Abstract

Real-time OFDM transmitters breaking the 100 Gbit/s barrier require high-performance, usually FPGA-based digital signal processing. Especially the Fourier transform as a key operation of any OFDM system must be optimized with respect to performance and chip area utilization. Here, we demonstrate an alternative to the widely adopted fast Fourier transform algorithm. Based on an extensive yet optimized use of pre-set look-up tables, our FPGA implementation supports fast reconfigurable channel equalization and switching times in the nanosecond range without re-loading any code. We demonstrate the potential of the concept by realizing the first real-time single polarization OFDM transmitter generating a 101.5 Gbit/s data stream by modulating 58 subcarriers with 16QAM.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008).
    [CrossRef] [PubMed]
  2. N. Cvijetic, “Optical OFDM for next-generation PON,” in Signal Processing in Photonic Communications, OSA Technical Digest (CD) (Optical Society of America, 2010), paper SPTuB6. http://www.opticsinfobase.org/abstract.cfm?URI=SPPCom-2010-SPTuB6 .
  3. X. Liu, S. Chandrasekhar, B. Zhu, P. Winzer, A. Gnauck, and D. Peckham, “448-Gb/s reduced-guard-interval CO-OFDM transmission over 2000 km of ultra-large-area fiber and five 80-GHz-grid ROADMs,” J. Lightwave Technol. 29(4), 483–490 (2011).
    [CrossRef]
  4. X. Liu, S. Chandrasekhar, B. Zhu, and D. Peckham, “Efficient digital coherent detection of a 1.2-Tb/s 24-carrier no-guard-interval CO-OFDM signal by simultaneously detecting multiple carriers per sampling,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OWO2. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2010-OWO2 .
  5. F. Buchali, R. Dischler, A. Klekamp, M. Bernhard, and Y. Ma, “Statistical transmission experiments using a real-time 12.1 Gb/s OFDM transmitter,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OMS3. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2010-OMS3 .
  6. R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated subcarriers,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWE5. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2011-OWE5
  7. Y. Benlachtar, P. M. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. C. Hoe, M. Püschel, M. Glick, and R. I. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express 17(20), 17658–17668 (2009).
    [CrossRef] [PubMed]
  8. B. Inan, O. Karakaya, P. Kainzmaier, S. Adhikari, S. Calabro, V. Sleiffer, N. Hanik, and S. Jansen, “Realization of a 23.9 Gb/s real time optical-OFDM transmitter with a 1024 Point IFFT,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMS2. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2011-OMS2
  9. D. Qian, T. Kwok, N. Cvijetic, J. Hu, and T. Wang, “41.25 Gb/s real-time OFDM receiver for variable rate WDM-OFDMA-PON transmission,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPD9. http://www.opticsinfobase.org/abstract.cfm?URI=NFOEC-2010-PDPD9 .
  10. N. Kaneda, Q. Yang, X. Liu, S. Chandrasekhar, W. Shieh, and Y. Chen, “Real-time 2.5 GS/s coherent optical receiver for 53.3-Gb/s sub-banded OFDM,” J. Lightwave Technol. 28(4), 494–501 (2010).
    [CrossRef]
  11. Q. Yang, N. Kaneda, X. Liu, S. Chandrasekhar, W. Shieh, and Y. Chen, “Towards Real-Time Implementation of Optical OFDM Transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OMS6. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2010-OMS6 .
  12. X. Q. Jin, R. P. Giddings, E. Hugues-Salas, and J. M. Tang, “Real-time demonstration of 128-QAM-encoded optical OFDM transmission with a 5.25bit/s/Hz spectral efficiency in simple IMDD systems utilizing directly modulated DFB lasers,” Opt. Express 17(22), 20484–20493 (2009).
    [CrossRef] [PubMed]
  13. C. R. Berger, Y. Benlachtar, and R. Killey, “Optimum clipping for optical OFDM with limited resolution DAC/ADC,” in Signal Processing in Photonics Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper SPMB5.
  14. S. G. Johnson and M. Frigo, “A modified split-radix FFT with fewer arithmetic operations,” IEEE Trans. Signal Process. 55(1), 111–119 (2007).
    [CrossRef]
  15. R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” (to be submitted).
  16. R. A. Shafik, M. S. Rahman, and A. H. M. R. Islam, “On the extended relationships among EVM, BER and SNR as performance metrics”, in Proceedings of 4th International Conference on Electrical and Computer Engineering, (Dhaka, Bangladesh, 2006) pp.408–411.

