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Abstract
Digital coherent transmission features a very large transmission bandwidth and has played a main role in core optical transmission networks. With the progress of semiconductor technologies, practical coherent transceivers with rates over 100 Gbaud are becoming feasible. With such advances, the transceiver components must have lower power consumption and lower costs, and it becomes important to know how each component contributes to the overall transmission performance. Here, to decompose the effects of noise factors in high-baud-rate DP-16QAM transmissions, we used the theoretical relationship between the bit error rate (BER) and noise-to-signal ratio (NSR) and performed linear analyses. The NSR could be decomposed into individual noise contributions according to dependences on the inverse signal and local photocurrents. The obtained parameters were shown to be useful for predicting required optical signal-to-noise ratio (ROSNR) characteristics.
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1. Introduction
Importance of large bandwidth communication networks has grown as society has evolved, such as through the recent popularization of teleworking, proliferation of services offered through data centers, and the introduction of wide-bandwidth mobile 5G networks. Among the optical internet technologies, optical coherent transmission [1] has played a crucial role in the core optical network; huge transmission bandwidth are enabled by the use of high bandwidth digital signal processors made with cutting-edge microfabrication technologies. Advances in semiconductor technologies and the requirement for low cost have also driven the increase in baud rates for shorter-reach applications; components must have low power consumption at a low cost; this increases the relative importance of noise and imperfections in transceiver components. To construct a more effective network with a smaller margin [2] using such devices, it has become increasingly important to understand the effects of all components on performance. Because of the highly complex polarization-multiplexing technologies and modulation and demodulation methodologies using local lasers, there are many more factors that degrade the transmission performance than in the conventional intensity modulation direct detection (IMDD) transmission technologies, and BER calculation using numerical simulations are suited for qualitative analyses rather than quantitative analyses.
To match the BER characteristics of transceivers with the theoretical predictions, [3] used parameter fitting to the signal power dependence of the BER characteristics to obtain various noise parameters. However, the number of parameters can be larger than the degrees of freedom and it is not possible to determine the validity of the fitting parameters or to tell whether deviations between the fitting and experiments are caused by insufficient fitting or parameters not included in the model.
In this study, by using the theoretical relationship between BER and NSR, we projected 16QAM (quadrature amplitude modulation) online BER characteristics into the NSR and performed linear analyses. We decompose the NSR into individual noise contributions, which is expected to be valid in case of low noise. The dependence of the NSR on the inverse signal and local photocurrents and OSNR were in good agreement with the theoretical analyses, and we could extract noise components from the dependencies. The obtained parameters were shown to be useful for predicting ROSNR characteristics. These analyses can be applied to the analyses and prediction of transmission characteristics under a wide range of conditions including baud rate, and and will be useful for developing high-baud rate transceivers.
2. Theoretical background
In this section, we derive the NSR in a form that can be compared with experimental values. Figure 1 is a schematic diagram of a coherent receiver. The input optical signal and local oscillator (LO) are split by beam splitters and input to a dual polarization optical hybrid and then to four dual photodiodes connected with transimpedance amplifiers (TIAs).
We analyze signal-to-noise ratio (SNR) corresponding to a single channel of the TIA, and express signal and noise components at the input of the TIA. It can be written as follows:
where $N_{tot}$ is the total input-referred noise density at the input of the TIA. and $S_0$ is the signal power occurring by the beat between signal power and local oscillator at the input of the TIA. $S_0$ can be written as [4,5]:Typical value of $C$ is 8, but can vary depending on a optical signal waveform.
Assuming that all of the noise terms are additive, which is expected to be valid under low BER conditions, and no correlation between the noise terms, the total noise $N_{tot}$ power can be approximated by the sum of independent noise terms. We decompose noise components according to the dependence on the photodiode currents.
