## Abstract

Orthogonal transmission with frequency division multiplexing technique is investigated for next generation optical communication systems. Coherent optical orthogonal frequency division multiplexing (OFDM) and single-carrier frequency division multiplexing (SCFDM) schemes are compared in combination with polarization-division multiplexing quadrature phase shift keying (QPSK) or 16-QAM (quadrature amplitude modulation) formats. Multi-granularity transmission with flexible bandwidth can be realized through ultra-dense wavelength division multiplexing (UDWDM) based on the orthogonal technique. The system performance is numerically studied with special emphasis on transmission degradations due to fiber Kerr nonlinearity. The maximum reach and fiber capacity for different spectral efficiencies are investigated for systems with nonlinear propagation over uncompensated standard single-mode fiber (SSMF) links with lumped amplification.

© 2013 OSA

## 1. Introduction

The continuously increasing growth of traffic in backbone networks pushes the demand for a more effective exploitation of the optical fiber capacity. Coherent detection obtains the full information of the optical field in both polarizations, enabling digital signal processing (DSP) techniques to compensate for transmission distortions, which could pave the way for approaching the fundamental Shannon limit of information capacity.

Orthogonal frequency division multiplexing (OFDM) is a well-established multi-carrier (MC) transmission scheme in the field of wireless communications [1], which stands out as a standard for many applications such as the Long Term Evolution (LTE) of cellular systems by the Third Generation Partnership Project (3GPP), Mobile Worldwide Interoperability for Microwave Access (WiMax), wireless local area network (LAN), etc. Coherent optical OFDM (CO-OFDM) has been recently extensively studied as a strong candidate for long-haul optical transmission. Terabit per channel transmission based on CO-OFDM technique has been reported by the research groups worldwide [2–6]. One of the main advantages of CO-OFDM is its resilience to the linear channel impairments such as chromatic dispersion (CD) and polarization mode dispersion (PMD). Moreover, OFDM has a rectangular-like spectrum, which provides the possibility of high spectral efficiency (SE). One can aggregate tightly spaced optical subcarriers to form a super-channel conveying ultra-high speed signals. Both Terabit transmission and ultra-dense wavelength division multiplexing (UDWDM) systems can be constructed based on the orthogonal technique.

However, OFDM suffers from high peak-to-average-power ratio (PAPR), which leads to inferior tolerance to fiber nonlinearity and inefficient power consumption [7]. To combat this problem, coherent optical single carrier frequency division multiplexing (CO-SCFDM) technique is proposed [8, 9]. If generated in frequency domain, SCFDM is also called discrete-Fourier-transform-spread (DFT-S)-OFDM [10], which has been employed in uplink transmission in wireless LTE scheme and it has an attractive feature of much reduced PAPR than conventional OFDM [10]. The numerical simulation shows that CO-SCFDM demonstrates superior nonlinear tolerance in comparison to CO-OFDM [8, 9].

Terabit per second super-channel transmission of polarization-division-multiplexing (PDM) CO-SCFDM signals has been experimentally demonstrated [11, 12]. In [11], 40 optical subcarriers tightly spaced at 9.375 GHz carry 1.08 Tb/s OFDM or SCFDM signals, transmitting over 2536 km or 3170 km standard single-mode fiber (SSMF), respectively. Compared with CO-OFDM, CO-SCFDM has about 1.0 dB more nonlinear tolerance, thus achieves a larger maximum transmission reach in the experiment [11]. In [12], 87 optical subcarriers spaced at 5.15625 GHz carry 1.45 Tb/s DFT-S-OFDM signals, transmitting over 480 km SSMF.

UDWDM is highly desired for high spectral efficiency transmission. Meanwhile, flexible bit-rate and/or bandwidth transmission can be achieved by controlling the amount or the granularity of the optical subcarrier in an OFDM/SCFDM super-channel. Grid-less UDWDM system would provide transport service from Gigabit to Terabit per second through tightly spaced super-channels. The super-channel can be transmitted or routed as a single entity. Each optical subcarrier within the super-channel can also be added or dropped to realize sub-wavelength allocation [13]. Limits of spectral efficiency and transmission reach are analyzed for grid-less OFDM super-channels [14]. In [14], adaptive WDM system is simulated through 5 channels with variable modulation format, symbol rate or channel spacing, while the OFDM signal always has a constant number of 120 data subcarriers.

