There is provided a wireless device in a communication system, comprising a transmitter (4) configured to transmit a Wake-Up Signal (WUS) message m from an input bit vector b comprising B input bits bi through a communication channel, the transmitter (4) comprising a set of transmit antennas, and :- a Multi-Carrier On-Off Keying (MC-OOK) modulator (42) applying a MC-OOK modulation to the input bit vector b = [b0, b1, ..., bB-1], which provides a MC-OOK modulated signal sm for the message m, comprising B elements si;- a Discrete Fourier Transform (DFT) precoder (44) applying DFT-precoding to the signal sm;- a single or multicarrier modulator (46) applying single or multicarrier modulation to the resulting signal Sm output by the DFT-precoder (44),the MC-OOK modulator (42) mapping a ON-signal a comprising KB elements to each element si of the MC-OOK modulated signal sm whenever the corresponding input bit bi is equal to one, and a zero value otherwise.