## Abstract

In this paper, an improved multi-carrier generation scheme based on single-side-band recirculating frequency shifter with optical finite impulse response (FIR) filter for amplified spontaneous emission (ASE) noise suppression is proposed and experimentally demonstrated. The carrier-to-noise-ratio (CNR) instead of tone-to-noise-ratio (TNR) is introduced to more reasonably and exactly evaluate the signal-to-noise-ratio of a multi-carrier source with non-flat noise floor. We have experimentally attain the worst case CNR of 22.5dB and 19.1dB for generated 50 and 69 flat low noise carriers, which has shown significant improvement than the previous cited works based on recirculating frequency shifter.

© 2014 Optical Society of America

## 1. Introduction

Multi-carrier source generation is crucial for achieving higher data rates optical communication systems with multi-carrier modulation formats, such as coherent dense wavelength division multiplexing (Co-DWDM) [1,2], coherent optical orthogonal frequency division multiplexing (Co-OFDM) [3–5] and Nyquist-WDM [6] based superchannel systems. Optical multi-carrier sources with high quality and large number of carriers are good candidates to serve as a laser array at transmitter end [1–5] or a local oscillator array at receiver end [7] for ultra-high speed and spectrum efficiency (SE) optical communication systems. On the other hand, these frequency locked carriers are very important to super-channel systems as small frequency drift of laser source would immediately lead to inter-channel crosstalk. Many endeavors have been made on generation of optical multi-carrier source such as multi-wavelength erbium-dropped fiber laser [8], cascaded modulators [5,9–11] and re-circulating frequency shifter (RFS) [3,4,11–13]. Among these technologies, single-side-band (SSB) modulation based RFS loop has attracted much attention due several advantages of relative simple structure, flexibility on frequency spacing control, low driving voltages, less sensitive to phase noise and ability to generate large number of flat carriers. Whereas, in most of SSB-RFS multi-carrier source applied terabits long reach transmission experiments, only 20~40 carriers (having a worst TNR of 20~25dB) are generated for signal loading. One of the reason is the noise nature of SSB-RFS method that ASE noise accumulates round by round, resulting limited number of available carriers, especially for cases of large desired carrier number (>50) and multi-EDFAs deployed in the loop [1,3,4]. Therefore, further investigations are required for low noise RFS based multi-carrier generation schemes. There are many improved RFS implementations techniques have been proposed to achieve better performance by halving required circulating times, such as multi-frequency shifting (MFS) method [14], double RFS structure [15] and complementary frequency shifter (CFS) loop [16,17], while increasing the complicity of the structures, doubling optical components, and limited noise characteristic improvements.

In this paper, we propose and experimentally demonstrate an improved SSB-RFS optical multi-carrier generation configuration with an ASE noise suppression scheme using an optical FIR filter. By applying this scheme, notable carrier-to-noise ratio (CNR) performance improvement is achieved. With proposed optical FIR ASE noise suppression scheme deployed in SSB-RFS loop, 50 and 69 stable and flat carriers with high CNR are generated.

## 2. Proposed scheme and noise characteristic analysis

#### 2.1 Proposed ASE noise suppression scheme

The proposed low noise SSB-RFS multi-carrier generator with ASE noise suppression scheme is illustrated in Fig. 1(a). This configuration includes a basic SSB-RFS loop and an optical FIR filter for noise suppression. In the basic SSB-RFS loop [3,4,12,13], the seed carrier of frequency *f _{0}* is provided by CW laser, and an I/Q modulator driven by two RF signals of frequency

*f*is used to implement carrier frequency shift. The exact polarization alignments are ensured by the polarization controllers (PCs) and the number of generated carriers is controlled by a band pass filter (BPF). The role of EDFA is to compensate the total loss suffered in one round trip (RT) with inevitable ASE noise accumulation that could result in a great system performance degradation. In our proposed scheme, an N-tap optical FIR structured notch filter is placed after EDFA to further reduce accumulated ASE noise, which ensures a significant improvement in overall system performance.

