1. Introduction

In recent years, network applications such as cloud computing, the internet of things, and telemedicine are coming into our daily life. These applications stimulate the growth of data center (DC) communication and necessitate the 800Gbps and 1.6Tbps transmission scene over distances ranging from 500m to 40km [1]. It has been reported that nearly 77% of the overall DC traffic is inside the intra-datacenter traffic [2]. However, as several optical transceivers are utilized for the optical-to-electrical (O/E) conversion in DC, the current optical transceivers are restricted to cost, power consumption, density, etc. [3]. Because the traditional optical coherent transceiver used in metro or long-haul communication seems too extravagant for DC communication, the self-homodyne coherent detection (SHCD) system becomes one of the most potential solutions [4]. In an SHCD system, only one laser source is separated by an optical coupler to be used as the signal carrier and the local oscillator (LO). By properly adjusting the fiber length difference between the signal carrier and LO, the impact of laser phase noise and frequency offset can be avoided. Therefore, the SHCD system allows the utilization of large linewidth lasers such as distributed feedback (DFB) lasers or even uncooled lasers [5]. Because no more phase recovery and frequency offset compensator are used, the power consumption, cost, and DSP complexity of the SHCD optical transceiver can be effectively reduced, which is compatible with data center applications.

High baud rate and high-order modulation format signals are widely used in 800Gbps and 1.6Tbps transmission scenes. However, the imperfections induced by the non-ideal characteristic of the SHCD optical transceiver will greatly degrade the transmission performance. For example, the attenuation in the high-frequency domain will significantly reduce the power of the payload signal, and the frequency-related phase response will also affect transmission performance. Besides, it has been reported that at the bit error rate (BER) of 1e-2 when no compensation algorithm is used in the receiver, the tolerance of in-phase(I)/quadrature-phase(Q) signals time skew induced by the physical path length difference for 16QAM and 64QAM signals with 1 dB signal-to-noise ratio (SNR) penalty is less than 11% and 4.2% of the symbol period, corresponding to 2.2/0.84 ps for 50GBaud signals, respectively [6]. In practice, the IQ amplitude/phase imbalance can be effectively compensated by precise modulator bias control and Gram-Schmidt orthogonalization procedure (GSOP) algorithms, and many well-established calibration methods have already been proposed [7–9]. Nevertheless, the calibration for bandwidth limitation of electrical and optical components and the transmitter (Tx)/receiver (Rx) side IQ skew is still challenging. Therefore, it becomes important to measure the value of amplitude-frequency response (AFR)/phase frequency response (PFR) and the Tx/Rx IQ skew.

In fact, due to the different impairment mechanisms on Tx/Rx side and the crosstalk between I and Q tributaries, it is quite difficult to extract the impairment characteristics from the received signals. To the best of our knowledge, the optical transceiver calibration methods targeting the AFR/PFR and Tx/Rx skew are mostly independent, which means the calibration of these impairments must be operated step by step. There are many types of research on AFR calibration, but most of these methods can only calibrate the Tx or Rx AFR [10–14]. Only a few types of research have been proposed to cope with the Tx PFR [15], and the research about the calibration of Rx PFR is fewer [16]. At the same time, many works have been proposed to individually deal with Tx or Rx skew [17–24], but only a few works are proposed to separate the Tx/Rx skew from the optical transceiver. The most common way to separate the Tx/Rx skew is utilizing the special ordered cascade DSP algorithms at the receiver side DSP module [25–27]. In these methods, the impairments from Tx/Rx side are compensated individually and separated by a slight ∼10 MHz frequency offset and laser phase noise effect. To be specific, many high complexity algorithms are required in these methods thus leading to the increased cost, and the estimated IQ skew accuracy/dynamic range is limited by the equalizer compensation capacity. Nevertheless, these methods are hard to be applied in the SHCD system because the effect of a slight ∼10 MHz frequency offset and laser phase noise does not exist. Therefore, the Tx/Rx impairments cannot be separated by the receiver side compensation algorithms. To sum up, the calibration of AFR/PFR and Tx/Rx skew are urgent to be solved, and a high-precision calibration scheme without additional devices for the SHCD transceiver is highly desired.

