## Abstract

In this paper we experimentally demonstrate transmission performance of optical DFT-spread OFDM systems in comparison with conventional OFDM systems. A 440.8-Gb/s superchannel consisting of 8 x 55.1-Gb/s densely-spaced DFT-S OFDM signal is successfully received after 1120-km transmission with a spectral efficiency of 3.5 b/s/Hz. It is shown that DFT-S OFDM can achieve an improvement of 1 dB in Q factor and 1 dB in launch power over conventional OFDM. Additionally, unique word aided phase estimation algorithm is proposed and demonstrated enabling extremely long OFDM symbol transmission.

©2011 Optical Society of America

## 1. Introduction

Coherent Optical OFDM (CO-OFDM) transmission has shown great promise of supporting single channel transmission data rate beyond 100 Gb/s [1–5]. On one hand, CO-OFDM has drawn great interests in recent years due to its high spectral efficiency and dispersion resilience [1–5]. On the other hand, CO-OFDM has drawbacks of high peak-to-average power ratio (PAPR) and sensitivity to laser phase noise. Particularly, high PAPR causes excessive nonlinear noise during fiber transmission [6]. Recently, discrete-Fourier-transform spread OFDM (DFT-S OFDM) was proposed as an attractive alternative to conventional CO-OFDM that possesses low PAPR within each OFDM sub-band [7,8].The superior nonlinear performance of DFT-spread (DFT-S) OFDM is predicted by simulation in comparison with conventional OFDM [7,9].

In this paper, we show the first experimental verification of nonlinear performance advantage of DFT-S OFDM systems over conventional OFDM systems. Densely-spaced 8 × 55.1-Gb/s DFT-S OFDM channels are successfully received after 1120-km transmission with a spectral efficiency of 3.5 b/s/Hz. We adopt a novel approach of consecutive transmission of both DFT-S-OFDM and conventional OFDM signals, enabling stable and repeatable comparison between these two formats. It is shown that DFT-S OFDM has advantage of about 1dB in Q factor and 1 dB in launch power over conventional OFDM. Additionally, unique word (UW) aided phase estimation algorithm is proposed and demonstrated enabling extremely long OFDM symbol transmission and subsequently improved spectral efficiency.

## 2. Principle of unique-word (UW) DFT-S OFDM

The concept of unique-word and its application were proposed for single carrier frequency-domain equalization (SC/FDE) [10]. Aided by the known UWs, better synchronization, channel estimation, and carrier phase estimation can be achieved for UW based systems compared with CP based counterparts [11,12]. The UW is derived from Zadoff-Chu sequence which will be defined later in this section.

Figure 1
illustrates the UW OFDM symbol structure for one of the two polarizations. The UWs are periodically inserted in the data sequence. In this paper, we choose the length of one DFT-S OFDM symbol to be 2048 points, including two 64-point UW patterns at two ends. Each 64-point UW pattern is cyclically extended by 16 points as shown in Fig. 1 (where GI_{1} and GI_{2} are 16-point GIs for UW_{1} and UW_{2,} respectively.), which results in an 80-point UW pattern at each side of OFDM symbol. An optional 8-point GI (GI_{sym}) is appended at the start of the OFDM symbol, which is a copy of the last 8-point of UW_{2}. The purpose of this optional 8-point is to keep data symbol length the same as training symbols. This GI is needed for training symbols so that no extra interpolation required when calculating channel matrix. But it is only optional for data symbols and thus can be dropped for data symbols without affecting any performance. The total length of one DFT-S OFDM symbol is 2056 points.

We adopt block-based decision-feedback (DF) phase estimation given by [13–16]

_{$\u3008\u3009$}represents ensemble average,

_{${\varphi}_{i}$}represents the carrier phase estimated for the

*i*-th segment, ${A}_{ij}^{}$and

*are respectively received and transmitted*

_{${A}_{ij}^{0}$}*j*-th point in the

*i*-th block of a OFDM symbol,

*M*is the OFDM symbol length, and

*K*is the block length for phase estimation. ${A}_{ij}^{0}$can be replaced with the recovered (or sliced) data after symbol decision on the received symbols when the transmitted symbols are not known. The procedure of UW-based DF phase estimation is as follows: the first block for the phase estimation in each OFDM symbol is calculated within the UW, where the transmitted symbols${A}_{ij}^{0}$are known. The constellation of the second block will be de-rotated using the phase estimated from the first block given by

*and*

_{${A}_{ij}^{}$}_{${A}_{ij}{}^{\prime}$}are the

*j*-th point in the

*i*-th block of a OFDM symbol before and after phase compensation, respectively. After constellation de-rotation, the symbol decision will be made to the phase compensated symbols

_{${A}_{ij}{}^{\prime}$}. Then another iteration of phase estimation and compensation will be made by applying Eqs. (1) and (2) (for arbitrary

*i*), which will be subsequently passed to the following block. The propagation will continue until the end of payload blocks. It is noted that the phase estimation can also be performed using UW

_{2}and propagate the phase estimation backward. In this paper, we use

*K*of 16 if not otherwise mentioned.

