Non-orthogonal frequency-division multiplexing

From HandWiki
Short description: Method of encoding digital data on multiple carrier frequencies
Passband modulation
Analog modulation
Digital modulation
Hierarchical modulation
Spread spectrum
See also

Non-orthogonal frequency-division multiplexing (N-OFDM) is a method of encoding digital data on multiple carrier frequencies with non-orthogonal intervals between frequency of sub-carriers.[1][2][3] N-OFDM signals can be used in communication and radar systems.

Subcarriers system

Subcarriers system of N-OFDM signals after FFT

The low-pass equivalent N-OFDM signal is expressed as:[3][2]

[math]\displaystyle{ \nu(t) = \sum_{k=0}^{N-1}X_k e^{j2\pi\alpha kt/T},\quad 0 \le t \lt T, }[/math]

where [math]\displaystyle{ X_k }[/math] are the data symbols, [math]\displaystyle{ N }[/math] is the number of sub-carriers, and [math]\displaystyle{ T }[/math] is the N-OFDM symbol time. The sub-carrier spacing [math]\displaystyle{ \alpha/T }[/math] for [math]\displaystyle{ \alpha \lt 1 }[/math] makes them non-orthogonal over each symbol period.

History

The history of N-OFDM signals theory was started in 1992 from the Patent of Russian Federation No. 2054684.[1] In this patent, Vadym Slyusar proposed the 1st method of optimal processing for N-OFDM signals after Fast Fourier transform (FFT).

In this regard need to say that W. Kozek and A. F. Molisch wrote in 1998 about N-OFDM signals with [math]\displaystyle{ \alpha \lt 1 }[/math] that "it is not possible to recover the information from the received signal, even in the case of an ideal channel."[4]

In 2001, V. Slyusar proposed non-orthogonal frequency digital modulation (N-OFDM) as an alternative of OFDM for communications systems.[5]

The next publication about this method has priority in July 2002[2] before the conference paper regarding SEFDM of I. Darwazeh and M.R.D. Rodrigues (September, 2003).[6]

Advantages of N-OFDM

Despite the increased complexity of demodulating N-OFDM signals compared to OFDM, the transition to non-orthogonal subcarrier frequency arrangement provides several advantages:

  1. higher spectral efficiency, which allows to reduce the frequency band occupied by the signal and improve the electromagnetic compatibility of many terminals;
  2. adaptive detuning from interference concentrated in frequency by changing the nominal frequencies of the subcarriers;[7]
  3. an ability to take into account Doppler frequency shifts of subcarriers when working with subscribers moving at high speeds;
  4. reduction of the peak factor of the multi-frequency signal mixture.

Idealized system model

This section describes a simple idealized N-OFDM system model suitable for a time-invariant AWGN channel.[8]

Transmitter N-OFDM signals

N-OFDM transmitter ideal.jpg

An N-OFDM carrier signal is the sum of a number of not-orthogonal subcarriers, with baseband data on each subcarrier being independently modulated commonly using some type of quadrature amplitude modulation (QAM) or phase-shift keying (PSK). This composite baseband signal is typically used to modulate a main RF carrier.

[math]\displaystyle{ s[n] }[/math] is a serial stream of binary digits. By inverse multiplexing, these are first demultiplexed into [math]\displaystyle{ \scriptstyle N }[/math] parallel streams, and each one mapped to a (possibly complex) symbol stream using some modulation constellation (QAM, PSK, etc.). Note that the constellations may be different, so some streams may carry a higher bit-rate than others.

A Digital Signal Processor (DSP) is computed on each set of symbols, giving a set of complex time-domain samples. These samples are then quadrature-mixed to passband in the standard way. The real and imaginary components are first converted to the analogue domain using digital-to-analogue converters (DACs); the analogue signals are then used to modulate cosine and sine waves at the carrier frequency, [math]\displaystyle{ f_\text{c} }[/math], respectively. These signals are then summed to give the transmission signal, [math]\displaystyle{ s(t) }[/math].

Demodulation

Receiver

N-OFDM receiver ideal.jpg

The receiver picks up the signal [math]\displaystyle{ r(t) }[/math], which is then quadrature-mixed down to baseband using cosine and sine waves at the carrier frequency. This also creates signals centered on [math]\displaystyle{ 2 f_\text{c} }[/math], so low-pass filters are used to reject these. The baseband signals are then sampled and digitised using analog-to-digital converters (ADCs), and a forward FFT is used to convert back to the frequency domain.

This returns [math]\displaystyle{ N }[/math] parallel streams, which use in appropriate symbol detector.

Demodulation after FFT

The 1st method of optimal processing for N-OFDM signals after FFT was proposed in 1992.[1]

Demodulation without FFT

Demodulation by using of ADC samples

The method of optimal processing for N-OFDM signals without FFT was proposed in October 2003.[3][9] In this case can be used ADC samples.

