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This work investigates the improvement of power amplifier efficiency through the reduction of peak-to-average power ratio (PAPR) of linearly precoded QAM data signals. In particular, we focus on the special cases of linear precoded modulation including the practical OFDM, OFDMA, and SC-FDMA signals that have been widely adopted in W-LAN and W-MAN. We apply the method of tone injection optimization for PAPR reduction. To reduce numerical complexity, we propose a linear programming algorithm which closely approximates the original tone injection optimization problem. Our comprehensive numerical results demonstrate substantial PAPR reduction and superior BER performance using several practical examples.