There is provided a wireless device comprising a transmitter (4) for transmitting a Wake-Up Signal (WUS) message m = 0,1, ..., 2B - 1 in a communication system (100), the transmitter (4) comprising :- a splitter (400) to split the input message m into Bv bits and Bh bits;- A vertical encoder (402) to encode the Bv bits into encoded bits c comprising elements ci;- a Multi-Carrier On-Off Keying (MC-OOK) modulator (42) to apply a MC-OOK modulation to the encoded bits c, which provides MC-OOK modulated signals sl,mv for the message m,- a horizontal encoder (404) to encode the Bh bits into an horizontal codeword wmh=w1,mh,w2,mh,…,wL,mh,- a combiner (14) to combine the MC-OOK modulated signals sl,mv with the horizontal codewords wl,mh,- a Discrete Fourier Transform (DFT) precoder (44) applying DFT-precoding to the combined sequence sl,m,- 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 sl,mv of the MC-OOK modulated signal sm whenever the corresponding encoded input bit ci is equal to one, and a value zero otherwise.