## Abstract

We present a detailed comparison of applying three advanced modulation formats including pulse amplitude modulation-8 (PAM-8), carrier-less amplitude and phase modulation-64 QAM (CAP-64), and discrete Fourier transform spread orthogonal frequency division multiplexing (DFT-S OFDM) with a bandwidth-limited direct-detection receiver for 100 Gb/s/λ optical transmission systems. These modulation formats are all experimentally demonstrated with corresponding digital signal processing (DSP) algorithms. The comparison is carried out to evaluate the performance of each modulation format in terms of nonlinear equalization, received optical power and optical signal to noise ratio (OSNR). Our experimental results show that only 112 Gbit/s DFT-S OFDM is successfully achieved over 50 km of SSMF under the hard decision-forward error correction (HD-FEC) threshold of 3.8 × 10^{−3}.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Nowadays, the demand of ultra-high data rate optical transmission is growing continuously in data center and other bandwidth hungry interconnect applications. Meanwhile, intensity modulation (IM) and direct detection (DD) optical transmission is considered to be the more attractive and feasible solution for 4-λ 100 Gbit/s wavelength-division-multiplex (WDM) optical interconnect due to the system construction cost, computation complexity and power consumption [1-2].

Recently, a comparison about pulse amplitude modulation-4 (PAM-4), carrier-less amplitude and phase modulation-16 QAM (CAP-16) and discrete multi-tone (DMT) modulation has been demonstrated for short reach optical transmission [3]. However, these experiments were carried out with low spectral-efficiency modulation formats, and they also transmitted signals at 1310 nm with 10 km of fiber transmission. To use 10G-class components for 100G signal transmission or detection can largely reduce the cost of the system. Also if we consider that Erbium-doped fiber amplifier (EDFA) wavelength response locates at ~1550nm, it is important to investigate the transmission performance at this wavelength.

There are a lot of published papers about these three modulation formats, respectively. Using direct detection, 100 Gb/s polarization-division-multiplexed (PDM) PAM-4 over 100 m of SSMF [4], 150 Gb/s PAM-8 over 2 km of SSMF [5] and 120 Gb/s PAM-8 over 2 km of SSMF or 20 km of large effective area fiber (LEAF) [6] are experimentally demonstrated. Bit rates of 221 Gb/s and 336 Gb/s are successfully achieved over 225 km and 451 km of SSMF employing PDM multi-band CAP and a coherent transceiver [7]. And 60 Gb/s CAP-64 over 20km of fiber in a direct-detection system has been reported in [8]. For Orthogonal frequency division multiplexing (OFDM), an 8 × 11.5 Gb/s single sideband (SSB) OFDM direct detection system is achieved over 1000 km of SSMF using eight-band signals [9]. One-band 128 Gb/s OFDM over 10 km of SSMF [10] and multi-band 100 Gb/s OFDM based on offset QAM of 64-QAM (OQAM-64QAM) over 80 km of fiber [11] are experimentally demonstrated. Besides, discrete Fourier transform spread (DFT-S) OFDM is proposed to suppress peak to average power ratio (PAPR) of OFDM signal. 560 Gb/s four-channel DFT-S OFDM transmission over 2.4 km of SSMF is successfully achieved [12].

However, to the best of our knowledge, the performance comparison of these three modulation formats in a bandwidth-limited system has not been reported, especially with a bandwidth-limited receiver. Such comparison is of great value considering the requirements of low cost in interconnect applications. Using the receiver with a 3-dB bandwidth less than 15GHz, PAM-8, CAP-64, or OFDM 64QAM, a relative high order modulation formats are required. In this paper, we present a comprehensive comparison of PAM-8, CAP-64 and DFT-S OFDM 64QAM with a bandwidth-limited direct-detection receiver and corresponding digital signal processing (DSP). These three typical advanced modulation formats are all realized at the same bit rate of 112 Gb/s/λ with a 15 GHz commercial photo detector with trans-impedance amplifier (TIA) integrated (PD, 15 GHz optical bandwidth and 11 GHz electrical bandwidth). The comparison is carried out to evaluate the performance of each modulation format in terms of nonlinear equalization, received optical power and optical signal to noise ratio (OSNR). Finally, only DFT-S OFDM is successfully achieved over 50 km of SSMF under the hard decision-forward error correction (HD-FEC) threshold of 3.8 × 10^{−3}. The reminder of this paper is organized as follows. Section 2 presents the DSP for three modulation formats. Section 3 presents the experimental setup and results in the back-to-back (BTB) case and fiber transmission cases. Section 4 concludes this paper.

## 2. DSP for three modulation formats

In this section, we describe the signal generation flow and recovery flow of PAM-8, CAP-64 and DFT-S OFDM. To compare these three modulation formats fairly, we use the same algorithms with the same parameter setting, such as the tap length and step size of the equalizer in this experiment. All these three modulation formats need mapping, pre-equalization, up- sampling and CD pre-compensation method in the generation process. While CAP has an extra need for IQ separation and shaping filters at the cost of convolution. DFT-S OFDM requires an extra Fast Fourier Transform (FFT) and inverse Fast Fourier Transform (IFFT).

