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This paper presents a new peak-to-average power ratio (PAPR) reduction method based on clipping and filtering for precoded orthogonal frequency division multiplexing (OFDM)-multiple-input multiple-output (MIMO) transmission. While the conventional clipping and filtering method adds roughly the same interference power to each of the transmission streams, the proposed method restricts the interference power applied to the streams that experience good channel conditions. Since the sum capacity is dominated by the capacity of the streams that experience good channel conditions and the interference caused by the PAPR reduction process severely degrades the achievable capacity of these streams, the proposed method can significantly improve the achievable sum capacity compared to the conventional clipping and filtering method for a given PAPR. Simulation results demonstrate the capacity gain when using the proposed method compared to that when using the conventional method.