In this contribution, we extend our previous experimental work in [28] and introduce the effect of fiber chromatic dispersion and bandwidth limitation in the SHCD system. In practice, the effect of fiber chromatic dispersion will occur before the Rx side imperfection, thus impacting the calibration for the whole transceiver. And the investigation of the fiber dispersion effect is also considered for the deployed optical transceiver and it may be the future online calibration tests process. Besides, the bandwidth limitation will greatly reduce the power/phase of high-frequency domain signals, which is another major imperfection that cannot be ignored in a high-speed optical transmission system. In our calibration scheme, a novel specially designed interleaved multi-tone signal is proposed to simultaneously obtain the Tx/Rx skew and AFR/PFR of the whole DP SHCD system. Benefiting from the no frequency offset/phase noise features of the SHCD system, these characteristics can be obtained by just one measurement without using any other optical/electrical devices even after long-distance fiber transmission. Then, the effect of Tx/Rx skew and bandwidth limitation can be mitigated after obtaining the non-ideal characteristics. The effect of AFR/PFR is pre-compensated at the Tx DSP module with linear pre-emphasis filters. The Tx/Rx skew is pre-/post- compensated by the frequency domain phase adder in Tx/Rx DSP module. The transmission BER performance improvement is experimentally demonstrated by transmitting 46GBaud DP-16QAM signals/35GBaud DP-64QAM signals in an SHCD transmission system with 10km standard single-mode fiber (SSMF), and the BER performance can be improved from 2.30e-2 to 2.18e-3/9.59e-2 to 2.20e-2 after compensating the effect of AFR/PFR and Tx/Rx skew.

2. Principle of the proposed calibration method

2.1 Transmission model of an SHCD system

Before introducing the proposed calibration scheme, it is necessary to derive the transmission model of a typical SHCD system. In our previous work [28], we have proposed a transmission model of the traditional transceiver on the condition of back to back (B2B). However, the effect of AFR/PFR and the fiber chromatic dispersion (CD) are not included in that model. As the transmission model of the Tx and Rx in the SHCD system are similar to the traditional ones, we can continue to derive a more complete transmission model. The schematic diagram of the typical Bi-directional SHCD transceiver is presented in Fig. 1.

 

Fig. 1. The schematic diagram of the typical Bi-directional SHCD transceiver.

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To be specific, we should derive the transmission model that includes the characteristic of AFR/PFR, IQ amplitude/phase imbalance, Tx/Rx skew, and CD. It should be noted that this transmission model only considers the static non-ideal imperfections listed above and does not consider the dynamic damage such as the rotation of state-of-polarization (RSOP) effect. Assume that the input signal $x(t )\textrm{ } = \textrm{ }{x_I}(t )\textrm{ } + \textrm{ }i{x_Q}(t)$, where ${x_I}(t )\textrm{ }$ and ${x_Q}(t)$ are the real-valued time-domain I and Q components, corresponding to ${X_I}(\omega )$ and ${X_Q}(\omega )$ in the frequency domain, respectively. Considering the order in which impairments occur, the output signals from the optical transmitter can be expressed as

Here ${H_{Taf}}(\omega )$, ${H_{Tpf}}(\omega )$, and ${H_{Tskew}}(\omega )$ are diagonal matrixes that represent the transmission model of AFR/PFR and Tx skew for the optical transmitter, respectively. Note that the IQ amplitude imbalance is included in the amplitude-frequency response, and ${H_{Tp}}(\omega )$ is the transmitter IQ phase imbalance. Besides, ${a_{Tm}}(\omega )$/${\varphi _{Tm}}(\omega )$ (m = I or Q) is the AFR/PFR of the transmitter for the I or Q tributary. ${\tau _1}$ and ${\beta _1}$ is the values of Tx skew and Tx IQ phase imbalance, respectively. ${Y_{TI}}(\omega )$ and ${Y_{TQ}}(\omega )$ represents the output signals from the optical transmitter. Therefore, the transmission model of the optical transmitter ${H_{Tx}}(\omega )$ can be described as

Similarly, the transmission model of the optical receiver ${H_{Rx}}(\omega )$ can be represented as

