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In this paper, we introduce cyclic space-frequency (CSF) filtering for orthogonal frequency division multiplexing (OFDM) systems using bit-interleaved coded modulation (BICM) and multiple transmit antennas for fading mitigation, and discuss the extension to orthogonal frequency division multiple access (OFDMA) systems. CSF filtering is a simple form of space-frequency coding (SFC) and may be viewed as a generalization of cyclic delay diversity (CDD) where the cyclic delays are replaced by CSF filters. CSF is applicable to both traditional multiple-input multiple-output systems with co-located transmit antennas and cooperative diversity systems with decode-and-forward relaying and distributed transmit antennas. Similar to CDD and in contrast to other SFC schemes, CSF filtering does not require any changes to the receiver compared to single-antenna transmission. Based on the asymptotic pairwise error probability of the overall system we derive an optimization criterion for the CSF filters for co-located and distributed transmit antennas, respectively. We show that the optimum CSF filters are independent of the interleaver if they do not exceed a certain length. If this length is exceeded, the adopted interleaver has to be carefully taken into account in the CSF filter design. For several special cases we derive closed-form solutions for the optimum CSF filters and for the general case we provide various CSF filter design methods. Our simulation results show that CSF filtering can achieve significant performance gains over existing CDD schemes.