1. Introduction

The demand for the amount of data from Internet has seen exponentially growth in the past decade. To meet the never-ending demand of Internet traffic growth, latest optical communication systems is moving towards 400-Gb/s and beyond per wavelength [1,2]. Besides increasing the modulation baud rate, higher data rate per wavelength is achieved through coherent detection and high-spectral-efficiency modulation formats, e.g., polarization division multiplexed (PDM) quadrature phase shift keying (QPSK) or quadrature amplitude modulation (QAM) [3,4].

On top of the optical transport network, there is a network layer which forwards the Internet protocol (IP) packet based on the IP address. Traditionally, the packet forwarding engine (PFE) application specific integrated circuit (ASIC) and the coherent optical transponder facing the optical line system (line-side optics) are located in different chassis. The client-side short-reach optical transponders, mostly relying on on-off key (OOK) modulation format and direct detection, interconnect the PFE and line-side optics. This traditional approach incurs extra cost and power consumption. Thus, it is very desirable to directly integrate the coherent transponder with PFE in the same physical equipment, which will remove the client-side optical transponders. This initiative is called as packet optical integration [5].

Figure 1 shows the architecture which closely integrates the PFE, the digital signal processing (DSP) ASIC, and coherent optical transponders. For example, the coherent optical transponder can be a CFP2 form factor analog coherent optics (CFP2-ACO) module [6]. The IP traffic is converted into optical signal through coherent transmitter and sent through the long-haul optical communication system which can include multiple reconfigurable optical add drop modules (ROADM). During the transmission, multiple optical impairments can accumulate. After coherent detection at the receiver and analog-to-digital (ADC) conversion, most impairments are compensated by the DSP ASIC in the digital domain.

 

Fig. 1 Architecture for packet-optical integration. FEC: forward error correction; FIR: finite impulse response; DAC: digital to analog conversion; OSNR: optical signal to noise ratio; CD: chromatic dispersion; PMD: polarization modal dispersion; PDL: polarization dependent loss; ADC: analog to digital conversion; CPE: carrier phase estimation.

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In the long-haul optical communication systems, optical amplifiers are used to compensate the attenuation introduced by optical fiber. While optical signal is boosted, additional noise is also added, which causes the decrease of optical signal noise ratio (OSNR) and the increase of bit error ratio (BER). Eventually, transmission distance can be limited, when BER is too high for forward error correction (FEC) to correct. Thus, BER vs. OSNR curve is one of the most important characteristic of coherent transponder for long-reach application. However a complicated setup is required to measure the BER vs. OSNR curve. This makes it difficult and complicated to measure this curve in the manufacturing environment and during the in-field operation. Thus, a laudable goal would be to have a simple way to measure this performance for coherent transponder.

Given the important role of OSNR, it is also highly desirable to monitor OSNR in optical communication system as well. Recently, several methods have been demonstrated using various methods [7–12]. In [7], the second order and the fourth order of the statistical moments of the output of the adaptive equalizer is used to estimate OSNR. In [8], periodic training sequence is added to the data stream, facilitating the monitoring of OSNR. In [9], periodic zero-power symbol is inserted into the data stream for OSNR measurement. In [10], variable phase difference phase portrait, acquired by a low-speed sampling channel, monitors the OSNR. In [11], a joint OSNR monitoring and modulation format identification is demonstrated. It relies on asynchronous single channel sampling. In [12], a non-intrusive OSNR monitoring scheme, utilizing the conventional optical spectrum analyzer (OSA), is demonstrated by detailed spectral analysis between the noise-free reference spectrum and the noise-loaded measurement spectrum. Although those innovative methods can monitor OSNR, it is desirable to monitor OSNR directly using the coherent receiver. The reason is that one need a coherent receiver to recover the transmitted symbol, and the pre-FEC BER is closely correlated with OSNR. Thus, it is desirable to directly monitor OSNR from pre-FEC BER reading using the built-in functionality of coherent transceiver.

