ture To realize sufficient flexibility with reasonable resource cost, we consider radix-2 values of K and M, which enable the implementation of DFT with flexible fast Fourier transform (FFT) intellectual property (IP) cores. This core allows the run-time reconfiguration of the size of DFT and setting the block either in DFT or IDFT mode. The architecture is illus- trated in Figure 4.11. This design consists of four flexible FFT cores with the configuration parameter Nx for the DFT size and Ix to set the core in the direct (D) or inverse (I) mode. Additionally, each FFT block can be enabled (E) or disabled (D) with the parameter Ex, such that the disabled block forwards the samples to the next stage. The fourth FFT core is optional depending on the desired domain of implementation. Moreover, one memory block is used to store the result of the first transform and performs the transpose by configur- ing the indexing unit. The modulator window is stored in a memory. This memory is always 5 The OTFS modulation follows the TD GFDM modulation. The data spreading E CMXK is denoted as the symplectic finite Fourier transform (SFFT). A window W E is applied. The resulting precoded data W, tx ODS are transmitted over K OFDM symbols of M subcarriers, such that xk D)[ k]. A CP can be inserted as well per OFDM symbol. 6 Early studies on GFDM are constrained by even K and odd M, as a consequence of the singularity problem, which results from the assumption of real symmetric prototype pulse. This limitation was tackled by the design of Hermitian symmetric filter with similar spectrum properties [25]. Flexible Transpose Flexible Complex Flexible Allocation Flexible memory multiplier memory Window indexing memory indexing Figure 4.11 Unified architecture for TD and FD GFDM processing. 4 Generalized Frequency Division Multiplexing: Unified Multicarrier Framework read incrementally and written with respect to the implementation domain. Furthermore, one high throughput complex multiplier is used to perform the element-wise multiplica-