Pilot-Aided Joint CFO and Doubly-Selective Channel Estimation for OFDM Transmissions

This paper studies the problem of pilot-aided joint carrier frequency offset (CFO) and channel estimation using Fisher and Bayesian approaches in orthogonal frequency division multiplexing (OFDM) transmissions over time- and frequency-selective (doubly selective) channels. In particular, the recursive-least-squares (RLS) and maximum-likelihood (ML) techniques are used to facilitate the Fisher estimation implementations. For the Bayesian estimation, the maximum-a-posteriori (MAP) principle is employed in formulating the joint estimation problem. With known channel statistics, the MAP-based estimation is expected to provide better performance than the RLS- and ML-based ones. To avoid a possible identifiability issue in the joint estimation problem, various basis expansion models (BEMs) are deployed as fitting parametric models for capturing the time-variation of the channels. Numerical results and related Bayesian Cramér Rao bounds (BCRB) demonstrate that the deployment of BEMs is able to alleviate performance degradation in the considered estimation techniques using the conventional block-fading assumption over time-varying channels. Among the considered schemes, the MAP-based estimation using the discrete prolate spheroidal (DPS) or Karhuen Loève (KL) basis functions would be the best choice that can provide mean-squared-error (MSE) performance comparable to BCRB in low signal-to-noise ratio (SNR) conditions (e.g., coded OFDM transmissions).