Current standardization process for Wake-up Radio (WuR) within the IEEE 802.11 Working Group, known as the IEEE 802.11ba, has brought interest to the IEEE 802.11-related technologies for the implementation of WuR systems. This paper proposes a new WuR system, where the Wake-up Transmitter (WuTx) is based on the legacy IEEE 802.11 Orthogonal Frequency Division Modulation (OFDM) Physical Layer (PHY) specification. Using the IEEE 802.11, OFDM PHY makes it possible for an IEEE 802.11a/g/n/ac transmitter to operate as WuTx for this WuR system. The WuTx generates a Wake-up Signal (WuS) coded with an amplitude-based digital modulation, achieving a bit rate of 250 kbps. This modulation, which we call Peak-Flat modulation, can be received using low-power receivers. A simulated proof of concept of the WuTx based on the IEEE 802.11g is presented and evaluated using MATLAB WLAN Toolbox. A method to generate the Peak-Flat modulated WuS from an IEEE 802.11a/g standard-compliant transmitter, using only software-level access, is explained. In addition, two possible low-power Wake-up Receiver (WuRx) architectures capable of decoding the presented modulation are proposed. The design of those receivers is generic enough to be used as a reference to compare the performance of the Peak-Flat Modulation with the other state-of-the-art approaches. The evaluation results conclude that the Peak-Flat modulation has similar performance compared to the other IEEE 802.11 WuR solutions on the reference receivers. Moreover, this solution provides a notorious advantage: legacy OFDM-based IEEE 802.11 transmitters can generate the Peak-Flat modulated WuS.