Here ${H_\theta }$ represents the impact of a global phase shift between the signal carrier and LO. ${H_{Raf}}(\omega )$, ${H_{Rpf}}(\omega )$, and ${H_{Rskew}}(\omega )$ are diagonal matrices that represent the transmission model of AFR/PFR and Rx skew for the optical receiver, respectively. ${a_{Rm}}(\omega )$/${\varphi _{Rm}}(\omega )$ (m = I or Q) is the AFR/PFR of the receiver for the I or Q tributary, respectively. ${\tau _\textrm{2}}$ is the value of Rx skew. ${Y_{RI}}(\omega )$ and ${Y_{RQ}}(\omega )$ is the output signal from the receiver. Therefore, the transmission model of the receiver ${H_{Rx}}(\omega )$ can be described as

It can be observed that the impact of the global phase shift $\theta$ will lead to the crosstalk between the I and Q tributaries. What’s more, the fiber transmission model only considering the chromatic dispersion can be expressed as

Here ${\sigma _2}$ is the chromatic dispersion parameter, L is the fiber length, and $\chi$ is the normalization parameter.

For an SHCD system, the effect of frequency offset and phase noise can be avoided by properly adjusting the fiber length difference between the signal carrier and LO, which has already been proved in [29]. Therefore, the transmission model of the whole transceiver ${H_{TRx}}(\omega ) = {H_{Rx}} \cdot {H_{CD}} \cdot {H_{Tx}}$ can be presented as

Here ${\varphi _{CD}} = \chi {\sigma _2}{\omega ^2}L$ is the chromatic dispersion-related parameter. In practice, ${\beta _1}$/${\beta _2}$ are the values of Tx /Rx IQ phase imbalance, and will be maintained within ±5 degrees. The global phase shift $\theta$ is usually a fast-changing random variable and will contribute equally to the four trigonometric terms. Therefore, these three parameters will almost not affect the calibration signals from different input/output ports. And the trigonometric terms can be removed after the normalization process. ${a_{XY}}/{\varphi _{XY}}$ (X, Y = I or Q) represent the amplitude/phase frequency response from different input and output channels, and it can be expressed as

It can be observed in ${H_{TRx}}(\omega )$ that the impairments of I and Q tributaries from the transmitter and receiver sides are all mixed. This effect will introduce inevasible crosstalk between the I and Q tributary signals and will greatly increase the difficulty of separating the non-ideal imperfection characteristics from the I/Q tributary and Tx/Rx side. Therefore, an effective and precise calibration method is very valuable.

2.2 Principle of the proposed calibration method

To cope with the impairment mixture effect of I and Q tributaries from the Tx/Rx side, specially designed multi-tone signals are proposed as the calibration signal, as shown in Fig. 2. In a dual-polarization SHCD system, the calibration signals are generated from the transmitter side digital to analog converters (DACs). After the transmission through optical fiber and coherent receiver, the non-ideal impairment parameters will be concluded in the received calibration signals. In our proposed scheme, the transmitted multi-tone calibration signals can be described as

Here ${X_{I/Q}}(t)$/${Y_{I/Q}}(t)$ is the calibration signal corresponding to the I/Q tributary of the X/Y polarization state. ${\omega _0}$ and $\Delta \omega$ represent the initial frequency and the frequency interval between the adjacent multi-tone signals, respectively. The preset random phase terms ${\phi _{XI/XQ/YI/YQ}}$ are applied to reduce the peak to average power ratio (PAPR) of the calibration signals [23], and each branch is different. Actually, the PAPR of the transmitted calibration signal is mostly determined by the preset random phase terms and the frequency interval. It can be observed that the multi-tone signals of different polarization states and different tributaries are interleaved in the frequency domain. Thus the crosstalk between each branch of calibration signals can be averted in the frequency domain. What’s more, as the RSOP effect can be avoided by using the mature technique proposed in [29], the calibration process of two polarization states can be operated individually. Therefore, for the sake of simplicity, we can illustrate the calibration process in just one polarization state. Take the calibration process for X polarization state optical transceiver as an example. The normalized Fourier transform of the transmitted signals (in the positive frequency domain) can be written as

 

Fig. 2. The schematic diagram of the specially designed multi-tone signals.

