2013 8th International Conference on Communications and Networking in China (CHINACOM)
Using Phase Inversion to Compensate Fiber Nonlinearity in Spectral-Amplitude Coding OCDMA Network 1 1,2
Jen-Fa Huang, 2Kai-Sheng Chen and 3Chao-Chin Yang
Department of Electrical Engineering, National Cheng Kung University, Tainan, Taiwan. 3 Department of Electro-Optical Engineering, Kun Shan University, Tainan Taiwan.
[email protected]
In a typical SAC-OCDMA system, each bit transmitted by different users is spectrally encoded onto an address code denoted by a code vector with several chips. However, when two or more chips having different wavelengths propagate simultaneously inside an optical channel, they induce cross-talk and interact with each other through the fiber nonlinearity. One nonlinear phenomenon lead by the intensity-dependent refractive index of the fiber is known as cross-phase modulation (XPM). This temporally varying index change results in a temporally varying phase change. The consequence is that the instantaneous optical wavelength assigned to each chip differs from its initial value. Different parts of chips undergo different phase shift because of the intensitydependent phase fluctuations. The time dependence of the phase manifests as spectral broadening. Similar to the case of self-phase modulation (SPM), a nonlinear effect occurring in a single wavelength transmission, the spectrum of each chip is broadened and develops into a multi-peak waveform. The broadened spectrum severely limits the performance of SACOCDMA since this technique is spectrally decoded in the receiver. Because the orthogonal property of signature code is lost due to fiber nonlinearities, MAI cannot be completely eliminated. Thus, SPM and XPM are seen as the ultimate limit of the number of active users that can be multiplexed simultaneously.
Abstract—Self-phase modulation (SPM) and cross-phase modulation (SPM) are leading nonlinear transmission penalty in Spectral-Amplitude Coding optical CDMA (SAC-OCDMA) systems. In nonlinear optical media, a phenomenon of the intensity dependence of the refractive index occurs through SPM or XPM, which leads to spectral broadening of optical pulses and therefore degrade system performance. A novel scheme for fiber nonlinearity compensation based on the principles of phase inversion compensation (PIC) is proposed to reduce the phase distortion. The phase of the data pulses is modulated in the middle of fiber spans. The magnitude of the phase modulation is proportional to the detected pulse intensity, and the sign is opposite to that of the nonlinear phase shift caused by SPM and XPM. Thus, the nonlinear phase noise induced in the first-half fiber is partially compensated for in the second-half fiber. Using an optimum value, we show by numerical simulations that a SAC-OCDMA format transmission in dispersion-managed system with such nonlinearities compensation can provide greater than 3 dB increase in launch power. Keywords- optical code-division multiple-access(OCDMA); spectral-amplitude coding (SAC); self-phase modulation (SPM); cross-phase modulation (XPM)
I.
INTRODUCTION
In recent years, optical code-division-multiple-access (OCDMA) systems are attractive because they offer several advantages such as security, privacy and flexibility. These techniques allow many users to access the common channel asynchronously and securely [1]. Since dedicated time or wave-lengths slots do not have to be allocated, high statistical multiplexing gain can be offered even in busty traffic. These characteristics distinguish OCDMA form other optical multiplexing schemes such as optical time-division multipleaccess (TDMA) and optical wavelength-division multipleaccess (WDMA). Until now, many researches on OCDMA focus on time spread OCDMA, frequency hopping OCDMA, phase-coding OCDMA and spectral-amplitude-coding (SAC) OCDMA [2]. Among these OCDMA schemes, SAC-OCDMA has the advantage of eliminating multiple access interference (MAI) and the avoiding sampling process in the optical encoder.
Several optical compensation schemes have been proposed to compensate for nonlinear phase noise. However, only few successful experiments have so far been reported—optical phase conjugation (OPC) [3], semiconductor optical amplifier (SOA)-based regenerative amplification, and phase-inversion compensation (PIC). The principle of PIC is to apply a phase modulation opposite to that produced by the Kerr nonlinearity. This phase modulation can be carried out at the transmitter, receiver, or in the middle of fiber by using digital signal processing (DSP) or photoelectric circuits [4]. In this paper, we propose a mid-span PIC to mitigate the nonlinear phase noise to remove SPM and XPM. The phase of data is detected after signal propagates through the first part of fiber. By applying a phase modulation on the signal opposite to that produced by nonlinear effect, then phase inversion is completed. We propose mid-span PIC, parallel to dispersion
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compensation fiber (DCF) to compensate fiber dispersion. Several numerical simulations show a PIC scheme can significantly enhance the performance of SAC-OCDMA. II.
