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We propose and experimentally demonstrate a no-guard-interval (No-GI) coherent optical orthogonal frequency division multiplexed (CO-OFDM) system that uses Fractionally-Spaced Time-Domain Equalizers (FS-TDE) to simultaneously demultiplex and equalize each subcarrier. Least-mean-squares algorithms (LMS) tune each FS-TDE to a subcarrier. A short unique training sequence is transmitted on each subcarrier, allowing each FS-TDE to lock onto its subcarrier. After the initial training, the adaptive blind equalizers remain tuned to their respective subcarriers. Unlike previous systems, this system does not require digital filtering or mixing of each subcarrier to baseband, so is more computationally efficient. Error-free transmission was measured over 800 km of fiber with a three-subcarrier 30 Gb/s system and a five-subcarrier 33.33 Gb/s system. The required OSNRs for a BER of 10−3 were 8.6 dB and 9.3 dB respectively, which are within 1.5 dB of the theoretical limit for coherent systems.
©2011 Optical Society of America
1. Introduction
Coherent optical communications systems have the ability to compensate for linear impairments such as chromatic dispersion (CD) and polarization mode dispersion (PMD) electronically [1], thus the capacity of any system is limited mainly by fiber nonlinearity [2]. Recent studies investigating fiber nonlinearity compensation for OFDM systems suggest minimizing the Peak-to-Average-Power-Ratio (PAPR) within narrow frequency bands is more beneficial than minimizing PAPR for the entire 100 Gb/s or 400 Gb/s signal [3, 4]. This suggests that it would be more optimal to transmit multiple closely-spaced low-rate carriers in preference to a single high-rate carrier.
No guard-interval coherent optical OFDM (No-GI CO-OFDM) uses several lower rate carriers, and is a suitable candidate for 100 GE optical transport for ultra-long haul distances [5, 6]. By using orthogonal subcarriers, the usual spectral guard bands present in WDM systems can be avoided, which maximizes spectral efficiency [6]. Recently, various methods of demultiplexing the subcarriers in No-GI CO-OFDM have been proposed, including optical [7, 8] and electrical [5, 9] methods. Optical methods involve building an optical circuit [10], such as an array of couplers [7] or an arrayed waveguide grating that has a similar response to a Discrete Fourier Transform (DFT) [8]. Optical methods minimize the digital complexity but require a separate coherent receiver for each subcarrier. Electrical methods involve receiving multiple subcarriers with a single coherent receiver and separating the subcarriers digitally. Previously proposed electrical methods have all used digital mixers and filters, which require a substantial amount of computation [5, 9].
In this paper, we propose a self-tuning digital receiver which simultaneously demultiplexes and equalizes multiple OFDM subcarriers. These subcarriers could be be generated in a transmitter using multiple lower-bandwidth optical modulators. Using a unique training sequence for each subcarrier, an adaptive fractionally-spaced time-domain equalizer (FS-TDE) can be made to search-out then lock onto a specific subcarrier, regardless of the spectral location of the subcarrier. After the initial training, blind adaptive equalizers can be used to track time-variant impairments. Our method of digital subcarrier demultiplexing does not require mixing down to baseband or filtering, thus reduces the number of computations.
We experimentally demonstrate a dual polarization (DP) three-subcarrier system carrying 30-Gb/s and five-subcarrier system carrying 33.33 Gb/s. This bit rate was limited by the Analog-to-Digital Converters (DAC), which are used to generate the multicarrier signal in this demonstration. After transition through 800 km of standard single mode fiber (S-SMF), error-free reception is observed for OSNRs above 15-dB for both systems. For a BER of 10−3, the three- and five-subcarrier systems require OSNRs of 8.6 dB and 9.3 dB (0.1 nm) respectively.
2. Equalizer description
Figure 1a shows a block diagram of the digital signal processing algorithms for a DP No-GI CO-OFDM as presented by Sano et al. [5]: the mixer and DFT are used to separate the subcarriers. The FS-TDE is an adaptive Finite Impulse Response (FIR) filter with N-taps and decreases the sampling rate by S, where S is the number of samples per symbol [11]. Because mixers, DFTs and FIR filters are all linear, it is possible to combine all three operations as shown in Fig. 1b. The FIR filters can be tuned to give any response with a maximum impulse response of Ntaps, where Ntaps is the number of taps used in the filter. A DFT of size NDFT has an impulse response length NDFT. Therefore, for cases where Ntaps>NDFT, it is possible to incorporate the response of the DFT into an FIR filter. A mixer can also be incorporated into the FS-TDE by multiplying all the taps in the FIR filter by the mixing frequency, which transforms a low-pass filter into a band-pass filter. The down-sampling in the FS-TDE will then cause subcarriers not centered on DC to be aliased back to baseband. Therefore, no additional computations are required in the FS-TDE for systems where the number of equalizer taps is greater than the number of subcarriers; this has been the case for all previously demonstrated No-GI CO-OFDM systems with digital PMD compensation [5, 9].
Fig. 1 Receiver structures: (a) previous design [5]; (b) proposed simplification where the Mixer, DFT and FS-TDE functions are replaced by a single FS-TDE function.