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Based on the optical transceiver transmission model ${H_{TRx}}(\omega )$ in Eq. (6), the calibration signals received from the coherent optical transceiver (in the positive frequency domain) can be written as

It can be observed that both ${R_I}(\omega )$ and ${R_Q}(\omega )$ will contain the impairment information from different transmitter ports. Due to the effect of fiber chromatic dispersion, the AFR curves will be modulated by ${\varphi _{CD}}$. According to the order in which impairment occurs, the chromatic dispersion can be compensated only after the compensation of the Rx skew. Fortunately, the phase terms of ${R_I}(\omega )$ and ${R_Q}(\omega )$ are almost unaffected by the chromatic dispersion. Define the four-receiver side phase terms as

Here we approximate that the difference between the PFR curves will contribute no effect to the value of the slope. In practice, the four-receiver side phase terms should be normalized by the unwrapping process. And after obtaining the value of Rx skew, the effect of fiber chromatic dispersion can be eliminated, and the AFR affected by the CD parameter can be recovered.

The bandwidth limitation caused by the AFR/PFR of the optical transceiver will also greatly reduce the signal transmission performance. As the effect of the bandwidth compensation process becomes poor after the signal is received, the transmitted signals should be pre-compensated in the Tx DSP module before sending to the DAC. However, as shown in Eq. (10), the payload signal sent by the I or Q tributary will be received at both the I and Q tributaries of the receiver. Therefore, the amplitude- and phase-frequency response of the transceiver can be expressed as

Here we suppose the probabilities of sending a signal to I and Q tributaries of the receiver are the same.

To sum up, by using our proposed calibration method, the AFR/PFR of an SHCD transceiver as well as Tx/Rx skew can all be obtained by just one measurement process even in the presence of long-distance transmission fiber.

2.3 Principle of the pre-/post- compensation algorithm

After obtaining the non-ideal impairment parameters, the specific compensation process can be implemented. In general, the Tx/Rx impairments should be compensated at the Tx/Rx side respectively. However, the high attenuation in the high-frequency domain of Rx AFR can hardly be compensated in the Rx-DSP module as the signal-to-noise ratio is fixed after acquisition by ADCs. In a traditional coherent optical transceiver, the AFR/PFR of the whole transceiver will be relevant to the dynamical frequency offset value. However, benefiting from the none frequency offset features, the AFR/PFR of the SHCD transceiver will be static and thus can be compensated at the Tx DSP module. By multiplying the transmitted signal with the inverting of the measured AFR/PFR, the compensation matrix ${H_{freq}}(\omega )$ can be described as

The compensation of the Tx/Rx skew can be applied to each side DSP module after obtaining the skew values. According to the Fourier transform relation, the delay in the time domain can be converted to the phase shift in the frequency domain. Therefore, the IQ skew compensation process realized by the DSP module can be expressed as

Here ${\tau _m}$ is the measured skew value (Tx or Rx side). It’s worth noting that the Tx/Rx skew can only be compensated at Tx/Rx side DSP module, thus the skew compensation process should be applied at both the transmitter and receiver sides separately. Combined with the precise measurement and compensation processes, the signal transmission performance in SHCD systems can be greatly improved.

3. Simulation setup and results

Based on the VPI Transmission Maker and MATLAB, a typical SHCD simulation system is constructed to verify the proposed calibration method. For the sake of simplicity, only a single polarization state and single direction are simulated, and the calibration process of the dual polarization transceiver is experimentally demonstrated in the next section. The simulation setup of the proposed calibration scheme for an SHCD transceiver is shown in Fig. 3(a).

 

Fig. 3. The simulation setup of the proposed calibration scheme for an SHCD transceiver (a). The envelope of calibration signals which are transmitted at point a (b), point b (c), point c (d), and point d (e).