In this paper, we develop an accurate analytical model to predict the BER vs. OSNR performance. Experimental studies show that the model can function well for high baud rate, up to 86 Giga baud per second (GBd/s), and advanced modulation format (PDM-16QAM). By considering the influence of baud rate on model parameters, we accurately predict the BER vs. OSNR curve for various baud rates. Inversely, the model allows the proper prediction of OSNR value based on the pre-FEC BER value, after the impairments from CD, PMD and nonlinearity are accounted for. This offers a simple and convenient solution of monitoring OSNR value based on existing hardware / DSP which are required to recover the signal.

The paper is organized as following: In section 2, we introduce the analytical model at fixed baud rate (32GBd/s) and PDM-QPSK modulation format. In section 3, we expand the analytical model to high baud rate (up to 86GBd/s) and advanced modulation format (PDM-16QAM). We also study the influence of baud rate on the analytical parameters and provide the physical insight. In section 4, we discuss a few potential applications of this model and the potential expansion of the model for the future works.

2. Analytical model for fixed baud rate

In [13], an analytical model with two fitting parameters, η (Eta) and κ (Kappa), has been developed to predict the performance of BER vs. OSNR curve as shown in Eq. (1).

Here, we use additive white Gaussian noise (AWGN) model for coherent detection system. With coherent detection, electrical field containing both the signal and amplified spontaneous emission (ASE) noise is linearly recovered. Thus, the noise source from OSNR can be added together with other noise source by AWGN assumption. As discussed above, this model cannot be applied to direct detection system since only the electrical amplitude is recovered after direct detection. A modified model can potentially meet the need to accurately predict the performance of direct-detected transponder.

Figure 2 shows the experimental setup to measure the BER vs. OSNR curve. A signal Erbium doped fiber amplifier (EDFA), working in constant output power mode, boosts the output signal from the coherent transmitter. The output from the amplified spontaneous emission (ASE) noise source is filtered by a tunable filter (TF 1), resulting a flat noise spectrum whose center is at the wavelength of coherent transmitter and whose spectral width is 3.2 nm. This narrow-band noise source is further amplified by a noise EDFA, resulting a strong noise pedestal around the signal’s wavelength. If the output from ASE is directly amplified by noise EDFA, the spectrum of the output of the noise EDFA will be across C band, leading to low noise level around the signal’s wavelength. Thus, this setup is necessary to achieve low OSNR at high receiver optical power (ROP). The output from signal EDFA and VOA 1 is further combined through a 3dB coupler. A second tunable filter (TF 2) controls the signal bandwidth and removes the out-of-band ASE noise. A second VOA (VOA 2) controls the ROP for the coherent receiver. As seen, the setup of BER vs. OSNR measurement is complicated. So there is a strong need to reduce the complexity of this measurement, so that the BER vs. OSNR measurement can be performed in the field operation.

 

Fig. 2 Experimental setup for BER vs. OSNR measurement.

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In this experiment, the coherent transponder is composed of a pluggable CFP2-ACO module and a DSP ASIC. The coherent transponder is plugged into an IP router with a built-in PFE which generate the traffic and count the BER. The block diagram of the DSP ASIC can be seen in Fig. (1). The optical transponder carries 100 Gigabit Ethernet (100GE) traffic using PDM-QPSK modulation format at 32 GBd/s. Nyquist pulse shaping [14] is not applied to the optical signal.

Figure 3 illustrates the measured BER vs. OSNR results at different ROP and the analytical results for each ROP value calculated from Eq. (1). However, for each ROP, a different set of η and κ values is needed. This is due to the fact that the signal power in electrical domain is proportional to ROP in optical domain. Thus, at the lower ROP, the electrical signal power is lower which leads to lower SNR and worse BER. It is very desirable to expand the model to take into consideration of ROP.

 

Fig. 3 Measurement vs. theory for BER vs. OSNR curves. Symbol: measurement; line: analytical results. Different [η, κ] are used to generate the analytical results.

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One advantage of extraction the analytical parameters η and κ from the curve fitting is the robustness against the fluctuation of pre-BER reading. Since multiple pre-FEC BER values are used to perform the curve fitting, any variation of pre-FEC BER reading on a single measurement point will be greatly averaged out. As shown in Fig. 3, the experimental results fit well with the analytical results.

