## Abstract

We demonstrate the transmission of a 30-GBd polarization-multiplexed probabilistically shaped 4096-ary quadrature amplitude modulation (QAM) signal over 50.9-km standard signal-mode fiber (SSMF), with a net single-carrier bit rate of 484.4 Gb/s carrying 16.1 information bits per symbol (a potential spectral efficiency of 15.9 bits/s/Hz when taking into account a 0.01 spectral roll-off). The signal is generated from 28-nm complementary metal-oxide-semiconductor (CMOS) digital-to-analog converters (DACs) with 8-bit nominal resolution and is received by an intradyne coherent receiver with a laser that has a linewidth of ∼1 kHz.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Optical transmission systems show a general trade-off between symbol rate and information rate (IR), i.e., the net data rate divided by the symbol rate [1]. One can use low symbol rates with each symbol carrying more information bits, or one can employ high-symbol-rate signals with each symbol carrying less information bits. This trade-off is not fundamental in terms of modulation, but rather comes from the fact that increasing the symbol rate in practice results in a lower end-to-end electrical signal-to-noise ratio (SNR).

Figure 1 shows recent record experiments at high IRs versus the demonstrated all-electronically generated symbol rates [2–15]. Note that these measurements are taken under very different experimental conditions, e.g. different amplification schemes (Raman amplifiers or Erbium-doped fiber amplifiers/EDFAs), different laser linewidths, different transmission fiber types and transmission distances. Nevertheless, the trade-off between symbol rate and IR can be clearly observed. For example, using integrated digital-to-analog converters (DACs), it is possible to achieve IRs of 19.9 bits/symbol with probabilistically shaped (PS) 4096-ary quadrature amplitude modulation (4096-QAM) at 3 GBd [2], 15.8 bits/symbol with 1024-QAM at 10 GBd [3], or 10 bits/symbol with 64-QAM at 100 GBd [10]. By externally multiplexing two or more DAC-generated signals in the time or frequency domain [11,13–15], IRs of 11.3 bits/symbol at 90 GBd [13] and 3.3 bits/symbol at 192 GBd [14] have been achieved. Typically, systems demonstrating high IRs (e.g. > 15 bits/symbol) use high-resolution DACs (10 bits or 14 bits) and narrow-linewidth lasers (< 400 Hz) and/or utilize analog phase locked loops (PLLs) [4].

In this paper, we demonstrate 16.1 bits/symbol with a 30-GBd PS-4096-QAM signal using standard 28-nm CMOS DACs with 8 bits of nominal resolution and 1-kHz-linewidth lasers. We transmit this signal over 50.9-km standard single mode fiber (SSMF) and receive it by an intradyne receiver without analog optical phase locking. The line rate [16] of our single-channel signal is 599.5 Gb/s and the net data rate after taking into account forward error correction (FEC) is 484.4 Gb/s. The signal uses root-raised-cosine (RRC) pulse shaping with a roll-off factor of 0.01 and consequently occupies an optical bandwidth of 30.3 GHz, potentially allowing for a spectral efficiency (SE) of 15.9 bits/s/Hz.

## 2. Optical measurement setup

The experimental setup for our 30-GBd PS-4096-QAM transmission system is shown in Fig. 2. The transmitter consists of a laser with a linewidth of 1 kHz operating at 1550.1 nm [17], and a LiNbO_{3} single-polarization I/Q Mach-Zehnder modulator (MZM) with a 3-dB bandwidth of 35 GHz and a V_{π} of ∼3.5 V. The modulator uses a laser input power of 23.3 dBm and is driven by 28-nm CMOS DACs. The DACs have a nominal resolution of 8 bits, operate at 88 GSa/s, and have a 3-dB bandwidth of ∼18 GHz. The DACs’ differential outputs (∼700 mV differential peak-to-peak swing) are converted to a single-ended signal via radio frequency (RF) baluns with 6-dB insertion loss to produce a single-ended signal of ∼350-mV peak-to-peak voltage. The electrical driver amplifiers have a gain of 23 dB, followed by RF attenuators with 13-dB attenuation. The signal used for driving the modulator has a peak-to-peak voltage of ∼1.1 V, allowing operation of the MZM in its linear region (drive voltage swing ∼V_{π}/3). The delay mismatch between in-phase (I) and quadrature (Q) components is measured and digitally compensated within the transmitter. The modulated light is amplified by an EDFA. Polarization-division multiplexing (PDM) is realized by a fiber-delay based PDM emulator with 10.9 meters of decorrelation delay (i.e., 54.5 ns or 1635 symbols). The transmission fiber is a single, dispersion-uncompensated 50.9-km span of SSMF with a loss of 0.2 dB/km and a chromatic dispersion of 17 ps/km/nm. We use an optimized launch power of -2 dBm, by varying the signal launch power from -5 dBm to 5 dBm and find the power level that gives the best normalized generalized mutual information (NGMI). The inset of Fig. 2 shows the signal spectrum at the transmitter (blue) and the receiver (orange). The received signal is amplified by an EDFA and detected by a standard intradyne coherent receiver. The optical signal-to-noise ratio (OSNR) before and after fiber transmission is 40 dB and 37.1 dB, respectively. The free-running local oscillator has a linewidth of 1 kHz and is kept to within a frequency offset of ∼900 MHz relative to the transmit laser. The signal is down-converted to the electrical domain via 4 balanced photodiodes (Finisar BPDV2150R) which have a 3-dB bandwidth of ∼45 GHz. The electrical signal is sampled by a 4-channel real-time oscilloscope operating at 256 GSa/s. The ∼8.5 $\times $ [ = 256 GSa/s /30 GBd] oversampled signal is down-sampled by a factor of ∼4.25 to a 2 $\times $ oversampling ratio before performing adaptive filter equalization. A digital anti-aliasing filter is used as part of the down-sampling process. As the down-sampling process averages the received signal across ∼4.25 samples, the digitizer’s effective number of bits (ENOB) is increased by ∼1 bit [18].

