arrier waveforms generator. 4.1.3.1 Transmitter The waveform generation can be achieved in four steps as illustrated in Figure 4.4: 1. Data symbol mapping: The data symbols are mapped to the active set of symbols Non = {n = k + mK} C Kon X Mon, such that dk,m = 0,k+ mK E Non. Therefore, an input data don CINonlX1 is mapped to db E CNx1 defined as db[k,m+K]= dk,m,b such 2. Core modulation: This refers to generating the modulated block, which can be expressed in a vector xb = Ad E CNx1 where A E CNxN is the modulation matrix defined as sA[nk+mK]: gk,mln]. 3. Additional processing: This processing involves adding CP/CS, which corresponds to overhead of size Ncp. Thus, the CP-block is defined - n = 0. , N +Ncp - 1. Windowing and/or filtering can be applied on top. Thus, the actual transmitted block is The filter increases the block length by the filter tail Nf. Thereby, the total transmitted block length is The additional processing can be summarized by linear operation using the matrix G(tx) E = 4. Block multiplexing: Block multiplexing is achieved by transmitting the signal with Ns samples spacing, such that x[n] = = - bNs]. The difference No = N - Ns rep- resents the overlapping between blocks. The case where No < 0 corresponds to zero padding. The main complexity arises from the core block modulation, which in general requires N2 complex multiplications. Nevertheless, this complexity can be significantly reduced by exploiting the modulation matrix structure. 4.1.3.2 Receiver Synchronization techniques are used for the detection of transmitted frames at the receiver. For example, in preamble-based synchronization, a reference sequence is transmitted in front of a frame to enable the detection of the start of the frame. After the preamble, a header signal is used to provide information about the number of blocks in the frame and other modulation parameters. Afterwards, inverse operations take place as shown in Figure 4.5. 1. Block demultiplexing: Block demultiplexing extracts the modulated blocks. Depending on the 