1. Introduction

Orthogonal Frequency Division Multiplexing (OFDM) and Pulse Amplitude Modulation (PAM) are two competing technologies initially considered for the 400Gb Ethernet standard [1, 2]. OFDM offers spectral efficiency combined with flexibility [3], whereas PAM is simple to implement [4]. The currently considered option for achieving 400Gb/s is 4PAM based transmission in the O band (1260nm to 1360nm) [1]. Recent results show short reach (up to 2km) OFDM transmission in excess of 100Gb/s for this band [5, 6]. The alternative to the O band is the more cost effective but challenging C band (1530nm to 1565nm). For this band, when using Standard Single Mode Fibre (SSMF), Chromatic Dispersion (CD) impairs transmission of large bandwidth signals. Nevertheless, OFDM transmission for long reach (up to 10km) in excess of 100Gb/s [7] has been shown. Also on this band, developments in device fabrication promise further cost reduction [8]. The main objective of this paper is to demonstrate the transmission performance of both OFDM and PAM for an interface based on a 3-bit high speed DAC at the alternative C band. We target to achieve at least 56Gb/s using PAM or OFDM modulation up to 2km and 10km using this high-speed low resolution interface, enabling usage of 8×56Gb/s to achieve 400Gb/s transmission. We start by introducing both modulation formats and then compare their channel adaptation capabilities. We then discuss the specific challenges faced when transmitting OFDM using this interface. We experimentally demonstrate OFDM transmission on 1km and 10km SSMF. Based on these results, we create a realistic simulation setup unencumbered by the limitations of a real setup in terms of fibre length, biasing and converter resolution. Using this setup, we focus our comparison on the performance of both modulation formats as well as the impact of the experimental interface limitations, mainly quantization noise and power fading caused by CD [9]. Later we explore the performance of both modulation formats for the case when the limitation in resolution is relaxed, thus reducing the impact of quantization noise. In our investigations, BER is estimated using Gaussian assumption and for the Forward-Error Correction (FEC) threshold we assume a conservative Bit-Error Rate (BER) of 1×10⁻³.

