Transmission of single lane 128 Gbit/s PAM-4 signals over an 80 km SSMF link, enabled by DDMZM aided dispersion pre-compensation

Qiang Zhang; Nebojsa Stojanovic; Changsong Xie; Cristian Prodaniuc; Piotr Laskowski

doi:10.1364/OE.24.024580

1. Introduction

With the rapid development of cloud services, high definition video, and broadband wireless communications, an extremely large amount of interconnection capacity is required for data transmission inside and between data centers (DCs). For the intra-DC scenario, low-cost multi-mode fibers with lengths below 1 km are widely used, together with low-cost multi-mode vertical-cavity surface-emitting lasers (VCSEL) [1]. For the inter-DC scenario, with ranges of several tens of kilometers for metropolitan (metro) DC interconnections (DCIs) and several hundred kilometers for long haul DCIs (LH-DCIs), standard single mode fibers (SSMFs) are used. Coherent systems are practically the only choice for LH-DCIs, because of the required high performance [2]; for metro DCIs, however, their use is still very challenging, because of their high cost. Two lines of research are being pursued to reduce the metro DCI cost: beyond 200 Gbit/s per lane coherent systems, and 100 Gbit/s per lane direct detection (DD) systems. Advanced modulation schemes and digital signal processing (DSP) are needed in DD systems to support 100 Gbit/s transmission over up to 80 km SSMF links. Pulse amplitude modulation (PAM) [3–5], carrierless amplitude and phase modulation (CAP) [6,7], discrete multi-tone (DMT) [8,9], and Nyquist single carrier modulation (N-SCM) [10,11] are the mainly used modulation schemes, and have been widely investigated and demonstrated. Among them, PAM needs the simplest DSP structure; four-level PAM (PAM-4) is a potential modulation scheme for the 400GE standard.

Chromatic dispersion (CD) is one of the most important system distortions in SSMF links of up to 80 km, and will induce a serious power fading penalty in C-band DD systems [9]. To overcome the influence of CD, dispersion compensation fibers (DCFs) or dispersion compensation modules (DCMs) based on fiber Bragg gratings are often used. However, they induce an extra cost and increase the total link losses. There is always some residual CD with DCF, but with increase of the baud-rate, the CD tolerance reduces to be just several tens of ps/nm [5] which is very challenging in the real deployment. While for the multi-wavelength DCM, the cost may be shared by multi-channels, the main problem is the insertion loss can reach up to 10 dB, which will greatly degrade the optical signal to noise ratio (OSNR) of the system especially when ring network architecture is applied to connect several sub-DCs or sites in the metropolitan range. So our target is focusing on DCF/DCM-free solution. Fortunately, CD pre-compensation can be done using complex signal modulators such as IQ Mach–Zehnder modulators (IQMZMs) or dual drive MZMs (DDMZMs). Of these two modulator types, DDMZMs have the simpler structure and potentially lower costs. Robert Killey et al. simulated CD pre-compensation with a DDMZM to enlarge the reach of 10 Gbit/s non-return-to-zero (NRZ) signals from 80 km to 800 km [12]. Recently, CD pre-compensation with a DDMZM was experimentally demonstrated with single sideband (SSB) N-SCM [11]. For the PAM-4 modulation scheme, the reported result is the IQMZM-based quasi-SSB Nyquist PAM-4 signal with CD pre-compensation, which supports 74.67 Gbit/s transmission over 20 km SSMF links [4]. In this paper, PAM-4 system with dispersion pre-compensation aided by DDMZM is investigated. An extra (j-1) multiplication is used in the dispersion pre-compensation process to align the modulated optical signal with the optical carrier. With this action, the 128 Gbit/s PAM-4 signals are managed to be transmitted over 80 km SSMF link with 4 dB OSNR penalty compared with back to back performance. The origin of the penalty is investigated by measuring different lengths of fiber and more than 2 dB penalty is observed when the fiber length is longer than 20 km. The carrier to signal power ratio (CSPR), peak to average power ratio (PAPR) are also optimized and the best values are found to be 7 dB and 9 dB, respectively.

