Modulation-format-free and automatic bias control for optical IQ modulators based on dither-correlation detection

Xiaolei Li; Lei Deng; Xiaoman Chen; Mengfan Cheng; Songnian Fu; Ming Tang; Deming Liu

doi:10.1364/OE.25.009333

1. Introduction

With the development of optical fiber communication technology, coherent optical communication systems using advanced modulation format have attracted great attention due to the extremely large transmission capacity [1, 2]. In coherent optical communication systems, the optical in-phase and quadrature (IQ) modulators are often deployed as the electrical-to-optical up-convertors [3, 4]. A single-polarization optical IQ modulator needs at least three bias signals to control its two child Mach-Zehnder modulator (MZM) and one parent MZM [5, 6]. However, the stability of the optical IQ modulator is easily influenced by some environment factors, such as temperature and mechanical vibration even the bias voltages remain unchanged [7, 8]. The drifting bias conditions will significantly degrade the transmission performance. Therefore, the auto bias control (ABC) module is essential to achieve long-term stability. Several ABC approaches have been proposed recently, including optical power monitoring techniques [9, 10] and dither signal monitoring techniques [11–14]. For instance, a dither-free method by monitoring optical power and analyzing the variance of optical power has been reported in [9], and a dither-added way of monitoring the electrical power of RF signal and dither signal respectively has also been proposed in [10]. For dither signal monitoring method, the power spectrum of 1st and 2rd dither harmonic frequency signals are analyzed and calculated carefully by fast Fourier transform (FFT) operation [11–14]. However, to meet the requirement of higher speed, longer transmission distance and more complex modulation format in current coherent optical communication system, auto bias control method with modulation format free, higher sensitivity and lower complexity is highly desired.

In this paper, we experimentally demonstrate an intelligent and effective ABC approach for optical IQ modulator. In the proposed scheme, the optimal bias conditions of two child MZMs and one parent MZM are achieved by using two different low frequency sine wave dither signals and dither-correlation detection. The designed dither-correlation detection doesn’t need frequency spectral analysis which is essential in the conventional dither signal based ABC method, and the results show that directional bias adjustment could be easily realized, resulting in the lower algorithm complexity and faster convergence rate. Moreover, the proposed ABC scheme is proved to have higher sensitivity and be modulation-format-free. For demonstration and evaluation purpose, we implement the proposed ABC method in both 10 Gb/s optical single carrier QPSK and 17.9 Gb/s optical 16QAM-OFDM signal transmission systems, and the experimental results show that the transmission penalty caused by ABC method is negligible.

2. Principle of the proposed ABC method

Figure 1 shows the proposed auto bias control configuration based on dither-correlation technique. To monitor and control the biases, a low bandwidth photo-detector (PD) is used to detect a small proportion (about 10%) of the optical signal power. A low speed (25 kHz) analog-to-digital converter (ADC) is adopted to sample the output signal of the PD. Two generated sine waves with the frequency of 3.9 kHz and 4.9 kHz are applied to dither the bias signal of the two child MZMs (BiasI and BiasQ) respectively. Meanwhile, these two dither signals are sampled by other ADCs for signal processing. A microprocessor unit (MPU) is then used to monitor both the average optical signal power and the correlation integration of the transmitted dither signals and the detected dither signals for auto bias control. Moreover, due to the use of ultra-low bandwidth PD, the wide-band RF signals (Signal I and Signal Q) are considered as white Gaussian noise.

Fig. 1 The proposed auto bias control configuration based on dither-correlation technique.

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The output optical signal can be written as

\begin{array}{l} S (t) = \frac{E_{i}}{2} [\cos (\frac{π}{2} \frac{V_{I} + V_{b i a s I}}{V_{π}}) + \cos (\frac{π}{2} \frac{V_{Q} + V_{b i a s Q}}{V_{π}}) e^{- j p}], \\ V_{b i a s I} = B i a s I - V_{I_{0}} \\ V_{b i a s Q} = B i a s Q - V_{Q_{0}} \end{array}

where p represents the phase difference between the two branches of the parent MZM.

V_{π}

is the half-wave voltage of the two-child MZMs at the bias port.

V_{I_{0}}

and

V_{Q_{0}}

are the bias voltages when the bias of two-child MZMs are set to be at their peak transmission point, and

V_{b i a s I}

and

V_{b i a s Q}

are the equivalent bias voltages for these two-child MZMs respectively.

