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We investigate the design of space-frequency codes and efficient feedback-aided precoding schemes for multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Inspired by the statistical structure of the MIMO-OFDM channel matrix, the proposed transceiver structure consists of two components: (i) a fixed space-frequency code, and (ii) a set of spatial precoding matrices that are adapted based on limited feedback from the receiver. For the fixed component, we propose a structured space-frequency coding scheme that spreads the source symbols across space and frequency. The space-frequency coded symbols are then processed with a spatial precoding matrix for each OFDM tone before transmission. The spatial precoding matrices use the limited feedback from the receiver to adapt the spatial directions and corresponding power allocation for different spatial symbols, in order to improve both the mutual information and error rate. Since the spatial channel statistics are invariant across frequency, one codebook of spatial precoding matrices suffices for all OFDM tones. This codebook is designed using a systematic algorithm that we had previously developed for narrowband spatially correlated MIMO channels. Finally, to reduce the computational complexity at the receiver and the amount of feedback to the transmitter, we propose a new interpolation algorithm in which the codebook indices are fed back to the transmitter for a subset of tones - precoding matrices for the other tones are computed at the transmitter using the precoding matrices for tones in the subset.