1. Introduction

Increasing the spectral efficiency has been shown to be an effective way when scaling up the data rate. Nyquist pulse shaping signal has rectangle-like spectrum which is similar to orthogonal frequency division multiplexing (OFDM), and they indeed have comparable spectral efficiency under the same modulation format. In [1] 7 × 224Gb/s Nyquist wavelength-division multiplexing (WDM) signal is demonstrated for transmission over 1200km SMF-28 with a spectral efficiency of 7.47b/s/Hz. In [2], PDM-32QAM Nyquist pulse shaping signal is generated for 450 Gb/s per-channel WDM transmission on the 50 GHz ITU-T Grid with a spectral efficiency of 8.4b/s/Hz. In both [1] and [2], blind equalization in time domain is implemented in the frame of multi-modulus constant modulus algorithm (CMA) based polarization de-multiplexing.

Frequency-domain estimation and equalization (FDE) has been proposed for wireless communication and adopted in 3rd generation long-term evolution [3]. Blind time domain equalization for Multi-level quadrature amplitude modulation (M-QAM) signal usually requires format-orientated multi-modulus phase recovery and polarization de-multiplexing. In contrast, FDE performs channel estimation based on training sequences, which offers a uniform frame to estimate transfer function of channel response for different M-QAM formats. FDE can be combined with both multicarrier (such as OFDM) and single carrier (the so called SCFDE) techniques. Both OFDM and SCFDE are resilience to linear channel impairments such as chromatic dispersion (CD) and polarization mode dispersion (PMD) due to cyclic extension in block-to-block operation with fast Fourier transform (FFT). However, the insertion of cyclic prefix (CP) and cyclic suffix (CS) requires more redundancy that decreases the spectral efficiency. Overlap FDE is thus used to combat inter-block-interference (IBI) [4], which, however, would increase calculation complexity compared to CP based FDE.

In Nyquist pulse shaping system, since the signal bandwidth is approximately equal to the symbol rate, the conventional FDE (processed by one sample per symbol) is effective according to the Nyquist sampling theorem. In this paper, we propose a scheme of combining Nyquist pulse shaping signal with the SCFDE technique, which is the so called Nyquist- SCFDE. Compared to OFDM, Nyquist SCFDE has lower peak-to-average-power ratio (PAPR) and similar frame of digital signal processing (DSP). Like OFDM, Nyquist SCFDE also has rectangle-like spectrum, which enables high-speed superchannel transmission with tightly spaced optical subcarriers. Moreover, to improve transmission efficiency, we develop a modified CP-free SCFDE technique by performing training sequence based channel estimation in frequency domain and finite impulse response (FIR) filter based channel equalization in time domain. This scheme is basically format-transparent, suitable for parallel implementation and independent of carrier phase recovery. Based on the above mentioned technique, we demonstrate the generation and transmission of Terabit Nyquist pulse shaping superchannel.

The paper is outlined as follows. In Section 2, we present the Nyquist SCFDE scheme and the principle of the modified SCFDE. Section 3 describes the experimental setup for the generation and transmission of a 7.06b/s/Hz, 1.76Tb/s PDM-16QAM superchannel with 40 subcarriers. In Section 4, the experimental results are reported after transmitting over 714 km standard single-mode fiber (SSMF). Finally, we summarize this paper in Section 5.

2. Nyquist pulse shaping and the modified SCFDE scheme

Figure 1 illustrates the diagram of the transmitter and receiver DSP of Nyquist-SCFDE systems. The information data would be firstly mapped into M-QAM format and then packed into Nyquist-SCFDE frames at the transmitter. After inserting pilots in the data, the preamble including both synchronization and training sequences are inserted into the front of Nyquist-SCFDE frame. After 2 samples per symbol up-sampling, both in-phase and quadrature components of the Nyquist-SCFDE signals are digitally shaped with root-raised-cosine (RRC) filters. After digital to analog convertors (DAC), low-pass filters are used as anti-aliasing filters to remove out-of-band radiation.

 

Fig. 1 (a) Generation of Nyquist pulse shaping signal. (b) Block diagrams of the receiver Offline DSP.