Another type of optical communication system is unamplified link, which is common in the interconnection between data centers. Without optical amplifier, the signal will experience attenuation during the transmission. The sensitivity of coherent transceiver determines the transmission distance. Here the most important measurement for unamplified link is BER vs. ROP (sensitivity) curve. The measurement setup only requires a VOA and a power meter (PM), which is very simple as shown in Fig. 4(a). Many coherent transponders, like CFP2-ACO module, have already integrated VOA and PM. An optical switch can be integrated as well. So a simple loopback, either external or internal (through optical switch), is sufficient for measuring BER vs. ROP.

 

Fig. 4 (a): setup for BER vs. ROP measurement. PM: power meter, OC: optical coupler. (b): correlation between BER vs. OSNR and BER vs. ROP. OSNR_ini = 10*log₁₀(ρ)

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The BER vs. OSNR curve and BER vs. ROP curve are intrinsically correlated. In BER vs. OSNR measurement, the noise increases while the signal remains constant when OSNR decreases; in BER vs. ROP measurement, the signal decreases while the noise remains constant when ROP decreases. Both scenarios lead to the decrease of SNR and the increase of BER. Two curves are put together in Fig. 4(b). Those two curves are almost overlapped, indicating strong correlation. Note that BER vs. ROP curve is shifted by 45dB since OSNR from the coherent transmitter is 45dB at 0dBm output power. Clearly, one can modify the model of BER vs. OSNR curve so that it can be applied to BER vs. ROP curve, as shown in Eq. (2). The fitting parameters derived from BER vs. ROP curve will be very close to the fitting parameters derived from BER vs. OSNR curve. The dashed line shows the analytical result which works for a large range of ROP, using the fitting parameters derived from Eq. (2). For ROP < −32 dBm, the BER reading is not accurate due to the presence of uncorrected code word (UCW). For > 0 dBm ROP, the noise floor of BER increases due to saturation of coherent receiver and high order nonlinearity like total harmonic distortion.

ROP^dB is the ROP value in dBm, ROP_cal is the ROP value after normalization against B and bw. Here the superscript ‘SEN’ indicates that the parameters are extracted from BER vs. ROP curve. Also, an additional parameter ρ (Rho) corresponds to the OSNR at the transmitter output, which is equivalent to 10^(45/10) = 31623. For the coherent transponders operating at certain baud rate, the OSNR value at the transmitter output remains relatively unchanged over different transponders. So it is possible to measure this parameters during the design verification testing (DVT) and apply the same parameters over different transponders.

From those observations, we can expand the BER vs. OSNR model to take consideration of ROP influence. The influence of ROP is treated as Gaussian noise, which can be added together with other noise source. Equation (3) shows the expanded model to predict BER vs. OSNR curve. The extracted fitting parameter [η^SEN, κ^SEN] from Eq. (2), and the ρ parameters determined during DVT, are used to predict BER vs. OSNR curve (BER_pred).

Figure 5 displays the comparison between the measurement result and the prediction result. As seen, they almost overlap with each other from 0 dBm to −25 dBm. We notice some deviation at the high OSNR region for ROP < −22 dBm. The likely root cause for this deviation can be found in Fig. 4(b). As seen, there is a slight deviation between BER vs. OSNR curve and BER vs. ROP curve at the high OSNR region. This leads to a slight difference between [η^SEN, κ^SEN] and [η^OSNR, κ^OSNR]. Here the superscript ‘OSNR’ indicates that the parameters are extracted from BER vs. OSNR curve. There is also a slighter deviation for ROP = 0 dBm. This is due to that at higher ROP, the influence of the shot noise (which does not follow the assumption of AWGN) and nonlinear effect like total harmonic distortion (THD) cannot be ignored. However, at low OSNR region where most long-haul optical communication systems operate at, the two curves are still well aligned from 0 dBm to −25 dBm.

 

Fig. 5 Prediction of BER vs. OSNR based on [η^SEN, κ^SEN, ρ], wrapped around different ROP value. Blue symbol: measurement results; red curve: analytical results.

