introduced by CFO is a linear function of the symbol index. The slope of the phase shift is given by

4.2

Figure 4.1 Illustration of the inter-symbol phase shift introduced by carrier frequency offset

From Equations 4.1 and 4.2 we can see that the only unknown in the common ...