#### 2.1 PAM-8 format

Figure 1 shows the block diagrams of a PAM-8 signal. At the transmitter side, the data is firstly mapped into real symbols of PAM-8 signal. Pre-equalization is employed in time domain with an inverted linear filter. The up-sampling factor is set as 2. A Kaiser window with shape parameter of 5 is used to avoid aliasing and imaging caused by the resampling process. The baud rate is set as 37.5 GBaud to get a 112 Gb/s PAM-8 signal, and the sampling rate of digital-to-analog converter (DAC) is 81.92 GSa/s. After resampling, the signal is pre-dispersed with the inverse of the phase delay cased by chromatic dispersion (CD) [13]. Because of the process of CD pre-compensation, the signal becomes a complex signal. The real and imaginary part of the signal are fed into the upper and lower arms of a dual-drive Mach-Zehnder Modulator (DDMZM) respectively.

During the offline process, the sampled signal is firstly processed by Gardner timing recovery algorithm. Then the data is sent into the nonlinearity equalization (NE) module using a Least Mean Square (LMS) Volterra filter. Considering the tradeoff between computation complexity and equalization performance, only the first-order and second-order terms of Volterra series are used in the calculation. The bit error ratio (BER) performance of the final data is measured after the direct-detection LMS (DD-LMS) and de-mapping process. The tap length of nonlinearity equalizer and DD-LMS are both set as 189 in the whole experiment, which is large enough to achieve the best performance for all the three modulation formats.

#### 2.2 CAP-64 format

Figure 2 shows the block diagrams of a CAP-64 signal. At the transmitter, the data is first mapped into complex symbols of 64-QAM signal. After pre-equalization in time domain with an inverted linear filter, the data is up- sampled by a factor of 4. An IQ separation is used to form a Hilbert pair and a square-root-raised-cosine shaping filter with a roll-off factor of 0.1 is used as a shaping filter. The center frequency is set as 10.3 GHz, while the baud rate of CAP-64 is 18.7 GBaud. The bit rate is still 112 Gb/s and the same CD pre-compensation process is carried out.

During the offline process, the signal is sent into the matched filter to separate the in-phase and quadrature components after the timing recovery and the nonlinearity equalizer. The BER performance of the final data is measured after DD-LMS and de-mapping process.

#### 2.3 DFT-S OFDM format

Figure 3 shows the block diagrams of a DFT-S OFDM signal. At the transmitter, the data is firstly mapped into complex symbols of a 64-QAM signal. Then, a 2048-point FFT is used to generate the DFT-S signal, and an IFFT is used to generate the OFDM signal with 2048 subcarriers after pre-equalization. 2040 subcarriers are used for data transmission due to the DFT-spread technique [12]. And 1 training symbol is used to recover the other 19 symbols for channel estimation. A 32-sample cyclic prefix (CP) is added to alleviate the inter-symbol interference (ISI) incurred by CD. After the parallel-to-serial (P/S) conversion, we do up-conversion to intermediate frequency to generate the real-value DFT-S OFDM signal [15]. In this experiment, the bandwidth of the OFDM signal is 20 GHz. The total bit rate is 111.8077 Gb/s (20 × 6 × $\frac{2048}{2048+32}$ × $\frac{2040}{2048}$ × $\frac{19}{20}$) and the same CD pre-compensation process is added.

During the offline process, the synchronized signal is firstly processed by a nonlinearity equalizer. The post equalizer is based on zero-forcing method utilizing 1 training symbol. The BER performance of the final data is measured after the DD-LMS and de-mapping process.

## 3. Experimental setup and results

The experimental setup is shown in Fig. 4. We generate the drive signals using an 81.92 GSa/s DAC with 20 GHz bandwidth and an offline Matlab® program. The bias of the two parallel PMs in the DDMZM (35 GHz bandwidth) is driven with a bias difference of ${V}_{\pi}$ /2 to achieve the function of IQ modulation [14]. Before driving the upper and lower arms of the modulator, the signals are amplified by electrical amplifiers (EA, 32 GHz bandwidth and 20 dB gain). A continuous wave (CW) light at 1542.9 nm is fed into the modulator. The signals are detected by a 15 GHz commercial photo detector with TIA integrated (PD, 15 GHz optical bandwidth and 11 GHz electrical bandwidth) after they are amplified by an EDFA. Finally, the signals are sampled by a digital real-time oscilloscope with an 80 GSa/s sampling rate and a 30 GHz electrical bandwidth. Main parameters are shown in Table 1. Figure 5 shows the measured end-to-end channel frequency response of the whole optical transmission link. According to the measured results, the bandwidth of the optical channel is 5.4 GHz of 3 dB, 11.1 GHz of 6 dB and 16.2 GHz of 10 dB.