_{s}In this work, two different structures of optical FIR filter implementations are taken into consideration, one is N-tap parallel structured FIR (direct implementation) and the other is N cascaded 2-tap one as illustrated in Figs. 1(b) and 1(c). The theoretical analysis of noise accumulation and reduction will be given out in the next part, and then the system performance improvement and experiment results.

#### 2.2 Analysis of noise accumulation and CNR definition

It is convenient to treat the output of SSB-RFS loop in frequency domain in the presence of ASE noise, and a recursive expression can be represented by Eq. (1).

*n*th (

*n*= 1,2,…N) RT. $l$ is the total loop loss including modulation loss and insertion loss, and ${g}_{n}$ is EDFA gain in

*n*th RT. A stable and flat output is always ensured by EDFA condition of ${g}_{n}\cdot l\approx 1$ .The transfer functions of IQ modulator is denoted by $T\left(f\right)\approx FFT\left({e}^{j2\pi {f}_{s}t}\right)=\delta \left(f-{f}_{s}\right)$. However, 3rd-order crosstalk is neglected for simplicity as this work mainly focus on processes of ASE noise accumulation and reduction. $\otimes $ denotes convolution operator and the BPF transfer function ${H}_{BPF}\left(f\right)$ is assumed ideal rectangle window here and represented by Eq. (2).

*n*th RT induced random ASE noise ${n}_{n}\left(t\right)$, that can be treated as bandwidth limited additive white Gaussian noise process obeying ${n}_{n}\left(t\right)~\left(0,{\sigma}^{2}\right)$. The statistical average quantity of $E\left[{\left|{n}_{n}\left(f\right)\right|}^{2}\right]$ accounts for the noise power spectrum density (PSD) $S\left(f\right)$, and can be derived from EDFA parameters of noise figure ${F}_{n}$ and power gain $G$ using Eq. (3).

*N*th channel can be calculated by Eq. (6).

Thus, the power of accumulated ASE noise in *N*th channel is represented by Eq. (7).

*N*. Where,

*N*times noise power accumulated on

*N*th generated carrier tone compared to first tone, would result in a great degradation on signal loading process. In this work, carrier-to-noise ratio (CNR) is defined and used to have a quick and accurate evaluation on noise characteristic of each channel instead of tone-to-noise ratio (TNR, defined as$10\mathrm{lg}\left({P}_{carrier}/{P}_{noisefloor}\right)$, ${P}_{carrier}$and ${P}_{noisefloor}$ are the readout powers of carrier tone and noise floor from OSA) in other works [13]. Although, TNR is suitable for the cases with flat noise power spectrum, but not for non-flat noise power spectrum as exploited in the present work. CNR of

*n*th channel with 0.1nm reference noise bandwidth likewise OSNR is defined as Eq. (8).

*n*th channel within channel spacing ${B}_{s}$, and ${B}_{r}$ is 0.1nm reference noise bandwidth. In a flat noise power spectrum case, CNR and TNR have a relationship of Eq. (9).where ${B}_{res}$ is resolution of optical spectrum analyzer (OSA). The CNR curve of ordinary SSB-RFS loop is depicted in Fig. 3 (blue line). It can be deduced that CNR decreases as required circulating times increases and 100th generated carrier tone is degraded 20dB in contrary to first tone. The simulation results of loaded Nyquist-16QAM signal degradation caused by CNR reduction are also shown in Fig. 3. In our simulation, the generated first carrier has a CNR value of 32dB that is consistent with the TNR value of first carrier observed from the experimental results in Fig. 8(a) and converted with the relationship of Eq. (6). The constellation of signal loaded on 1st-carrier has a very clear QAM pattern having an error vector magnitude (EVM) of 5.4% while blurred constellation is observed on 100th carrier having an EVM of 19.8% as depicted in Fig. 3. Moreover, the constellation points at the range of outer circles have a more scattered distribution than inner ones which implies that the impairments induced by accumulated ASE noise would act like Gaussian distribution phase noise.