A similar OFDM symbol structure to that shown in Fig. 1 can be drawn for the second polarization by using different UWs. The reason to use two UWs within one OFDM symbol is compatibility with polarization diversity where the first and second UWs are orthogonal to each other when combining the two OFDM symbols for two polarizations in a Jones vector form. The two UWs for the two polarizations, $\left(\begin{array}{c}U{W}_{x1}\\ U{W}_{y1}\text{\hspace{0.05em}}\end{array}\right)$and$\left(\begin{array}{l}U{W}_{x2}\\ U{W}_{y2}\end{array}\right)$ are given by

*ZC*is the Zadoff-Chu sequence expressed as a row vector of size

*N*[17]. $circshift(\text{\hspace{0.05em}}\text{\hspace{0.05em}})$denotes a circular shift of the sequence by half of the sequence length and * denotes complex conjugate. The circular shift ensures that UWs for two polarizations, e.g., $U{W}_{x1}$and$U{W}_{y1}$are uncorrelated so long as the channel length is shorter than half of the sequence length. Such configuration can aid fast synchronization and channel estimation (not explored in this paper). Fast synchronization and channel estimation for UW based DFT-OFDM will be discussed in a separate submission.

_{zc}UW aided phase estimation can be very effective in comparison with phase compensation method in conventional OFDM system. Since the phase estimation compensation is implemented in the time domain, it is possible to perform intra-symbol phase noise estimation rather than conventional symbol-wise phase estimation. Additionally, because of known UWs are used to initiate phase estimation, the errors resulting from wrong symbol decisions do not prorogate beyond one OFDM symbol.

Figure 2 shows the signal flow diagram for DFT-S OFDM transmitter and receiver. At the transmitter, after serial to parallel conversion, the UWs are added with data, and converted to frequency domain by applying an M-point DFT. The DFT spread signal is then mapped onto an N-point vector which is subsequently converted to a time-domain signal by IDFT. Typically N is an integral larger than M. In this paper, we choose M of 2048 and N of 4096. The subcarrier mapping is a localized mapping [18], which means subcarriers are placed continuously and are occupying the center part of the spectrum in this paper. The guard-interval is inserted before digital-to-analog conversion (ADC) to avoid inter-symbol interference. The comparison of RF spectra between DFT-S OFDM and conventional OFDM is shown in Fig. 3 . The spectra are plotted under the condition that the two signals have exactly the same root mean square (RMS) value. For conventional OFDM signal, it uses 128-point FFT size. The reason we choose FFT size of conventional OFDM different from that of DFT-S OFDM signal is due to the phase noise. The conventional OFDM FFT size is limited by the phase noise and FFT of 128 is chosen. However, for DFT-Spread OFDM, the phase noise can be estimated in the time domain. After the IFFT at receiver, the signal is transformed back to the time domain where a proper averaging window can be chosen for phase estimation. In this way, the FFT size is not limited by phase noise. As a result, the OFDM symbol length can be relatively large. Meanwhile, due to the 160-point UW used, a long OFDM symbol is required to reduce the overhead. Consequently, we choose quite different sizes for DFT-S and conventional OFDM: FFT size of 4096-point for DFT-Spread, and 128 for conventional OFDM. From Fig. 3, both signals have the same bandwidth and identical gap width in the middle to avoid impairment from DC. It can be seen that DFT-S OFDM signal has less power fluctuation and out-of-band leakage because it has much larger FFT size of 4096 than FFT size of 128 in conventional OFDM.