2. General principles

2.1 Complex signal generation with DDMZM

The DDMZM consists of two independent phase modulators. Each phase modulator will induce a phase shift proportional to the applied voltage. The DDMZM output signal can be written as [9]:

E_{o u t} = \frac{1}{2} e^{j ω t} (e^{j \frac{V_{1}}{V_{π}} π} + e^{j \frac{V_{2}}{V_{π}} π}) = e^{j ω t} \cos (\frac{V_{1} - V_{2}}{2 V_{π}} π) e^{j \frac{V_{1} + V_{2}}{2 V_{π}} π},

where V₁ and V₂ are the voltage signals applied to each one of the two branches, and V_π is the voltage needed to induce a π phase shift in each branch. One can note that the DDMZM is the cascade of an amplitude and phase modulators, and that it can be used to generate the complex signal.

The driving voltage signals (V₁ and V₂) include two components: a direct current (DC) component, and a radio frequency (RF) component. The DC voltages will induce a constant phase shift between the upper and lower branches to adjust the bias point. The RF signals carry the information to be sent. The drive signals can be written as:

V_{1} = V_{b 1} + s_{1}, V_{2} = V_{b 2} + s_{2},

where

V_{b 1}

and

V_{b 2}

are the bias voltages for the upper and lower branch, respectively, and

s_{1}

,

s_{2}

are the respective RF signals. When the upper and lower branches are biased with

V_{b 1} = ​ ​ V_{π} / 4

and

V_{b 2} = ​ - ​ V_{π} / 4

, the DDMZM works at the quadrature point, and the phase shift between the two branches is π/2. In this case, the output signal can be written as:

E_{o u t} = \frac{1}{2} e^{j ω t} e^{j π / 4} (e^{j \frac{s_{1}}{V_{π}} π} - j e^{j \frac{s_{2}}{V_{π}} π}) .

If the RF signal is small, the approximation of

e^{x} \approx 1 + x + O_{2}

can be used and the modulator can linearly convert the signal from the electrical to the optical domain, as expressed in the following expression [9]:

E_{o u t} = \frac{1}{2} e^{j ω t} e^{j π / 4} (1 + j \frac{s_{1}}{V_{π}} - j + \frac{s_{2}}{V_{π}} + O_{2}),

where s₁ and s₂ are the RF signals in the upper and lower branches, respectively, and O₂ are the higher order components of the resulting signal. One can see that the electrical signals are linearly mapped to the optical electric field; signals s₁ and s₂ are mapped to the amplitudes of the real and imaginary parts, respectively. The optical intensity can be written as:

I = E_{o u t} \cdot E_{o u t}^{*} \approx 1 - \frac{s_{1}}{V_{π}} + \frac{s_{2}}{V_{π}} + S S B I + O_{2},

where SSBI stands for the signal to signal beating interference (SSBI) and can be written as:

S S B I = {(\frac{s_{1}}{V_{π}})}^{2} + {(\frac{s_{2}}{V_{π}})}^{2} .

In the back to back condition, differential driven (

s_{1} = - s_{2}

) is always used to reduce the driven voltage. The optical signal is:

E_{o u t} = \frac{1}{2} e^{j ω t} e^{j π / 4} (1 + j \frac{s_{1}}{V_{π}} - j - \frac{s_{1}}{V_{π}} + O_{2}) = \frac{1}{2} e^{j ω t} e^{j π / 4} [1 - j + \frac{s_{1}}{V_{π}} (j - 1) + O_{2}] .

