In this study, we propose an approach to constructing on-off keying (OOK) symbols for wake-up radios (WURs) by using sequences in the frequency domain. The proposed method enables orthogonal multiplexing of wake-up signals (WUSs) and orthogonal frequency division multiplexing (OFDM) waveforms. We optimize the sequences with a tractable algorithm by considering the reliability of WUSs in fading channels. The proposed algorithm relies on an alternating minimization technique, i.e. cyclic algorithm-new (CAN), which was originally proposed for obtaining a unimodular sequence with good aperiodic correlation properties. In this study, we extend CAN to generate OOK waveforms with Manchester coding. We demonstrate the performance of four optimized sequences and compare with state-of-the-art approaches. We show that the proposed scheme improves the wake-up radio receiver (WURx) performance by controlling the energy distribution in frequency domain while removing the interference-floor at the OFDM receiver.