N 2 ∂ri ∂2r i 2 = − β2i 2i + iri ( γi ri + 2∑ γ j rj ) ∂z 2 ∂t j ≠i
where ri(z,t) is the inverse Fourier transform of Ri(z,ω), β2i is the dispersion parameter at the carrier wavelength λi, and γi is the nonlinear parameter defined as (4)
IMPACT OF NOLINEAR EFFECTS ON SAC-OCDMA
A typical fiber-optic SAC-CDMA network consist K transmitter and receiver pairs connected in a star configuration to share the same optical fiber channel. At the transmitter, each bit of information from the k-th user is on-off keying (OOK) the broadband light source to fulfill the E-O modulation. The optical field corresponding to each data bit is encoded by spectral slicing. With a properly written SAC-OCDMA pattern, the light field from the output of encoder will be spectrally encoded onto and address code denoted by code vector Ck = [ck(1), ck(2),…, ck(N)]. Here, N is the length of the code or the number of chips per bit, ck(i) ∈ {0,1}, for 1 ≤ i ≤ N, is the i-th chip value of the k-th user. The SAC-OCDMA encoder will spectral encode an incoming broadband spectrum into N component chips with centered wavelengths (λ1, λ2,…, λN). A K × 1 passive coupler is connected to the fiber in the system to transmit the combined signal spectrum, which is a sum of signal spectra of all active users. The power spectrum density (PSD) of the transmitted optical signal R(z,ω) at distance z is represented as (1). K
N
k =1
i =1
R ( z , ω ) = ∑ bk ∑ ck (i )Vi ( z , ω )
(3)
γi =
2πn2 cAeff λi
(4)
where n2 is the nonlinear index coefficient and Aeff is the effective core area, λi is the i-th carrier wavelength and c is the speed of light in free-space.
Consider the case that the dispersion effect is not severe and the second-derivative terms in (3) can be neglected. Because the pulse shapes do not change in the absence of dispersion effect, (3) can be solved analytically. The general solution at z = L is given by (5)
ri ( L, t ) = ri (0, t )e jφi (t )
(5)
where the time-dependent nonlinear phase shifts are obtained from (6)
(1)
N
φi (t ) = (γ i ri (0, t ) + 2∑ γ j ri (0, t ) ) L 2
2
(6)
j ≠i
where bk ∈ {0,1}, for 0 ≤ k ≤ K, are the information bit of kth user, Vi(z,ω) is PSD of the i-th chip in the code vector. Let Ri(z,ω) denote the PSD of i-th element in the transmitted vector R(z,ω), which can be written as (2).
Thus, for the same power in all channels, the factor of 2 in (6) indicates that XPM is twice as effective as SPM. The total phase shift induced by XPM now depends on the power in all channels and would vary from bit to bit depending on the bit pattern of the neighboring channels.
K
Ri ( z , ω ) = ∑ bk ck (i )Vi ( z , ω )
To demonstrate the effect of SPM and XPM, we take the example of Table I. Assuming the pulse of each chip is Gaussian, the spectra of SAC-OCDMA input pulse for several values of the transmission distance is shown in Fig. 1. For the fiber component properties, we disable attenuation effects. The bit rate is 2Gb/s, the centered frequency is 193.1THz, with each chip 10GHz-spaced. The fiber channel has nonlinear coefficient of 1.3km1W-1 and dispersion of 16.75 ps/nm/km.
(2)
k =1
An example is illustrated in Table I for N = 7 chips msequences address code. In the receiver, a correlation function is applied to the incoming signal to extract the bit stream of desired user. In order to reduce the influence of MAI, orthogonal (or nearly orthogonal) codes are required. However, when two or more optical fields with different frequencies transmit inside a fiber, they influence each other because of the fiber nonlinearity. The nonlinearity induced by Kerr effect couples two optical fields through XPM, which is always accompanies SPM when two or more optical fields propagate simultaneously in an optical fiber. To see the spectral and temporal changes occurring as a result of XPM interaction between two or more co-propagating chips, a set of coupled nonlinear Schrodinger equations can be used to express the propagation. For simplicity, fiber losses, group-velocity mismatch are neglected, and the resulting equation for ri(z,t), for 1 ≤ i ≤ N, becomes
TABLE I. User Number 1 2 3 4 5 6 7 Combined Spectrum
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1 0 1 0 0 1 1
CODED 7-CHIP SPECTRAL SEQUENCES
Assigned Address Sequence 1 1 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0
0 1 0 0 1 1 1
Data Bit 1 1 1 0 1 0 1
1 0 1 0 0 0 1
Transmitted Optical Signal 1 1 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0
0 1 0 0 1 0 1
3 3 4 2 3 2 3
1× N
N ×1
Figure 2. Schematic drawing of a mid-span phase inversion for compensating SPM and XPM; OPM-optical phase modulator. Figure 1. SPM and XPM in SAC-OCDMA system.
photo-diodes and electrical filters and the SAC-OCDMA system must first be de-multiplexed to detect power fluctuations for different channels.
Fig. 1 shows the feature of SPM and XPM-induced spectral broadening, the entire frequency range covered by an oscillatory structure. Usually, there are many peaks consisted in the spectrum and the outmost peaks have most intensity. We can understand the origin of oscillatory structure from (6), which shows the time-dependent frequency chirp induced by SPM and XPM. In general, at two distinct points, the same chirp occurs, so that there is the same instantaneous frequency at tow values of T. Two waves with the same frequency but different phases are represented by these two points, and according to their relative phase difference, they can have constructive or destructive interference. Such interference results in the multi-peak structure in the pulse spectrum.