In the equation, (1-j) stands for the optical carrier which is decided by the bias point of the DDMZM; while

\frac{s_{1}}{V_{π}} (j - 1)

is the modulated optical signal by the RF signals. One can note that compared with the original PAM4 signal

s_{1}

, the modulated signal is multiplied by (j-1) and this can makes the optical signal align with the optical carrier and get the maximum beating value between the optical carrier and the modulated optical signal. In the system, the amplitude of

s_{1}

will be optimized which can be characterized by carrier to signal power ratio (CSPR) value. Higher CSPR can help to reduce the SSBI but will degrade the amplified spontaneous emission noise tolerance of the system. The CSPR value can be adjusted by changing the amplitude of the RF signals of

s_{1}

and

s_{2}

.The high-order distortion can be reduced using a Cartesian to polar conversion [12]. If we ignore the constant phase part of the optical signal, the target optical electric field without high-order distortion can be written as:

E_{t x} = \frac{1}{2} (1 + j \frac{s_{1}}{V_{π}} - j + \frac{s_{2}}{V_{π}}) = | E_{t x} | e^{j Φ} .

With this target signal, we can invert the DDMZM transfer function and recalculate signals V₁ and V₂ as Eq. (9) to obtain [12,13]:

V_{1} = \frac{V_{π}}{π} [ϕ + \cos^{- 1} \frac{| E_{tx} |}{{| E_{tx} |}_{max}}], V_{2} = \frac{V_{π}}{π} [ϕ - \cos^{- 1} \frac{| E_{tx} |}{{| E_{tx} |}_{max}}] .

2.2 Bandwidth and dispersion pre-compensation

Bandwidth pre-compensation is usually supported by off-line measurements of the channel response (CR) amplitude. However, the CR phase is also very important for high baud-rate signals. In our performed tests, we used a shared clock to synchronize the transmitter (an arbitrary waveform generator; AWG) and the receiver (a digital sampling oscilloscope; DSO), thus allowing a precise CR phase measurement, as shown in Fig. 1. The DUT in the figures means device under test and is the end to end transmission system in our measurement. First, the time delay between the AWG and DSO was tested, using an NRZ signal as training sequence. The observed delay was then corrected using the AWG DSP. Then, an unequally spaced discrete multi-tone signal was generated and sent to the receiver. The unequal spacing used at this step helped to reduce the influence of high-order system nonlinearities. At the receiver side, the CR could be obtained by dividing the received signal by the transmitted signal in the frequency domain. The response at frequencies that had not been used (this happens because only an unequally spaced DMT signal is sent) could be derived by interpolation. Finally, the target pulse shape was divided by the CR, to obtain the bandwidth pre-compensation (BWC) function.

Fig. 1 Bandwidth pre-compensation, as implemented in this work.

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When a broadband signal goes through a SSMF, the different frequency components of the signal will present temporal mismatches with each other. The pre-distorted optical signal waveform can be written as [12]:

E_{T x} (ω) = E_{T A R} (ω) exp (- j \frac{β_{2} {Lω}^{2}}{2}),

where

β_{2}

is the fiber dispersion, L is the fiber length, and

E_{T A R} (ω)

is the target waveform desired at the received side. In our case,

E_{T A R} (ω)

is the PAM-4 waveform. The CD pre-compensation function is a complex-valued all-pass filter, whose phase value depends on the absolute value of ω at a determined distance. This breaks the Hermitian property of the PAM-4 signal, and the CD pre-compensated signal therefore becomes complex-value. This process is not feasible for an intensity modulator, such as an electro-absorption modulated laser. Digital pre-compensation can be carried out with DDMZM, because of the complex field modulation characteristic of this modulator. One important setting in our experiment is that we use one extra (j-1) multiplication in the dispersion pre-compensation process as mentioned in Eq. (7) to align the optical carrier and modulated optical signal at the received side.

