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This paper is concerned with the problem of turbo (iterative) processing for joint channel and carrier frequency offset (CFO) estimation and soft decoding in coded multiple-input-multiple-output (MIMO) orthogonal frequency-division-multiplexing (OFDM) systems over time- and frequency-selective (doubly selective) channels. In doubly selective channel modeling, a basis expansion model (BEM) is deployed as a fitting parametric model to reduce the number of channel parameters to be estimated. Under pilot-aided Bayesian estimation, CFO and BEM coefficients are treated as random variables to be estimated by the maximum a posteriori technique. To attain better estimation performance without sacrificing spectral efficiency, soft bit information from a soft-input-soft-output (SISO) decoder is exploited in computing soft estimates of data symbols to function as pilots. These additional pilot signals, together with the …