In wireless LTE scheme, the downlink is based on the OFDM technique while the uplink is based on the SCFDM technique. For optical communication, it is of great importance to provide a comprehensive study of the feasibility of orthogonal transmission with OFDM/SCFDM signals in UDWDM systems. In this paper, we concentrate on the study of UDWDM coherent optical OFDM/SCFDM transmission with multiple granularities. Consider a uniform design rule of OFDM/SCFDM frame for different granularities, the optimum guard band, the maximum transmission reach and fiber capacity are discussed in terms of quadrature phase shift keying (QPSK) or 16-QAM (quadrature amplitude modulation) formats.

The paper is outlined as follows. In Section 2, we present a general theoretical treatment of PDM-CO-OFDM and PDM-CO-SCFDM systems. In Section 3, we provide a uniform frame design of OFDM/SCFDM for different granularities. Section 4 compares the basic performance of CO-OFDM/SCFDM systems at back to back (BTB) scenario. The PAPR character is also discussed in both BTB case and dispersive channels. Section 5 shows nonlinear transmission performance of UDWDM systems based on OFDM/SCFDM techniques. The fiber capacity and the maximum transmission reach are studied in terms of various modulation formats, granularities and guard bands. Cross phase modulation (XPM) induced performance distortions are also specified. Finally, in Section 6, we comment on our results and draw the conclusions.

## 2. Basic theory

The DSP diagrams of both the transmitter and the receiver of PDM-CO-OFDM and PDM-CO-SCFDM system are shown in Fig. 1 . It can be found that the structures of the two block-transmission schemes are very similar. For PDM-CO-OFDM, the transmitted data stream passes through modulation mapping to produce the information sequence which is grouped into several transmitted data blocks. After pilot insertion, the ith transmitted data block ${a}_{i}$ is described as ${a}_{i}={\left[\begin{array}{cc}{a}_{ix}& {a}_{iy}\end{array}\right]}^{T}$. Here${a}_{ix}={\left[\begin{array}{cccc}{a}_{ix}\left(0\right)& {a}_{ix}\left(1\right)& \cdots & {a}_{ix}\left(N-1\right)\end{array}\right]}^{T}$ and ${a}_{iy}={\left[\begin{array}{cccc}{a}_{iy}\left(0\right)& {a}_{iy}\left(1\right)& \cdots & {a}_{iy}\left(N-1\right)\end{array}\right]}^{T}$ are the transmitted data for the two polarization branches, respectively. The transmitted data are converted to time domain by $N$-point inverse DFT (IDFT). Then cyclic extension is added to eliminate inter-symbol interference (ISI) induced by linear effects in optical fiber channel such as CD and PMD. After inserting the preamble consisting of some special training sequences, the two signal tributaries are sent to the front end to be modulated on optical carriers with orthogonal polarizations. In the front end, digital-to-analog converters (DACs) and optical modulators convert the baseband signal directly into optical domain. Then two polarization branches are multiplexed by a polarization beam combiner (PBC) and sent into optical fiber channel. The received signal together with the output of local oscillator (LO) laser are fed into the receiver front end, which consists of two 90° hybrids and two pairs of balanced photo detectors (BPDs). At the phase and polarization diversity receiver, I and Q tributaries of polarization $x$ and y signals are down-sampled with analog-to-digital converters (ADCs). Considering all linear effects in optical fiber channel, i.e. the combined effects of CD, PMD and polarization dependent loss (PDL), after removing cyclic extension, the received signals are transformed to frequency domain by DFT. We can obtain

PDM system can be modeled with a 2 × 2 multiple-input multiple-output (MIMO) technique. ${h}_{xx}$, ${h}_{yx}$, ${h}_{xy}$and ${h}_{yy}$ are time domain channel impulse response (CIR) vectors of the four equivalent MIMO channels with a memory length of $l-1$.

