GFDM principles

Generalized Frequency Division Multiplexing (GFDM) is a flexible multicarrier modulation scheme. The modulation is performed block by block, where each GFDM data block consist of certain number of subcarriers and subsymbols. By setting the number of subcarriers and the number of subsymbols to 1, GFDM allows single-carrier frequency domain equalization (SC-FDE) and CP-OFDM as its special cases, respectively. Furthermore, pulse shaping with a prototype filter $g_{0,0}(m)$ is another flexibility in GFDM to reduce out-of-band (OOB) emissions. In contrast to linear convolution used in FBMC, GFDM brings circular convolution into play. Let $g_{k,n}$ denote the pulse shape corresponding to the data symbol $s_{k,n}$, that is transmitted at subcarrier $n$ and time $k$, it can be written as $$ g_{k,n}[m] = g_{0,0}[(m-kN_{\textrm{sub}})~ \textrm{mod} ~(N_{\textrm{sub}}K)]\cdot e^{j2\pi \frac{n}{N_{\textrm{sub}}}m} $$ where $K$ denotes the number of sub-symbols within a GFDM block. Thus the time domain signal $x(m)$ of a GFDM block is expressed as $$ x[m] = \sum_{n=0}^{N_{\textrm{sub}}-1}\sum_{k=0}^{K-1}g_{k,n}[m]s_{k,n} $$ Optionally, cyclic prefix (CP) and cyclic suffix (CS) can be added in the GFDM data block.

In the following demo slide, raised-cosine filter with configurable roll-off factor $\alpha$ is used.