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Modulation constellation extension (CE) schemes provide good peak-to-average power ratio (PAPR) reduction performance for orthogonal frequency division multiplexing (OFDM) signals. However, they usually require a complicated algorithm to find the optimal signal for transmission. In this paper, we propose a low-complexity CE scheme to reduce the PAPR of OFDM signals, in which some low-complexity conversion matrices are used to generate multiple candidate signals for selection. Also, we develop a mechanism to limit the increase in the average transmitted power that results from the constellation extension to an acceptable level. As compared to the related work using the CE technique, the proposed CE scheme can achieve close PAPR reduction performance with much lower computational complexity and lower transmitted power.