#### 2.3 Analysis of ASE noise power reduction

Before investigating CNR performance improved by proposed noise suppression scheme, the reduced ASE noise power by optical FIR filter should be analyzed first.

### CASE I: Parallel FIR implementation

The power transfer function of N-tap FIR filter could be represented by Eq. (10).

### CASE II Serial FIR implementation

The serial FIR structured implementation can be treated as N cascade 2-tap FIR (both tap coefficients are 1/2) or N-tap FIR with *m*th tap coefficient equals ${\left(1/2\right)}^{N}\cdot {C}_{N}^{m}$. Hence, the power transfer function is Eq. (13).

In Fig. 4, the power transfer functions of two structured optical FIR filters are illustrated, considering tap number of 2, 8 and stage number of 8. Apparently, with same tap number, more noise power would be filtered as parallel structured FIR employed in contrary to serial structured FIR, but the later maybe easier to implement.

The principle of proposed scheme on improving system performance can be easily understood. In existent application, the generated sub-carriers are firstly separated by a de-multiplexer, such as arrayed waveguide grating (AWG) which has a relatively flat window with bandwidth equal to channel spacing. Then the desired carrier, together with accumulated ASE noise (within bandwidth of channel spacing) will be sent into the transmitter. The signal constellation will thus be blurred while being loaded onto a “noisy” carrier. This scheme works because the carrier bandwidth without modulation is quite small, which allows us to “clear” the generated carriers using a notch filter with narrow 3dB bandwidth, such as N-tap optical FIR filter, resulting less noise accumulates within channel. The “cleared” carrier is selected and modulated, contributing an improved signal quality after modulation. And the detailed system performance (CNR, EVM and EDFA efficiency) improvements will be discussed in the following section.

#### 2.4 System performance improvements with the proposed ASE noise suppression scheme

### CNR improvement

When N-tap optical FIR structured ASE noise suppression scheme employed in the loop, the output of SSB-RFS after *N* RTs could be denoted by Eq. (15).

*N*th channel can be represented by Eq. (16).

*N*th channel has been overlapped

*N*times and 2) ASE noise induced in

*m*th trip has passed FIR filter

*N*-

*m +*1 times. Therefore, the power of residual ASE noise after FIR filtering in

*N*th channel can be represented by

*N*th channel with 0.1nm equivalent reference noise bandwidth is

### EVM improvement of loaded signals

As revealed above, CNR evaluation for the naked carrier tone is in close relationship with error vector magnitude (EVM) evaluation for the quality of loaded signal, which also implies the performance of whole transmission system. In Fig. 5, this relationship is illustrated in detail for different SSB-RFS schemes, including ordinary SSB-RFS, SSB-RFS with N-tap (N = 2, 4, 8) FIR ASE noise suppression, SSB-RFS with 2-frequency shifting (2-FS), and combined scheme of N-tap optical FIR and 2-FS. In order to load the signal on the carrier, we must select it with a WDM de-multiplexer, which in our simulation a 10-order super-Gaussian filter of 28GHz bandwidth is used (almost the MUX and DEMUX window). The filtered carrier is loaded with 28Gbaud Nyqusit-16QAM signal and detected with coherent detection. The linewidth of both signal laser and local oscillator is set to 0kHz. A match filter is applied on received signal without phase recovery algorithm for digital signal processing (DSP). The EVM of signals loaded on ordinary SSB-RFS carriers significantly increases with number of carriers as denoted by the blue line, having 15 carriers with EVM values better than 11% and about 25 carriers better than 13% (BER≈3.8e-3). Apparently, the last several tens carriers cannot support higher-order modulation format systems. In the results of SSB-RFS with 2-FS, a limited performance improvement is achieved as only a small part of the noise is reduced. Whereas an outstanding improvement can be found as optical FIR filter based ASE noise scheme deployed in the loop. Even a 2-tap case can help improve the EVM performance of generated 100th carrier from 19.7% to around 10%, and additional EVM improvement could be achieved when the 2-tap case combined with 2-FS. Notably, when 8-tap optical FIR deployed in the loop, EVMs of all 100 generated carriers have values of less than 6.5%, which is comparable with first several carrier tones generated by ordinary scheme. This is very meaningful especially for multi-carrier source based super-channel transmission systems since higher order modulation formats such as 16QAM and 32QAM could be loaded on large amounts of carriers. We can also conclude that among all the improved SSB-RFS multi-carrier generation schemes, optical FIR structured ASE noise suppression scheme would contribute most significant improvement to system performance.

