Investigation of the Noise Variance and the SNR Estimators for OFDM Systems with Imperfect Frequency Synchronization

Orthogonal frequency division multiplexing (OFDM) systems require the knowledge of signal-to-noise ratio (SNR) at the receiver in order to maximize the system performance. In general, the noise variance is required by the SNR estimator and the knowledge of noise variance also improves the performances of carrier frequency offset (CFO) and channel state estimations. This paper first investigates the maximum likelihood noise variance estimator (ML-NVE) in OFDM systems with imperfect frequency synchronization. Theoretical derivations show that both the mean and the variance of the ML-NVE are functions of the CFO. The mean and the variance of the SNR estimate are then derived by utilizing the derivation results of the ML-NVE. Finally, the validity of the theoretical observations is confirmed by simulation experiments.