A solution to the power leakage minimization problem in discrete Fourier transform (DFT) based communication systems is presented. In a conventional DFT based system, modulated subcarriers exhibit high sidelobe levels, which leads to significant out-of-band power leakage. Existing techniques found in the literature either do not achieve sufficient sidelobe suppression or suffer from significant spectral efficiency loss. Precoding can be seen as a general linear processing method for power leakage reduction, however, how to design the optimal linear precoder is still an open problem. In this paper, the power leakage suppression is first treated as a matrix Frobenius norm minimization problem, and then the optimal orthogonal precoding matrix design for the power leakage suppression is proposed based on singular value decomposition (SVD). By further exploiting the extra degrees of freedom in the precoding matrix, two kinds of optimized precoding matrices, one with multi-carrier property and the other with single-carrier property, are developed to take the advantages of orthogonal frequency division multiplexing (OFDM) and single carrier frequency division multiple access (SC-FDMA), respectively. Simulation results show that both the multi-carrier and the single-carrier precoding schemes achieve significant power leakage suppression, and have similar peak-to-average power ratio (PAPR) and bit-error-rate (BER) to those of OFDM and SC-FDMA systems, respectively.