# What is difference between OFDM and GFDM?

I am trying to understand the difference(s) between OFDM (Orthogonal Frequency Division Multiplexing) and GFDM (Generalized Frequency Division Multiplexing) which are used as a multicarrier modulation techniques in wireless communication. As far as I know the OFDM uses the orthogonal subcarriers and the GFDM is with the non-orthogonal subcarriers when designing a transmitter. The GFDM is possibly going to be the modulation technique for 5G systems as it has been discussed in a research area.

Could anyone please explain further about GFDM design and its differences from OFDM? What is the purpose of using GFDM when designing a transmitter? The subcarriers are created just after the IFFT?

In GFDM, how does the IFFT block work when creating the subcarriers?

What about the subcarrier pulse shaping in GFDM?

• This might help: webdemo.inue.uni-stuttgart.de/webdemos/08_research/waveform5G/… – Deve Apr 1 '15 at 15:28
• Thank you for sharing this link! Excellent explanations and spectrum showings! – tuner May 4 '15 at 9:55
• How you know that the GFDM is possibly going to be the modulation technique for 5G system? – Val Costa Jun 26 '15 at 13:50
• @Deve your link is excellent and answers this question perfectly; can you paste it below so that we can upvote it? – Dan Boschen May 14 '17 at 14:03
• @DanBoschen Done – Deve Jun 5 '17 at 9:43

There is a great interactive demonstration of GFDM by Xiaojie Wang and Stephan ten Brink explaining the differences between OFDM and GFDM.

To sum it up, GFDM uses generalized pulse shaping filters that can span

• a subset of $N_\mathrm S$ subcarriers out of a total number $N_\mathrm{S,tot}$ of subcarriers and
• a set of $N_\mathrm Y$ symbols

OFDM is a special case of GFDM where $N_\mathrm Y = 1$, $N_S = N_\mathrm{S,tot}$, and the pulse shaping filter is rectangular in frequency domain. This can be implemented using an IFFT at the transmitter and an FFT at the receiver.

The implementation of GFDM is generally not that simple. I could think of an implementation using $N_\mathrm{S,tot}/N_\mathrm S$ IFFTs of length $N_\mathrm{S,tot}$ where at every IFFT just a subset of $N_\mathrm S$ inputs is used and the others are zero padded to realize the frequency allocation of one subset of subcarriers. Each IFFT output would be followd by a specific pulse shaping filter spanning $N_\mathrm Y$ symbols. Finally, all filter outputs would be added up and converted to an analog signal using an digital-to-analog converter (DAC).

The purpose of GFDM is to achieve, amongst others:

• lower out-of-band radiation (better spectral efficiency)
• higher robustness against carrier frequency offset (CFO)
• higher robustness against sampling time offset

when compared to OFDM.

GFDM is also motivated by the fact that in Long-term evolution (LTE) mobile communications, users are allocated so-called physical ressource blocks (PRB). PRBs consist of a set of adjacent subcarriers and symbols.

Here is a nice reference in the academic literature. He starts the derivation with OFDM, then shows how GFDM can be derived from that.

In Figure 3, the pulse shaping coefficients $c_k$ precede the IFFT block.

• the link you provided does not work. – sky-light Dec 27 '16 at 14:21