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On the transmitter side, the interleaved multi-tone signals are generated from MATLAB and uploaded to the I/Q tributary of the transmitter in the VPI transmission system, as shown in Fig. 3(a). In our simulation, multi-tone signals combined with 166 tones of 150 MHz frequency interval are applied in the 25 GHz bandwidth system. The linewidth and wavelength of the optical source are set as 4 MHz and 1550 nm to emulate the large linewidth DFB laser in the real SHCD system, and the fiber length difference between the signal carrier and LO is set as 0.05 m. To emulate the bandwidth limitation, experimentally measured parameters of the AFR/PFR are utilized to construct the low pass filters (LPFs). The Tx skew is induced by the time delay module. In the transmission link, the universal fiber module is used to emulate the SSMF. The OSNR module is applied to induce the impact of channel noise. Two optical attenuators are used to control the optical power of the signal and LO. On the receiver side, the integrated coherent receiver (ICR) is constructed by the optical hybrid and balanced photodiodes (BPDs). The bandwidth limitation and Rx skew are introduced in the same way as the transmitter side. The envelope of the multi-tone signals when transmitted at a specific point is given in Figs. 3(b-e). Figure 3(b) is the estimated AFR envelope curve without adding any bandwidth limitation effect, and the non-flat feature is caused by the quantization noise and Gaussian-distributed white noise in this simulation system, which is tolerated as a measurement error. In point b, the AFR curve is affected by the transmitter as shown in Fig. 3(c). The power fading effect induced by fiber dispersion is shown in Fig. 3(d) at point c, and Fig. 3(e) contains the receiver side AFR besides all of the impairments mentioned above at point d.

The calibration performance of the proposed scheme is evaluated in a 25GHz bandwidth SHCD system with 50km SSMF. The Tx and Rx IQ skew are set as 5ps and 7ps respectively. The OSNR value is set as 20dB in the operation bandwidth and the optical power of the signal and LO are set as -10dBm and 8dBm respectively. It should be noted that the fiber attenuation is not considered to maintain the fixed receiver side optical power and only investigate the effect of fiber dispersion. As mentioned in Section 2.2, the skew values are obtained from the difference between the specific phase frequency response. Moreover, as shown in Fig. 4(a), the fiber chromatic dispersion effect will introduce some power null points at AFR curves and thus reduce the signal power near these points, resulting in an inevasible phase error.

 

Fig. 4. The simulation results of the AFR curves affected by the chromatic dispersion effect (a), the estimated PFR curves after the unwrapping process (b), the difference between the specific phase curves (c), the AFR curves and the estimated error after compensating the chromatic dispersion effect (d), the PFR curves and estimated error (e), the amplitude error of the AFR in different dispersion compensation lengths (f), Tx/Rx skew estimation performance at different fiber length (g), the estimated skew values within ±30ps range (h).

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The estimated PFR curves after the unwrapping process are given in Fig. 4(b), and it can be observed that these four curves are separated apart due to the effect of Tx/Rx skew. Besides, as the phase near the frequency of power null points will fluctuate on the continuous phase curve, we should avoid using these phase points for the estimation process. The difference between the specific phase curves is presented in Fig. 4(c). And the slope of the difference between the curves of ${\varphi _{II}}$ and ${\varphi _{QI}}$ besides the difference between the curves of ${\varphi _{IQ}}$ and ${\varphi _{QQ}}$ represent the Tx skew value. The slope of the difference between the curves of ${\varphi _{II}}$ and ${\varphi _{IQ}}$ besides the difference between the curves of ${\varphi _{QI}}$ and ${\varphi _{QQ}}$ represent the Rx skew value. The estimated Tx and Rx skew under this simulation condition are 5.05ps and 6.83ps (originally set as 5ps and 7ps). According to the transmission model in Eq. (6), the fiber dispersion effect occurs before the Rx skew. Therefore, the AFR should be obtained after compensating for the Rx skew. The estimated AFR after compensating for the Rx skew and fiber dispersion is given in Fig. 4(d). It can be observed that the estimated error is within ±1dB in 25GHz bandwidth, and the estimated error gradually increases due to the reduced SNR in the higher frequency domain. In practice, an operation such as increasing the time length of calibration signals and the implementation of the frequency domain average process can improve the calibration accuracy of AFR. But the longer time length will lead to the limitation of DAC/ADC RAM storage, and the frequency domain average process scheme may increase the complexity of the calculation. If the condition permits, these methods can further improve the calibration accuracy. Similarly, the estimated PFR after compensating for the Tx and Rx skew can be obtained in Fig. 4(e). Except for the fluctuated phase point, the phase estimated error is within ±0.15 rad in 25 GHz bandwidth. To quantitatively analyze the AFR estimated error between the residual dispersion, the fiber compensation length is set as 49, 49.5, 50, 50.5, and 51 km as presented in Fig. 4(f). It can be observed that the amplitude error can still be maintained within about ±1 dB when the dispersion compensation length is 49.5∼50.5 km, which means the error tolerance of the dispersion compensation length can reach 0.5 km. What’s more, with the increasing error of the fiber dispersion compensation length, the amplitude error becomes larger in the high-frequency domain. This can be explained by the dispersion induced phase ${\varphi _{CD}} = \chi {\sigma _2}{\omega ^2}L$, where ${\varphi _{CD}}$ becomes larger in the higher frequency domain and affects the AFR curves more. To evaluate the IQ skew estimation performance at different fiber lengths, we have scanned the fiber length from 0 to 100 km considering the application scenarios of the real SHCD system. The simulation result is presented in Fig. 4(g) and the estimation error is within ±0.3ps in this range. With the increase of fiber length after 100 km, the calibration precision will gradually decrease. Therefore, our proposed calibration method is more compatible with the short/medium transmission system currently. Finally, the calibration accuracy in the case of different IQ skew values for 50 km transmission is stimulated, and the Tx and Rx skew are randomly preset within ±30ps and the estimated skew values are shown in Fig. 4(h). The simulation results indicate that the IQ skew absolute estimated error of the proposed calibration scheme can reach 0.3 ps in the range of dozens of picoseconds.