3. Experimental setup

Based on the above-discussed body of knowledge, we setup a testbed (shown in Fig. 2) to verify the feasibility and measure the performance of CD pre-compensated PAM-4 signals using a DDMZM. An arbitrary waveform generator (AWG, M8196A from Keysight) with a sampling rate of 92 GSa/s and a 30 GHz bandwidth was used to generate the electrical signals. The AWG has an 8 nominal number of bits and more than 4.5 effective number of bits (ENOB) at 30 GHz. The electrical signals were then amplified by two 50 GHz bandwidth drivers (SHF S807) to a peak-to-peak value of 2 V, and drove a 30 GHz DDMZM (FTM7937EZ from Fujitsu). The launch power to the 80 km SSMF is 4 dBm with fiber loss of 16.5 dB. After removing the out of band optical noise with a 100 GHz optical band-pass filter (OBPF), the signal was received by a photo-detector (PD: XPDV2320R from Finisar) with a 50 GHz bandwidth, which performed the opto-electrical conversion. Finally, the electrical signal was captured by a DSO (DSO-Z 634A from Keysight) operating at 160 GSa/s, with a cutoff frequency of 63 GHz.

Fig. 2 Experimental setup and offline DSP used in the experiment.

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Data generation and processing proceeded as follows. At the transmitter side, a pseudo-random bit sequence with length of 2¹⁵-1 was used for the bit-to-PAM-4 symbol mapping. The generated 64 GBaud PAM-4 symbols were up-sampled by inserting zeros between symbols. Pulse shaping and bandwidth pre-compensation were then performed, to reduce the influence of bandwidth limitations. A root raised cosine (RRC) pulse shape with a 0.35 roll off value was used as target shape. The bandwidth pre-compensation process with pulse shape was carried out in time domain by using FIR filter with tap number of 160. The signal was then re-sampled to 92 GSa/s and CD pre-compensation was performed. During the CD pre-compensation process, the real signal after the bandwidth pre-compensation is multiplied with (j-1) to align the optical carrier and modulated optical signal. After that, a complex signal was obtained. A Cartesian to polar conversion was carried out to reduce the modulator nonlinearities. After removing the DC parts, the RF signals (RF1 and RF2) from the output of the Cartesian to polar conversion were clipped to reduce the peak to average power ratio (PAPR) of the RF signals. Finally the RF signals were quantized with 8 bits and were loaded to the AWG. At the receiver side, the offline data was first digitally down-sampled from 160 GSa/s to 128 GSa/s. A timing recovery procedure with Mueller and Muller phase detector [14] was then used to remove the timing offset and jitter from the signal. Afterwards, the fractional spaced feed-forward equalizer (FFE) removed most of the linear distortion from the system, while a maximum likelihood sequence estimator (MLSE) removed the residual linear and nonlinear distortion. Finally, the bit error rate (BER) was calculated. If we exclude the frame structure and soft decision forward error correction (SD-FEC) code overheads, the net data-rate was 100 Gbit/s with a SD-FEC threshold of 2.4 × 10⁻² [15].

4. Experimental results and discussion

Figure 3(a) shows the measured total system transfer function. The 3-dB bandwidth is approximately 7.5 GHz, which is far below the optimal bandwidth [16]. This strong filtering effect is induced by the cascaded filtering of electric and optical components. The benefit of using high bandwidth components is that the 10-dB bandwidth of the system can reach up to 27 dB. The phase response is not linear in frequency (even without the SSMF), which is an indication of the intrinsic dispersion of the system. The amplitude attenuation is approximately 15 dB at the Nyquist frequency. Figures 3(b) and 3(c) show the optical eye-diagram before and after BWC; a great improvement in the eye-diagram quality can easily be seen. This improvement can also be verified in the optical spectra with resolution of 0.02 nm as shown in Fig. 4. Without BWC, there is an obvious roll off in the spectrum; with BWC, the spectrum becomes more flat within the bandwidth.

Fig. 3 (a) System transfer function. (b, c) Eye-diagrams (b) before and (c) after bandwidth pre-compensation.

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Fig. 4 Optical spectra of the transmitted signal.

