Non-linear phase Generalized DFT

Could someone help me on this, please

I am studying about the newly developed non-linear phase Generalized DFT proposed by Akansu.
https://web.njit.edu/~akansu/PAPERS/Akansu-Agirman Sarnoff2009.pdf
https://web.njit.edu/~akansu/PAPERS/Akansu-AgirmanEUSIPCO2009.pdf
(It's not that long, if you have time, please help)

The system is basically replacing IFFT and FFT block in the OFDM system with DFT matrix * G matrix
where G can be anything, for example rational function, diagonal matrix, or defined by the phase shaping function

Now, I applied this so-called GDFT into my MIMO-OFDM system over the correlated multipath channel that also considers Rician-K factor, angle of arrival/departure, doppler shift and so or, making it as realistic as possible

My question is, by using the non-linear phase transform, does it make the OFDM signal not to be orthogonal?
My result is that the GDFT performs a little bit better than traditional DFT if there is deep fade in the channel and there's only one receive antenna. But for other no. of receive antenna, the results are comparable to the traditional DFT system.

If you can, could you explain why is the result like this?
I mean, I am confused a bit. Does normally non-linearity is undesired in OFDM? but in his paper, he said it can be applied to CDMA and OFDM... Or is there any difference between non-linear amplitude and non-linear phase?
Normally you talk about non-linear phase noise from the amplifier, right? I think this non-linearity acts the different way, am I right?

Also, about the test based on correlation metric. Does he mean we choose optimize the dft parameter a2 and b2 in order to get lowest BER? In the code, he suggest that Rcc should be used with OFDM, but why the correlation Rcc of the GDFT for OFDM case is higher than traditional DFT? Should it be lower for it to be beneficial to OFDM system?

Please, anyone, please help me, I really need answer urgently.

Thanks in advance, guys

Re: Non-linear phase Generalized DFT (Cool Stuff)

Hi,

I read about GDFT from links you copied. That is fascinating. How come no one thought about it since Fourier. I googled this guy his did the same for walsh codes (he called them wals like codes) with nonlinear phase. I missed that work.
(Walsh-Like Nonlinear Phase Orthogonal Codes for Direct Sequence CDMA Communications
https://ieeexplore.ieee.org/Xplore/...er=4244642&isnumber=4244641&authDecision=-203 )

Let me try to answer your questions.

1) GDFT is always orthogonal (see orthogonality in Akansu papers).
https://web.njit.edu/~akansu/PAPERS/Akansu-Agirman Sarnoff2009.pdf
https://web.njit.edu/~akansu/PAPERS/Akansu-AgirmanEUSIPCO2009.pdf

2) I don't see any reason OFDM demands linear phase. The opposite, nonlinear phase GDFT they proposed gives freedom to design carriers with synch advantages. They claim correlations of DFT is boosted with its generalization (nonlinear phase). They all unity amplitude sample transforms, it makes sense to me. Phase is the only dimension you have freedom to plat with. That is cool.

3) Nonlinearity of RF PA is something else. They are talking about nonlinear phase functions of GDFT basis functions instead of linear phase DFT basis functions. They show GDFT has much superior correlations to DFT.

4) It is my understanding from what I read you can optimize phase for best Rac and/or Rcc. It depends what you want to do. He gave examples in his papers. You should design nonlinear phase functions (he calls it phase shaping function) for your goals like ICC, ISI, PAPR reduction. You emphasize metrics important for your design. You can design your own GDFTs. Don't limit yourself to his examples. It is a design method.

Thanks a lot for bringing GDFT to the forum. This is the coolest engineering math stuff I've seen since wavelets. Dis you do Fast GDFT? Post your findings.

Good luck in your research.