Demodulation after discrete Hartley transform

N-OFDM+MIMO

N-OFDM+MIMO system model

The combination N-OFDM and MIMO technology is similar to OFDM. To the building of MIMO system can be used digital antenna array as transmitter and receiver of N-OFDM signals.

Fast-OFDM

Fast-OFDM[10][11][12] method was proposed in 2002.[13]

Filter-bank multi-carrier modulation (FBMC)

Filter-bank multi-carrier modulation (FBMC) is.[14][15][16] As example of FBMC can consider Wavelet N-OFDM.

Wavelet N-OFDM

N-OFDM has become a technique for power-line communications (PLC). In this area of research, a wavelet transform is introduced to replace the DFT as the method of creating non-orthogonal frequencies. This is due to the advantages wavelets offer, which are particularly useful on noisy power lines.[17]

To create the sender signal the wavelet N-OFDM uses a synthesis bank consisting of a [math]\displaystyle{ N }[/math]-band transmultiplexer followed by the transform function

[math]\displaystyle{ F_n(z) = \sum_{k=0}^{L-1} f_n(k) z^{-k},\quad 0 \leq n \lt N }[/math]

On the receiver side, an analysis bank is used to demodulate the signal again. This bank contains an inverse transform

[math]\displaystyle{ G_n(z) = \sum_{k=0}^{L-1} g_n(k) z^{-k},\quad 0 \leq n \lt N }[/math]

followed by another [math]\displaystyle{ N }[/math]-band transmultiplexer. The relationship between both transform functions is

[math]\displaystyle{ \begin{align} f_n(k) &= g_n(L - 1 - k) \\ F_n(z) &= z^{-(L-1)} G_n * (z - 1) \end{align} }[/math]


Spectrally-efficient FDM (SEFDM)

N-OFDM is a spectrally efficient method.[6][18] All SEFDM methods are similar to N-OFDM.[6][19][20][21][22][23][24]

Generalized frequency division multiplexing (GFDM)

Generalized frequency division multiplexing (GFDM) is.