Here the superscript $H$ and $T$ stand for Hermitian transpose and transpose, respectively. ${w}_{i}$of size $2N\times 1$ denotes additive white Gaussian noise (AWGN).

For CO-OFDM, a few (${N}_{virtual}$) side subcarriers are usually turned off to spectrally separate the aliasing products generated by DAC processing. For PDM-CO-SCFDM transmission, the mapped information sequence at the transmitter is first grouped into data blocks of length $M$($M\le N$). The elements of the *i*th data block ${a}_{i}$ for two polarizations are ${a}_{ix}={\left[\begin{array}{cccc}{a}_{ix}\left(0\right)& {a}_{ix}\left(1\right)& \cdots & {a}_{ix}\left(M-1\right)\end{array}\right]}^{T}$ and ${a}_{iy}={\left[\begin{array}{cccc}{a}_{iy}\left(0\right)& {a}_{iy}\left(1\right)& \cdots & {a}_{iy}\left(M-1\right)\end{array}\right]}^{T}.$ ${a}_{ix}$ and ${a}_{iy}$ are transformed into frequency domain by $M$-point DFT, respectively. Then the $M$-point DFT outputs are mapped to $N$ orthogonal subcarriers by allocating virtual subcarriers at both sides of the band. After the $N$-point IDFT which transforms the signal to time domain, cyclic extension is inserted for each block before the data sequence is transmitted. Therefore, for PDM-CO-SCFDM transmission, the received signal ${r}_{i}$ is

Intra-symbol frequency-domain averaging (ISFA) [15, 16] based channel estimation and equalization is considered in this paper. At the transmitter, the training sequences ${P}_{x}$ and ${P}_{y}$ for the two polarization branches are inserted, respectively, which consist of a pair of correlated dual-polarization (CDP) training symbols as

The estimation of $H$ is denoted by $\widehat{H}$, which can be derived with the ISFA method as

## 3. Multi-granularity design principle

In this section, we discuss the design of OFDM/SCFDM symbols with a uniform methodology for multiple granularities of optical carriers. The parameters of OFDM/SCFDM symbols should be carefully designed to transport a target net bit rate ${R}_{net}$ via the specific transmission link. The OFDM/SCFDM related redundancies and the overhead for both Ethernet and forward error correction (FEC) should be taken into account. The granularities are chosen to convey a net bit rate of 25, 50 and 100 Gb/s if PDM-QPSK mapped. 100GE operation requires a raw line rate of usually 112 Gb/s to include overhead for Ethernet (64B/66B) and FEC coding [17]. The overhead due to the cyclic and the preamble should be limited to about 8% in order to realize a line rate about 120 Gb/s before oversampling.

The virtual subcarriers for oversampling provide a guard band in the frequency domain to reduce the out-of band radiation. The optical subcarrier within one super-channel may pass a reconfigurable optical add–drop multiplexer (ROADM). The guard band between optical subcarriers should also account for optical filtering effect. Moreover, in practice, a frequency drift may exist when optical subcarriers come from different sources, a guard band can increase the tolerance to this kind of orthogonal misalignment. Therefore, an oversampling ratio of about 120% is adopted in this work.

We consider uncompensated transmission over a SSMF link with 17 ps/nm/km local chromatic dispersion. The target transmission reach for 100GE is set as 1280 km, which requires a minimal cyclic guard interval of 6.5 ns/symbol.