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Inversely, the OSNR value can be predicted from pre-FEC BER value using the proposed analytical model, as shown in Eq. (4). Figure 6 shows the error of this OSNR monitoring scheme over different ROP value. As seen, the absolute value of the error is less than 0.3dB between 0 to −22 dBm. Even at −25 dBm, the absolute value of the error is still less than 0.5dB for low OSNR region (below 16dB OSNR) where most coherent transponders operate at. This demonstrates the feasibility of OSNR monitoring scheme proposed over a large range of ROP value. The monitoring accuracy is in-line with the results presented in [7–12].

 

Fig. 6 Accuracy of OSNR monitoring based on pre-FEC BER value.

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Furthermore, the influence of channel wavelength on the fitting parameters is studied. The wavelength of the CFP2-ACO module was tuned over C band in 50-GHz grid. We performed BER vs. OSNR measurement for each wavelength at −18dBm ROP, and extracted the fitting parameters [η^OSNR, κ^OSNR]. Figure 7 shows the fitting error (Err_rms) and the fitting parameters η^OSNR, κ^OSNR for all channels. As seen, the analytical model works well over different wavelength, and the variation of fitting parameters over different wavelength is small.

 

Fig. 7 Variations of the fitting parameters, fitting error, BER noise floor and estimation error using average analytical parameters over wavelength.

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We notice that both η^OSNR and κ^OSNR vary over wavelengths. However, there is no clear correlation between two parameters. So we still need to use both parameters to predict BER vs. OSNR values. The possible root cause for those small variations are the noise fluctuation from the hardware implementation. One example is the dependency of the phase noise of the local oscillator on the wavelength. Another example is the radio-frequency (RF) bandwidth variation of modulated signal over wavelengths. In Fig. 7, we also plot the estimation error if we use the average values of η^OSNR and κ^OSNR to predict the BER vs. OSNR curve over all wavelengths. As seen, the estimation error using the average value of the fitting parameters will be increased by roughly an order of magnitude with maximum around 7%. This demonstrates that the analytical model is robust against the small variation of fitting parameters, and can be applied over different wavelengths at a small trade-off of accuracy.

In Eq. (1) to (4), the OSNR / ROP is normalized against two times of baud rate. This is justified since Nyquist pulse shaping is not applied to the optical signal. Thus, the optical spectrum spreads from v-B to v + B, where v is the central frequency of optical signal. It is noticeable that the underlying assumption of this model, AWGN and coherent detection, is independent with the shape of optical spectrum. Hence, the model can be applied to the case with / without the Nyquist pulse shaping. We validate this by studying the coherent transponder without the Nyquist pulse shaping in Section 2 and the coherent transponder with the Nyquist pulse shaping in Section 3.

The DSP ASIC is an essential components of coherent transponders. The analytical parameters are closely linked to the performance of DSP ASIC. For example, the bandwidth limitation of ADC and DAC within DSP ASIC contributes to η, which is related to the mismatching between transmitter’s bandwidth and receiver’s bandwidth. The noise from DSP ASIC contributes to the noise floor of BER, which is related to κ in turn. Thus it is essential to find the analytical parameters for the model with the DSP ASIC. If a new DSP ASIC is used, the analytical parameters need to be measured again. On the other hand, if the DSP ASIC remains the same, but the baud rate changes, one does not need to calibrate the analytical parameters for every baud rate. The variation of the analytical parameters over the baud rates will be the subject of study in Section 3.

3. Analytical model over various baud rate

Having demonstrated that the analytical model works at fixed baud rate (32 GBd/s) and PDM-QPSK modulation format, we further extend the model above to cover the user case of high baud rate (up to 86 GBd/s) and advanced modulation format (PDM-16QAM). One aspect is to expand the existing model to various baud rates, so that the performance of coherent transponder at various baud rate (B) can be predicted without first measuring the transponder at that particular baud rate.

The change of baud rate can be attributed to either the underlying data rate or the overhead of forward error correction (FEC). Higher underlying data rate increases the throughput, and larger overhead of FEC increase the tolerance to ASE noise. In general, the industry evolves towards higher baud rate [15]. Flex-grid ROADM enables the transmission of signal with various baud rates over the optical line system by dynamically allocating the passband for optical carrier [16].

