Carrier frequency offset estimation in time-selective Rayleigh flat-fading channels

This paper focuses on carrier frequency offset (CFO) estimation in the presence of time-selective Rayleigh fading (i.e., Gaussian multiplicative noise) channel. The time-variant fading is modeled by considering the Jakes' and the first order autoregressive AR(1) correlation models. A high signal-to-noise-ratio maximum likelihood (ML) estimators based on the AR(1) correlation model and for slow-fading channels are derived when the channel statistics are unknown. The main objective is to reduce algorithm complexity to a single-dimensional search on the CFO parameter alone. Closed-form expressions of the Cramér-Rao lower bound (CRB) for the CFO parameter alone are derived for fast-fading and slow-fading channels. Approximate analytical expressions for the CRB are derived for low and high SNR that enable the derivation of a number of properties that describe the bound's dependence on key parameters such as SNR, channel correlation. Finally, simulation results illustrate the performance of the estimators and confirm the validity of the theoretical analysis.