Novel Optical Fast Fourier Transform Scheme Enabling Real-Time OFDM Processing at 392 Gbit/s and Beyond

D. Hillerkuss1, A. Marculescu1, J. Li1, M. Teschke1, G. Sigurdsson1, K. Worms1,

S. Ben Ezra2, N. Narkiss2, W. Freude1, J. Leuthold1 1: Institute of Photonics and Quantum Electronics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany,

2: Finisar Corporation, Nes Ziona, Israel Author e-mail address: Hillerkuss@kit.edu

Abstract: An optical FFT scheme is implemented and tested at 392 Gbit/s. It enables OFDM sig-nal processing way beyond the bandwidth limits of electronics. The scheme operates with little energy as it exp loits passive optical components. ©2010 Optical Society of America OCIS codes: (060.4510) Optical communications; (070.2025) Discrete optical signal processing.

1. Introduction OFDM holds promise for next generation transmission systems ‎[1], because large spectral efficiency, high band-width and ultra-long haul transmission without dispersion compensation can be expected. However, trans mitter and receiver need to calculate the inverse fast Fourier transform (IFFT) or the fast Fourier transform (FFT), respectively. While electronic signal processing is possible at 10 Gbit/s and potentially at 40 Gbit/s, future core channel bitrates are expected to operate at 100 Gbit/s and up to 1 Tbit/s ‎[2], where electronic processing is difficu lt and severe power consumption issues arise.

An optical implementation of the FFT has been demonstrated by Sanjoh et al. in 2002 ‎[3]. Here, an N × N wa-veguide grating router arrangement has been chosen. A number of N phase stabilization elements were simulta-neously optimized with respect to their relat ive phases. While this is an interesting approach, it still requires the sta-bilization of N phases, and the complexity is unnecessarily high if, e .g., only one subcarrier is to be received.

In this paper, we introduce a simple all-optical implementation of a FFT algorithm performing simultaneous serial-to-parallel (S/P) conversion and FFT calculation within a cascade of delay interferometers (DIs). An equiva-lent IFFT scheme would apply for the transmitter. We demonstrate real-time FFT processing of a 392 Gbit/s OFDM signal, and direct detection of its 9 OFDM subcarriers. As our new scheme requires only passive DIs (as in all such schemes, time gating/sampling elements are required in addit ion), it scales well with the bitrate (potentially enabling Tbit/s-OFDM), and it requires a very s mall amount of energy. 2. All optical fast Fourier transform The discrete signal spectrum Xm is the discrete Fourier transform, a sum of weighted time-samples xk,

1 j 2

0, 0, 1

mkNN

m kk

X x e m Nπ− −

=

= = …, −∑ . (1)

The FFT performs this operation for a sample number N = 2n more efficiently. In 1987 Marh ic ‎[4] suggested an opt-ical FFT implementation. We depict this solution in Fig. 1(a) for N = 4. The S/P conversion, FFT processing and time gating provide the frequency-samples Xk. The number of couplers is the complexity std 21 ( / 2)logC N N N= − + ,

TS/2TS/4

3TS/4

SamplingOptical FFT

∆

∑

∆

∑

∆

∑

∆

∑

S/P Conversion

SamplingCombined S/P Conversion & Optical FFT

SamplingCombined S/P Conversion & Optical FFT

SamplingCombined S/P Conversion & Optical FFT

TS/4

(c)

(b) (d)

(a)

(-j)

(-j) (-j)

(-j)

TS/4

TS/4TS/4

TS/2

TS/2

TS/2

TS/4TS/2

3TS/4

Fig. 1: Exemplary 4-point optical FFT ‎[4] for OFDM symbol duration 1 /ST f= ∆ . (a) Implemented traditionally ‎[5] with S/P conversion, FFT and sampling, two paths are switched (b), leading to a structure consisting of two delay interferometers with the same differential delay. The additional TS/4 delay is moved out of the second DI (c), which leads to two identical DI that can be replaced by a single DI followed by signal splitters (d). This scheme represents our new simplified S/P conversion and FFT scheme.