At the receiver, after the signal is down-converted to baseband, timing synchronization and serial-to-parallel conversion is made. Then the guard-interval is removed and a proper N -point window is selected to apply DFT. After the DFT, the frequency-domain signal is down-sampled and equalized with a one-tap equalizer. We use a hybrid of short and long training symbols for channel estimation. Only 2 short training symbols and 2 long training symbols are used in this paper. The short and long training symbols consist of 128- and 4096-point Zadoff-Chu sequence respectively. Figure 4
shows the detailed channel estimation procedure: the first step is to calculate a coarse channel matrix (or *H* matrix) by using short training symbols. This coarse channel matrix will be interpolated and then expanded to the same length as long symbols. The next step is to perform frequency-domain equalization to the long symbols by using coarse *H* matrix. The equalized long symbols are further transformed back to time domain to estimate intra-symbol phase noise. This estimated phase noise is then used to apply phase compensation on the original long training symbols. After the phase noise compensation, the conventional maximum-likelihood channel estimation can be performed to obtain updated *H* matrix [16]. The same process can be repeated a few times until an accurate *H* matrix can be obtained. In this paper, no iteration is used since it is found a single round of channel estimation is sufficient. After the frequency-domain equalization, M-point IDFT is applied to the equalized signal to rewind the DFT spreading at the transmitter. The UWs are employed to seed the DF aided phase estimation and compensation as described previously. Finally, symbol decision is made to the phase compensated OFDM symbols.

The nonlinear advantage of multi-band DFT-OFDM has been theoretically analyzed [7,9]. In multi-band DFT-OFDM systems, each subband is essentially filled with a digitally-generated single-carrier signal. It has been shown that DFT spreading significantly lowers the PAPR for DFT-S OFDM compared with conventional OFDM [8]. For instance, DFT-S OFDM signal exceeds a PAPR of 7.5 dB for less than probability of 0.1%, and this PAPR is 3.2 dB lower than the value in conventional OFDM with the same probability [8]. Furthermore, one of the important findings of DFT-OFDM for optical transmission is that there exists an optimal bandwidth within which the subbands should be partitioned. The reason for this optimal bandwidth with respect to nonlinearity performance is as follows [7,9]: if In the case of small number of subbands, e.g., single carrier, the subband bandwidth becomes too broad. Although the PAPR within each subband is low at launch, due to large walk off among frequency components within each subband, the PAPR of each subband will grow rapidly thus inducing nonlinearity penalty; In the case of large number of subbands, the subband bandwidth becomes too narrow. Neighboring subbands interact just as narrowly-spaced OFDM subcarriers, generating large inter-band nonlinear crosstalk and thereby large penalty due to narrow subband spacing. Subsequently there exists a sweet spot in number of subbands that gives the optimal nonlinearity performance. In this experiment, each DFT-OFDM subband is 5 GHz, which is close to the optimal subband bandwidth predicted in [7,9].

Due to one extra DFT at transmitter and one extra IDFT at receiver, the complexity of digital signal processing (DSP) of DFT-S OFDM is higher than that of conventional OFDM. However, due to the improved nonlinearity tolerance, DFT-S OFDM may be a good choice where additional system margin is needed.

## 3. Experimental results and nonlinear performance analysis

The experimental setup is shown in Fig. 5 . At the transmitter, 8 CW lasers are combined and fed into an intensity modulator to impress 3 tones onto each wavelength. The tone spacing is controlled by the drive RF frequency at 5.3125-GHz, and wavelength spacing is set to be 16.4375-GHz. The optical signal is then split with a 3-dB coupler for separate modulation on the two polarizations. The OFDM signal for each individual band is generated by a Tektronix Arbitrary Waveform Generator (AWG). The time-domain OFDM waveform is first generated in a Matlab program with the parameters as follows: total number of subcarriers is 4096 with 4QAM encoding, guard interval is 16/4096 of the observation period, and middle 2145 subcarriers out of 4096 are filled, from which 160 subcarriers are occupied by UW patterns, and 97 subcarriers in the middle are left null to avoid contamination from DC. The real and imaginary parts of the OFDM waveforms are uploaded onto the AWG operated at 10-GS/s to generate two corresponding analog signals. The two polarization signals from 3-dB couplers are separately fed into two optical IQ modulators that are driven by the two AWGs. Consequently, the baseband OFDM signals are impressed onto all the 24 optical tones. The optical spectra of 8-lasers, 24-tones with and without data modulation are shown as insets. The spectrums have flatness over 1.1nm bandwidth.

The optical outputs from the two IQ modulators are combined with a polarization-beam combiner (PBC), forming a dual-polarization 8-channel DFT-S OFDM signal, with each channel carrying 55.1-Gb/s data. The signal is coupled into a recirculation loop for 1120-km transmission. The recirculation loop is consisted of two spans of 80-km SSMF fiber, with two EDFAs at the end of each span to compensate fiber loss. After transmission the signal is received with a polarization diversity coherent receiver. The RF signals from the coherent receiver are then input into a Tektronix real-time sampling scope at 50-GS/s, and processed with a Matlab program using a 2x2 MIMO-OFDM model. To gain stable and repeatable comparison, DFT-S OFDM and conventional OFDM waveforms are cascaded in time domain digitally before loading onto AWG, with the same RMS value. Parameters for conventional OFDM signal are as follows: total number of subcarriers is 128 with 4QAM encoding, guard interval is 1/8 of the observation period, middle 67 subcarriers out of 128 are filled, and DF-based common phase error is calculated for phase estimation. 3 subcarriers close to DC are unfilled to avoid degraded performance due to DC. As such, the unfilled portion of the spectra are kept the same for both DFT-S and conventional OFDM.