In Section 3.1, we present the experimental and analytical results for coherent transponder with high baud rate and advanced modulation format. The experimental results agree well with the analytical results. In Section 3.2, we analyze how the fitting parameters change over baud rate and presented a model which allows the prediction of BER vs. OSNR performance at various baud rates.

3.1 Experimental results vs. analytical results

The experimental setup for BER vs. OSNR measurement is the same as that shown in Fig. 2, and the experimental setup for BER vs. ROP measurement is the same as that shown in Fig. 4(a). We build the coherent transmitter and the coherent receiver using the discrete components to achieve high baud rate and advance modulation format. The coherent transmitter is composed by a high-speed digital-to-analog converter (DAC, 92G samples/s), a tunable laser, a dual-polarization IQ modulator, and an automatic bias control circuit. Nyquist pulse shaping with roll-off factor of 0.1 is applied to the transmitter’s signal. The coherent receiver is composed by 90 degree optical hybrid, balanced photo diode, tunable laser serving as local oscillator, and real-time oscilloscope serving as high speed ADC (160G samples/s). Offline DSP is used to recover the signal and count the BER, which is similar to that in [17]. After the high speed ADC, the following DSP building block is used: static equalization to compensate the static impairment and chromatic dispersion; adaptive equalization to perform polarization de-multiplexing and compensation of polarization mode dispersion; time recovery using Gardner’s method; frequency offset estimation; carrier phase recovery; and symbol estimation and recovery.

Figure 8 shows BER vs. OSNR curves at various baud rates (45, 56, 64 and 86 GBd/s) over different ROP value. We measured 0, −5, −10, and −15dBm for 45 GBd/s and 56 GBd/s; we measured 0, −5, and −10dBm for 64 GBd/s and 86 GBd/s due to the fact that BER at −15dBm was above the FEC threshold, which is 4.2e-2 according to 25% overhead used in [18].

 

Fig. 8 BER vs. OSNR measurement and prediction. Symbol: measurement result; line: prediction result.

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The symbols in the plots correspond to the measurement results, and the curves in the plots correspond to the analytical model. As seen, two results are very close with each other, particularly at the low OSNR region where most long-haul optical communication systems operate at. At high OSNR region, there is a small difference between the measurement and prediction. This is due to the estimation error in κ. Some possible causes are non-AWGN type of noise, receiver saturation and nonlinearity like total harmonic distortion. Overall, the prediction results agree well with the measurement results, clearly demonstrated how powerfully and accurately our expanded model works over various baud rates.

The analytical model is described in Eq. (3) with three model parameters. In the next section, we will discuss how to extract those parameters from BER vs. ROP curve, and how those parameters vary over different baud rates.

3.2 Influence of baud rate on model parameters

Figure 9 shows the BER vs. ROP curve at different baud rate, measured by setup shown in Fig. 4(b). We have noticed that to calculate [η^SEN, κ^SEN] value from BER vs. ROP curve, it is necessary to just use the portion where ROP is smaller than −7dBm. This is due to the fact that at larger ROP, other nonlinearity or noise also contributes to overall SNR. For example, shot noise, receiver saturation or total harmonic distortion distorts the AWGN model. The experimental results agree well with the analytical predictions once we apply this methodology. The value of ROP_th −7dBm is a hyper-parameter for the model, which could be transponder-dependent and should be determined during DVT.

 

Fig. 9 BER vs. ROP measurement. The dashed line indicates ROP_th.

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To determine ρ, one needs to overlay the curve of BER vs. OSNR at 0dBm ROP with the curve of BER vs. ROP, which is similar to Fig. 4(a). For BER vs. ROP curve, the x axis value is ROP + 10*log₁₀(ρ). This is related to the fact that ρ represented the OSNR value at 0dBm ROP. As shown in Fig. 10, two curves overlapped well, especially at the low OSNR or small ROP region. This indicates that if [η^SEN, κ^SEN] parameters derived from BER vs. ROP curves are used to predict BER vs. OSNR curves, the prediction will match the measurement well. In our experiment, the receiver bandwidth is set at 0.8*B. Since white noise is proportional to the receiver bandwidth and the signal remains unchanged, ρ, which is OSNR at 0dBm ROP, will be inversely proportional to baud rate B.

