We investigate the performance and DSP resource requirements of digitally generated OFDM and sinc-shaped Nyquist pulses. The two multiplexing techniques are of interest as they offer highest spectral efficiency. The comparison aims at determining which technology performs better with limited processing capacities of state-of-the-art FPGAs. It is shown that a novel Nyquist pulse shaping technique, based on look-up tables requires lower resource count than equivalent IFFT-based OFDM signal generation while achieving similar performance with low inter-channel guard-bands in ultra-dense WDM. Our findings are based on a resource assessment of selected DSP implementations in terms of both simulations and experimental validations. The experiments were performed with real-time software-defined transmitters using a single or three optical carriers.
© 2012 OSA
Digital signal processing (DSP) resources ultimately limit the maximum speed of real-time multiplexing techniques such as orthogonal frequency division multiplexing (OFDM)  or Nyquist wavelength division multiplexing (N-WDM) . These two multiplexing methods are attractive, because in theory they both offer a spectral efficiency (SE) close to or at the Nyquist limit . Yet, despite their similarities , where OFDM is mathematically described by a superposition of sinc-shaped subcarriers, while N-WDM is made up of temporal sinc-pulses, the actual implementation and thus the DSP resource requirements are quite different depending on the selected processing technique. The question remains: Which of the two techniques can be implemented more efficiently with respect to DSP resources?
Spectrally efficient ultra-dense WDM networks call for optimum channel utilization without inter-channel interference (ICI). At best, the channel spectra should be of rectangular shape. This way, independent channels can be added without overlap. This enables independent channels which need not be synchronized and use free-running independent laser sources as optical carriers. Due to their potentially high SE, both Nyquist pulse shaping and multiband OFDM  are promising options. Spectra for these two multiplexing techniques are schematically depicted in Fig. 1 . We briefly discuss the concepts and focus on the relevant parameters for generating nearly-rectangular spectra with either of the schemes.
Option 1 – OFDM: Electrically generated OFDM signals comprising multiple subcarriers (SC) can be transmitted in independent WDM channels, Fig. 1(a). With an increasing number of SCs per channel within a fixed bandwidth, the OFDM spectrum approaches a rectangle. Therefore, by a proper choice of SC number, inter-channel guard-bands can be reduced without introducing ICI.
Option 2 – N-WDM: Electrically generated Nyquist pulses are shaped with so-called finite duration impulse response (FIR) filters, have nearly rectangular spectra, and are transmitted in independent WDM channels (N-WDM), Fig. 1(b). The higher the filter order R is, the closer the spectrum approaches a rectangle. If R is chosen appropriately, then inter-channel guard-bands can be kept small without introducing ICI.
Several real-time transmitter (Tx) concepts producing digitally generated OFDM and Nyquist pulses have been demonstrated. Here we confine the discussion to implementations with the potential of generating 100 Gbit/s using a dual-polarization scheme. For real-time OFDM, recent publications demonstrated data rates of 101.5 Gbit/s  and 85.4 Gbit/s  in a single polarization and 93.8 Gbit/s  in a polarization division multiplexed (PDM)  configuration. So far, real-time Nyquist sinc-pulse Tx were demonstrated at speeds of 112 Gbit/s  and 150 Gbit/s , both using PDM.
In this paper we compare the system performance and DSP resource requirements of OFDM and Nyquist sinc-pulse generation for two selected DSP approaches, exemplarily. This work is an in-depth discussion of our work previously published in  extended by simulations of the implemented DSP and a discussion of the receiver. First, the implemented code to be run on field programmable gate arrays (FPGA) is evaluated in terms of achievable performance and resource utilization. Second, both a single-channel and an ultra-dense WDM scenario with three carriers are experimentally assessed, using two software-defined Tx  to generate either OFDM with 80 SCs or Nyquist sinc-pulses formed with FIR filters of order R = 32, 64, and 128. With both multiplexing techniques we transmitted either the format quadrature phase shift keying (QPSK) or we used 16-ary quadrature amplitude modulation (16QAM). Finally, we briefly discuss potential OFDM and Nyquist pulse receivers (Rx).
2. VHDL/Verilog simulations and resource requirements
First we investigated the potential performance of the two pulse shaping techniques in terms of signal quality and spectral shape using the target field programmable gate arrays (FPGA) that were to be used in the experiments. To this end, the designs developed with the hardware description languages Verilog (for the inverse fast Fourier transform only, IFFT) and VHDL (very high speed integrated circuit hardware description language) were investigated on the register transfer level (RTL), a design abstraction which models the signal flow of synchronous digital circuits. The simulations (performed with the Modelsim software) used a test bench (Xilinx ISE software) for obtaining the bit-level-accurate outputs to be expected from the FPGAs. Additionally, we determined the resource requirements of each DSP design. The DSP blocks are pictured in Fig. 2(a) (OFDM) and in Fig. 2(b) (N-WDM), respectively.