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and the optical phases in all 2log ( )N N arms of the FFT structure must be stabilized with respect to each other, the-reby limiting N to a small number for practical cases. An implementation of the Marhic approach for N = 4 needs a total number of 7 optical couplers and 8 differentially phase-stabilized arms. Nonetheless, this way, 100 Gbit/s OFDM transmission with N = 2 subcarriers processed in a single FFT stage has been demonstrated recently ‎[5].

However, the 2log ( )N N scaling of the required stabilized phase shifters renders the scheme impract ical for large N. Yet, a simplification is possible. After combin ing and rearranging the elements of the S/P and FFT stage (see Fig. 1(b,c,d)), a functionally equivalent structure results. The new optical FFT processor consists only of 1N − cascaded DIs with a small complexity of only DI 2( 1)C N= − couplers, where DI stdC C N≤ ∀ . Also, in this implemen-tation only the phase of 1N − DIs needs stabilizat ion, and no inter-DI phase adjustment is required. The subsequent time gates define the FFT window. It has to be aligned to the OFDM symbols fo r suppressing intersymbol and inter-carrier interference. For N = 4 the new solution requires only 3 phase stabilizations and 6 couplers.

An additional simplification is obtained for N > 4. It can be shown that the first two DI stages have the largest impact on the overall performance, so that only two DI stages are needed, and any additional DI can be replaced by passive splitters and bandpass filters thereby simplify ing the FFT processing even further. It needs to be clarified, that for N = 2 our new implementation and the implementation by Marhic ‎[4 ‎,5] lead to an identical structure. Our novel FFT scheme has a reduced complexity DI stdC C< for N > 2, or if on ly a subset of subcarriers is to be received.

In the following, we demonstrate an FFT for N = 9 subcarriers using only the first two stages of the DI cascade together with a bandpass filter for selecting the subcarrier of interest. 3. Experimental implementation and results The OFDM receiver-transmitter pair is shown in Fig. 3. The transmitter is quite similar to the coherent-WDM transmitter proposed in ‎[6] but it does not require any phase stabilization. It employs a 50 GHz optical comb genera-tor ‎[7] to generate 9 OFDM subcarriers (A). A disinterleaver separates the odd and even subcarriers that are indivi-dually encoded with DBPSK (B) and DQPSK (C) signals, respectively. The OFDM signal is generated by combin-ing the odd and even channels (B/C) in an optical coupler (D).

The signal with the spectrum D is really an OFDM signal, and not a dense WDM signal. First, one clearly sees from B/C and D that the subcarriers strongly overlap with neighboring subcarrier sidebands. Second, we checked the quality of reception experimentally and with simulat ions for many possible receiver filter shapes. A penalty-free detection is only possible with an FFT receiver. As the orthogonality of the subcarriers has to be maintained for the duration of the OFDM symbols 1 / 20psST f= ∆ = , rise and fall t imes Rise, FallT of the available transmitters have to be excluded by introducing a guard time GT . This results in a symbol rate R that is lower than the frequency spacing ∆f of the subcarriers. An additional increase of the guard time increases the available sampling window for the re-

Fig. 2: Setup of OFDM transmission system. Two cascaded Mach-Zehnder modulators generate an optical frequency comb A, which is split by a disinterleaver into 4 odd and 5 even channels. Spectrally adjacent subcarriers are modulated differently using decorrelated DBPSK B or DQPSK modulators C, respectively. All subcarriers are combined in a coupler ( ) and transmitted D. The OFDM nature of the signal is demonstrated by the spectral overlap of subcarriers with neighboring subcarrier sidebands, B/C and D. The received OFDM signal D is processed using the “S/P converter & FFT” (D, E), where following DI stages are replaced by passive splitters ( ) F and optical bandpass filters. The resulting signals are sampled by electro-absorption modulators (EAM) G and detected using DBPSK and DQPSK receivers. Ei-ther eye diagrams D, G, H, J, or bit error probabilit ies BER (Fig. 3) were measured with a BERT. Spectra are plotted with 20 dB/div (verti-cally) and 2 nm/div (horizontally) in a resolution bandwidth of 0.01 nm, center of plotted spectra located at 1550 nm.