Photodiode currents $I_{tot}$ are expressed as follows:
where $I_{sig}$, $I_{lo}$ are the photodiode current of the optical signal and that of the local oscillator corresponding to one of two photodiodes connected to each TIA, and $I_{dark}$ is the photodiode dark current. By using the signal and local input optical powers, $P_{sig}$ and $P_{lo}$, and the signal and local responsivities $R_{sig}$ and $R_{lo}$, for each photodiode, the photodiode currents can be expressed as $I_{sig} = P_{sig}\cdot R_{sig}$ and $I_{lo} = P_{lo}\cdot R_{lo}$. We consider the case when $I_{sig}$ and $I_{dark}$ can be ignored compared with $I_{lo}$. We also ignored the noise term, which has quadratic dependence on the signal current and is affected by the common mode rejection ratio of the receiver, since such noise term can be ignored except in the case of colorless reception, which is out of the scope of this paper.In such a case, we decompose total noise $N_{tot}$ according to the dependencies on the signal current:
where $N_{0}$ is constant noise which does not depend on photodiode currents, $N_{1}$ is the noise term proportional to the photodiode current, and $N_{2}$ is proportional to the product of $I_{sig}$ and $I_{lo}$.Constant noise $N_0$ is considered to be mostly TIA thermal noise. $N_{1}$ corresponds to shot noise. Since we consider the case when $I_{sig}$ and $I_{dark}$ are much smaller than $I_{lo}$, $N_1$ for a single channel, which includes two photodiodes, can be expressed as:
where $e$ is the electron charge, and $f_{shot}$ is the shot-noise bandwidth in the receiver.The noise term $N_{2}$ is the term which is proportional to the signal power $S_0$ and we included two components:
where OSNR is the optical signal-to-noise ratio, $f_0$ is the reference bandwidth corresponding to 0.1 nm at the signal wavelength and is 12.5 GHz at 1.55 $\mu$ m, and $f_{ase}$ is the amplified spontaneous emission (ASE) noise bandwidth in the receiver.In Eq. (6), first term corresponds to LO-ASE beat noise, and the second term, which has constant NSR of $\alpha$, includes all imperfections whose NSR does not depend on signal power, local oscillator power, or ASE noise power. Main imperfection in this term is considered to be the transmitter imperfection. When condition of transmitter does not change, NSR regarding that imperfection is constant, regardless of the signal power or loaded ASE noise, as far as all imperfections are considered to be additive. Among other imperfections included in $\alpha$ are phase error of the optical hybrid uncompensated by the DSP, and noise caused by the finite dynamic range of the DSP, since such imperfections accompany constant NSR, which does not depend on the signal, local oscillator power or ASE noise.
In order to treat the effects of the noise terms separately, the noise-to-signal ratio (NSR) is better suited for analyses compared with the signal-to-noise ratio. From Eqs. (1), (2), (4) to (6), the NSR($=1/SNR$) can be expressed as:
Equation (8) can be expressed as follows:
where $P_0$ and $P_1$ areHere, $P_1$ can be expressed as
whereIf the constant noise only includes TIA thermal noise, $P_{11}$ can be written as follows:
where $I_{eq}$ is input-referred equivalent noise density of the TIA and $f_{th}$ is the thermal noise bandwidth of the receiver. In this case, NSR can be rewritten asThese formula will be used in the following sections to obtain the noise parameters from the experimental BER characteristics.
3. Measurement and analyses
3.1 Measurement setup
Figure 2 shows the setup for measuring online BER characteristics. The transmitter comprised an integrated tunable laser array (ITLA), modulator driver, an in-phase quadrature modulator, and a transmitter DSP. The transmitter’s optical signal, to which amplified spontaneous emission (ASE) noise source is loaded, is input to the receiver. Optical bandpass filter (OBPF) with the 3-dB bandwidth of 5.5 nm was used to limit bandwidth of ASE noise before amplification. An optical coupler was used to tap the signal for monitoring the OSNR, and a variable optical attenuator (VOA) was used to control the optical power. OBPF with the 3-dB bandwidth of 1 nm was also inserted to filter out-of-band optical noise.