Option 1 – OFDM: The DSP blocks used for real-time OFDM generation are depicted in Fig. 2(a). A pseudo random binary sequence (PRBS) generator produced binary data (periodicity: 215 – 1) that served as input. Following this, bit mapping to the QPSK/QAM states was performed. In the next processing block, a 128 point IFFT based on a mixed-radix Cooley-Tukey fast Fourier transform (FFT, radices 16 and 8, generated with the Spiral tool)  produced a complex-valued OFDM waveform with 80 SCs carrying either QPSK or 16QAM data. Four additional pilot tones were used for equalization. The remaining SCs were set to zero leading to an oversampling factor of 128 / 85 ≈1.5. Oversampling is needed to remove the image spectra produced by digital-to-analog converters (DAC) with realizable low-pass filters. The generated signals had an optical bandwidth close to 13 GHz carrying either 25 Gbit/s (QPSK) or 50 Gbit/s (16QAM) of data. The computational precision of the IFFT was 10 bit and the output waveform was quantized and clipped to 6 bit according to the DAC resolution of the target system. Clipping reduces the peak-to-average power ratio (PAPR) of the signals . The simulated OFDM spectrum (assuming an ideal 6 bit DAC) is depicted in Fig. 3(a) . The frequency is normalized to the sampling rate Fs (in the experiments Fs = 20 GSa/s) of the used DACs. Four pilot tones can be identified as spectral lines in Fig. 3(a), since their amplitudes and phases were kept constant throughout all OFDM symbols. The simulated constellation diagram for 16QAM modulated SCs is shown in Fig. 3(b). In this diagram all 80 SCs contribute. It can be seen, that some of the SCs produce constellation points with an offset to the lower left. This has been compensated for at the receiver (Rx). The simulations predicted an achievable error vector magnitude (EVM)  of 4.2%. The residual error is due to limited computational precision, clipping and quantization noise.
Option 2 – Nyquist sinc-pulse generation: The DSP blocks used for real-time Nyquist sinc-pulse shaping are depicted in Fig. 2(b), where the same PRBS generator was used and the binary data was mapped to QPSK/16QAM symbols. Instead of using an IFFT, this time QPSK/16QAM data fed an FIR filter which processed 128 samples in parallel within each clock cycle. The impulse response of this filter was sinc-shaped, resulting in a near-rectangular signal spectrum. For Nyquist pulse shaping we used two-fold oversampling, i. e., two samples were generated for each transmitted symbol. Due to the use of look-up tables (LUT) , no multiplications during runtime were needed, a significant advantage when it comes to processing complexity and resource requirements. FIR filters of orders R = 32, 64, and 128 were implemented. As expected, the spectrum evolved towards an ideal rectangle with increasing filter order. The computational precision was dynamically adjusted according to , leading to an effective precision of 9.9 bit. Again a clipping module lowered the PAPR by removing amplitude peaks for quantizing the output waveform with 6 bit. Spectra obtained from the simulations of the VHDL designs using random input data are depicted for a filter order R = 32 (Fig. 4(a) ) and for a filter order R = 128 (Fig. 4(b)), respectively. Due to two-fold oversampling, the spectra are confined to the region |f / Fs| ≤ 1 / 4. Even the lower-order R = 32 filter shows a good out-of-band suppression and would be expected to perform well in ultra-dense WDM experiments. The generated Nyquist signals had a bandwidth close to 10 GHz for a symbol rate of 10 GBd. The data rates were either 20 Gbit/s (QPSK) or 40 Gbit/s (16QAM). Unlike OFDM DSP, Nyquist pulse shaping with 2s-fold oversampling (integer s) shows no residual EVM. This is due to the fact that each pulse maximum coincides with zeros of all other pulses, independent of the filter order that has been implemented.
Resource requirements: Table 1 summarizes the necessary FPGA resources for implementing the OFDM and N-WDM Tx. All numbers are based on synthesis results using the Xilinx XC5VFX200T FPGA. We compare the required resources for generating a complex-amplitude OFDM or Nyquist sinc-pulse waveform and conclude: While the number of slice registers and slice LUTs break even for the OFDM and Nyquist signals with filter orders around 64, our LUT-based Nyquist pulse shaping technique removes the need for any DSP48E slices as they support multiple functions (e. g. resource-hungry multiplications).