### Amplification efficiency improvement of EDFA

Another contribution of proposed ASE noise suppression scheme is improvement of amplification efficiency of EDFA. In our previous analysis, EDFA is modeled as constant gain coefficient with adequate saturation output power [12]. In reality, EDFA is specified with a parameter of saturation output power${P}_{s}$, but the different carrier number requires different saturation output powers. Considering saturation output power, the EDFA power gain $G$ is given by the implicit expression of Eq. (19) [18].

where ${G}_{0}$ is the peak gain and ${P}_{in}$ is input power. In Fig. 6, the required saturation power is shown against number of carriers, considering ASE suppressed SSB-RFS scheme with different tap numbers. In the ordinary scheme, when generating 100 carriers, a saturation power of 29dBm is required. For SSB-RFS with 2-tap ASE noise suppression scheme, the required saturation power is reduced by 1dB. By analyzing all curves in Fig. 6, it can be concluded that 1dB saturation power will be saved as tap number doubles, which means that, by applying optical FIR filter based noise suppression scheme in the loop, more carriers can be generated with a certain EDFA saturation output power.## 3. Experimental setup and results

Experimental setup is shown in Fig. 7(a). In this experiment, a 2-tap optical FIR filter case is carried out, which is implemented by Mach-Zehnder delay interferometer (MZ-DI). The seed laser is centered at 1559.5nm with linewidth of several tens kilohertz and the output power is set to be 16dBm. An I/Q modulator with insertion loss of 7dB is used here to implement frequency shifting, and both of its arms are biased at null points. A phase shift of $\pi /2$ between I and Q branches is ensured by adjusting bias voltage of phase modulator. The frequency of sine and cosine RF driven signals applied to I/Q modulator is 10.7GHz. Both amplitudes and phases of the driven signals are carefully adjusted by electrical amplifier and phase shifter, resulting that, as shown in Fig. 7(b), only 1st order line (the desired shifted frequency carrier tone) remains on the spectrum (about 40dB power larger than the seed tone, −1st, ± 2nd and −3rd order tone) when the loop is set open, which indicates a minimum harmonic crosstalk remained and helps to achieve good fatness of the generated multi-carriers [12]. After I/Q modulator, a tunable band pass filter (BPF) with insertion loss of 6dB is used to limit the number of generated carriers. The role of EDFA is to compensate the total loop loss suffered in every round trip.

In this experiment, the EDFA works at automatic power control (APC) mode and has being applied with setting saturation output power of 25dBm. The noise figure of EDFA is less than 5.5dB at −10dBm input power and 25dBm output power. Exactly polarization alignments between I/Q modulator and EDFA are ensured by the two PCs. In the first experiment, 3dB bandwidth of BPF is set to about 4.4nm to allow 50 carriers pass. The generated 50 carriers without applying MZ-DI (2-tap FIR filter) in the loop are shown in Fig. 8(a), compared to 1st carrier, the noise floor of last one has been raised about 18dB that is consistent with our simulation results in Fig. 3, having an equivalent CNR with 0.1nm noise bandwidth of 14dB (the value of transferred from TNR of 42 dB calculated through Eq. (9)). To improve the CNR, a MZ-DI (2-tap FIR filter) with parameters of fixed FSR = 10.7GHz, insertion loss of 1.54dB and extinction ratio of 36dB is inserted after EDFA in our experimental setup. The phase arm of MZ-DI is adjusted to align the middle of FSR window to the generated carrier tones, and corresponding output optical spectrum is shown in Fig. 8(b), where the CNR of 50th tone has been increased to 22.2dB.