2011

2010

2009

2008

2007

S. G. Johnson and M. Frigo, “A modified split-radix FFT with fewer arithmetic operations,” IEEE Trans. Signal Process. 55(1), 111–119 (2007).
[CrossRef]

Bao, H.

Benlachtar, Y.

Bouziane, R.

Cartolano, A.

Chandrasekhar, S.

Chen, Y.

Frigo, M.

S. G. Johnson and M. Frigo, “A modified split-radix FFT with fewer arithmetic operations,” IEEE Trans. Signal Process. 55(1), 111–119 (2007).
[CrossRef]

Giddings, R. P.

Glick, M.

Gnauck, A.

Hoe, J. C.

Hugues-Salas, E.

Jin, X. Q.

Johnson, S. G.

S. G. Johnson and M. Frigo, “A modified split-radix FFT with fewer arithmetic operations,” IEEE Trans. Signal Process. 55(1), 111–119 (2007).
[CrossRef]

Kaneda, N.

Killey, R. I.

Koutsoyannis, R.

Liu, X.

Milder, P.

Peckham, D.

Püschel, M.

Rangaraj, D.

Shieh, W.

Tang, J. M.

Tang, Y.

Watts, P. M.

Winzer, P.

Yang, Q.

Zhu, B.

IEEE Trans. Signal Process.

S. G. Johnson and M. Frigo, “A modified split-radix FFT with fewer arithmetic operations,” IEEE Trans. Signal Process. 55(1), 111–119 (2007).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Other

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” (to be submitted).

R. A. Shafik, M. S. Rahman, and A. H. M. R. Islam, “On the extended relationships among EVM, BER and SNR as performance metrics”, in Proceedings of 4th International Conference on Electrical and Computer Engineering, (Dhaka, Bangladesh, 2006) pp.408–411.

Q. Yang, N. Kaneda, X. Liu, S. Chandrasekhar, W. Shieh, and Y. Chen, “Towards Real-Time Implementation of Optical OFDM Transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OMS6. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2010-OMS6 .

X. Liu, S. Chandrasekhar, B. Zhu, and D. Peckham, “Efficient digital coherent detection of a 1.2-Tb/s 24-carrier no-guard-interval CO-OFDM signal by simultaneously detecting multiple carriers per sampling,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OWO2. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2010-OWO2 .

F. Buchali, R. Dischler, A. Klekamp, M. Bernhard, and Y. Ma, “Statistical transmission experiments using a real-time 12.1 Gb/s OFDM transmitter,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OMS3. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2010-OMS3 .

R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated subcarriers,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWE5. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2011-OWE5

N. Cvijetic, “Optical OFDM for next-generation PON,” in Signal Processing in Photonic Communications, OSA Technical Digest (CD) (Optical Society of America, 2010), paper SPTuB6. http://www.opticsinfobase.org/abstract.cfm?URI=SPPCom-2010-SPTuB6 .

B. Inan, O. Karakaya, P. Kainzmaier, S. Adhikari, S. Calabro, V. Sleiffer, N. Hanik, and S. Jansen, “Realization of a 23.9 Gb/s real time optical-OFDM transmitter with a 1024 Point IFFT,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMS2. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2011-OMS2

D. Qian, T. Kwok, N. Cvijetic, J. Hu, and T. Wang, “41.25 Gb/s real-time OFDM receiver for variable rate WDM-OFDMA-PON transmission,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPD9. http://www.opticsinfobase.org/abstract.cfm?URI=NFOEC-2010-PDPD9 .

C. R. Berger, Y. Benlachtar, and R. Killey, “Optimum clipping for optical OFDM with limited resolution DAC/ADC,” in Signal Processing in Photonics Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper SPMB5.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Experimental setup. Real-time OFDM transmitter comprising FPGAs, DACs, and an external cavity laser (ECL) source with an optical IQ-modulator. Both FPGA boards are fed with identical spectral data sequences Xk (in fact, these pseudo-random data are generated on the FPGA boards themselves). The boards generate the corresponding complex OFDM symbols xn by an inverse Fourier transform, Eq. (1). FPGA1 and FPGA2 then feed the real part of xn to DAC1 for the I-channel and the imaginary part of xn to DAC2 for the Q-channel modulation, respectively. A short standard single-mode fiber connects the transmitter to an offline OFDM receiver comprising an EDFA, a polarization controller and an Agilent OMA, where the signal is sampled at 80 GSa/s. The received signal is then processed offline using standard OFDM algorithms.