When the magnitude of the phase modulation is twice than the phase shift of the signal in the first–half fiber and with opposite sign, the mid-span phase inversion can be achieved. An electrical low-pass filter is placed in the output of the photo-diode to mitigate the noise. The output of the filter is used to mitigate the noise by driving the phase modulator to apply extra phase modulation. Thus, the nonlinear phase noise of signal in the second-half fiber is partially cancelled by this extra phase modulation. IV.
SIMULATIONS RESULTS ON THE COMPENSATED SYSTEMS The simulation setup is shown in Fig. 3. The data transmission bit rate is 2Gb/s. On the transmitter side, a bit stream is generated used a pseudo random binary sequence generator, and the data is encoded by a 127-chip m-sequence encoder. The SLD is used to convert electrical carriers to optical wave centered at 193.1THz. Fiber dispersion and attenuation are fully compensated. In the receiver, the optical field is down-converted into electrical domain by photodetectors. A set of balanced-detectors is used to mitigate MAI.
III.
FIBER NONLINEARITY COMPENSATION OF SPM AND XPM FOR SAC-OCDMA A common way to mitigate the nonlinear phase noise is phase inversion compensation. Here, a scheme for SPM compensation based on mid-span phase inversion is proposed. The phase inversion is employed in the identical fiber span .The phase noise induced by fiber nonlinearity is cancelled by inversing the phase of signal in the middle of the channel. We can show that it is an effective way to mitigate nonlinear phase noise and enhance the system performance.
The main benefit of nonlinearity compensation is to be able to increase the nonlinear threshold, so systems can be operated at higher powers to allow increased amplifier spacing or longer transmission distances. Fig. 4 shows the electrical bit-error rate (BER) versus the power per chip with and without PIC compensation. The chip power is varied from -14dBm to 6dBm. System without PIC compensation is compared with PIC compensation. At low powers, the SAC-OCDMA signals with or without compensation have similar BER. The reasons are that, under low input power level, the fiber nonlinearities do not take effect and the fiber can be modeled as a linear channel, which is dominated by linear dispersion. When optical power increases, the system BER increases and the SPM and XPM effects become stronger. By adding the PIC compensation, the system can take higher launch power and reach lower BER. For single mode fiber, the input power can be increased up to 3 dB using PIC compensation alone for a given BER.
The proposed mid-span phase inversion scheme is shown in details in Fig. 2. It can be shown that the SPM and XPM can be effectively removed. A photo-detector is used to detect the instantaneous power of the incoming data stream. Then the original signal is phase modulated by a phase modulator in front of the second-half fiber to reach the phase-inversed operation. The magnitude of the phase modulation is proportional of the detected data intensity and the sign is opposite to that of the SPM-induced nonlinear phase shift in the first-half fiber. XPM compensation signal for each wave-length should is different. The power of each wavelength should be detected using separate photo-diodes and electrically filtered with different low-pass filters (LPF). The compensation signal should then be the sum of all the filtered signals. The factor of 2 for optical amplifiers means that under the same intensity fluctuations, XPM is twice as effective as SPM. However, as the number of channels increases, this would require multiple
794
1× K
K ×1
Figure 3. SAC-OCDMA simulation setup
less transmission length because of high nonlinearity due to higher power variations. For a required BER of 10-9, the reach in this link is increased from under 40 km to over 60 km. V.
CONCLUSIONS
In summary, a novel method of fiber nonlinearities compensation based on mid-phase inversion is proposed to reduce the phase distortion in SAC-OCDMA. A phase modulator is used to modulate the phase of the data pulses at the beginnings of second-half fiber. The magnitude of the phase modulation is directly proportional to the detected pulse intensity, and the sign is opposite the nonlinear phase shift caused by SPM or XPM. Thus the nonlinear phase noise induced by amplitude fluctuation and SPM in the firsthalf fiber is partially compensated for in the second-half fiber.
Figure 4. BER versus fiber input power for 100-km long fiber
In the proposed compensation schemes, only a single tuning parameter is used in the mid-span compensation, so little knowledge is required of the actual fiber plant to achieve a reasonable benefit. The actual value of this parameter need not be accurate, by the optimization process; the compensation can handle for dynamic variations in the system. Then it would be robust against variations in input power and transmission distance. We how by numerical simulations that SAC-OCDMA at 2Gb/s with such a fiber nonlinearities can provide near 3dB of improvement in optical transmissions. REFERENCES
Figure 5. BER versus transmission distance with and without compensation
[1]
The system BER of launch power at -6dBm as a function of reach up to 100km is shown in Fig. 5. For shorter distance, the performance of SPM and XPM compensation is limited. As the transmission distance getting longer, the phase shift of the optical signal is more severe, and thereby degrades the system performance. The compensated system with PIC can take larger launch power and reach longer distance for a given BER. Because the phase distortion is proportional to the signal power and transmission distance, the effect of nonlinear compensation is more notable at high launch power and long distance. However, PIC can only support
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