2. OFDM and PAM for 400Gb Ethernet

OFDM spectral efficiency arises from using low-speed subcarriers, each supporting dense constellations. The use of low-speed subcarriers enables the use of tight Nyquist filtering resulting in a compact spectrum. With bit-and-power loading each subcarrier can be independently configured allowing greater flexibility. OFDM also presents an added resilience to CD due to its many low-rate subcarriers which effectively reduce InterSymbol Interference (ISI). By adding a Cyclic Prefix (CP) to the OFDM frame, further resilience to CD is attained. Despite these advantages, OFDM requires processing at the transmitter and receiver in order to perform the inverse Discrete Fourier Transform (iDFT) and Discrete Fourier Transform (DFT) respectively. Although the iDFT generates a complex valued signal, it is possible to complex conjugate half of the subcarriers in order to generate a real-valued baseband signal. This is known as Discrete Multi Tone (DMT) [3]. The modulated subcarriers at the output of the iDFT essentially represent an analogue signal. Changes to this signal translate directly into changes in the received constellation, for this reason, a highly linear transmission channel is required. In Itensity Modulation/Direct Detection (IM/DD) systems, OFDM is impaired by Subcarrier to Subcarrier Intermixing Interferences (SSII) due to subcarrier to subcarrier beating [10], the interaction between chirp and CD leads to larger SSII [11]. As SSII are modulation index dependent, their magnitude can be reduced by using a low modulation index, leading to less signal power at the receiver. This approach is of limited effectiveness as OFDM already has reduced signal power, compared to PAM, due to the concentration of the signal around the DC bias point. Furthermore, to represent this signal, the Digital to Analog Converter (DAC) resolution needs to be accounted for. Low resolutions will cause high levels of quantization noise thus decreasing the Signal-to-Noise Ratio (SNR) for all subcarriers. The required DAC resolution to support a specific number of bits-per-symbol does not grow linearly. Nevertheless it is possible to derive it by assuming a given BER threshold [12]. This relation becomes more complex when different subcarriers have different constellations and/or power loading. One final aspect to consider, especially for a low resolution DAC, is the high Peak-to-Average Power Ratio (PAPR) of OFDM [12]. Without further processing after the iDFT most of the signal is limited to the central levels of the DAC output. This causes the signal to suffer from increased quantization noise, as if it was generated by a lower resolution device. Amplitude clipping mitigates this problem, even though distortion is introduced, and can be optimized [13] to provide a better distribution of the signal among the very limited dynamic range of the DAC. The effect of high clipping can be seen in Fig. 1(a) for the histogram of the generated OFDM signal before quantization. PAM simplicity arises from it being a one dimensional baseband modulation format. It enables simple decoding at the receiver where only sampling and level decision are needed. At the transmitter side, the multilevel digital signal can be generated simply by the addition of binary tributaries without any digital signal processing. Another approach is to encode one tributary into several levels and then generate the multilevel electrical signal with a DAC. In both cases, the DAC sample rate can be fully utilized as PAM uses one sample per symbol. OFDM on the other hand is composed by subcarriers that require a minimum of two samples per symbol to be represented. The one dimensional nature of PAM limits its spectral efficiency where high numbers of levels are affected by noise in the transmission system earlier than for OFDM where information is encoded in the complex plane, or in other words in two dimensions. Finally, PAM is also affected by the non-linear transfer function of the modulator leading to unequal level distribution and reduced eye opening. PAM transmission can be adapted to the transfer function by adjusting the amplitude of the binary tributaries. Due to being a large bandwidth single carrier modulation format, PAM is affected by CD and the low-pass channel characteristic.

 

Fig. 1 Experimental OFDM@32Gbaud (a) 8PAM@60Gbaud (b) at the DAC output. For reference, the original OFDM signal is shown (a).

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2.1. OFDM vs. PAM transmission

Both modulation formats can adapt to the channel by changing the number of bits-per-symbol, or by baudrate reduction. Assuming the use of hardware with a fixed sample rate, PAM baudrate reduction is achieved simply by symbol repetition, which leads to large steps in terms of capacity. For OFDM, smaller decrements are possible as single subcarriers can be disabled. The transmission performance of these modulation formats can be significantly improved through the use of digital equalization, for instance: Volterra filtering for OFDM [14] and Decision Feedback Equalization (DFE) for PAM [1]. A DFE increases the requirements of PAM in terms of signal processing and allows for a direct comparison between the two formats.

2.2. Transmission using a high speed 3-bit interface

In order to successfully achieve OFDM transmission using a 3-bit high baudrate IM/DD interface at 1550nm, two challenges need to be overcome. The first challenge arises from high baudrate signal generation in combination with nonzero dispersion wavelength transmission. This makes the system sensitive to CD, which causes power fading in the signal bandwidth at specific fibre lengths [7, 9]. The second challenge arises from the low resolution of the DAC. 3-bit resolution is the nominal requirement to transmit an 8PAM signal, as can be seen in Fig. 1(b). In order to minimize quantization noise, OFDM is usually transmitted using higher resolutions. Nevertheless, low baudrate OFDM Back-to-Back (BTB) transmission has been demonstrated using 3 bits [12]. Our experimental BTB results are shown in Fig. 1(a) using a 3-bit DAC, emphasizing the strong performance limitation posed by this low resolution. For comparison, Fig. 1(a) also shows the histogram before quantization, demonstrating the quasi-analogue time-dynamics of a typical OFDM signal. For this resolution, the maximum density when using all subcarriers at the same power is Quadrature Phase Shift Keying (QPSK) [12].