Then in the second experiment, the 3dB bandwidth of BPF is set to 6nm (the maximum value of our instrument) to generate 69 tones with EDFA saturation output power of 26dBm. The corresponding output spectrum is shown in Fig. 9, and both the measured and theoretical CNR values of 69 carriers are all depicted in Fig. 10(a). The measured CNR values of SSB-RFS with and without 2-tap filter decrease with the number of generated carriers in the trend of theoretical results. The measured CNR values of 67th carrier in two cases are about 17.9dB and 9.2dB respectively, showing 8.7dB CNR increment by using proposed scheme. All these results are observed using the optical spectrum analyzer APEX AP2440A with a resolution of 0.16pm (20MHz). The measured $\Delta CN{R}_{n}$ values are also shown in Fig. 10(b), where we can find that the measured $\Delta CN{R}_{n}$ has a small difference from the theoretical value, thus the improved CNR can be derived using Eq. (20), without resorting to integration.

*n*th channel and is read from Fig. 3. Moreover, in our previous experiment results of 50 carrier tones with 12.5GHz spacing having a worst TNR of 20dB observed with a resolution of 0.02nm OSA [13] (corresponding TNR of 41dB at 20MHz OSA resolution and equivalent CNR of 13dB at

*B*= 12.5GHz), EDFA saturation output power is about 29dBm while in this work only 25dBm output power is needed to generate 50 flat carriers but with much higher CNR. It is consistent with theoretical analysis above that, not only ASE noise power is reduced by 2-tap optical FIR filter but also the EDFA amplification efficiency is improved.

_{r}## 4. Conclusion

In this paper, ASE noise accumulation of SSB-RFS multi-carrier generation is analyzed. To improve CNR performance of generated multi-carrier, a low noise SSB-RFS multi-carrier generation configuration with optical FIR filter based ASE noise suppression scheme is proposed and corresponding analysis of amount of noise reduction is given out. Theoretically, the worst CNR can be improved about 9.5dB (2-tap) and 16.4dB (8-tap) with the proposed noise suppression scheme when 100 carriers are generated, which would enable all generated 100 carriers supporting 16QAM or higher modulation formats. An experimental demonstration is also carried out, and 50 flat carriers with and without proposed noise suppression scheme are generated, having a worst CNR of 14dB and 22.2dB respectively. After that, 69 carriers covering 6nm range with 10.7GHz frequency spacing and high flatness (<1dB) are generated, having a high CNR about 17dB for the worst carrier tone. The achieved results will pave the way to support higher order modulation formats and long-distance transmission.

## Acknowledgments

This work is partly supported by the National Natural Science Foundation of China (Grant No.61205065), Open Fund of State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, China (Grant No. 2013G- ZKF031310), Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110005110014), and Open Fund of IPOC (BUPT) (IPOC2013B005).

## References and links

**1. **F. Tian, X. Zhang, L. Xi, A. Stark, S. E. Ralph, and G. K. Chang, “Experiment of 2.56-Tb/s, polarization division multiplexing return-to-zero 16-ary quadrature amplitude modulation, 25 GHz grid coherent optical wavelength division multiplexing, 800 km transmission based on optical comb in standard single-mode fiber,” Opt. Eng. **52**(11), 116103 (2013). [CrossRef]

**2. **D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, and J. Leuthold, “Single-laser 32.5 Tbit/s Nyquist WDM transmission,” J. Opt. Commun. Netw. **4**(10), 715–723 (2012). [CrossRef]

**3. **Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express **17**(11), 9421–9427 (2009). [CrossRef] [PubMed]

**4. **S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-carrier no-guard-interval coherent OFDM superchannel over 7200-km of ultra-large-area fiber,” European Conference on Optical Communications, paper PD2.6, Vienna, Austria (2009).

