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In this paper, the effect of a general spatial and temporal fading correlation structure on the performance of coded multiple-input multiple-output (MIMO)-orthogonal frequency-division multiplexing (OFDM) systems is studied. The analysis handles an arbitrary joint transmit-receive spatial correlation model, including the non-Kronecker model. An upper bound on the maximum achievable diversity order for frequency-selective MIMO-OFDM systems with general temporal and spatial correlation is derived. Furthermore, a space-time-frequency code design that can achieve the upper bound for any arbitrarily correlated channel scenario is provided. The general framework of the analysis includes space-frequency (SF)-coded systems as a special case. For the SF-coded MIMO-OFDM system, it is shown that any SF code designed to achieve full diversity in the independent fading channel can achieve full diversity in an arbitrary spatially correlated channel. The derived analytical results are consistent with those in the existing literature for special correlation structures. Extensive simulation results are provided to confirm the theoretical analysis.