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At the receiver, a FIR filter roughly compensates the accumulated CD. Then the carrier frequency recovery is conducted by a phase increment estimation algorithm well known in wireless communication [5]. A matched receiving RRC filter is adopted to satisfy the Nyquist first criterion. After synchronization, the training sequences are picked up for channel estimation, and then the modified SCFDE is performed. The phase is corrected with pilots and then averaged with the Viterbi-Viterbi method [6].

Figure 2 compared the conventional and the modified SCFDE algorithm. In the conventional SCFDE, data symbols are grouped into blocks, and cyclic insertion in both data and training sequences ensures that no IBI exists. In Fig. 2(a), after removing CP and CS, the training sequences are transformed into frequency domain to estimate channel transfer function. Then one-tap zero forcing equalization is performed in frequency domain. After equalization, the data signal is transformed to time domain for further DSP. The conventional SCFDE requires ${\rm O}(2N{\log }_2(N)+2N)$ multiplications for a block of N-point fast Fourier transform (FFT), which has lower complexity than TDE with long channel impulse response, such as the case of large amount CD accumulation. For short channel impulse response, we propose a modified SCFDE technique, in which transfer function is estimated in frequency domain with training sequence and channel equalization is performed in time domain by transforming the inverse of transfer function to FIR filter.

 

Fig. 2 Block diagrams of (a) the conventional SCFDE, and (b) the modified SCFDE.

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_{$s_{tr}(n)$} and $r_{tr}(n)$ are the sending and receiving training sequences respectively, and their frequency domain form are $S_{tr}(k)$and $R_{tr}(k)$.$C(k)$is the conventional frequency domain equalizer taps.$\tilde{H}(k)$is the estimated channel transfer function.$c(l)$is the FIR taps and $c(l)=IDFT(C(k))$. Time domain FIR equalization takes ${\rm O}(L)$multiplications for each symbol, where $L$ is the amount of non-zero taps. Note that in the modified SCFDE, frequency domain channel estimation is based on training sequence with cyclic extension, while data always keeps in time domain. In doing so, there is no need to insert CP/CS into data signal, resulting in higher transmission efficiency. If$L<2{\log }_2(N)+2$, which means the accumulated CD is not too large or it has been compensated upon receiving, the modified SCFDE has lower complexity than the conventional SCFDE.

3. Experimental setup

Figure 3 shows the experimental setup for the generation and transmission of 1.76Tb/s PDM-16QAM Nyquist-SCFDE superchannel. Four lasers with 62.5GHz spacing are combined by cascaded 2x1 polarization-maintain optical couplers (OC). An arbitrary waveform generator (Tektronix AWG7122B) operating at 11.2GSample/s with 2-point DAC upsampling generates baseband electrical Nyquist signals of 5.6Gbaud/s. Root-raised-cosine (RRC) filters with a roll-off factor of 0.07 are chosen for Nyquist pulse shaping. Analog electric low-pass filters (ELPF) with 3dB bandwidth of 4.4GHz are used as anti-aliasing filtering.

 

Fig. 3 Experimental setup of Nyquist-SCFDE superchannel generation and transmission.

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Four original odd subcarriers are obtained after IQ modulator 1 and then split into two streams by OC. The lower stream passes directly without any change while the upper one is frequency shifted through a single-sideband modulator [7], which is implemented by driving IQ modulator 2 with 6.25GHz radio frequency (RF) signal. We use two phase shifters (PS) to adjust the phase difference between two arms. Before being combined by OC, the even and odd subcarriers are delayed by different length of patch cords for de-correlation. Then the eight coupled subcarriers pass through a 5-tone generator, which is realized by driving the intensity modulator with the combination of 12.5GHz and 25GHz RF signals [8]. PDM is emulated with a polarization beam splitter/combiner (PBS/PBC), and a tunable optical delay line. After PDM emulator, a Nyquist PDM-16-QAM superchannel with 40 subcarriers is obtained with 6.25GHz subcarrier spacing. The transmission loop has a length of about 238km, which consists of three spans of SSMF with Erbium-doped fiber amplifier (EDFA) only amplification. No inline chromatic dispersion compensation is used. In the loop, we apply an optical band pass filter (OBPF) with a bandwidth of 2.07nm to suppress noise accumulation. A loop controller drives the two optical switches and triggers the acquisition of the oscilloscope.