Table 1 gives a list of OFDM/SCFDM parameters. Note that a fast Fourier transform (FFT) or inverse fast Fourier transform (IFFT) is an efficient algorithm to compute DFT and its inverse. An FFT size of 4096 is chosen for 100G operation with a sampling rate of 37 GS/s. The symbol duration is 117.1 ns and the cyclic overhead is 5.86%. The effective symbol duration ${T}_{eff}$ without cyclic extension is 110.6 ns. If a preamble ratio is set as 2.44%, a total of 8.3% overhead are obtained. For multiple optical granularities operation, FFT simply scales to different sizes, while electrical subcarrier spacing $\Delta f$ remains the same value of 9.04 MHz. Therefore both the symbol duration and cyclic overhead keep unchanged for multi-granularity optical carriers. An FFT size of 1024, 2048 and 4096 corresponds to a respective sampling rate ${S}_{p}$ of 9.25, 18.5 and 37 GS/s. The above scenarios can be referred as fine, medium and coarse granularities, which have effective bandwidths ${B}_{eff}$ of 7.75, 15.5 and 31 GHz, respectively. Grid-less UDWDM systems can be constructed on the basis of such tightly spaced optical carriers. As cyclic overhead is the same for different granularities, cyclic supported transmission reach should be doubled when the granularity downs to half size.

## 4. Basic comparison of OFDM and SCFDM

In this section, we make a comparison between OFDM and SCFDM systems in both BTB and linear transmission scenarios. The simulations are carried out via commercial software VPItransmissionMaker 8.6. The fiber link consists of multiple spans of 80 km SSMF with an average loss of 20 dB each. Fiber dispersion is 17 ps/km/nm. Fiber nonlinearity is not considered in this section. An Erbium-doped fiber amplifier (EDFA) with a noise figure of 5dB fully compensates fiber attenuation in each span. No inline chromatic dispersion compensation is used. At the coherent receiver, the specific channel is selected by a fourth order super-Gaussian optical filter with a 3 dB bandwidth of ${S}_{p}$. As the main task of this work is to provide a fundamental study of nonlinear performance of OFDM/SCFDM UDWDM systems, both the transmitter and the LO lasers are assumed with zero linewidth. The alignment of the LO to the optical carrier center frequency is assumed ideal. After optical hybrid, four BPDs are used to detect the received signal. The electrical signals are then filtered by a 5th-order low-pass Bessel filter with 3 dB bandwidth of 0.7${S}_{p}$. The electrical noise in BPDs is not considered. Both DACs and ADCs are assumed with unlimited bandwidth and without quantization noise. In our simulation, the training symbols consist of Chu sequences, which are polyphase sequences that have a constant magnitude in both the time domain and the frequency domain [18]. The phase of each OFDM/SCFDM block is first corrected with pilots, and then averaged through the Viterbi–Viterbi algorithm [19]. Note that for 16-QAM, a modified Viterbi–Viterbi algorithm is applied to partition the square-16-QAM into QPSK constellations for carrier phase estimation [20].

Figures 2
and 3
show constellation diagrams of PDM CO-OFDM/SCFDM systems at BTB scenario for QPSK and 16-QAM signals mapped, respectively. The optical signal to noise ratio (OSNR) is set as 25 dB at a resolution of 0.1 nm. Before equalization, the constellation diagrams will be influenced by optical and electrical filtering at both the transmitter and the receiver sides. After equalization, the signal can be recovered with only the degradation from amplified spontaneous emission (ASE) noise remains. Note that before equalization, two polarizations will superimpose on each other and virtual subcarriers remain around the constellation origins. The constellations of OFDM and SCFDM are different before equalization due to the extra FFT and IFFT processing in SCFDM systems. After equalization, similar performances are observed for both OFDM and SCFDM systems. The back-to-back performance of OFDM/SCFDM-PDM-QPSK signals, in terms of OSNR needed to achieve a bit error rate (BER) of 10^{−3} is 7.9, 10.9, and 13.9 dB for the granularities of 7.75, 15.5 and 31 GHz, respectively. For PDM-16-QAM signals, the corresponding required OSNRs are 14.7, 17.7, and 20.7 dB, respectively.