Probabilistic constellation shaping is realized within the framework of the real-time implementable probabilistic amplitude shaping (PAS) architecture [19]. 64-level amplitude shaping is independently performed for the I and Q components of the 4096-QAM signal, in a block of 89364 symbols. We use a family of Maxwell-Boltzmann (MB) distributions with varying shaping parameter β to adjust the PS-4096-QAM signal, where β is the entropy of the positive half of the 64-level amplitudes that are made symmetric around zero through multiplication with the sign bit as part of the PAS architecture. Using a distribution matcher (DM) that produces a negligible shaping gap to the ideal DM, such as the constant composition DM [20], the maximum IR supported by the constellation can be quantified by the entropy rate as

*R*of 0.8402 (19.02% overhead). Post-FEC bit error ratio (BER) performance of the rate-0.8469 SC-LDPC code is shown in Fig. 3. The error-free decoding of our FEC code for PS-4096-QAM can be accurately predicted by the NGMI [25]. We determine the maximum β that yields a measured NGMI greater than the

_{c}*NGMI threshold*(NGMI*) [16,24] to maximize the net data rate with a fixed FEC rate. For our SC-LDPC code, the post-FEC BER is below the outer BCH threshold BER of $1.1 \times {10^{ - 6}}$ for NGMI $\ge \,$ 0.8798, as per the simulation results shown in Fig. 3, hence we conservatively take NGMI

^{* }= 0.8798.

The receiver digital signal processing (DSP) consists of chromatic dispersion compensation, frequency offset compensation, frame synchronization, and 2 $\times $ oversampled least mean square (LMS)-based 4 $\times $ 4 real-valued multiple-input multiple-output (MIMO) channel equalization [26–27]. The equalizer uses pilot-assisted pre-convergence followed by blind equalization. Only the blindly recovered data are used for subsequent NGMI calculation from the digitally recovered symbols. Clock recovery and carrier phase recovery are done by a digital PLL inside the LMS equalizer. The LMS filters have 281 taps (4.68 ns), which is significantly shorter than our PDM delay (54.5 ns). A total of 1.18 $\times $ 10^{6} recovered symbols are used for NGMI estimation.

For the success of PS-4096-QAM transmission, it is critical to optimize transmitter and receiver settings. In particular, the following three aspects are important: *(i)* Electrical distortions are avoided as much as possible. For instance, both differential outputs from the CMOS DAC are used to minimize degradations from clock leakage and other distortions. This may either be done using a differential-input RF amplifier, or (as in our setup) by an RF balun converting the differential DAC output signals to a single-ended signal, followed by a single-ended RF amplifier. Our setup uses discrete components, and RF cables are kept as short as possible to minimize RF loss at higher frequencies; *(ii)* Any I/Q time skew in the transmitter and receiver must be carefully compensated. In particular, to compensate for the transmitter I/Q skew, we digitally vary the transmitter I/Q delay of a single-sideband test signal until we observe a maximum image-band suppression ratio on an optical spectrum analyzer (OSA). We minimize the receiver I/Q skew by bypassing the PDM emulator and loading a binary signal on only one of the two DAC channels, and varying the receiver channel delays until the cross correlations of the received four tributaries are maximized; *(iii)* The I/Q amplitude balance is also critical to the performance. We adjust the amplitudes of the transmitter’s I and Q branches by tuning the gain of our RF drivers; *(iv)* the modulator bias positions are precisely adjusted. In our setup, we vary the modulator DC bias in 1-mV steps to find the optimal bias position.

