y John Wiley & Sons Ltd. 4 Generalized Frequency Division Multiplexing: Unified Multicarrier Framework as a result of the channel delay spread. Considering the frequency domain equalization (FDE) of a single carrier system, which was first proposed in [10], it can be seen as pre- coded OFDM, where the precoding matrix is the DFT matrix as noted in [11]. The idea of precoded-OFDM is extended to cover several OFDM symbols. Another famous precoding is DFT-spread-OFDM, which is exploited for the uplink multiple access under the name single carrier-frequency division multiple access (SC-FDMA) [12, 13]. Another family of waveforms uses periodic pulse shaping and windowing, which leads to circular filtering. It is worth noting that OFDM also follows this principle. To generalize the concept of circular filtering, generalized frequency division multiplexing (GFDM) [14] was proposed as an extension of OFDM using general circular filtering [15]. At the begin- ning, GFDM is introduced as a system of parallel single carrier (SC)-CPs, which are filtered to reduce the ICI. The tail-biting idea, which is equivalent to circular filtering, is used to reduce the CP length due to the filtering. In this scheme described in [14], a finite number of symbols per subcarrier, denoted as subsymbols, are circularly filtered with a prototype filter and shifted to the corresponding channel. Moreover, the modulated blocks can be iso- lated by means of guard interval that is longer than the channel delay to prevent inter-block interference [14]. Circular filtering is also introduced for OQAM-OFDM to facilitate the CP insertion [16]. The common thread among all multicarrier techniques is the transmission of data in parallel streams, which are then superimposed to formulate the final signal. Each stream can be seen as a single-carrier modulation with a specific pulse shape. In the state of the art multicarrier systems, pulse shapes are generated by a shift of the prototype filter¹ in the frequency-domain (FD) and each stream is denoted as a subc