For linear transmission, we evaluate the PAPR distribution with complementary cumulative distribution function (CCDF), which gives the probability of the PAPR higher than a certain threshold. Figure 4 shows the CCDF curves of the PAPR for OFDM and SCFDM systems. The fine granularity with QPSK and 16-QAM encoded is chosen as an example. 12800 OFDM/SCFDM symbols are transmitted to calculate the PAPR samples. SCFDM demonstrates much lower PAPR at BTB scenario. After transmission, the PAPR of SCFDM increases with accumulated dispersion. In contrast, the PAPR distribution of OFDM keeps almost unchanged with transmission. After thousands of kilometers SSMF propagation, SCFDM demonstrates similar PAPR distribution as OFDM. This confirms that SCFDM has the single carrier character, which has been observed in single carrier frequency domain equalization (SCFDE) systems [21]. Due to the low PAPR, SCFDM has superior nonlinear performance compared to OFDM, which is shown in Section 5. It is interesting to note that for OFDM system, similar PAPR distribution is observed for both QPSK and 16-QAM signals regardless of propagation distance. In contrast, for SCFDM, 16-QAM yields larger PAPR than QPSK, although the difference becomes trivial after longer propagation.

## 5. Nonlinear performance

In this section, we carry out a detailed simulation of nonlinear performance of UDWDM systems with orthogonal transmission based on OFDM/SCFDM signals. Fiber nonlinear coefficient is 1.32 /km/W. Other parameters of the fiber link are detailed in Section 4. We first discuss the optimum time and frequency averaging in channel estimation, and then explain simulation bandwidth choice and investigate the maximum reach and fiber capacity under the influence of fiber Kerr nonlinearity. Note that when transmission distance is close to or longer than the cyclic extension supported length, we simply adopt an ideal dispersion compensating fiber to compensate the extra dispersion beyond the mitigation capability of cyclic extension.

Each UDWDM channel is polarization-multiplexed and encoded with different and uncorrelated pseudo-random binary sequence (PRBS). A time window of 64 ${T}_{eff}$ is chosen to perform simulation. We first study UDWDM systems with optical carrier spacing of ${S}_{p}$. The corresponding guard bandwidth is $GB={N}_{virtual}\Delta f$. Then we change the guard bandwidth to see how it influences the performance of UDWDM systems.

#### 5.1 Time and frequency domain averaging

${N}_{training}$ training symbols are implemented in the center channel for channel estimation. Both the time domain averaging based on multiple training symbols and the frequency domain averaging ISFA method based on subcarriers are employed to obtain a more accurate estimation of channel matrix.

Figures 5
and 6
show the performance of the time and frequency averaging channel estimation for QPSK and 16-QAM mapped OFDM/SCFDM systems with the granularity of 7.75 GHz. As shown in the next subsection, to make a good estimation of nonlinear distortions, a 28-channel UDWDM system is simulated and the optical channel spacing is ${S}_{p}\text{=9}\text{.25}$GHz. The BER values of the center channel are evaluated with direct error counting. The BER is converted to ${Q}_{BER}$ in dB using the relationship ${Q}_{BER}=20\mathrm{log}\left[\sqrt{2}erf{c}^{-1}\left(2BER\right)\right]$. Here erfc^{−1} is the inverse complementary error function. A BER target of 10^{−3} corresponds to a ${Q}_{BER}$ value of 9.8 dB. It is clear that SCFDM always has a superior performance compared to OFDM. ${Q}_{BER}$ does improve, but tends to saturate with the increasing of training symbols and the averaged subcarriers. We also test other granularities and make similar observations.

Note that the number of averaged subcarriers of ISFA processing is ultimately limited by phase variation induced by large amount of residual dispersion [15]. For less than about 1 rad phase difference between the center subcarrier and the farthest subcarrier in the averaging process of the ISFA, the criterion is deduced in [15] and we rewrite it again with the parameters defined in our paper.