The filter coefficients for a FS-TDE that receives multiple subcarriers cannot be easily found using blind techniques such as the Constant-Modulus-Algorithm (CMA) [12]. For each subcarrier, there will be a local minimum in the error vector of the CMA. Unfortunately the CMA cannot differentiate between these minima [12]; thus it is possible that each FS-TDE will converge (tune) to the same subcarrier. As a solution, we propose transmitting a short, unique training sequence at the start of each subcarrier. This allows a training-based algorithm, such as the Least-Mean-Squares algorithm (LMS), to select the subcarrier with the expected training sequence, so long as the receiver knows the training sequences for the subcarriers. Optimally, the training sequences should be close to orthogonal to one another such as pseudo random bit sequences generated with well-chosen seeds. This training is only required once on system startup. After the filter response has converged on the desired subcarrier, the error vector for the CMA will lock to the local minimum. Time-varying effects such as PMD can then be tracked with the CMA, which will make minor adjustments to the filter tap coefficients to keep the FS-TDE locked. Alternatively, it should be possible to set the initial values of the equalizer taps directly such that each FS-TDE is initially centered on a different subcarrier. However, such an implementation was not investigated in this paper.
Figure 2a shows the amplitude response of the converged filters for a single polarization, three-subcarrier, back-to-back system. LMS was used on a 512-symbol training sequence to converge the filters around the three subcarriers before switching to CMA for another 2048 symbols. It can be seen that the final responses of the filters are close to sinc functions, with characteristically-strong sidelobes and overlapping passbands. Each output of a Discrete Fourier Transform (DFT) also has a sinc response [8, 10]. Thus each FS-TDE behaves as one output of a DFT once trained. The received constellations of this three-subcarrier optical back-to-back system are shown in Fig. 2b. The small spread around each data symbol suggests that the crosstalk between subcarriers is very low, confirming that the filters are acting like a DFT in that they maximize the orthogonality of the subcarriers.
Fig. 2 Results from a single-polarization 3-subcarrier back-back system: (a) amplitude response of the FS-TDE after locking; (b) equalized constellations. SC – subcarrier.
3. Long-haul experimental setup
Figure 3 shows the experimental setup for an 800-km system. The OFDM signal was generated in MATLAB. A Tektronix AWG7102 Arbitrary Waveform Generator (AWG), with two outputs operating at 10 Gsample/s, was used as DACs to generate the In-phase and Quadrature components of the signal. Two 5-GHz electrical low pass filters (LPF) were used to remove the image from the generated electrical signals. Minicircuits® 14-GHz microwave amplifiers were used to drive a Sumitomo 40-Gbps C-MZM. The optical source was an Agilent External Cavity Laser (ECL) with a linewidth of ~100 kHz. The modulated optical signal was split with a polarization beam splitter (PBS) with its input polarization aligned so that the power was split evenly between the two outputs. A one-meter long polarization maintaining fiber patch lead was used as a delay line to decorrelate the two signals before they were recombined with another PBS to generate a polarization multiplexed signal. DACs were used to generate the subcarriers because of the cost of five C-MZMs. We expect the receiver to work for subcarriers generated from separate optical modulators at higher bit-rates as long as they are orthogonal.
The optical link consisted of 10×80-km spans of S-SMF. The loss of each span was compensated by an EDFA. The optical launch power into each span was kept below −4 dBm in order to avoid fiber nonlinearity. The effects of fiber nonlinearity will be investigated in a subsequent paper. The received Optical Signal to Noise Ratio (OSNR) was controlled by changing the launch powers of the EDFAs and the attenuation of variable optical attenuator (VOA) and measured using an Agilent 86142B Optical Spectrum Analyzer (OSA) with a resolution bandwidth of 0.1 nm. A Finisar WaveShaper (programmed to have a 50-GHz passband centered on the laser wavelength) was used as an optical filter to remove the out-of-band ASE before the receiver. At the receiver, a Kylia dual-polarization 1×8 optical hybrid and four pairs of u2t Photonics balanced photodiodes detected the optical signal. The optical local oscillator (LO) was taken from the transmitter laser with a 3-dB optical coupler. The propagation delay through 800 km of fiber is well in excess of the coherence time of the laser; thus, the LO is uncorrelated with the transmitter laser. A Tektronix DSA72004 real-time digital sampling oscilloscope (DSO), sampling at 50 Gsample/s on each of its four inputs, was used as the ADCs.
Two different systems were tested: a three-subcarrier system and a five-subcarrier system. The three-subcarrier signal was generated with a four-point IFFT and the five-subcarrier signal was generated with a six-point DFT. For both, only the Nyquist frequency was zeroed, with all other subcarriers carrying data. The three-subcarrier system had a bit rate of 30 Gb/s and 97436 randomly generated symbols were transmitted, which contained 1.17 million bits. The bit rate for the five-subcarrier system was 33.33 Gb/s and 64957 symbols were transmitted; this corresponds to 1.3 million bits. The sampling rate of the DACs limited the maximum transmission rates that could be used. The optical spectra of the two systems were measured with an Agilent High-Resolution Spectrometer (HRS) and are shown in Fig. 4 .