Figure 6 shows an example of phase evolution over 16 DFT-S OFDM symbols (or about 6.5 µs). The phase noise within 12th symbol is shown in inset. It can be seen that due to the long symbol length, the phase can varies more than 0.6 rad within one OFDM symbol. It is obvious that the symbol-wise phase noise compensation is not suitable for extra long symbols. Thus it is necessary to introduce the UW-based time-domain phase compensation.

Figure 7
gives the BER sensitivity of 18.4-Gb/s, 55.1-Gb/s, and 8 × 55.1-Gb/s signal at back-to-back for both DFT-S OFDM and conventional OFDM, which corresponds to one-band, three-band (or one wavelength), and 24-band (or 8 wavelengths) OFDM signal. For 18.4- and 55.1 Gb/s system, the BER is respectively measured over 1,208,320 and 3,624,960 bits. Figure 7 suggests that DFT-S OFDM and conventional OFDM have the same linear performance at back-to-back. The OSNR requirement for a BER of 10^{−3} is about 6-dB, 11-dB, and 21-dB for 18.4-Gb/s, 55.1-Gb/s, and 440.8-Gb/s system respectively.

Figure 8
shows the nonlinear performance of both DFT-S OFDM signal and conventional OFDM signal for 440.8-Gb/s after 1120-km transmission. Figure 8 (a) shows signal launch power vs. Q factor. It can be seen that DFT-S OFDM has better nonlinear performance, with 1dB optimal Q factor improvement, and about 1 dB improvement in optimal launch power. The effectiveness of DFT-S OFDM system is more evident at high nonlinear region. For instance, at launch power of 7 dBm or 8 dBm, the Q factor of DFT-S OFDM is improved by more than 2 dB. The constellations measured at launch power of 7 dBm are shown as inset in Fig. 8 (a). It is evident that DFT-S OFDM has better performance after 1120-km transmission. To further isolate the nonlinear effect from the phase noise effect, we conduct signal processing by using phase estimation block size *k* of 64. Since the conventional OFDM is also using phase estimation window of 64 points, the phase noise has the same impact on both DFT-S and conventional OFDM. The Q factor difference between DFT-S and conventional OFDM is shown in Fig. 8 (b) when both have the same phase estimation window size of 64. As can be seen in the figure, when the launch power is higher than 1 dBm, with the increasing power level, the advantage of DFT-S OFDM increases, e.g., 2.8 dB at the launch power of 8 dBm. Because DFT-S and conventional OFDM shall have the same linear phase noise impact due to using the same phase estimation window size, the Q factor difference between these two formats in Fig. 8 (b) is clearly caused by nonlinearity tolerance.

We also measure performance after transmission for the 24 OFDM sub-bands of 8 lasers. The launch power is 4 dBm, which is the optimal power for 440.8-Gb/s DFT-S signal. The Q factors are shown in Fig. 9 . We can see that the advantages of DFT-S OFDM system have been preserved over all the sub-bands, about 1 dB on average. It is noted that due to the middle portion of the spectrum is unfilled (Fig. 2 (b)), the DFT-OFDM signal in this paper is not strictly a single-carrier one. Nevertheless, this demonstration shows not only this quasi-single-carrier format can be received properly for long-haul transmission, it also possess nonlinear advantage over the conventional OFDM. Additionally, because of the long OFDM symbol used, the overhead is reduced to below 10% as opposed to 20-25% in conventional CP based OFDM systems [1].

## 4. Conclusion

We have shown the first experimental verification of nonlinear performance advantage of DFT-S OFDM systems over conventional OFDM systems. Densely spaced 8 × 55.1-Gb/s DFT-S OFDM channels are successfully received after 1120-km transmission with a spectral efficiency of 3.5 b/s/Hz. We adopt a novel approach of consecutive transmission of DFT-S-OFDM and conventional OFDM enabling stable and repeatable measurements. It is shown that DFT-S OFDM has advantage of about 1 dB in Q factor and 1 dB in launch power over conventional OFDM. Additionally, unique word (UW) aided phase estimation algorithm is proposed and demonstrated enabling extremely long OFDM symbol transmission.

## Acknowledgment

This work was supported by Australian Research Council (ARC) and National ICT of Australia (NICTA). NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT centre of Excellence program.

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