${D}_{ISFA}$ is the residual dispersion prior to the ISFA. ${B}_{eff}$ is the effective bandwidth of OFDM/SCFDM signals. As $2m+1$ is the averaging subcarrier number of the ISFA window, $m\Delta f$is the optical frequency difference between the center subcarrier and the farthest subcarrier in the ISFA averaging process. For instance, after 50 spans transmission in Fig. 5, the residual dispersion is 68000 ps/nm, which yields the dispersion limited ISFA window with less than 17 subcarriers ($m<8.3$). We test the ISFA window with the averaging subcarrier number larger than 17, the system performance will degrade due to the criterion of Eq. (12).

The residual dispersion${D}_{ISFA}$is less than the cyclic supported values, which is inversely proportional to the effective bandwidth ${B}_{eff}$. Therefore, the averaging ISFA window should be approximately the same for different granularities.

More training symbols and ISFA subcarriers would also increase preamble overhead and DSP complexity. For a trade-off, we choose ${N}_{training}\text{=}4$ pairs for time domain averaging and 11 subcarriers for frequency domain averaging in the following studies, which provide sufficient channel estimation accuracy and fulfill the criterion of Eq. (12).

#### 5.2 Simulation bandwidth choice

It is essential to keep the physical bandwidth constant to ensure a fair comparison between multiple granularities, since the nonlinear distortion due to XPM and four-wave-mixing (FWM) depends on the frequency separation between the interacting optical carriers. As an example, Fig. 7
shows nonlinear degradation of OFDM system performance with the increase of physical bandwidth. Both QPSK and 16-QAM formats with different granularities are tested with the following parameters shown in Table 2
. According to the optimization results in Fig. 8
shown in the next subsection, the transmission distance and optical power are chosen to approximately obtain a BER target in the order of 10^{−3}.

The nonlinear penalty increases with the bandwidth expanding of UDWDM system and tends to saturate when UDWDM system assembles more and more channels. For instance, a 27-channel OFDM-QPSK system with fine granularity suffers a ${Q}_{BER}$degradation of 1.61dB compared to the single channel transmission, while a further increase of 12 channels only brings 0.1dB additional nonlinear penalty. Similar results are observed in both QPSK and 16-QAM systems with different granularities. Therefore we choose the number of simulated tightly aggregated optical carriers as 28, 14, and 7 at the granularities of 7.75, 15.5 and 31 GHz, respectively. With an optical channel spacing of ${S}_{p}$, the same bandwidth occupancy of 259 GHz is obtained for all three configurations, which ensures a fair comparison between different granularities. It is worthy to note that 259 GHz bandwidth is appropriate to evaluate nonlinear degradation of UDWDM systems. Further increase of simulation bandwidth will observe slightly difference of nonlinear penalty, while result in unrealistic computer time. When extrapolating the results to the entire C-band, we implicitly assume that the nonlinear distortions of optical carriers can be well approximated by such UDWDM systems.

#### 5.3 Maximum reach and fiber capacity

For OFDM and SCFDM systems with different granularities, we assess the maximum transmission distance still ensuring a BER below the FEC threshold of BER = 4 × 10^{−3}. The transmission reach for BER≤4 × 10^{−3} is shown in Fig. 8 for QPSK and 16-QAM formats, as a function of optical launch power. For UDWDM operation, optical channel spacing is set as ${S}_{p}$. We can draw the following observations from Fig. 8. SCFDM has a larger maximum transmission reach in both QPSK and 16-QAM systems with various granularities for both single channel and UDWDM scenarios. In the left column of Fig. 8, with QPSK mapped, although suffers the most serious XPM degradation, the fine granularity still has the longest maximum reach, compared to the medium and the coarse granularities. For the coarse granularity, the maximum reach decreases slightly at UDWDM systems compared with the single channel scenario, indicating that the nonlinear distortions mainly result from intra-channel effect instead of inter-channel ones. The right column of Fig. 8 demonstrates the transmission reach for OFDM and SCFDM systems with 16-QAM mapped. For single channel operation, the transmission reach decreases at the larger granularity, this is the same as the QPSK cases. For 16-QAM format, the inter-channel nonlinearities strongly degrade the system performance, especially in the smaller granularities. Therefore, for UDWDM systems, it is interesting almost the same maximum reach is observed for different granularities.