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Figure 5(a) shows the statistic transfer function of DDMZM with differential drive mode. The insertion loss of the DDMZM is measured to be about 8 dB. The extinction ratio is about 25 dB. The quadrature bias voltage is 3.9 V. During the experiment, shifting the bias voltage a little close to the null point of the DDMZM can improve the system performance as shown in Fig. 5 (b). The best bias voltage is found to be 4.25 V. Because of the dispersion pre-compensation, the PAPR of the signal is very large and it can be controlled by using hard clipping method [17]. During the clipping process, the real value signals, , are clipped with amplitude A as follows [17]:

S_{out} = {\begin{matrix} - A, {if S}_{in} < - A \\ S_{in}, if - A \leq S_{in} \leq A \\ A, {if S}_{in} > A, \end{matrix}

where A is the clipping level,

S_{in}

is the un-clipped signal and

S_{out}

is the clipped signal. The ratio between the clipping amplitude A and the root mean square value of the signal

σ

is usually used to characterize the clipping process. After the clipping process, the maximum power of the RF signal is

A^{2}

while the mean power of the signal is

σ^{2}

, so the PAPR value ( =

10 {log}_{10} (A^{2} / σ^{2})

) of the RF signal can be controlled by hard clipping process. The influence of the PAPR is indicated in Fig. 5 (c) and the best PAPR value is found to be 9 dB. For the DD system, the carrier to signal power ratio (CSPR) is also a very important parameter to characterize the system. In the experiment, the CSPR values are estimated by using the measured optical spectrum. The modulated signal power far away from the optical carrier can be easily got by the measured power values. For the modulated signal near the optical carrier (

\pm 0.05 nm

of the optical carrier), considering the flat power distribution character of the signal, the average power value in the range of 0.1~0.15 nm away from the optical carrier is used to estimate the overlapped part with the optical carrier. After the signal power is obtained, the optical carrier power can be estimated by summing up the optical carrier part. The CSPR can be adjusted by changing the bias condition or the drive amplitude of the RF signals. In Fig. 5 (b), the best bias voltage is fixed at 4.25 V, and the CSPR is then scanned by using different drive amplitude of the RF signals and the result is shown in Fig. 5 (d). One can see that the best CSPR value is about 7 dB for PAM4 signal with dispersion pre-compensation.

Fig. 5 (a) Statistic transfer function of DDMZM; experimental parameters optimization over 80 km SSMF: (b) bias voltage; (c) RF PAPR; and (d) CSPR.

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With the optimization above, the measured BER versus optical signal to noise ratio (OSNR) in both the back-to-back (B2B) case and after 80 km SSMF transmission is shown in Fig. 6. In the offline processing chain, the number of FFE taps was chosen to be 41, and the memory length of MLSE was four. After 80 km SSMF transmission, a BER below the SD-FEC threshold was obtained. The longest previously reported reach for a 100 Gbit/s direct detection PAM-4 system over a DCF-free link was 4 km [18]. In this work, we greatly extended this reach to 80 km, making it possible to support the metro DCI scenario. The OSNR values required to reach the SD-FEC threshold for these two cases are 25.5 dB and 29.5 dB, respectively. MLSE does not help too much in reducing the required OSNR, but is helpful in reducing the error floor in the B2B condition. The OSNR penalty over an 80 km SSMF link is 4 dB; this degradation can also be observed by checking the eye-diagrams after the FFE, as shown in the insets of Fig. 6: the eye-diagram is much clearer in the B2B condition. The four levels are not exactly equally spaced, because we slightly suppressed the bias point near the null point as mentioned above, to reduce the carrier to signal power ratio and thus contribute to improve the sensitivity and OSNR performance of the system. With the fiber link, the eye-diagram becomes considerably blurred. As analyzed in the introduction part, (j-1) multiplication can align the optical carrier with the modulated optical signal. To show the improvement of this action, we also compared the system performance with and without (j-1) multiplication during the dispersion pre-compensation process as shown in Fig. 7. One can see that without the (j-1) multiplication in DDMZM system, we cannot get a BER below the FEC limit. The system performance with fiber lengths of 10, 20, 40 km is also measured to investigate the penalty relationship with the fiber lengths as shown in Fig. 8. The OSNR penalties with 10, 20, 40 and 80 km SSMF are 0.6 dB, 2.6 dB, 3.4 dB and 4 dB, respectively. One can see that once the fiber lengths reach 20 km and above, the penalty increases greatly. The error floor also increases with increasing the fiber length.

