 set of pulse shapes defined by the active subsymbol set Mon={mL+1,1<mL+1<M} Therefore, the final block is a superposition of L GFDM blocks, such that (4.9) kekon memon" An alternative reformulation can be achieved in the FD representation with respect to 8k,m[q] (4.7). Here, the design is adjusted such that P = ATF's = K and Q=M resulting in the prototype pulses the sets on{kL+,<kL+1<K. General Multiple Prototype Pulses This approach can be generalized to design a waveform with L prototype pulses {g ()[[n]}. Each prototype pulse is associated with the sets 1Con(1) and Mon(1), as shown in Figure 4.2. Thus, for (k, m) E = the input data symbol can be further preprocessed prior to modulation, for instance, to produce OQAM [20]. 4 Generalized Frequency Division Multiplexing: Unified Multicarrier Framework Kon(0) Mon(0) Symbol x(0) [n] mapping modulator Kon (L-1) Mon(L-1) g(L-1) Symbol d(L-1) x(L-1) [n] mapping modulator Figure 4.2 GFDM with multiple prototype pulses. Symbol x(0) [n] mapping modulator k is even dream Symbol j(L-1) mapping modulator x(1) [n] Figure 4.3 OQAM preprocessing. Example: OQAM-OFDM In this waveform, Q = M and P = K/2; first, the complex QAM data symbols split into two OQAM precoded streams, d(1) = as illustrated in Figure 4.3, where The streams are then fed to two GFDM modulators with the parameters g(0) = g[n], = - = = = M = M - Ms + 1 is the overlapping factor of the prototype filter g[n] as shown in Figure 4.1. The output block is a superposition of both GFDM blocksi.e.xn]xon]x"[n].The = blocks are multiplexed with spacing Ns = M&K, and thus, = 4.1.3 Generalized Block-Based Multicarrier In addition to the pulse shaping, further processing can be performed on top of the mod- ulated block, including CP/cyclic suffix (CS) insertion, windowing, and filtering. Accord- ingly, we introduce a generic multicarrier framework. 4.1 Overview of Multicarrier Waveforms Symbol x(cp) Windowing/ x(LXX) Block Core block Overhead mapping filtering multiplexing [db](Non)=dbon ib=Adb Figure 4.4 Stages of multic