The receiver comprised a coherent optical subassembly (COSA) module [6], ITLA, and receiver DSP. The receiver part of the COSA contains a SiPh PIC that contains optical mixers and Ge PDs, and the transimpedance amplifiers (TIAs). The wavelength of the ITLA was set to 1547nm. The DSP-ASICs [7] in the transmitter and the receiver were fabricated with 16-nm Fin-FET CMOS technology. They were used to perform analog/digital conversion along with digital signal processing. Receiver DSP, which performs the task including equalization, polarization de-multiplexing, and carrier-phase recovery, was used to obtain BER in this experiment. The modulation format was dual polarization(DP)-16QAM, and the FEC limit is about 5.7 dB.
The optical signal power was varied using the VOA. The optical power of the local oscillator was varied from 10 to 16 dBm. Before the BER measurements, fixed equalizers in the transmitter and receiver DSPs were optimized with the method described in [8], in a way that the frequency response of transmitter and receiver are compensated. One pair of transmitter and receiver was used for all measurements, and the optimization was done at a fixed signal power $P_{sig}$ of -10 dBm, for each local oscillator power and baud rate.
Transmission performance is evaluated by the pre-FEC Q-margin, defined as the difference between measured Q-factor and Q-limit. Q-factor was calculated from the BER by using the following formula:
and the Q-limit is the Q-value at the pre-FEC limit.Here, we use the following formula [9,10], corresponding to 16-QAM modulation format, to convert the BER value into an NSR value. This conversion means making a projection from BER to phenomenological NSR, which includes all noise contribution in each constellation, thus obtaining NSR referred at BER level.
Although Eq. (17) assumes uniform constellation, we use it in the following analyses since we assume low BER condition in which the effects of imperfections are considered to be additive and the crosstalk between distortion and other imperfections can be neglected.
3.2 Dependence on OSNR
Figure 3(a) shows the dependence of the Q margin on OSNR(dB/0.1nm) at three baud rates. The optical signal powers for 34, 50, and 67 Gbaud are −10, −10, and −5 dBm, respectively. As OSNR increases, optical noise decreases and the Q margin increases. From Eq. (8), the noise bandwidth $f_{ase}$ acquired by DSP should be able to be obtained from the slope of the NSR plotted against linear OSNR. Figure 3(b) plots NSR margin with respect to linear OSNR, and we can see that the data almost fall on lines. In Fig. 4, its slope is plotted against baud rate, and $f_{ase}$ was calculated from the slope. We obtained the result that $f_{ase}$ is proportional to the baud rate with the coefficient of 0.53.
3.3 Dependence on optical signal power and local oscillator power
In this subsection, dependence of the Q value on optical signal power and local oscillator power are analyzed. Figures 5(a)(b)(c) plots the Q margin against the optical input signal power for three baud rates. Each figure includes three plots for different local oscillator powers $P_{lo}$. The OSNRs for 34, 50, 67 Gbaud are 25, 35, and 35 dB, respectively. In the weak signal region, the Q margin decreases as $P_{sig}$ decreases. This is because the ratio of thermal and shot noise to signal amplitude increases with decreasing signal power. Decrease in the Q margin in the high optical signal region ($P_{sig} >$ −5 dBm) is caused by distortion in the TIA.
Fig. 5. Dependence of Q margin on input signal power for different local oscillator powers $P_{lo}$ (10, 13, 16 dBm) and baud rates
To evaluate each noise term using Eq. (9), we converted the Q margin into an NSR margin and plotted it in Fig. 6, as a function of inverse signal photocurrent. The data in $P_{sig} <$ −10 dBm, which corresponds to 1/$I_{sig} >$ 110, fall on a line, which implies that $P_0$ and $P_1$ in Eq. (9) are nearly constant in this region. Therefore, $P_0$ and $P_1$ can be obtained from the Y-intercept and slope, respectively. We can also see that, while the slope depends on the local oscillator power, the intercept $P_0$ does not. In high optical signal power region, which is low $1/I_{sig}$ region in Fig. 6, the data deviate from the line, which quantitativly indicates the distortion at the TIA.
