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We demonstrate a mitigation of fiber nonlinearity based on μ-law companding transform in coherent optical OFDM transmissions. High peak-to-average power ratio (PAPR) increases fiber nonlinear impairments caused by the Kerr effect in optical fiber. The μ-law companding modifies amplitude profile of OFDM signal with time domain signal processing, which reduces high PAPR of OFDM signal. The effects of companding parameter on noise enhancement and PAPR variation are presented. The impacts of companding transform on system performances are evaluated in a single polarization system as well as polarization multiplexed system. The resolution of analog-to-digital converter (ADC), dispersion map of transmission link, and launch power tolerance are also considered. The results of bit-error-rate (BER) measurements show that the μ-law companding improves OSNR margin over 5.5 dB after transmission of 1,040 km over SMF.
©2011 Optical Society of America
1. Introduction
Compared to conventional on-off-keying modulation format, phase-shift-keying with coherent detection is an attractive solution for high speed optical communication system since it offers high polarization-mode-dispersion (PMD) and chromatic dispersion (CD) tolerance, receiver sensitivity, and spectral efficiency [1, 2]. Orthogonal frequency division multiplexing (OFDM) brings similar benefits as a single carrier based coherent format while one-tap equalizer for each subcarrier reduces implementation complexity of channel equalizer [3, 4]. In addition, optical OFDM could share the same optical front-end with a single carrier quadrature phase shift keying (QPSK), and would be easily scalable to high data rate without changing optical front-end [5]. As a result, OFDM has recently been under active study for future optical systems.
However, one inherent drawback of OFDM is its high peak-to-average power ratio (PAPR) which requires a high dynamic range of linear power amplifier, DA/AD-converters, and optical modulator/demodulator. In optical CO-OFDM systems, the high PAPR increases fiber nonlinear impairments caused by the Kerr effect in optical fiber. Thus, it induces low optical signal-to-noise ratio (OSNR) in signal after transmission, and eventually limits the maximum reach. Several methods have been investigated to reduce the high PAPR of OFDM signal, such as clipping [6], pre-coding [7], partial transmission technique [8], selective mapping [9], and optical phase modulator [10]. A clipping is the simplest method and is widely employed for real-time implementation, but it causes additional clipping noise that degrades system’s performance. Other methods add additional complexity, coding overhead, or require additional optical components.
In this paper, we demonstrate fiber nonlinear suppression with a μ-law companding transform in coherent optical OFDM transmission. This approach is based on blind signal processing operating at time domain. The effects of companding parameters on noise variation and PAPR reduction are investigated. The impacts of companding transform on system performances are evaluated in a single polarization system as well as polarization multiplexed system. The resolution of analog-to-digital converter (ADC), dispersion map, and launch power tolerance are also considered. The results of bit-error-rate (BER) measurements show that the μ-law companding improves OSNR margin over 5.5 dB after transmission of 1,040 km over SMF. The results also show that μ-law companding outperforms clipping for reducing fiber nonlinearity.
2. Modified μ-law companding
Nowadays, integrated photonics for transmitter and receiver defined by optical internetworking forum (OIF) are already available for the realization of optical OFDM transceiver. Optical OFDM could use the same optical front-end with a signal carrier QPSK, and would be easily scalable to high data rate without changing optical front-end. As a result, to implement optical OFDM transceiver, one of remaining issues would be digital signal processing (DSP) algorithms. Many DSP algorithms well established in wireless link could be used in optical link such as time & frequency synchronization, cyclic prefix, training symbol, and equalization, and so on. However, there is fundamental difference between wireless link and optical link, as shown in Fig. 1 . A frequency selective fading due to multi-path interference is one of main problems in wireless link, whereas non-linear channel characteristic in optical fiber is one of main problems in optical link.
As optical OFDM signal is transmitted through transmission link, optical fiber attenuates power, spreads waveform, and induces nonlinear phase noise in the signal. Temporal variation in the intensity creates a temporal variation in refractive index, which leads to nonlinear signal distortions as optical OFDM signal is transmitted over hundreds of kilometers. Because OFDM signal has many high power components, nonlinear distortion due to temporal variation of signal is serious problem in optical OFDM. High PAPR means high peak power for a given average power or optical signal to noise ratio (OSNR), which produces high nonlinear interactions. Since the effects of high PAPR become worse for higher number of subcarriers, reducing PAPR is critically important in high data rate. This is because high number of subcarrier is desirable in high data rate due to DSP implementation.
The PAPR can be modified by companding technique. The OFDM signal is compressed at transmitter and expanded at receiver. Compression is performed according to modified μμ-law companding profile [11].