See also

  • OFDM
  • COFDM

References

  1. ↑ 1.0 1.1 1.2 RU2054684 (C1) G01R 23/16. Amplitude-frequency response measurement technique// Slyusar V. – Appl. Number SU 19925055759, Priority Data: 19920722. – Official Publication Data: 1996-02-20 [1]
  2. ↑ 2.0 2.1 2.2 Slyusar, V. I. Smolyar, V. G. Multifrequency operation of communication channels based on super-Rayleigh resolution of signals// Radio electronics and communications systems c/c of Izvestiia- vysshie uchebnye zavedeniia radioelektronika.. – 2003, volume 46; part 7, pages 22–27. – Allerton press Inc. (USA)[2]
  3. ↑ 3.0 3.1 3.2 Slyusar, V. I. Smolyar, V. G. The method of nonorthogonal frequency-discrete modulation of signals for narrow-band communication channels// Radio electronics and communications systems c/c of Izvestiia- vysshie uchebnye zavedeniia radioelektronika. – 2004, volume 47; part 4, pages 40–44. – Allerton press Inc. (USA)[3]
  4. ↑ W. Kozek and A. F. Molisch. "Nonorthogonal pulseshapes for multicarrier communications in doubly dispersive channels," IEEE J. Sel. Areas Commun., vol. 16, no. 8, pp. 1579–1589, Oct. 1998.
  5. ↑ Pat. of Ukraine № 47835 A. IPС8 H04J1/00, H04L5/00. Method of frequency-division multiplexing of narrow-band information channels// Sliusar Vadym Іvanovych, Smoliar Viktor Hryhorovych. – Appl. № 2001106761, Priority Data 03.10.2001. – Official Publication Data 15.07.2002, Official Bulletin № 7/2002
  6. ↑ 6.0 6.1 6.2 M. R. D. Rodrigues and I. Darwazeh. A Spectrally Efficient Frequency Division Multiplexing Based Communications System.// InOWo'03, 8th International OFDM-Workshop, Proceedings, Hamburg, DE, September 24–25, 2003. - https://www.researchgate.net/publication/309373002
  7. ↑ Vasilii A. Maystrenko, Vladimir V. Maystrenko, Alexander Lyubchenko. Interference Immunity Analysis of an Optimal Demodulator Under Peak Multiplexing of N-OFDM Spectrum.//Conference Paper of 2017 International Siberian Conference on Control and Communications (SIBCON).· June 2017. - DOI: 10.1109/SIBCON.2017.7998458
  8. ↑ Vasilii A. Maystrenko, Vladimir V. Maystrenko, Evgeny Y. Kopytov, Alexander Lyubche. Analysis of Operation Algorithms of N-OFDM Modem in Channels with AWGN.// Conference Paper of 2017 Dynamics of Systems, Mechanisms and Machines (Dynamics). November 2017. DOI: 10.1109/Dynamics.2017.8239486
  9. ↑ Maystrenko, V. A., & Maystrenko, V. V. (2014). The modified method of demodulation N-OFDM signals. 2014 12th International Conference on Actual Problems of Electronics Instrument Engineering (APEIE). doi:10.1109/apeie.2014.7040919
  10. ↑ Dimitrios Karampatsis, M.R.D. Rodrigues and Izzat Darwazeh. Implications of linear phase dispersion on OFDM and Fast-OFDM systems.// London Communications Symposium 2002. - http://www.ee.ucl.ac.uk/lcs/previous/LCS2002/LCS112.pdf.
  11. ↑ D. Karampatsis and I. Darwazeh. Performance Comparison of OFDM and FOFDM Communication Systems in Typical GSM Multipath Environments. // London Communications Symposium 2003 (LCS2003), London, UK, Pp. 360 – 372. - http://www.ee.ucl.ac.uk/lcs/previous/LCS2003/94.pdf.
  12. ↑ K. Li and I. Darwazeh. System performance comparison of Fast-OFDM system and overlapping Multi-carrier DS-CDMA scheme.// London Communications Symposium 2006. - http://www.ee.ucl.ac.uk/lcs/previous/LCS2006/54.pdf.
  13. ↑ M.R.D. Rodrigues, Izzat Darwazeh. Fast OFDM: A Proposal for Doubling the Data Rate of OFDM Schemes.// International Conference on Communications, ICT 2002, Beijing, China, June 2002. - Pp. 484 – 487
  14. ↑ Bellanger M.G. FBMC physical layer: a primer / M.G. Bellanger et al. - January 2010.
  15. ↑ Farhang-Boroujeny B. OFDM Versus Filter Bank Multicarrier//IEEE Signal Processing Magazine.— 2011.— Vol. 28, № 3.— P. 92— 112.
  16. ↑ Behrouz Farhang-Boroujeny. Filter Bank Multicarrier for Next Generation of Communication Systems.//Virginia Tech Symposium on Wireless Personal Communications. — June 2–4, 2010.
  17. ↑ S. Galli; H. Koga; N. Nodokama (May 2008). "Advanced signal processing for PLCS: Wavelet-OFDM". 2008 IEEE International Symposium on Power Line Communications and Its Applications. pp. 187–192. doi:10.1109/ISPLC.2008.4510421. ISBN 978-1-4244-1975-3. https://www.researchgate.net/publication/4330667. 
  18. ↑ Safa Isam A Ahmed. Spectrally Efficient FDM Communication Signals and Transceivers: Design, Mathematical Modelling and System Optimization.//A thesis submitted for the degree of PhD. — Communications and Information Systems Research Group Department of Electronic and Electrical Engineering University College London. — October 2011.- http://discovery.ucl.ac.uk/1335609/1/1335609.pdf
  19. ↑ Masanori Hamamura, Shinichi Tachikawa. Bandwidth efficiency improvement for multi-carrier systems. //15th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, vol. 1, Sept. 2004, pp. 48 — 52.
  20. ↑ Li. D. B. A high spectral efficiency technology and method for overlapped frequency division multiplexing [P]. 2006, PCT/CN2006/002012 (in Chinese)
  21. ↑ Xing Yang, Wenbao Ait, Tianping Shuait, Daoben Li. A Fast Decoding Algorithm for Non-orthogonal Frequency Division Multiplexing Signals // Communications and Networking in China, 2007. CHINACOM '07. — 22-24 Aug. 2007, P. 595—598.
  22. ↑ I. Kanaras, A. Chorti, M. Rodrigues, and I. Darwazeh, "A combined MMSE-ML detection for a spectrally efficient non orthogonal FDM signal, " in Broadband Communications, Networks and Systems, 2008. BROADNETS 2008. 5th International Conference on, Sept. 2008, pp. 421 −425.
  23. ↑ I. Kanaras, A. Chorti, M. Rodrigues, and I. Darwazeh, "Spectrally efficient FDM signals: Bandwidth gain at the expense of receiver complexity, " in IEEE International Conference on Communications, 2009. ICC ’09., June 2009, pp. 1 −6.
  24. ↑ Bharadwaj, S., Nithin Krishna, B.M.; Sutharshun, V.; Sudheesh, P.; Jayakumar, M. Low Complexity Detection Scheme for NOFDM Systems Based on ML Detection over Hyperspheres. 2011 International Conference on Devices and Communications, ICDeCom 2011 - Proceedings, Mesra, 24-25 February 2011, Pp. 1-5.



Retrieved from "https://handwiki.org/wiki/index.php?title=Non-orthogonal_frequency-division_multiplexing&oldid=3372849"