The tolerance to 1-kHz laser phase noise comes naturally from the high symbol rate. Compared with a symbol rate of 3 GBd [2], a 30-GBd signal has a 10-times higher tolerance to laser linewidth [28].

## 3. Results and discussion

With 50.9-km fiber transmission, we vary the shaping factor β to maximize the data rate under the best available OSNR (37.1 dB) and find a shaping factor that still yields an NGMI greater than the FEC’s NGMI threshold. We use target values for β of 3.9, 4.0, 4.1, and 4.2, which yield actually implemented values for β of 3.896, 3.996, 4.096, and 4.198, with a discrepancy of < 0.004 between the target and implemented β values because of the finite block length due to limited memory of our DACs. The measured NGMI with different shaping factors after 50.9-km transmission is plotted in Fig. 4(a). As can be seen, a shaping factor of β=3.996 yields an NGMI of 0.8903, which is comfortably above the NGMI threshold. The measured pre-FEC BER is shown for reference as a function of β in Fig. 4(b). The recovered raw BER is 3.1 $\times $ 10^{−2} and the measured constellation SNR is 26.2 dB. The electrical SNR derived solely from amplified spontaneous emission (ASE) noise as per the measured 37.1-dB OSNR is 33.3 dB [ = 37.1 dB – 10 $\times $ log10(30 GBd/12.5 GHz)]. Therefore, we observe a ∼7-dB penalty from back-to-back implementation penalty plus uncompensated nonlinear distortions from fiber transmission.

It is important to mention that although PS-4096-QAM with β=3.996 has an entropy rate (9.99 bits/symbol/pol) very close to uniform (U)-1024-QAM (10 bits/symbol/pol), it is still beneficial to use PS-4096-QAM, as constellation shaping offers a gain over U-1024-QAM of the same entropy rate. To see this, we plot in Fig. 5 the AIRs of bit-metric decoding for four relevant modulation formats (PS-4096-QAM, U-4096-QAM, PS-1024-QAM, and U-1024-QAM) in the additive white Gaussian noise (AWGN) channel, estimated by their GMI as mentioned in Sec. 2. The AIRs shown in this figure are *achievable*, meaning that the post-FEC BER can be made arbitrarily low when information is transmitted at a rate of the AIR, by using an ideal FEC coding scheme with an arbitrarily adjustable code rate. Here, ‘ideal FEC’ means that the coding uses infinite code length and unlimited decoding complexity, and ‘arbitrarily adjustable code rate’ means that the code rate can be adapted to perfectly match the channel SNR. More details about the operational meaning of various AIRs and their calculations can be found in, e.g., Refs. [22,23]. Assuming this, we see that at our measured constellation SNR of 26.2 dB, PS-4096-QAM (solid red curve) has an AIR of 8.70 bits/symbol/pol, which is 0.46-bits/symbol/pol higher than U-1024-QAM (dashed blue curve). In principle, we could also obtain a higher AIR of 8.60 bits/symbol/pol than U-1024-QAM using the smaller PS-1024-QAM (solid blue curve). However, in practice, it is typical to use only one or a few selected fixed FEC rates; e.g., we use a fixed code rate of 0.8402, in which case the AIR of PS-1024-QAM cannot be made greater than 8.402 using any value of β allowed for the 1024-QAM template [16]. On the contrary, PS-4096-QAM enables us to use the fixed FEC code rate of 0.8402 to maximize the AIR solely by adjusting β. Here, although the merit of PS-4096-QAM with β=3.996 over U-1024-QAM is explained in an ideal FEC scenario, the same explanation can easily be extended to a practical non-ideal FEC [29], making PS-4096-QAM the most suitable format for our experimental link.

The transmitted probability distribution of the PS-4096-QAM constellation with β=3.996 is shown in Fig. 6(a). Figure 6(b) illustrates the histogram of the real part of the transmitted signal. The recovered constellations for the two polarizations are plotted in Fig. 6(c). With Ref. to [16] and at a code rate of ${R_c}\, = \; \,$ 0.8402, we have $\gamma $ = 0.0412 which can be calculated as

*R*is 599.5 Gb/s, which is calculated from

_{Line}*R*is 484.4 Gb/s, which is calculated from

_{info}## 4. Conclusions

We have demonstrated the transmission of 30-GBd PDM PS-4096-QAM signals over 50.9-km SSMF with an optimum shaping factor of β=3.996. The line rate of our single-channel signal is 599.5 Gb/s and the net data rate is 484.4 Gb/s. The signals are generated via standard 28-nm CMOS DACs with a nominal resolution of 8 bits and received by an intradyne coherent receiver.

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