 

Fig. 10 Correlation between BER vs. OSNR curves and BER vs. ROP curves for different baud rates. Rho: ρ. The amount of the shift applied to ROP curve is determined by Eq. (5).

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Ideally, the filter mismatching between coherent receiver and signal should remain nearly constant since the receiver bandwidth is 0.8*B. However, we have noticed that the filter mismatching parameter η changes linearly with the baud rate at a small slope as shown in Fig. 11(a). This deviation is likely due to non-perfect implementation of coherent transponder within the experimental setup. For example, the arbitrary waveform generator works at 92Gsample/s. At 86G baud rate, the sample per bit is 1.07, well below the 2 samples per bit required by Nyquist theorem. This will introduce distortion to the coherent signal and cause η to change at various baud rates. As seen, the relationship between η and B can be expressed as a linear curve fitting:

 

Fig. 11 Analytical model parameters vs. baud rate. (a) η vs. baud rate, (b) κ vs. baud rate, (c) Q²_ceiling vs. baud rate. Two sets of parameters and their linear fittings are shown. One is extracted from the BER vs. OSNR curves, the other one is extracted from the BER vs. ROP curves. As seen, two sets of parameters agree with each other.

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We noticed the noise floors of BER in BER vs. OSNR curves increase when the baud rates increase. This is similar for BER vs. ROP curves. From BER vs. ROP curves, we can extract model parameters [η^SEN, κ^SEN], and we can calculate noise floor of BER from Eq. (1)

Having determined how fitting parameters change over baud rate, we can predict BER vs. OSNR curve based on the following parameter: [ρ(B₀), ROP_th, α₀, β₀, α₁, β₁]. The values of those parameters are listed in Table 1 below. As shown in Fig. 9 of section 3.1, the analytical results and the measurement results agree with each other. Note that those analytical results used the fitting parameters [ρ(B₀), ROP_th, α₀, β₀, α₁, β₁] for all baud rates. In comparison, the analytical results in section 2 use the fitting parameters [η^SEN, κ^SEN, ρ(B₀)] at a fixed baud rate. This demonstrates that the fitting parameters can be extracted from the measured BER vs. ROP curves at a few baud rates. The extracted fitting parameters can be used to predict the analytical result over all baud rates.

Table 1. Fitting parameters used to predict BER vs. OSNR curves shown in Fig. 9

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The fitting parameters shown in Table 1 are extracted from η^SEN and κ^SEN, which are further extracted from BER vs. ROP curves at different baud rate. Since the curve fitting method is used on each BER vs. ROP curve which contains multiple BER measurement points, the fluctuation of pre-FEC BER reading is greatly mitigated. Thus the fitting parameters in Table 1 is robust as well.

Note that η^SEN and κ^SEN are extracted from Eq. (2), where ROP value is normalized against two times of the baud rate, which is suitable for the signal without Nyquist pulse shaping. For simplicity of the model, we keep Eq. (2) unchanged even for the signal with Nyquist pulse shaping. As demonstrated in Fig. 9, the analytical results fit well with the experimental results over a large range of ROP values and different baud rates. This demonstrates that the analytical model is agnostic with the spectrum shape of the signal. This is as expected since the fundamental assumptions of coherent detection and AWGN still hold for various spectral shape of the signal.

4. Application of analytical model

There are multiple applications for the expanded BER vs. OSNR model. Firstly, the model allows a simple process of measuring BER vs. OSNR performance. Instead of relying on a complicated setup as shown in Fig. 2, one can use a simple loopback, either internally or externally, as shown in Fig. 4(a). During the initial power-up without live traffic, an internal built-in optical switch can loop the signal between coherent transmitter and coherent receiver. Using the built-in VOA and photo diode, BER vs. ROP curve at a few baud rates can be measured. And α₀, β₀, α₁, β₁ can be determined. Once the initial calibration is done, the coherent transponder can be used to carry the live traffic. Periodically, during the maintenance window, one can repeat the calibration process and determine α₀, β₀, α₁, β₁ again. By comparing with earlier values of α₀, β₀, α₁, β₁, one can monitor the degradation in coherent transponder through the analytical model. Once a coherent transponder degrades too much, it can be either replaced, or re-assigned to a shorter router, or re-adjusted to a lower baud rate.