,where PR(peak ratio)=peak amplitude of compressor/peak of actual signal and x = instantaneous amplitude of input signal, and μ is companding paratemer. Expanding is simply the inverse of Eq. (1).Figure 2 represents companding profile as a function of PR and μ. When PR equals to 1, companding transform produces higher amplitude gain for lower amplitude signal while the peaks remain unchanged. On the other hand, choosing PR >1 results in a gain greater than unit for the peaks and a much higher gain for the lower amplitude signals. Varying μ with higher value induces more gain for lower amplitude signals. Thus, through the companding, we can re-distribute the profile of signal amplitude and reduces PAPR of OFDM signal.
3. Noise enhancement and PRPR reduction
One drawback of companding is noise enhancement. The signal power as well as noise power is increased as it is companded. The noise increment by companding transform for constant signal-to-noise ratio can be expressed as [12]
,where Es is the energy of OFDM signal. In order to avoid significant noise enhancement by companding transform, it is necessary to choose appropriate values of companding parameters.Figure 3 shows the effects of μ and PR on the noise increment and PAPR reduction when OFDM signal is generated with 128 point IFFT and QPSK mapping. In order to reduce fiber nonlinearity and SNR degradation, large reduction of PAPR and low noise enhancement are required. To suppress noise increment as low as possible, high PR is desirable. However, high PR results in lower gain of PAPR reduction. In addition, higher μ enhances higher noise increment as well as higher PAPR reduction. Thus, compromise between μ and PR is required to achieve large reduction of PAPR and low noise enhancement. In this analysis, we set μ and PR to be 8 and 4, respectively. At this value, the PAPR reduction and noise enhancement are 2 dB and 1.2 dB, respectively.
The probability density function (PDF) of OFDM signal before and after companding is plotted in Fig. 4(a) . The PDF is obtained by discretizing the OFDM signal and counting the number of each discrete value that occur in the OFDM signal. The PDF of OFDM signal before companding has Gaussian distribution. After companding, the occurrence of lower amplitude signal is reduced and the OFDM signal is more evenly distributed. Figure 4(b) shows the complementary cumulative distribution functions (CCDF) of PAPR for original signal and companded signal. The CCDF curves show the probability that the PAPR of an OFDM signal comprising N subcarriers exceeds the PAPR value specified on the PAPR axis. Obviously, the PAPR of the companded signal is lower than that of original signal. Companding OFDM signal with μ = 8 gives the 10% probability of PAPR reduction as 2 dB.
Fig. 4 Companding transform of OFDM signal with 128 point IFFT and QPSK mapping (a) probability density function (b) Complementary cumulative distribution function (CCDF) of PAPR.
4. SPM compensation in optical CO-OFDM system
We used Monte Carlo simulations to evaluate the transmission performance of an optical CO-OFDM system using μ-law companding, as show in Fig. 5(a) . The OFDM data was generated and decoded by Matlab, and optical up/down conversion and transmission were done by VPI TransmissionMaker. The OFDM signal consisted of 128 subcarriers from which 98 subcarriers carried data and 30 subcarriers were zero padded. A QPSK was used for symbol mapping, and the cyclic prefix length was 14 samples (1.4 ns) per OFDM symbol. Thus, together with cyclic prefix, the OFDM symbol length was 14.2 ns. After companding, real and imaginary part of companded OFDM signal are applied to optical IQ modulator, and then modulated signal is transmitted 1,040 km over conventional single mode fiber (SMF). Two types of transmission line were used for this evaluation as shown in Fig. 5(b); inline-dispersion-compensated or dispersion-uncompensated SMF link. The dispersion-compensated link would be highly susceptible fiber nonlinearity, but it was widely deployed in optical transmission system. The dispersion compensation fiber (DCF)-free link was also considered for the green-field deployment. The local oscillator (LO) laser’s linewidth and frequency offset to transmitter laser were set to be 100 kHz and 50 MHz, respectively. After down conversion and analog to digital conversion (ADC), the digitized signals was expanded and then phase noise of laser was compensated by the data-aided phase estimation. The resolution of ADC/DAC was assumed to 6 bits. The bit-error-rate was calculated by comparing decoded bit with transmitted bit, and total 262,144 bits were used. For comparison, we also investigated the performance of clipping. In this case, the PAPR of clipped signal was set to have the same value with that of companded signal.
