Brij, I think the answer to this question, why the DCT may be more efficient than the DFT (FFT algorithm), boils down to the same thing: a DCT approach does not involve imaginary numbers. Therefore, computationally simpler. As far as I can tell, this also applies to OFDM.

FFT has (cos wt + jsin wt) but DCT has only cos wt

Hello Brij,

As mentioned in the previous answers that the difference between DFT and DCT is the imaginary part.

So this technique is useful for systems that use intensity modulation (IM/DD Systems) such as visible light communication as discussed in :

1- J. Zhou et al., "FOFDM Based on Discrete Cosine Transform for Intensity-Modulated and Direct-Detected Systems," in Journal of Lightwave Technology, vol. 34, no. 16, pp. 3717-3725, 15 Aug.15, 2016.

2- J. Zhou, Y. Qiao, Z. Cai and Y. Ji, "Asymmetrically Clipped Optical Fast OFDM Based on Discrete Cosine Transform for IM/DD Systems," in Journal of Lightwave Technology, vol. 33, no. 9, pp. 1920-1927, 1 May1, 2015.

Moreover some papers have proposed that DCT-OFDM system outperform DFT-OFDM system in case of frequency offset errors, and in frequency-selective fast-fading environments.

As discussed in papers below:

1- G. D. Mandyam, "On the discrete cosine transform and OFDM systems," 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)., Hong Kong, 2003, pp. IV-544.

2- P. Tan and N. C. Beaulieu, "A Comparison of DCT-Based OFDM and DFT-Based OFDM in Frequency Offset and Fading Channels," in IEEE Transactions on Communications, vol. 54, no. 11, pp. 2113-2125, Nov. 2006.

3- H. A. Leftah and S. Boussakta, "Novel OFDM Based on C-Transform for Improving Multipath Transmission," in IEEE Transactions on Signal Processing, vol. 62, no. 23, pp. 6158-6170, Dec.1, 2014.

Hope this answers your question :)

Best wishes

DCT-OFDM is a Fast-OFDM because it has twice the bandwidth efficiency compared to FFT-OFDM. DCT is much simpler indeed than FFT. However, only single-quadrature modulation formats are used (e.g. ASK-4, ASK-8). There are ways though to work around with QAM and Fast-OFDM.

The benefits of DCT-OFDM over FFT-OFDM are as follows:

1) As mentioned in the previous answer, DCT-OFDM has twice the bandwidth efficiency compared to FFT-OFDM. However, only 1D constellation alphabets can be used, thus, the spectral efficiency of both DCT-OFDM and FFT-OFDM is the same.

2) DCT inherently is simpler compared to FFT. However, for DCT, convolution in time domain is not multiplication in the frequency domain, thus, classical equalizations schemes for FFT-OFDM are not compatible for DCT-OFDM. It is possible to use appropriate cyclic prefix and use the following operations at the receiver FFT -> Classical Equalization -> IFFT -> DCT before estimating the constellation alphabets. Thus, if we consider the overall complexity of DCT-OFDM, it might be higher than FFT-OFDM.

3) The bit error rate performance for both DCT-OFDM and FFT-OFDM is expected to be the same in AWGN channel, however, DCT-OFDM outperforms FFT-OFDM in the presence of frequency offset, and in frequency-selective fast-fading environments. See ' A Comparison of DCT-Based OFDM and DFT-Based

OFDM in Frequency Offset and Fading Channels' by Peng and Beaulieu.

4) You should also see ' DCT-OFDM With Index Modulation' by Chafii et al., where the authors have shown that amalgamating DCT-OFDM with Index modulation can help achieve higher spectral efficiencies compared to FFT-OFDM.

Hope my answer has provided enough information for you to determine whether DCT-OFDM is efficient than FFT-OFDM.