4. Experimental setup and results

To experimentally evaluate the calibration performance of the proposed scheme, a DP SHCD transmission system is constructed. Moreover, the transmission performance improvement after compensating for the non-ideal impairments based on the estimated impairment parameters is also tested. The experimental setup of the DP SHCD transmission system and the Tx/Rx DSP module are presented in Fig. 5. On the transmitter side, a DFB laser with a maximum optical power of 14.5dBm is used as the optical source, and the linewidth of this laser is about 4MHz at about 1550nm. The emitted light is separated by a 3dB optical coupler and then transmitted to a 22GHz DP IQ modulator (DP-IQM, Fujitsu FTM7961EX) and the LO port of the receiver side. The 65GSa/s four-channel arbitrary waveform generator (AWG, Keysight M8195A) with 8 bits vertical resolution is applied to generate the target signals. A 30GHz four-channel modulator driver amplifier (MDA, Centellax, OA3MHQM) is used to amplify these signals. The modulated signals are then transmitted to a 10km SSMF. Before the LO side transmitted 10km SSMF, a motorized delay line (MDL, General photonics, MDL-002) with the path length adjustment accuracy of 0.3 µm is utilized to match the fiber length between the signal carrier and LO, and the fiber mismatch length is controlled within 0.02m. A polarization controller (PC) is used to align the polarization states of the LO and signal optical carrier. On the receiver side, a 22GHz integrated coherent receiver (ICR, Fujitsu FIM24706) is applied to reconstruct the optical field. The recovered signals are then captured by a 50GSa/s four-channel digital sampling oscilloscope (DSO, Tektronix DPO73304D) with a 3dB bandwidth of 23GHz. It should be noted that the bi-directional transmission is not considered in our experiment due to the lack of laboratory devices. But this will not affect the verification of our calibration scheme. For the calibrated system, in the Tx DSP module, the frequency response and Tx skew of the payload signal will be pre-compensated before being transmitted to the AWG. In the Rx DSP module, the received signal will be compensated by using an Rx skew compensator, modified Gardner clock recovery algorithm, GSOP algorithm, polarization division demultiplexing algorithm, and joint constant modulus algorithm (CMA) +decision-directed least mean square (DDLMS) blind equalization algorithm. For the uncalibrated system, only the modified Gardner clock recovery algorithm, GSOP algorithm, polarization division demultiplexing algorithm, and joint CMA + DDLMS blind equalization algorithms are used to compensate for the transceiver imperfection.

 

Fig. 5. The experimental setup of the dual-polarization SHCD transmission system.

