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By providing both spatial diversity and multiplexing gains simultaneously, double space-time transmit diversity (D-STTD) is considered a promising technique for future multiple antenna wireless systems. Although originally proposed D-STTD is an open-loop scheme, transmit antenna grouping (also called antenna shuffling) with low-rate feedback information from the receiver can significantly improve the performance of open-loop D-STTD even in spatially correlated Rayleigh fading channels, since the antenna grouping method selects the best antenna grouping pattern corresponding to the channel realization. In this paper we propose a new antenna grouping method based on the criterion of maximum mutual information. Showing the same performance improvement as the existing antenna grouping method based on the criterion of maximum post-processing signal-to-noise ratio (SNR), the proposed low-complexity mutual information-based antenna grouping method can be performed with less complexity. We verify the effectiveness of our proposed method by numerical simulations even for a spatial correlation channel model based on practical channel measurements.