Fig. 4 Transmitted optical spectrum measured with a HRS: (left) 3-subcarriers; (right) 5-subcarriers. Colored arrows illustrate the positions of the subcarriers within the signal.
Digital equalization was performed in MATLAB® using the equalizer described in Section 2. Firstly, the digital signal was down sampled to 10 Gsample/s to match the sampling rate of the transmitter’s DACs. The bulk of the CD was removed from all subcarriers with a frequency domain equalizer using the overlap-add algorithm [5, 9]. The values of the FS-TDE for each subcarrier were set with an LMS algorithm [11]; the first 512 data symbols from each subcarrier were used as training. The step size used for LMS was 0.02. CMA [12], with a step size of 0.001, was then used to fine tune and update the filter coefficients in the FS-TDE. Finally, the phase noise from each subcarrier was compensated independently with the Viterbi-Viterbi algorithm [13].
4. Experimental results
Figure 5 shows the received constellation after transmission over 800 km of S-SMF for the three-subcarrier system (a), and five-subcarrier system (b). A 12-tap FS-TDE was used for the three-subcarrier system. The received OSNR, measured with the OSA set to a resolution bandwidth of 0.1 nm, was 15.3 dB. The five-subcarrier system used a 16-tap FS-TDE and the received OSNR was 15.2 dB. Error-free transmission was achieved in all subcarriers of both systems. After receiving all of the symbols, the filter response of the adaptive FS-TDE remained centered on the subcarrier selected by LMS during training.
Fig. 5 Received constellations after 800 km arranged according to the subcarrier’s frequency: (a) 3-subcarrers, OSNR of 15.3 dB; (b) 5-subcarriers, OSNR of 15.2 dB.
The Qconst, shown for each subcarrier in Fig. 5, is calculated from the spread in the equalized constellations [14]. This shows that the signal qualities were similar for all subcarriers, with the outer most subcarriers having a slightly lower Qconst. Degradation from linear crosstalk would be most significant on the middle subcarrier because it has the maximum number of neighbors. This suggests linear crosstalk is not a significant source of degradation and the proposed equalizer is effective in subcarrier demultiplexing after 800 km of transmission. The degradation of the outer channels could be due to the truncation of their sinc responses, due to the DAC’s response, the subsequent image rejecting electrical LPFs and other bandwidth limitations, as studied in [8].
The received QBER is plotted against the OSNR in Fig. 6 for both systems after 80 km (◊) and 800 km (◯).An 80-km system was used instead of an optical back-to-back system because the 80-km link was required to decorrelate the phases of the transmitter laser and LO. The received QBER was calculated from the average BER count of all the subcarriers assuming a Gaussian distribution. The FEC limit is shown at a Q of 9.8 dB which corresponds to a BER of 10−3. The ASE-limited Q (green dashed lines) are calculated from the OSNR assuming that the only source of degradation is additive white Gaussian noise, generated by Amplified Spontaneous Emission (ASE). Note that the ASE-limited Q is 0.5 dB lower for the five-subcarrier system because of the higher bit rate.
Fig. 6 Average BER against OSNR measured in a 0.1 nm bandwidth: (a) 3-subcarriers; (b) 5-subcarriers.
The graphs show that the degradation in QBER after the 800-km link, compared to the 80-km link, for both systems was very small, indicating that the fiber impairments are almost fully compensated by the digital equalizer. For the three-subcarrier 30 Gb/s system, the required OSNR for a BER of 10−3 was 8.5 dB after 80 km and 8.6 dB after 800 km, around 1-dB higher than the ASE-limited Q of 7.6 dB. For the five subcarrier 33.33 GB/s system, OSNRs of 9.5 dB and 9.3 dB were required after 80 km and 800 km respectively, less than 1.5-dB above the ASE-limited Q of 8.1 dB. This suggests that the OSNR penalty from linear crosstalk was negligible after 800 km for a BER of 10−3.
5. Conclusion
In this paper, we have proposed and experimentally demonstrated a novel method which simultaneously demultiplexes and equalizes No-GI CO-OFDM signals. An adaptive FS-TDE was used to separate and equalize each subcarrier. By using a unique training sequence for each subcarrier, the LMS algorithm converged to give a bandpass filter with a sinc-like response, minimizing linear crosstalk. Separate digital filters, DFTs or mixers used in previously proposed systems were not required. The multiple subcarriers were generated with an IFFT followed by a DAC, which allowed multiple lower-rate subcarriers to be generated with a signal C-MZM. Error-free transmission after 800 km was experimentally demonstrated for a three-subcarrier 30 Gb/s system and a five-subcarrier 33.33 Gb/s system. The required OSNR after 800 km for a BER of 10−3 was 8.6 dB for the three-subcarrier system and 9.3 dB for the five-subcarrier system. This shows that the proposed demultiplexing and equalization method is suitable for long-haul optical systems with multiple orthogonal subcarriers.
Acknowledgements
This work is supported under the Australian Research Council’s Discovery funding scheme (DP1096782).
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