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The proposed calibration method is applied in the 10km SHCD system mentioned above to investigate the calibration performance experimentally. Using the same calibration process in Section 3, the AFR/PFR of the transceiver and Tx/Rx skew can be obtained as shown in Fig. 6. The frequency interval of the multi-tone signals is set as 75MHz and the operating bandwidth is about 23GHz which is the maximum bandwidth of the used DSO. As the calibration results of the two polarization states are independent but similar, Fig. 6 only includes the calibration results in the X polarization state. The dotted curves in Figs. 6(a-b) represent the original AFR curves without compensating for the fiber dispersion effect. The AFR and the absolute estimated error of XI/XQ tributaries in 8 tests after compensating the fiber dispersion are also presented in Figs. 6(a-b). It should be noted that the absolute estimated error is the maximum absolute value of the difference between these 8 curves and the average curve. According to the test results, the power attenuation of this system is about 11dB in 20GHz and larger than 25dB in 23GHz. Besides, the absolute estimated error is less than 0.6dB in the whole operation bandwidth. Analogously, the 8 test results of PFR in XI/XQ tributaries are presented in Figs. 6(c-d). It can be observed that the phase response of the system gradually decreases with the increase of frequency and the phase attenuation is about 3.5 rads in 23GHz. The absolute estimated error in most of the operating bandwidth is less than 0.2 rad and the estimated error in the beyond 22.5GHz frequency domain suddenly increases because of the reduced signal power. After obtaining the frequency response characteristics, the payload signals are pre-compensated at the Tx DSP module based on Eqs. (14) and (15). And the optical spectra of the signal with different compensation depths $\gamma$ at the output of the optical transmitter are shown in Fig. 6(e). When increasing the compensation depth, the power at high frequency gradually increases and the frequency at low frequency gradually decreases. Note that, only the AFR needs to be multiplied by the compensation depth $\gamma$ because the PFR compensation will not affect the power distribution of the signal, and $\gamma$=0 means the original signal. The electrical spectra of the received Nyquist 46 GBaud 16QAM signals whether using the frequency response compensation process are presented in Fig. 6(f). It can be seen that the received signal spectrum without the frequency response compensation will drop rapidly after 22 GHz, and the signal spectrum is uneven within 0∼22 GHz. However, the received signal spectrum after the frequency response compensation is flatter thanks to the precise calibration. Besides, the signal power is distributed more evenly over the entire transmission bandwidth after calibration. Furthermore, the estimation accuracy for the Tx/Rx skew of our proposed method is tested by adding an additional skew value on the Tx/Rx side as shown in Figs. 6(g-h). The original Tx skew is measured as -10.34 ps and the additional Tx skew is set as +10, +5, -5, and -10 ps. The estimated Tx skew is obtained from the slope of the phase curves between 0∼13 GHz considering the SNR of the multi-tone signals. And the relative accuracy of each Tx skew measurement is within ±0.3 ps. Meanwhile, an additional Rx skew is added in the receiver side DSO digital module. The original Rx skew is 5.18 ps and the additional Rx skew is set as +40, +20, -20, and -40 ps. The minimum additional value of the Rx skew is 20 ps due to the 50 GSa/s sample rate limitation. Similarly, the estimated Rx skew is obtained from the slope of phase curves between 0∼13 GHz. And the relative accuracy of each Rx skew measurement is also within ±0.3ps. The reason for calculating the Tx/Rx skew only using 13 GHz frequency bandwidth is for the calibration precision. More specifically, the measured AFR curves of this optical transceiver are shown in Figs. 6(a-b). There is a 7 dB power reduction at 13 GHz, which means a relatively low SNR for the calibration signals. Besides, it can be observed in Figs. 6(c-d) that the absolute error of the measured phase gradually increases to more than 0.1 rad after 13 GHz, which will also gradually increase the calibration precision of our proposed method. These experimental results indicate the high accuracy for measuring the exact frequency response and IQ skew value of the SHCD system by using our proposed method.

 

Fig. 6. The experimental results of the AFR curves of XI/XQ tributaries and the absolute estimated error (a-b), the PFR curves of XI/XQ tributaries and the absolute estimated error (c-d), the optical spectra of the transmitted signal with different compensation depth (e), the electrical spectra of the received signals whether using the frequency response compensation (f), the calculated Tx skew when additional skew values of +10, +5, -5, and -10 ps are preset (g), the calculated Rx skew when additional skew values of +40, +20, -20, and -40 ps are preset (h).

