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.