Consider the guard band of $GB=n\Delta f$ ($n=1,2,3,\cdots $) between two adjacent UDWDM channels, the SE can be calculated with $SE={R}_{net}/\left({B}_{eff}+GB\right)$. Consider an available bandwidth ${B}_{C}$ in the C-band, which equals to approximately 4THz (32 nm), the total link capacity is $Capacity=SE\cdot {B}_{C}$. Decreasing of the guard band implies a reduction in bandwidth occupation, corresponding to an increase in spectral efficiency and fiber capacity.

The above discussions assume UDWDM systems with optical channel spacing of ${S}_{p}$. In the following paragraphs, we study UDWDM performance as a function of guard bandwidth. In order to compare the different granularities in a general frame, we define the normalized guard band with regard to the effective bandwidth$G{B}_{normal}=GB/{B}_{eff}$.

Figures 9 and 10 show the maximum reach ${L}_{\mathrm{max}}$ in terms of fiber capacity and spectral efficiency for PDM-OFDM/SCFDM systems with QPSK and 16-QAM formats, respectively. The spectral efficiency varies from 1.48 to 3.15 bit/s/Hz for QPSK, and from 2.96 to 6.30 bit/s/Hz for 16-QAM. The corresponding normalized guard band varies from 1.178 to 0.026. For QPSK, the maximum reach decreases significantly with the increase of SE at the fine and medium granularities. For the coarse granularity, it is interesting to see that the maximum reach changes slightly with different SE, indicating that XPM distortion is not serious for this scenario. For 16-QAM, the maximum reach is much less than that of QPSK due to both the high OSNR requirement and large nonlinear distortions. Figure 10 shows the maximum reach increases moderately with the SE decreases for all granularities we considered.

As shown in Figs. 9 and 10, we can see that the high SE, or equivalently, large fiber capacity usually corresponds to short transmission distance. We thus use the widely known SE-distance product to measure the performance of UDWDM systems. Figures 11 and 12 , which are derived from the data of Figs. 9 and 10, plot the values of $SE\times {L}_{\mathrm{max}}$ achievable with both QPSK and 16-QAM PDM-OFDM/SCFDM signals over SSMF as a function of the normalized guard band.

For QPSK, the SE-${L}_{\mathrm{max}}$product is similar for the fine and the medium granularities, but significantly degrades for the coarse granularity. For 16-QAM, the SE-${L}_{\mathrm{max}}$ product is similar for all the three granularities considered, indicating that multi-level formats such as 16-QAM or above can only increase system capacity with a limited transmission reach. For orthogonal transmission with OFDM/SCFDM, the maximum value of SE-distance product is usually achieved at the small guard band.

## 6. Conclusion

In this paper, we numerically investigate orthogonal UDWDM transmission based on PDM CO-OFDM and CO-SCFDM techniques at various granularities. Compared to OFDM, SCFDM shows better nonlinear performance over uncompensated SSMF transmission with EDFA amplification. If PDM-QPSK mapped, both the fine and the medium granularities demonstrate significantly larger SE-distance product than the coarse granularity. For instance, PDM-QPSK can achieve a capacity of 12.6 Tb/s with a maximum reach of 5120 km for SCFDM and 4400 km for OFDM at the fine granularity. However, if 16-QAM mapped, the maximum reach becomes much smaller compared to QPSK scenario. The SE-distance product is slightly different for these three granularities. For instance, PDM-16-QAM can achieve a capacity of 25.2 Tb/s with a maximum reach of 1120 km for SCFDM and 1024 km for OFDM at the fine granularity. For UDWDM system with orthogonal transmission, tightly spaced optical carriers usually show better performance in terms of SE-distance product.

## Acknowledgment

This work is supported by Natural Science Foundation of China (No. 61077053, 60932004 and 61275005), National Hi-tech Research and Development Program of China (No.2012AA011302), National Basic Research Program of China (No. 2010CB328201) and Program for New Century Excellent Talents in University.

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