3. Reference experimental setup

The OFDM signal is generated offline and separated into three bitstreams. They are loaded into the Bit-Pattern Generator (BPG), which is an SHF 12104A feeding the SHF 613A 3-bit@60Gbaud DAC. The optical modulator is the Mach-Zehnder based SHF 46215B (23GHz optical bandwidth) followed by the SHF 45210C optical amplifier. The Mach-Zehnder Modulator (MZM) is biased for intensity modulation. On the other side of the link, a PIN (70GHz bandwidth) is connected to a Tektronix DSA8300 sampling oscilloscope having 16bit@128GS/s. A schematic of the experimental setup is shown in Fig. 2. We use VPIlabExpert for signal upload/download to/from the lab equipment and also for offline processing with respect to signal generation, visualization, decoding, filtering and BER estimation. The memory of the sampling oscilloscope limited the number of frames, and consequently the number of subcarriers. We found the optimum number of subcarriers to be 32 which led to 128 OFDM frames (140ns), therefore the DFT size was 64 (31 subcarriers, first subcarrier is discarded). A PRBS pattern length of 2¹⁴−1 was used. We used a DMT signal with 32Gbaud, 10% cyclic prefix and with clipping optimized to 10%. The transmitted power and modulation index were optimized in optical BTB and the power was found to be 7.6dBm whereas the modulation index was close to 100%. This high modulation index leads to increased signal distortion in two ways. The first is due to the Mach-Zehnder non-linear transfer curve, exacerbated by the fact that the high clipping of OFDM causes a large amount of samples to be transmitted in the non-linear region of the transfer function. The second is related to the relative small difference between the power of the optical carrier and sidebands, leading to large SSII (subcarrier to subcarrier beating) already for the optical BTB case. In this case, the amplifier and receiver noises are dominant, therefore high signal power with low amplifier gain are desired. We performed optical OFDM transmission while adapting the signal to the transmission link using bit loading and subcarrier suppression. In our experimental setup we did not perform powerloading in order to have the same quantization noise for all the subcarriers. This allowed us to better analyse how the transmission affected the SNR. Initially, QPSK was tested for all subcarriers. Whenever BER was above the threshold, Binary Phase Shift Keying (BPSK) was used. For optical BTB we achieved a net capacity of 48.6Gb/s (8 subcarriers using BPSK). For 1km transmission, a net capacity of 45Gb/s was possible (8 subcarriers using BPSK). For 10km transmission, there was a power fading null at 20GHz (see Fig. 3(a)). At the null no subcarriers were able to be transmitted. For frequencies above the null the attenuation is still high which caused SNR to be too low to support subcarrier transmission, therefore, all subcarriers above subcarrier 16 were disabled, resulting in a net transmission rate of 27Gb/s.

 

Fig. 2 Experimental setup where the BPG+DAC feed an intensity driven MZM.

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Fig. 3 Simulated OFDM spectra showing power fading evolution (a). Capacity comparison between PAM and OFDM with 3-bit resolution (b) (black stars show experimental results).

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4. OFDM vs. PAM performance comparison and capacity considerations

As our experiments are limited to specific fibre lengths, we used these results to characterize the system and its components to build realistic numerical simulation setups using VPItransmissionMaker Optical Systems. With the aid of device parameters we were able to model the bandwidth limitation and electrical noise of the DAC and insertion loss, optical amplifier noise and photodiode noise and bandwidth. These characteristics were then used to evaluate the system capacity achieved by OFDM and PAM for transmission distances up to 20km SSMF.