Fig. 6 BER versus OSNR for different equalization configurations; the insets are the eye-diagrams after FFE, for an OSNR of 36 dB.

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Fig. 7 BER versus OSNR with and without (j-1) multiplication.

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Fig. 8 System performance with different fiber lengths.

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To find out the origin of the degradation, we first analyze the power spectral density (PSD) of the received electrical signals in both the B2B case and after 80 km SSMF transmission, as shown in Fig. 9. One can see that the PSDs are approximately the same. The power-fading free PSD after the 80 km SSMF also shows the effectiveness of the CD pre-compensation. However, the power ripple is enhanced after the CD pre-compensation is carried out, as shown in the inset of Fig. 9. The ripple can also be observed in the optical spectrum (OS) of the signal after the transmitter, as shown in Fig. 10. Because the OS is measured immediately after the transmitter, we ascribe the origin of the ripple to modulator nonlinearity. In the back-to-back condition, the second order component of this nonlinearity will be cancelled during the direct detection process [19]. When CD pre-compensation is carried out, this relationship does not hold anymore, and the second (and higher) order components of the nonlinearity will remain. The Cartesian to polar conversion can—in theory—remove this nonlinearity when both the number of samples per symbol (NSPS) and the number of DAC quantization bits are high enough. However, the sampling rate of AWG is 92 GSa/s and the baud-rate reaches as high as 64 GBaud, which means the NSPS value is only 1.4375. If the limited bandwidth of the system and limited effective number of bits are also taken into account, this ratio becomes even closer to unity. In this condition, Cartesian to polar conversion will also have a compensation penalty. When the NSPS value reaches unity, the penalty is 1.8 dB for a 10 Gbit/s NRZ signal with CD pre-compensation over a 100 km SSMF [12]. In our case, both the baud-rate and modulation order are higher; the penalty is therefore reasonable for the DDMZM. One must also consider that the frequency ripple will induce inter-symbol-interference (ISI) with long memory lengths. In our measurements, the maximum memory length of MLSE was set to be four, which stands for 256 possible states and is almost the maximum capacity that could be implemented; this memory length is, however, still too small to compensate the ripple induced ISI, especially when the signal is transmitted over the 80 km SSMF.

Fig. 9 Power spectral density (PSD) of the received signals in the B2B condition, and after the 80 km SSMF link.

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Fig. 10 Optical spectra of the received signals in the B2B condition and with the 80 km SSMF link.

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5. Conclusion

We achieved successful transmission of a 128 Gbit/s PAM-4 signal over an 80 km SSMF link without DCF, which represents the longest reported distance for the direct detection of 100 Gbit/s (and beyond) PAM-4 systems. A synchronized bandwidth pre-compensation method is used to enable the generation of 64 GBaud PAM-4 signals in a system with a 7.5 GHz 3-dB bandwidth. The DDMZM is used as a complex signal modulator, to generate a CD pre-compensated optical signal capable of supporting DCF-free transmission over SSMFs. The values of OSNR required for the B2B condition and 80 km SSMF transmission are 25.5 dB and 29.5 dB, respectively. A 4 dB penalty is observed; its origin is analyzed and ascribed to the nonlinearity of the modulator and the limited ENOB of the AWG.

Acknowledgments

The authors thank Keysight for supplying the high performance AWG (M8196A) for the measurements.

References and links

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Transmission of single lane 128 Gbit/s PAM-4 signals over an 80 km SSMF link, enabled by DDMZM aided dispersion pre-compensation

Abstract

1. Introduction

2. General principles

2.1 Complex signal generation with DDMZM

2.2 Bandwidth and dispersion pre-compensation

3. Experimental setup

4. Experimental results and discussion

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (10)

Equations (11)

Optics Express