3. Experimental setup
The experimental setup is depicted in Fig. 5 . Three single-polarization WDM channels were generated using tunable external cavity lasers (ECLs) and a pair of nested LiNbO3 Mach-Zehnder modulators (MZM), which were connected in a configuration such that the two outer channels were modulated independently from the center channel. We employed two software-defined transmitters  each based on pairs of FPGAs (Xilinx Virtex 5 XC5VFX200T) and high-speed Micram DACs with 6 bit resolution. The DACs operated at 20 GSa/s and were followed by anti-aliasing filters with 12.5 GHz bandwidth. These transmitters generated the modulator drive waveforms (Tx I for the center channel, Tx II for the two outer channels in Fig. 5). A 215 − 1 PRBS was generated on the FPGAs and transmitted. The polarization states of the WDM channels were adjusted to obtain the worst-case ICI penalty. An optical spectrum analyzer (OSA) measured the WDM signal spectra and the optical signal-to-noise ratio (OSNR) for single channel configuration. The OSNR and therefore the relative amplified spontaneous emission (ASE) noise loading were adjusted with a variable optical attenuator (VOA). The center channel was selected with an optical filter, coherently detected using an Agilent optical modulation analyzer (OMA), and the data recovered using off-line DSP.
In order to obtain an equal data rate of 20 Gbit/s (QPSK) and 40 Gbit/s (16QAM) for the OFDM and Nyquist-WDM Tx signals, the OFDM signal should have been sampled with 16 GSa/s whereas for Nyquist-WDM a sampling rate of 20 GSa/s would have been appropriate. This stems from the fact that the Nyquist-WDM DSP uses two-fold oversampling and the OFDM DSP oversamples by a factor of 128 / 85 ≈1.5. However, the available anti-alias low-pass filters with a cutoff-frequency of 12.5 GHz would not have removed the whole of the image spectra at 16 GSa/s DAC operation. For this reason we have chosen 20 GSa/s for OFDM. In order to guarantee a fair comparison (independent of signal bandwidth) between OFDM and Nyquist signaling, we derived the actual SNR from the measured OSNR0.1nm .
4. Experimental results
4.1 Single channel characterization
In a first experiment, we tested the signal-to-noise ratio (SNR) sensitivity of single channel OFDM signals generated by the 128 point IFFT and compared the results with those obtained with Nyquist pulse-shaped signals generated with FIR filters of orders R = 32, 64 and 128.
The results of the EVM  measurements as a function of SNR are plotted in Fig. 6 . For OFDM we take the average EVM of all 80 SCs. It can be seen that the quality of the Nyquist signal is independent of the filter order as was expected from the simulations. Furthermore, it can be concluded that in the case of QPSK modulation, both OFDM and Nyquist pulse shaping show very similar SNR performance, see Fig. 6(a).
For 16QAM OFDM, however, the EVM was found to be slightly worse than for Nyquist-WDM, see Fig. 6(b). We attribute this increased implementation penalty in part to the 10 bit precision of the IFFT core, which was limited by the available resources on the FPGAs. Another limitation was imposed by the finite DAC resolution of 6 bits. Both limitations more seriously affect high order modulation formats.
Constellation diagrams are plotted for 16QAM Nyquist pulse shaping (Fig. 7(a) , blue) and SC 26 of the OFDM signal (Fig. 7(b), red) in back-to-back configuration. In Fig. 7(c) the EVM as a function of SC index is plotted. Subcarriers far away from the optical carrier are degraded due to a decreased SNR caused by the roll-off of the analog electronics. This could have been compensated for by pre-emphasizing SCs with lower SNR. However, in doing so, the power of other SCs reduces, so that the average SNR throughout all SCs remains constant.
4.2 Multi channel characterization
In order to assess the achievable SE we tested all designs in an ultra-dense WDM experiment comprising three free-running carriers. Since only the linear inter-channel crosstalk affecting the middle channel was investigated, three channels were sufficient as little additional information (for linear operation) can be gained from increasing the number of channels beyond this. The OSNR was set to its maximum achievable value. With the wavelength of the center channel kept constant, the outer channel wavelengths were varied to adjust the SE of the WDM signal. The guard-band between the edges of the signal bands was varied from 10 GHz down to zero for Nyquist-spacing. Figure 8 shows the WDM spectra with 5 GHz and 500 MHz guard bands.
To investigate the potential SE of both pulse shaping techniques in ultra-dense WDM networks, we measured the EVM penalty as a function of inter-channel guard-band width. The results for QPSK modulation are depicted in Fig. 9(a) . For guard-bands > 1 GHz there was virtually no influence of the Nyquist pulse-shapers’ filter order R on the signal quality. The ICI was negligible. For very small guard-bands (< 1 GHz), high filter orders perform slightly better. At some point, however, severe crosstalk is observed. This stems mostly from the fact that we use independent, free-running lasers whose center frequencies are not perfectly stable. Despite this, we can conclude that, even for small guard-bands, low Nyquist filter orders R suffice.
