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Orthogonal frequency division multiplexing (OFDM) systems that adopt the cyclic-delay diversity (CDD) scheme require only one inverse discrete Fourier transform (IDFT) operation at the transmitter. Therefore, the CDD provides a low-complexity means of increasing the transmission diversity in multiple-input multiple-output (MIMO) OFDM systems. However, the optimal pilot sequences which minimize the mean square error (MSE) of the channel estimate in traditional MIMO-OFDM systems are inapplicable to CDD-OFDM systems. Accordingly, this paper commences by deriving the criteria which yield the minimum MSE of both the least square (LS) channel estimate and the minimum mean square error (MMSE) channel estimate in CDD-OFDM systems. The derived criteria are then used to develop a general methodology for determining the optimal pilot sequence. Significantly, the proposed design methodology enables the status of the channel to be estimated using just one OFDM symbol. The simulation results confirm that the proposed pilot design minimizes the MSE of both the LS and the MMSE channel estimates.