There are a number of approaches to estimating carrier frequency offset (CFO) that causes inter-carrier interference (ICI) in orthogonal frequency division multiplexing (OFDM) systems: self-cancelation method, the extended Kalman filler (EKF), particle filter, H-infinity filter (HF), etc. In particular, the HF is of interest because prior statistical noise information is not necessarily required in its application. Cost reference particle filter (CRPF), newly developed in the particle filtering framework, has the same feature as HF; it also does not require the prior noise information of the state and the measurement equation. In this letter, we compare and analyze the performances of two similar methods. The simulation results show that CRPF outperforms HF, particularly when the bit energy to noise ratio of the measurement is low. Therefore, CRPF is very effective and robust, especially when the noise statistics are unknown with a low bit energy to noise ratio.