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ceiver. The chosen guard time of 15.7 ps effectively reduces the symbol rate R to 28 GBd, Eq . (2),

/

1 1 1, .SS G S Rise Fall

R TT T T T f

= ≤ =+ + ∆

(2)

Both DBPSK as well as in -phase and quadrature DQPSK signals were electrically decorrelated by RF delays. The resulting signals are combined to generate the 392 Gbit/s OFDM signal (D) with a symbol rate of 28 GBd. The limi-tations of our setup restrict us to 27 − 1 long PRBS for BER measurements.

The receiver comprises the new all-optical FFT scheme followed by a p reamplified receiver with differential d i-rect-detection. The FFT processor comprises a cascade of two DI, fo llowed by passive splitters and bandpass filters (explained in the previous section), and the EAM sampling gates. The first DI suppresses every second subcarrier (E), the second DI every fourth subcarrier (F). The bandpass filter finally selects one of the remain ing carriers (G). The intercarrier and intersymbol interference (see eye diagram G) is suppressed by an optical gate, which sets the FFT window. Bit erro r probabilities (BER) fo r each subcarrier have been measured (J, H).

For evaluating the FFT performance we compared the optically processed subcarriers with back-to-back (B2B) signals delivered by the DBPSK and DQPSK trans mitters, respectively. The results depicted in Fig. 3 show no pe-nalty compared to the B2B performance for DBPSK and only a small penalty for the DQPSK channels. The outer channels −4 and 4 perfo rm worse, because their subcarriers have 11 dB less power compared to the center channel. 4. Conclusions We demonstrated for the first time an all-optical FFT based on cascaded DI, and implemented an OFDM receiver that showed showing no penalty compared to single-channel B2B performance. The scheme potentially enables ul-tra-fast OFDM transmission with state-of-the-art electronics. Acknowlegements David Hillerkuss and Jingshi Li acknowledge financial support from the Karlsruhe School of Optics & Photonics (KSOP) and the German Research Foundation (DFG). 5. References [1] W. Shieh et al., “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett., vol. 42, no. 10, pp. 587–589, (2006). [2] D. J. Geisler et al., “3 b/s/Hz 1.2 Tb/s packet generation using optical arbitrary waveform generation based optical transmitter,” in Proc.

OFC‘09, JThA29 (2009). [3] H. Sanjoh et al., “Optical orthogonal frequency division multiplexing using frequency/time domain filtering for high spectral efficiency up to

1 bit/s/Hz,” Proc. OFC 2009, ThD1 (2009). [4] M. E. Marhic, “Discrete Fourier transforms by single-mode star networks,” Opt. Lett., vol. 12, no. 1, pp. 63–65, (1987). [5] Y.-K. Huang et al., “Dual-polarization 2×2 IFFT/FFT optical signal processing for 100-Gb/s QPSK-PDM all-optical OFDM,” Proc. OFC

2009, OTuM4 (2009). [6] A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett., vol. 17, no. 2, pp.

504–506, (2005). [7] T. Healy et al., “Multi-wavelength source using low drive-voltage amplitude modulators for optical communications,” Opt. Express, Vol. 15,

no. 6, pp .2981-2986, (2007)

-45 -40 -35 -30 -25 -2011

9

7

5

3

-log(

BER)

Rx Input Power [dBm]

DQPSK CH -4 DBPSK CH -3 DQPSK CH -2 DBPSK CH -1 DQPSK CH 0 DBPSK CH 1 DQPSK CH 2 DBPSK CH 3 DQPSK CH 4 DQPSK Back-to-Back DBPSK Back-to-Back

DBPSK Carriers

DQPSKCarriers

Fig. 3: BER performance of different subcarriers. No penalty compared to back-to-back performance for DBPSK carriers (−3, −1, 1, 3), no significant penalty for the central DQPSK carriers (−2, 0, 2), a 5 dB penalty or error floor for the two outer DQPSK subcarriers with 11 dB less power in the optical comb (−4, 4).

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