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The combination of differential space-frequency modulation (DSFM) with orthogonal frequency-division multiplexing (OFDM) is attractive for transmission over time-and frequency-selective multiple-input-multiple-output (MIMO) channels and detection without the need for channel-state information (CSI) at the receiver. It is well known that a simple differential detection already results in a high error floor for moderate time and frequency selectivities of the channel. A more sophisticated multiple-symbol differential detection (MSDD), which jointly processes multiple received symbols, overcomes this limitation, usually at the price of higher detection complexity. In this paper, we consider the DSFM for the MIMO-OFDM transmission and MSDD at the receiver. Inspired by previous work presented in literature, we devise a novel DSFM scheme, which makes use of spatial and/or spectral (multipath) diversity and is particularly suited for the MIMO-OFDM and power-efficient low-delay MSDD. We further investigate the application of a 2-D observation window to the MSDD (2-D MSDD) in order to exploit channel correlations in both time and frequency directions. We develop a representation of the detection problem that is amenable to tree-search decoding, whose application leads to a tremendous reduction in the MSDD complexity or a "fast" MSDD. An analytical approximation of the symbol-error rate of the 2-D MSDD for the MIMO-OFDM under spatially correlated fading is derived, which enables quick and accurate performance evaluations. Numerical and simulation results corroborate the efficacy of our approach and show that power efficiency close to that of a coherent detection with a perfect CSI is feasible in all standard fading scenarios at reasonable decoder complexity.