**5. **X. Liu, S. Chandrasekhar, X. Chen, P. J. Winzer, Y. Pan, T. F. Taunay, B. Zhu, M. Fishteyn, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “1.12-Tb/s 32-QAM-OFDM superchannel with 8.6-b/s/Hz intrachannel spectral efficiency and space-division multiplexed transmission with 60-b/s/Hz aggregate spectral efficiency,” Opt. Express **19**(26), B958–B964 (2011). [CrossRef] [PubMed]

**6. **G. Bosco, V. Curri, A. Carena, P. Poggiolini, and F. Forghieri, “On the performance of Nyquist-WDM terabit superchannels based on PM-BPSK, PM-QPSK, PM-8QAM or PM-16QAM subcarriers,” J. Lightwave Technol. **29**(1), 53–61 (2011). [CrossRef]

**7. **N. K. Fontaine, “Spectrally-sliced coherent receivers for THz bandwidth optical communications.” European Conference on Optical Communications, paper Mo.3.C.1, London, UK (2012). [CrossRef]

**8. **M. A. Mirza and G. Stewart, “Multi-wavelength operation of erbiumdoped fiber lasers by periodic filtering and phase modulation,” J. Lightwave Technol. **27**(8), 1034–1044 (2009). [CrossRef]

**9. **J. Zhang, J. Yu, N. Chi, Z. Dong, X. Li, Y. Shao, J. Yu, and L. Tao, “Flattened comb generation using only phase modulators driven by fundamental frequency sinusoidal sources with small frequency offset,” Opt. Lett. **38**(4), 552–554 (2013). [CrossRef] [PubMed]

**10. **X. Zhou, X. Zheng, H. Wen, H. Zhang, and B. Zhou, “Generation of broadband optical frequency comb with rectangular envelope using cascaded intensity and dual-parallel modulators,” Opt. Commun. **313**, 356–359 (2014). [CrossRef]

**11. **J. Zhang, N. Chi, J. Yu, Y. Shao, J. Zhu, B. Huang, and L. Tao, “Generation of coherent and frequency-lock multi-carriers using cascaded phase modulators and recirculating frequency shifter for Tb/s optical communication,” Opt. Express **19**(14), 12891–12902 (2011). [CrossRef] [PubMed]

**12. **J. Li, X. Zhang, F. Tian, and L. Xi, “Theoretical and experimental study on generation of stable and high-quality multi-carrier source based on re-circulating frequency shifter used for Tb/s optical transmission,” Opt. Express **19**(2), 848–860 (2011). [CrossRef] [PubMed]

**13. **F. Tian, X. Zhang, J. Li, and L. Xi, “Generation of 50 stable frequency-locked optical carriers for Tb/s multicarrier optical transmission using a recirculating frequency shifter,” J. Lightwave Technol. **29**(8), 1085–1091 (2011). [CrossRef]

**14. **J. Zhang, J. Yu, N. Chi, Z. Dong, Y. Shao, L. Tao, and X. Li, “Theoretical and experimental study on improved frequency-locked multi-carrier generation by using recirculating loop based on multi-frequency shifting single-side band modulation,” IEEE Photon. J. **4**(6), 2249–2261 (2012). [CrossRef]

**15. **J. Zhang, J. Yu, N. Chi, Y. Shao, L. Tao, J. Zhu, and Y. Wang, “Stable Optical Frequency-Locked Multicarriers Generation by Double Recirculating Frequency Shifter Loops for Tb/s Communication,” J. Lightwave Technol. **30**(24), 3938–3945 (2012). [CrossRef]

**16. **J. Li and Z. Li, “Frequency-locked multicarrier generator based on a complementary frequency shifter with double recirculating frequency-shifting loops,” Opt. Lett. **38**(3), 359–361 (2013). [CrossRef] [PubMed]

**17. **J. Li, C. Yu, and Z. Li, “Complementary frequency shifter based on polarization modulator used for generation of a high-quality frequency-locked multicarrier,” Opt. Lett. **39**(6), 1513–1516 (2014). [CrossRef]

**18. **G. P. Agrawal, *Applications of Nonlinear Fiber Optics* (Academic Press, 2001), Chap. 4.