Fig. 6. Dependence of NSR margin on input signal power for different local oscillator powers $P_{lo}$ (10, 13, 16 dBm) and baud rates
The slopes of the curves in Fig. 6, which corresponds to $P_1$, are plotted against $1/I_{lo}$ for three different baud rates in Fig. 7(a). We can see that $P_1$ is linearly dependent on the inverse local oscillator current, which is in agreement with Eq. (12). $P_{10}$ and $P_{11}$ obtained from the intercept and slope are plotted in Fig. 7(b). $P_{10}$ and $P_{11}$, which are expressed by Eqs. (13) and (14), respectively, are proportional to the noise bandwidth $f_{shot}$ and $f_{th}$. Each type of noise is determined by the total receiver transfer function [11].
Fig. 7. (a) Dependence of $P_1$ on inverse local oscillator current and baud rate and (b) dependence of P$_{10}$ and P$_{11}$ on baud rate
When all constant noise is regarded as thermal and signal amplitude coefficient $C$ takes a typical value of 8, and setting $f_{shot}=f_{ase}$, $I_{eq}$ is 21, 19, and 19, pA/$\sqrt {Hz}$, at baud rate of 67, 50, and 34 Gbaud, respectively. $I_{eq}$ is considered to be larger at higher baud rate since input-referred noise is generally larger at higher frequency.
Theoretical value of shot noise can be estimated by setting $f_{shot}=f_{ase}$. Shot noise obtained from $P_{10}$ were 1.4, 1.2, and 1.3 times larger than the theoretical expectation, at the baud rate of 67, 50, and 34 Gbaud, respectively. The reason of the discrepancy is not clear, but the result might be affected by the change of amplitude coefficient in real electronic waveforms.
3.4 Calculation of ROSNR characteristics
In this section, the required OSNR (ROSNR) characteristics calculated from the constants obtained in the previous section are shown to reproduce the measured values. ROSNR is the required OSNR value to take the Q-limit.
The following formula can be obtained from Eqs. (8), (13–14).
To show ROSNR performance, we define $\Delta$ROSNR(dB) and $\Delta$ROSNR$_{linear}$ by the following formula:
where $\Delta \rm {ROSNR}_0(dB)$ and ROSNR$_0$(linear) are defined by:Figure 8(a) plots the calculated and measured dependences of the raw $\Delta \rm {OSNR}$ on the inverse signal current at 67 Gbaud. The measured data lie close to the calculated data in Fig. 8(a). Figure 8(b) plots ROSNR on a dB scale against optical signal power. We can see that calculated characteristics reproduce the measured results. ROSNR performance under a wide range of conditions including baud rate should be able to be obtained from the changes in each parameter for various conditions and devices.
4. Summary
In summary, we measured and analyzed the online transmission characteristics of a high-baud-rate 16QAM digital coherent receiver. Using the theoretical relationship between BER and NSR, we projected the 16QAM online BER characteristics into the NSR and performed linear analyses. Analyses of the NSR dependencies on the inverse signal and local oscillator photocurrents showed that the data fall on the theoretically-predicted line and we could decompose the NSR into noise terms corresponding to shot noise, constant noise, ASE noise, and noises included in the signal. The obtained parameters were shown to be useful for predicting ROSNR characteristics.
These analyses can be applied to the analyses and prediction of transmission characteristics under a wide range of conditions including baud rate, and and will be useful for developing high-baud rate transceivers.
Acknowledgment
The authors thank S. Kamei for encouragement of this work, and T. Yamashita for her assistance in the measurements.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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