Similarly to Nyquist-WDM, good performance is also observed with the OFDM transmitters, even with small guard-bands between channels. The OFDM signal quality degrades gradually for guard-bands < 3 GHz which can be explained by the lower out-of-band suppression of the OFDM spectrum as compared to that of the Nyquist filtered signals. To reduce this effect, a larger number of SCs would be needed to make the signal spectrum more rectangular. The lesser increase in EVM penalty with reducing guard-band width for OFDM, compared to that observed with Nyquist pulse shaping can be explained by the outermost SCs of the OFDM signal being affected by ICI. At some point they can no longer be used for data transmission, while the inner-SC EVM remains low. The results for 16QAM modulation are shown in Fig. 9(b). These results follow the observations made in the QPSK measurements.
5. Discussion on receiver complexity for OFDM and Nyquist pulse shaping
So far, only a few real-time optical receivers (Rx) for OFDM [4, 15, 16] and single carrier M-ary QAM  have been demonstrated. Due to the increased complexity of the Rx as compared to the Tx, achieved data rates are significantly lower than for real-time Tx [3–7].
The main difference between a multicarrier OFDM Rx and a single carrier Nyquist pulse Rx is the process of data extraction and equalization. An OFDM Rx comprises an FFT which demultiplexes the orthogonal SCs . While the OFDM signal can be made tolerant to chromatic dispersion (CD) and polarization mode dispersion (PMD) through the addition of a cyclic extension , which can be achieved with low complexity DSP, this comes at the cost of increased overhead and thus reduced SE. It is preferable in high SE systems to employ FIR filters to equalize CD and PMD, avoiding the need for a large cyclic extension. Likewise, for Nyquist pulse Rx, FIR filters are needed to compensate for CD and PMD, and also to effectively remove spectral components from neighboring channels. An extensive analysis of receiver complexity for single carrier (e. g. Nyquist pulse modulation) and multi carrier (OFDM) systems is given in . In general, high order FIR filters are more effectively realized in the frequency domain using FFTs by employing frequency domain equalization (FDE) .
Analog electrical low-pass filters at the Rx can also contribute to the removal of unwanted components of the neighboring WDM channels for both multiband OFDM and Nyquist pulse transmission. Such analog filters relax the requirement on the Nyquist pulse Rx digital filter significantly. The non-flat frequency response of the transceiver electronics along with accumulated CD can be pre-compensated at the Tx , hence further reducing processing efforts for single carrier Rx.
We directly compared, for the first time, performance and DSP resource requirements of FPGA based OFDM and Nyquist pulse shaping. Two real-time implementations were compared, namely Nyquist pulse shaping with LUTs  and OFDM generation using the Spiral IFFT core . There are several studies on DSP complexity from a theoretical point of view  concluding that OFDM and Nyquist pulse shaping are similarly complex. An actual implementation using state-of-the-art FPGAs and DACs, however, reveals the strengths and weaknesses of each technique from a practical point of view. For instance, the LUT based Nyquist pulse shaping approach offers the possibility to compensate for the frequency response of the hardware by simply changing the pre-computed filter responses stored in the LUTs whereas for OFDM, the implemented IFFT core was optimized with respect to the specific 16QAM SC modulation format. Hence it did not allow for the OFDM typical one-tap equalizer  to be made use of in this Tx configuration. As future work, real-time OFDM and Nyquist pulse Rx ought to be compared.
Experiments were performed for a single wavelength and in an ultra-dense WDM scenario. Both, OFDM and Nyquist-WDM channels can be placed next to each other close to the Nyquist limit without experiencing significant inter-channel crosstalk, even though free-running lasers provided the optical carriers. However, the Nyquist sinc-pulses offer similar or slightly better performance than OFDM for very small guard-band widths (over the range 0.5–1 GHz). This can be explained by better out-of-band suppression of the N-WDM signals which calls for an increase in the number of SCs for OFDM. The overall OFDM signal quality in our experiments was essentially determined by the limited precision of the implemented IFFT and the limited effective resolution of the DACs. For Nyquist pulse shaping, an increase in filter order beyond R = 128 is not expected to further significantly minimize the crosstalk. At small guard-bands (i.e. lower than 10% of the channel spacing), even relatively low order (e.g. 32nd order) low-resource Nyquist pulse shaping suffices.
This work was supported by the projects ACCORDANCE, CONDOR, Micram Microelectronic GmbH, EPSRC UNLOC (EP/J017582/1), Piano + IMPACT and OTONES, as well as by the Xilinx University Program (XUP), and the Agilent University Relations Program. We further acknowledge financial support from Karlsruhe School of Optics & Photonics (KSOP), and the Open Access Publishing Fund of the Karlsruhe Institute of Technology (KIT).
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