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A transmission performance comparison is realized experimentally based on the constructed DP SHCD transmission system and the estimated imperfection parameters. The Tx/Rx skew of X polarization is -10.34ps/5.18ps as mentioned before, and the Tx/Rx skew of Y polarization is estimated as -8.35ps/6.43ps. In order to guarantee the reasonability of this comparison experiment, the Rx DSP modules of the transmission system with/without using the calibration process are the same except for Rx skew compensation. The peak-to-peak voltage (Vpp) of the output signals from AWG is optimized as 400mV to balance the effects of modulation nonlinearity and SNR, and the experimental results are shown in Fig. 7. Noted that the transmission performance of the dual-polarization states is the combination of X/Y polarization state transmission performance.

 

Fig. 7. The measured EVM performance of DP-16QAM signals versus different compensation depths and with different compensation items (a), the measured BER performance of DP-16QAM signals versus different symbol rates whether using the proposed calibration method (b), the measured BER performance of DP-16QAM/64QAM signals versus different laser optical power whether using the proposed calibration method (c), the constellations of the received 35GBaud DP-64QAM/46GBaud DP-16QAM signals whether using the proposed calibration method (d-g).

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We first investigate the effect of compensation depth as presented in Fig. 7(a). The transmitted signal is a 46GBaud Nyquist DP-16QAM signal with a roll-off factor of 0.01. It can be observed that with the increase of the compensation depth, the transmission performance gradually improves as more energy is injected into the attenuated high-frequency domain. However, the transmission performance starts to degrade when $\gamma$> 0.6, because the compensation for the high-frequency domain will reduce the signal power in other frequency domains. In other words, when $\gamma$> 0.6, the transmission performance improvement brought by the compensation in the high-frequency domain will counteract the performance degradation in the lower frequency domain, resulting in the degradation of the overall transmission performance. What’s more, the transmission performance of the signals without skew compensation or frequency response compensation is also proposed. These experimental results indicate almost the same importance for skew and frequency response compensation for high baud-rate signal transmission. To further evaluate the calibration performance of the proposed scheme, the BER performance of the same 46GBaud DP-16QAM signals is measured with different baud rates, and the experimental results are plotted in Fig. 7(b). The experiment result shows that our calibration scheme can still contribute a great performance improvement even for 20GBaud signal transmission. The performance improvement can be attributed to the skew compensation as the bandwidth limitation is no longer severe in this situation. At last, the transmission performance with the optical power of the DFB laser from 9∼14 dBm is investigated as shown in Fig. 7(c). 46GBaud Nyquist DP-16QAM and 35GBaud Nyquist DP-64QAM signals with the roll-off factor of 0.01 are transmitted. It can be observed that the calibrated 46GBaud DP-16QAM signals can reach the 7% overhead hard-decision forward error correction (HD-FEC) threshold of 3.8e-3 even with 12dBm laser optical power. However, the same signals without the calibration process can just reach the 24% overhead SD-FEC threshold of 4.5e-2 with 14dBm laser optical power. Besides, the measured 35GBaud DP-64QAM signals can exceed the 24% overhead SD-FEC threshold after the calibration process. But the BER of the same DP-64QAM signals without calibration is about 1e-1 which means the failure of the transmission. In order to illustrate the difference between the signals whether using the calibration process, the constellations of the received 46GBaud DP-16QAM/35GBaud DP-64QAM signals are presented in Figs. 7(d-g). It can be observed that the constellations of calibrated signals are much clearer than the not calibrated signals. And the measured BER value of 46GBaud DP-16QAM signals/35GBaud DP-64QAM signals with 14dBm laser optical power is improved from 2.30e-2 to 2.18e-3/9.59e-2 to 2.20e-2 with the help of the proposed calibration method.

5. Conclusion

We have proposed and experimentally demonstrated a highly precise and cost-effective calibration method, with the capacity of simultaneously characterizing the frequency response and IQ skew for the DP SHCD optical transmission system. The measurement error of the AFR/PFR for the coherent optical transceiver is less than ±1 dB and ±0.15 rad in the target frequency domain, respectively. The measurement error of the Tx/Rx skew is less than ±0.3 ps. The proposed scheme is confirmed experimentally by transmitting 46 GBaud DP-16QAM and 35GBaud DP-64QAM signals in a 4MHz SHCD system with an 11 dB attenuation of 20 GHz. The measured BER performance is significantly improved after the calibration process. The experimental results indicate the potential of the proposed method as a precise calibration method to mitigate the inherent impairments of the SHCD system and reveal the potential of being applied in a high baud rate and high-order modulation format transmission system with low cost.