At the receiver, a waveshaper (Finisar-4000s) with a minimum 3dB bandwidth about 10GHz is used as receiving filter to remove out-of-band noise. As the subcarrier spacing is 6.25GHz, the adjacent subcarriers will be partially included and should be removed by further electrical filtering in the receiver side DSP. The coherent receiver consists of 90° optical hybrid, an optical local oscillator (LO) and four balanced detectors (BD). The real-time sampling oscilloscope (Tektronix DPO72004B) operating at 50GSample/s stores the electrical waveforms for processing offline. Both the transmitter and the LO lasers have a linewidth of about 100 kHz.

The frame structure of Nyquist-SCFDE signals is shown in Fig. 4. Two 63-bit M-sequences are used for synchronization. Pairs of time-multiplexed training sequences are across the two polarizations, denoted as$t_1$ and $t_2$.

 

Fig. 4 Frame structure of PDM-Nyquist SCFDE signals.

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Figure 5(a) shows the optical spectrum of 1.76Tb/s PDM 16-QAM Nyquist-SCFDE signal. The superchannel occupies 2.0nm bandwidth with two subcarriers in each 12.5GHz grid. The resolution is set as 0.01nm to see spectrum details of the subcarriers. The black line shows the signal spectrum for the back-to-back case. The red line shows the spectrum after 238km SSMF transmission and the blue line shows the spectrum after 238km transmission and OBPF filtering. Figure 5(b) shows the received 37th subcarrier optical signal after filtering with part of two neighbors included.

 

Fig. 5 Optical spectra of (a)PDM 16-QAM Nyquist-SCFDE signal of back-to-back and after 238 km SSMF transmission; (b)the received optical signal after filtering.

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4. Results and discussions

Figure 6 shows the back-to-back bit-error-rate (BER) performance of the superchannel as a function of optical signal-to-noise ratio (OSNR) at 0.1nm resolution. The original single carrier is the signal out of the modulator 1 in Fig. 3 with only one laser on. The required OSNR of the superchannel at the BER of 1.0 × 10⁻³ is 30.5dB, which is 16.3dB larger than the original single carrier, showing that the PDM-16QAM Nyquist pulse shaping signal has a small penalty of 0.3dB for subcarrier aggregation. The insert in Fig. 6 shows a typical recovered constellation of the 37th subcarrier at OSNR = 36.3dB.

 

Fig. 6 Back-to-back BER performance

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Figure 7 shows the BER of 37th subcarrier versus launch power per subcarrier over 714km SSMF. The optimal power is −10dBm/subcarrier. The performance of the modified FDE is comparable to the 3-stage time domain equalization strategy [9], which consists of the CMA, the cascaded multi-modulus algorithm (CMMA), and the decision-directed least-mean-square (DD-LMS) algorithm. Figure 8 shows the measured BER results of all 40 subcarriers after 714km SSMF transmission with the optimal launch power. The inserts are constellations of both polarizations of the 30th subcarrier, which has the worst performance. The BER of each subcarrier is lower than 3.8 × 10⁻³, which is the threshold for 7% forward error correction (FEC) overhead. The BER of each subcarrier is measured based on 10⁶ bits data, and the average BER for the entire superchannel is 2.2 × 10⁻³.

 

Fig. 7 Measured BER of 37th subcarrier over 714km SSMF.

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Fig. 8 Measured BER for Nyquist pulse shaping superchannel over 714km SSMF

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5. Conclusions

We experimentally demonstrate the generation and transmission of 1.76Tb/s PDM-16QAM Nyquist pulse shaping signal with spectral efficiency of 7.06b/s/Hz using the modified SCFDE technique. Considering its high spectral efficiency and low penalty in multi-carrier aggregation, Nyquist pulse shaping signal with high order modulation such as 16-QAM format is a good choice for superchannel transmission.