Bayesian Joint Estimation of CFO and Doubly Selective Channels in MIMO-OFDM Transmissions

This paper studies the problem of pilot-aided joint carrier frequency offset (CFO) and channel estimation using a Bayesian approach in multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) transmissions over time- and frequency-selective (doubly selective) channels. Unlike the joint CFO and channel impulse response (CIR) estimation over block-fading channels, the joint CFO and time-variant CIR estimation gives rise to the identifiability problem where the number of observations (received samples) is smaller than that of both CFO and time-variant CIR parameters to be estimated. To reduce a large number of the time-variant CIR parameters to be estimated, various basis expansion models (BEMs) are deployed as fitting parametric models for capturing the time variation of the MIMO channels. As the main purpose of using BEMs, the resulting dimension reduction in the time-variant channel representation helps to avoid the identifiability issue in the joint estimation problem. Under Bayesian estimation, CFO and BEM coefficients are treated as random variables to be estimated by the maximum-a-posteriori (MAP) technique. Numerical results demonstrate that the deployment of BEMs is able to alleviate performance degradation in the considered estimation technique using the conventional assumption of block fading over time varying channels.