Fig. 2
Fig. 2

FPGA and high speed DAC with digital signal processing (DSP) blocks and GTX interface. A pseudo random binary sequence (PRBS) generator feeds the input of the IDFT core which produces the representation of the time domain OFDM signal. A clipping and rescaling module (CLIP) trims the signal to the physical resolution of the Micram DAC. The FPGA’s 24 high-speed synchronized GTX transmitters drive the DAC at 7 Gbit/s each. Onboard 4:1 multiplexers before the DAC core translate to an output sampling rate of 28 GSa/s with 6 bit of physical resolution.

Fig. 3
Fig. 3

The FPGA’s internal realization of the IDFT operation. All M possible products of modulation coefficients Xk and k th complex harmonic are sampled, quantized, and stored within look-up tables (LUT). There are LUTs for the real part and for the imaginary part of each complex harmonic. For simplicity we show only one set of LUT, namely the one for the real part which corresponds to the inphase component I. An onboard PRBS generator selects symbols to be transmitted by addressing the corresponding LUTs. For each sample of each of the subcarriers, an addition forms the output samples (k = 0…N−1) of the transformed signal. To improve the computation efficiency additions are realized by a binary adder tree with log2 N stages.

Fig. 4
Fig. 4

Real output sample values of a 64-point IDFT for subcarriers (a) k = 6 and (b) k = 4 with the specific modulation symbols X 6 = X 4 = 1. The time sample number n on the horizontal axis can be interpreted in units of an arbitrary time interval Δt. The solid blue line represents the interpolated “physical” subcarrier time function, if n is assumed to be continuous. (a) Subcarrier k = 6 is doubly periodic within the IDFT window. It has the “physical” non-integer period pk = 64 / 6 = 32 / 3 ≈10.67 and a minimum integer period pn = 64 / 2 = 32 = 3 × pk . Therefore only 32 samples have to be processed. (b) Subcarrier k = 4 is singly periodic with a minimum integer period pk = 64 / 4 = 16 = pn , so that only 16 samples out of 64 need to be processed.

Fig. 5
Fig. 5

LUT contents for subcarrier k and a set of M = 4 symbols (QPSK). (a) LUT with N values for each symbol in the constellation. (b) Only one LUT needs to be stored. Phases exceeding the stored range are folded back due to the function’s periodicity.

Fig. 6
Fig. 6

Simulated output spectrum and constellation diagram of all modulated subcarriers and pilot tones showing the proper functionality of the FPGA design. (a) Spectrum with four pilot tones. (b) Constellation diagram. Distortions are due to quantization and clipping noise. A residual EVM of 4.8% is found for an optimized relation between clipping and quantization noise.

Fig. 7
Fig. 7

Experimental spectrum, error vector magnitude and constellation diagrams. (a) Received (red) and simulated (black) electrical power spectrum of the transmitted OFDM signal. The simulation is performed for logical signals on the FPGA, and the resulting arbitrary power density is scaled to match the maximum power density of the measured signal. Four pilot tones are used for phase recovery and symbol window synchronization. (b) EVM of modulated subcarriers. Standard limits of the bit error ratio (BER) for forward-error corrected (FEC) “error-free” reception are indicated. (c) Constellation diagram for subcarrier 27, EVM = 7.6%. (d) Constellation diagram of subcarrier 51 with EVM = 9.7%.

Fig. 8
Fig. 8

Comparison between an ideal time discrete signal xn (t) and an ideal DAC output time signal (left) and frequency domain (right). The DAC impulse response is described by a rectangular function r(t) of area 1 and a temporal width equal to the sampling interval. (a) An ideal time discrete signal has a periodic spectrum. Periodic repetitions are in faded blue. A properly chosen anti-aliasing filter blocks these unwanted parts of the spectrum. (b) The ideal DAC output spectrum results from multiplying the (blue) periodic spectrum Fig. 8(a) with the (red) sinc-function R(f).

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

x n = k = 0 N 1 X k e j 2 π k n N ,     k , n = 0 , 1 , , N 1 , M  complex data symbols  X k  per  k ,
P = N 2 .
P = 1 + k = 1 N 1 N GCD ( N , k ) .
P q = 1 + m = 0 q 1 2 q m × 1 2 2 q m = 1 + 1 2 2 2 q m = 0 q 1 4 m = 1 + 1 2 N 2 m = 0 q 1 4 m , lim q P q = 1 2 N 2 1 1 1 4 = 2 3 N 2 .
α ( N ) = 8 3 N log 2 N 16 9 N 2 9 ( 1 ) log 2 N + 2 ,
μ ( N ) = 4 3 N log 2 N 38 9 N 2 9 ( 1 ) log 2 N + 6.

Metrics