Secondly, it allows abstraction of performance of coherent transponder to a set of fitting parameters [ρ(B₀), ROP_th, α₀, β₀, α₁, β₁]. Those values can be determined during design verification testing. Those parameters can be stored in EEPROM of the line-card. The network management layer or the multi-layer optimization tool can extract those parameters, and perform network management and optimization. This is well suited for future software defined network (SDN).

Thirdly, this approach allows the capability of accurate OSNR monitoring. FEC layer can correct certain amount of BER and report the per-FEC BER. One can use the pre-FEC BER to reversely predict the OSNR. The advantage of the proposed approach is that no extra hardware is required. All the necessary hardware has been implemented in coherent receiver and the following digital signal processing circuits.

Having established that the expanded model to predict BER vs. OSNR curve, we can further develop a new scheme of coherent optical channel monitor (OCM). Essentially this OCM is composed of components in the receiver path of a coherent transponder, namely variable optical attenuator, 90 degree optical hybrid, balanced photo diodes, linear trans impedance amplifier, integrated tunable laser assembly (ITLA) and DSP chip etc. Once the parameters of the model described earlier are calibrated for this coherent OCM, this coherent OCM can be used to monitor many parameters within an optical channel. Most importantly, OSNR value can be reversely calculated from BER value based on the model. Other parameters, like chromatic dispersion, differential group delay and frequency offset, can be monitored as well.

The results above are obtained during the back-to-back measurement. During the optical transmission over long distance, additional optical impairments, for example the chromatic dispersion (CD) and polarization mode dispersion (PMD), are built up. Coherent transponder together with digital signal processing can recover the signal with large amount of CD and PMD present. Also coherent receiver can report estimated CD value, and differential group delay (DGD) value which is average PMD value [19]. However, additional BER degradation is present due to those optical impairments. The penalty in Q² factor introduced by CD or DGD is approximately linearly proportional with CD or DGD value [20]. During DVT, one can determine those linear coefficients and remove the influence of CD or DGD accordingly. This will further improves the OSNR monitoring accuracy. Another influence is the nonlinear penalty from four wave mixing. The noise generated can be treated as AWGN using the GN model, and the influence on pre-FEC BER can be estimated as well [21,22].

This accurate analytical model can be implemented in a central processing unit (CPU). For example, in the scenario of the packet optical integration, a routing engine (RE), which is essential a CPU used to established routing table for Internet traffic, can implement the curve fitting using sequential quadratic programming [23]. Another example is that in the scenario of SDN, the central SDN controller can implement this analytical model.

Since the initial inception of probability shaping constellation (PSC) [24], the advantage and flexibility of PSC has made this technique as the essential de-factor modulation format for next generation coherent DWDM system [25]. Other types of advanced modulation format, like geometrical shaping [26], high-dimensional shaping (for example, 8D-2QAM and 4D-8QAM) [27,28] have been also developed to improve the performance of coherent DWDM system. The analytical model developed in this work relies on the assumption of coherent detection and AWGN, which also hold for those advance modulation formats. Intrinsically, this analytical model can be applied to predict the performance of BER vs. OSNR for those coherent transponder. The influence of the advanced modulation formats on the analytical parameters will be an important topic for future study.

5. Conclusion

In this paper, we have demonstrated an accurate model allowing the prediction of BER vs. OSNR performance of coherent transponders over various baud rates and modulation formats. The model’s parameters can be extracted from the BER vs. ROP curves measured at a few baud rates. The prediction results from the model agree well with the measurement results.

By adopting this model, one can easily predict the most important performance metrics for coherent transponder, which is BER vs. OSNR performance, without using a cumbersome and complicated setup. It allows the abstraction of coherent transponder into a set of modeling parameters, well suited for application in software defined network. This model also allows the accurate monitoring of OSNR from BER values without requiring extra hardware or DSP building block. A coherent optical channel monitor based on this model will be a powerful monitoring tool for whole optical network.