4.1. Experimental 3-bit interface for 400G Ethernet

Initially we used numerical simulations to expand our experimental results for distances up to 20km SSMF using only bit loading and subcarier suppression. Volterra filtering was tested, but as the system was mainly quantization noise limited, its use showed no capacity improvement. For PAM simulations, we reduced the modulation index to ≈70% allowing sufficient eye opening to transmit 8PAM. We selected the highest capacity available for each transmission distance: 8PAM@32Gbaud up to 3km, where the power fading null is starting to affect the signal. From 4km to 7km 4PAM@32Gbaud was used, here the power fading null is inside the signal bandwidth. After 7km, 4PAM baudrate was halved to 16Gbaud. 4PAM@16Gbaud can be transmitted up to 16km similarly to [4], this limit is due to the power fading null being present in the high frequency portion of the signal bandwidth. PAM shows higher capacity than OFDM with bit loading for nearly all transmission lengths below 17km, as seen in Fig. 3(b)(blue squares). Unlike PAM, OFDM can cope with power fading anywhere in its signal bandwidth by disabling subcarriers. OFDM transmission can be further improved by the use of power loading, as seen in Fig. 3(b)(green triangles). A denser constellation can now be supported, we opted for Circular 16 Quadrature Amplitude Modulation (C16QAM) as it is known to present slightly better noise requirements than square 16QAM. From this point onwards, all OFDM results use bit-and-power loading. OFDM now outperforms PAM for all distances larger than 7km. In order to further increase PAM performance, a fractionally-spaced DFE was applied at the receiver. The 8 forward and 3 feedback tap coefficients were obtained using a training signal. As seen in Fig. 3(b)(orange diamonds), the use of the DFE allows an increase in achievable distance by 3km for 8PAM@32Gbaud and 4PAM@32Gbaud. It also enables the use of 8PAM@16Gbaud up to 20km. With the use of the equalizer, PAM is more resilient to power fading. 8PAM can now support a power fading null in the high frequency part of its spectrum. 4PAM can support a power fading null at almost half of its bandwidth. In summary, OFDM can cope with power fading in small decrements of capacity whereas PAM shows large steps. Nevertheless, PAM without DFE performs better than OFDM only for lengths below 8km, whereas PAM with DFE outperforms OFDM for all considered lengths.

4.2. Relaxed resolution limitation

As DSP-enabled PAM outperformed OFDM for all lengths, the comparison between both modulation formats was extended by the removal of the resolution limitation. We studied the impact of several DAC resolutions on capacity for optical BTB and 10km SSMF. Results are presented in Fig. 4(a). Here we see that OFDM requires a minimum of 6-bit to match PAM in capacity. As previously, we perform simulations for OFDM up to 20km, seen in Fig. 4(b)(brown triangles). Here, OFDM shows the same trend as previously seen in Fig. 3(b)(green triangles) albeit at a higher capacity. The initial capacity loss is due to the appearance of the power fading null at 4km. After 6km the null has progressively lower frequency and the subcarriers with frequencies above the null can be reused. Unlike PAM, OFDM is able to adapt to the changes in frequency of the null and is insensitive to its position on the signal spectrum. After 11km, the second null is present and capacity reduces progressively even when frequencies above the second null are available. This is due to their higher attenuation causing a lower SNR than the ones after the first null. At 20km, both transmission formats achieve the same capacity.

 

Fig. 4 Capacity comparison using simulations. PAM and OFDM transmissions at BTB and 5km for different DAC resolutions (a) and PAM with DFE and 6-bit OFDM with bit-and-power loading (b).

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5. Conclusions

We experimentally demonstrated 27Gb/s OFDM transmission at 1550nm over 10km SSMF using our 3-bit high baudrate IM/DD interface. Using simulations based on experimental results, we were able to compare OFDM and PAM. DFE-enabled PAM achieved 64Gb/s up to 10km, which makes it possible to reach the 400Gb/s goal by using 7×64Gb/s. OFDM is strongly limited by quantization noise using this low resolution interface. We performed further simulations where a 6-bit DAC was used. At this resolution, OFDM is not quantization noise limited. For transmission up to 2km, both modulation formats show similar performance, but PAM can be used without DFE. For transmission between 2km and 10km, both modulation formats show similar performance. For transmission above 10km, OFDM has a clear advantage as its multi-carrier nature allows adaptation to power fading.