Firstly, we investigate the BER performance of PAM, CAP and DFT-S OFDM with and without the nonlinear equalization in the BTB case. The results are shown in Fig. 6(a). The received optical power is measured after the EDFA at the receiver side to show the sensitivity of the receiver. We observed that PAM signal has the best BER performance after using nonlinear equalization. The reason is that in PAM modulation the signal is digital multi-level signal, while in CAP and DFT-S OFDM they are the analog signals. In this experiment, PAM, CAP and DFT-S OFDM generated by the DAC have the same signal output amplitude. However, PAM signal has higher average output power compared with the other two modulation formats due to lower peak to average power ratio (PAPR). As shown in Fig. 7, the high-levels of PAM-8 signal suffer significant nonlinear impairment, which directly causes large bit errors after decision. When using nonlinear equalization, the nonlinear effects can be mitigated. The performance is dominated by SNR other than the nonlinearity. So PAM signal outperforms both the CAP and DFT-S OFDM signals with nonlinear equalization due to the higher SNR (higher average output power). We also take into account the effect of Volterra filter taps on system performance. The results are shown in Fig. 6(b). The data are transmitted over 40 km of fiber. From the figure, we can see that the system performance becomes better with the increase of the tap numbers. However, the minimum number of taps that is close to the best performance is different for three modulation formats. Therefore, in order to reduce the impact of the tap numbers on the system performance, we will choose a larger tap number to ensure that the system has the best performance. Therefore, the number of 189 is chosen as the tap number and NE will be used in the all fiber transmission cases.

Then, fiber transmission is demonstrated as shown in Fig. 8. We compare the BER performance in the BTB, 10 km, 25 km and 40 km cases. For PAM signal, the penalty of the received optical power from BTB to 10 km is 3.4 dB at the HD-FEC threshold of 3.8 × 10^{−3}, while it is 2.5 dB for CAP and 2 dB for DFT-S OFDM. After the fiber transmission, DFT-S OFDM signal outperforms both the PAM and CAP signals. There are two reasons. One is the changed PAPR after the CD pre-compensation process. We evaluate the PAPR of the three modulation formats with and without CD pre-compensation as shown in Fig. 9(a). The figure shows the relationship between Complementary Cumulative Distribution Function (CCDF) and PAPR. After CD pre-compensation, PAM, DFT-S OFDM and CAP have the same PAPRs. Another reason is the bandwidth-limited receiver. As the optical bandwidth of the PD is only 15 GHz, while the total bandwidth is 37.5 GHz for PAM, 20.57 GHz (18.7 × 1.1) for CAP and 20 GHz for DFT-S OFDM. The frequency spectrums are shown in Fig. 9(b)-9(d). These two factors have resulted in DFT-S OFDM having the best performance after fiber transmission.

We also investigate the BER performance versus OSNR in the BTB, 25 km and 40 km cases. A variable optical attenuator (VOA) is used to change the OSNR. The results are shown in Fig. 10. For PAM signal, the penalty of the OSNR from BTB to 25 km is 5.2 dB at the HD-FEC threshold of 3.8 × 10^{−3}, while it is 2.9 dB for CAP and 1.2 dB for DFT-S OFDM. However, the penalty of the OSNR from 25 km to 40 km at the HD-FEC threshold is almost the same for three modulation formats. It is also because their PAPR changes are relatively slight from 25 km to 40 km.

Finally, 50 km SSMF fiber transmission with DFT-S OFDM is experimentally demonstrated under HD-FEC threshold of 3.8 × 10^{−3} as shown in Fig. 11. While it is 5. 75 × 10^{−3} for PAM signal, and 6.24 × 10^{−3} for CAP signal. The constellations of DFT-S OFDM and CAP and the diagram of PAM signal are all shown in Fig. 11. The results show the feasibility for employing DFT-S OFDM in 100 Gb/s/λ optical transmission systems with a bandwidth-limited direct-detection receiver compared with PAM-8 and CAP-64.

## 4. Conclusions

In conclusion, a comprehensive comparison is presented among PAM-8, CAP-64 and DFT-S OFDM with a bandwidth-limited direct-detection receiver for 100 Gb/s/λ optical transmission systems. The optical bandwidth of the receiver (15 GHz) is less than the total bandwidth of signals (37.5 GHz for PAM, 20.57 GHz for CAP and 20 GHz for DFT-S OFDM). In the BTB case, PAM signal is less robust to the nonlinearity compared with other modulation formats. Whereas, it shows the best performance using the nonlinear equalization due to its lowest PAPR. In the fiber transmission case, three signals have the similar PAPRs after the process of CD pre-compensation. DFT-S OFDM signal outperforms both the PAM and CAP signals because of the smallest total bandwidth. Finally, 50 km SSMF fiber transmission with DFT-S OFDM is experimentally achieved under HD-FEC threshold of 3.8 × 10^{−3}, While it is 5. 75 × 10^{−3} for PAM signal, and 6.24 × 10^{−3} for CAP signal. The results show that DFT-S OFDM is a potential candidate in the future low-cost short reach system with a limited bandwidth at the receiver.

## Funding

National Natural Science Foundation of China (NSFC) (61325002, 61527801, 61571133, 61720106015 and 61675048); State Grid Corporation of China (SGCC) Research on Key Technologies of High Reliability and Short Distance Wireless Communication in Power Complex Electromagnetic Environment; Open Fund of IPOC(BUPT)(IPOC2015B002).

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