Figure 6(a) shows waveforms of OFDM signal measured at back-to-back. The vertical axis represents normalized amplitude obtained by dividing absolute value of OFDM signal with mean amplitude. The original OFDM signal has many high power components, whereas companding transform suppresses peak power components. As a result, the PAPR is reduced from 9.78 dB to 7.78 dB. When clipping is employed, high power components are intentionally removed to make the same PAPR of clipped signal with that of companded signal. Figure 6(b) represents the effects of ADC resolution on back-to-back sensitivity measured at the BER of 10−3. It is shown that OSNR sensitivities for clipping and non-companded signal have the similar value, whereas there is 0.5 dB penalty at the BER of 10−3 for companded signal due to noise enhancement. When the resolution ADC resolution is higher than 6 bits, there is no sensitivity variation due to low quantization noise. Thus, we used 6 bits ADC for all following analysis. It should be noted that, unlike speech processing or wireless link, the PAPR reduction due to companding does not affect the results of ADC resolution since quantization noise at 5 ~6 bits resolution, – 30~– 36 dB, is much lower than measured OSNR for BER analysis (– 8~– 9 dB).
Fig. 6 (a) optical OFDM Waveform (b) back-to-back sensitivity at the BER of 10−3 as a function of ADC resolution.
Figure 7 . shows the comparison of BER performance under various operation conditions of OFDM systems after 1,040 km over SMF link. The results were obtained without any companding and with companding by the μ-law transform. The comparison was also made with clipping. The launch power was – 2 dBm. In the case of dispersion compensated link, OFDM signal with companding shows 5.5 dB and 2.5 dB OSNR improvement at the BER of 10−3 over non-companded and clipped signal, respectively, as shown in Fig. 7(a). Figure 7(b) represents performances comparison between dispersion compensated link and DCF-free link. When companding transform is used, the sensitivity of dispersion compensated link is only 0.5 dB higher than that of DCF-free link. This indicates that the single channel nonlinearity would not prevent OFDM from viable dispersion-compensated transmission. On the other hand, the performance difference between dispersion compensated link and DCF-free link becomes 4.8 dB without companding.
Fig. 7 Transmission performance after 1,040 km over SMF (a) dispersion compensated link (b) performances comparison between dispersion compensated link and DCF-free link
The system performance as a function of launch power was investigated, as shown in Fig. 8 . The nonlinearity threshold is defined as the launch power at which point the Q reaches the FEC threshold (i.e 9.8 dB). The results show that the μ-law companding transform is effective in reducing nonlinearity penalty. In the case of dispersion compensated link as shown in Fig. 8(a), for example, at the launch power of – 0.5 dBm, the Q value is improved by over 2 dB. The launch power of the nonlinear threshold is increased from –1.7 dBm to – 0.5 dBm with companding, an improvement of 1.2 dB. The companding transform is also effective in the DCF-free transmission link as shown in Fig. 8(b). When companding is used, the nonlinear threshold in dispersion compensated link is similar with that in DCF-free link.
Fig. 8 Launch power tolerance after 1,040 km over SMF (a) dispersion compensated link (b) DCF-free link.
The performance of nonlinearity suppressing by the μ-law companding in PDM system was also investigated as shown in Fig. 9(a) . The PDM-OFDM signal contained two orthogonal x- and y-polarization, each of which consisted of 128 subcarriers. Polarization demultiplexing was realized by using a pair of correlated dual-polarization training symbol. Transmission link was consisted of dispersion compensated 1,040 km of SMF. Transmission speed was doubled compared to that in Fig. 5 due to polarization multiplexing. Other parameters were similar with those in Fig. 5. Figure 9(b) shows that companding transform suppresses optical nonlinearity. In addition, the companding transform changes error-floor to error-free operation at the BER of 10−3. The OSNR sensitivity at the BER of 10−3 is about 17 dB when companding transform is employed. All these results indicate that the μ-law companding effectively suppress optical nonlinearities without using additional optical components.
5. Summary
We have demonstrated a suppression of fiber nonlinearity using μ-law companding transform in coherent optical coherent-OFDM transmission. The μ-law companding modifies amplitude profile of OFDM signal with time domain signal processing, which reduces PAPR of OFDM signal. The compromising between peak ratio and companding parameter resulted in PAPR reduction with minimum noise enhancement. The effects of ADC resolution and dispersion map were also investigated. After transmission of 1,040 km over dispersion-managed SMF link, OFDM signal with companding produced 5.5 dB OSNR improvements over non-companded signal. The ADC resolution over 6 bits was enough to achieve low quantization noise. When μ-law companding transform was employed, we could achieve the similar performance in dispersion compensated and dispersion-uncompensated link, and OSNR sensitivity difference between two dispersion maps was less than 0.5 dB. The results confirmed that μ-law companding was effective for the reduction of optical nonlinearity in a single polarization as well as polarization multiplexed system, and presented better performance than clipping.
Acknowledgments
This work was supported by the IT R&D program of MKE/IITA. [2008-F017-04, 100Gbps Ethernet and optical transmission technology development].
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