# What benefits can we get from the use of GFDM?

Existing literatures say that the generalized frequency division multiplexing (GFDM) has lower out-of-band emission (OOBE) levels compared to orthogonal frequency division multiplexing (OFDM). However, this is actually untrue in a fair manner. In the previous papers, the OOBE levels of these two schemes have been compared under the assumption of the same number of subcarriers. But such an assumption is very unfair!

Obviously, the total number of subcarriers of OFDM system (denoted by 'K') is determined by considering the coherence time and bandwidth expected. Therefore, under the same (or similar) circumstances, it is fair to set the number of samples in the GFDM symbols to be equal to 'K', which means that MN=K (M: number of subsymbols in GFDM system, N: number of subcarriers in GFDM system). In short, comparing the OOBE levels under the condition of K=N is quite unfair because GFDM requires the longer coherence time than OFDM in that case, and two systems have different spectral efficiencies. Instead, assuming MN=K is fair.

However, when MN=K, there is no gain of OOBE of GFDM systems compared to the OFDM one because of circular filtering, and I have already checked it up through both mathematical analysis and computer simulations.

So, I want to know what benefits we can get from the use of GFDM. As I know, the improved PAPR performance can be expected. But I'm not sure it is meaningful because of high implementation complexity of GFDM transceiver. In my opinion, the OFDM with PAPR reduction techniques may be preferable.

How do you think about it? Am I missing something? If it is, can you please let me know what benefits we can obtain from GFDM?

Thank in advance

## 1 Answer

In a system where subcarrier crosstalk is not defined by how well the parties are synchronized, synchronization can might more easily be implemented. Whether that really compensates for the more complex filtering structure is up to research or even questionable.

Point is that you can actually, in math and simulation bring down OOBE with GFDM, not even considering different comparison bases for the number of subcarriers:

Consider this: The pulse shape of a single OFDM subcarrier is inherently a sinc. Hence, the first side lobes of the outermost carriers can only be $\approx13$ dB lower than the desired signal, and will continue periodically, whereas such a statement cannot be universally made for GFDM.

• Thank you for your kind answer. But the GFDM system cannot provide the boundary continuity required for the relaxed synchronization due to the circular convolution in time domain. Since the circular convolution is equivalent to the applying the rectangular window in time domain, no difference of OOBE level between OFDM and GFDM is made when MN=K. The OOBE performance of GFDM can be easily improved by inserting null subsymbols. However, such an approach can be only acceptable with large M. – J Choi Feb 1 '16 at 3:47
• With the same number of subcarriers, the OOBE level of GFDM is obviously lower than that of OFDM. In this case, K=N and the length of a GFDM symbol is M-fold longer than that of OFDM. That means, considering the coherence time, we can increase the number of subcarrires of OFDM system up to 'MN'. Consequently, those two systems have the same OOBE level as I mentioned before. – J Choi Feb 1 '16 at 4:03