V_{I}

and

V_{Q}

are the dither signals which could be denoted as

\begin{array}{l} V_{I} = A \sin (2 π f_{1} t) \\ V_{Q} = A \sin (2 π f_{2} t), \end{array}

where the phase and amplitude differences between these two dither signals are ignored for simplicity, and

f_{1}

and

f_{2}

are the dither signals with the frequency of 3.9 kHz and 4.9 kHz respectively. Subsequently, the output optical power at the PD could be given by

\begin{array}{l} {| S (t) |}^{2} = I^{2} (t) + Q^{2} (t) + 2 I (t) Q (t) \cos p \\ I (t) = \cos (\frac{π}{2} \frac{A \sin (2 π f_{1} t) + V_{b i a s I}}{V_{π}}) . \\ Q (t) = \cos (\frac{π}{2} \frac{A \sin (2 π f_{2} t) + V_{b i a s Q}}{V_{π}}) \end{array}

Around the optimum bias point ( $V_{b i a s I} \approx V_{π}$ , $V_{b i a s Q} \approx V_{π}$ and $p \approx \pm π / 2$ ), Eq. (3) can be rewritten as

\begin{matrix} I (t) \approx A [\sin (2 π f_{1} t) + Δ b_{1}] \\ Q (t) \approx A [\sin (2 π f_{2} t) + Δ b_{2}] \\ {| S (t) |}^{2} \approx A^{2} [\sin^{2} (2 π f_{1} t) + \sin^{2} (2 π f_{2} t), \\ + 2 Δ b_{1} \sin (2 π f_{1} t) + 2 Δ b_{2} \sin (2 π f_{2} t) \\ + 2 \sin (2 π f_{1} t) \sin (2 π f_{2} t) \cos p] \end{matrix}

where

Δ b_{1}

and

Δ b_{2}

are the errors of

V_{b i a s I}

and

V_{b i a s Q}

respectively. It could be clearly observed in Eq. (4) that if

V_{b i a s I}

is set to its optimum value which means

Δ b_{1} = 0

, the electrical power of the dither fundamental frequency (

f_{1}

) in

{| S (t) |}^{2}

is minimum. Similarly, if

V_{b i a s Q}

is set to its optimum value, the electrical power of the dither fundamental frequency (

f_{2}

) in

{| S (t) |}^{2}

is minimum. Moreover, if

p

is set to its optimum value which means

\cos p = 0

, the electrical power of the dither inter-modulation frequency (

f_{1} \pm f_{2}

) are minimum. These feature are widely used in the conventional ABC methods based on frequency spectrum analysis [14]. In these methods, FFT based frequency spectrum analysis is adopted to calculate the power of the fundamental harmonic component and the inter-modulation frequency component. However, the bias adjustment around the optimum point are obviously non-directional and non-linear in these methods. Figures 2(a) and 2(b) show the electrical power of dither inter-modulation frequency (

f_{1} \pm f_{2}

) and low frequency RF signal curves in the conventional dither signal monitoring [14] and dither-free ABC scheme [15] respectively. In this simulation, the bias voltage of the parent MZM is scanned from

V_{o p t} - 0.05 V_{π}

to

V_{o p t} + 0.05 V_{π}

, where

V_{o p t}

is the optimum bias value of the parent MZM, so the phase

p

is varied from

0.45 π

to

0.55 π

, and the electrical power of dither inter-modulation frequency is normalized by the electrical power of

f_{1} + f_{2}

when

p = 0.55 π

.

Fig. 2 The simulated power of dither inter-modulation frequency ( $f_{1} \pm f_{2}$ ) (a), low frequency RF signals (b) and the correlation integral coefficients $C I_{P}$ versus bias voltage (c).

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To address these issues, an effective ABC approach based on dither-correlation detection is proposed in our scheme. The proposed correlation integration operations can be written as

\begin{array}{l} C I_{I} = \int_{0}^{T} {| S (t) |}^{2} \sin (2 π f_{1} t + φ_{1}) d t \\ C I_{Q} = \int_{0}^{T} {| S (t) |}^{2} \sin (2 π f_{2} t + φ_{2}) d t, \\ C I_{P} = \int_{0}^{T} {| S (t) |}^{2} \sin (2 π f_{1} t + φ_{1}) \sin (2 π f_{2} t + φ_{2}) d t \end{array}

where

φ_{1}

and

φ_{2}

are the initial phase of these two dither signals respectively.

T

is the acquisition time, normally

T

is set to be about 100 times of the dither signal’s period to reduce the effect of noise.

C I_{I}

,

C I_{Q}

and

C I_{P}

are the correlation integral coefficients which are related to the bias states of two-child MZMs and one parent MZM respectively. According to the statistical theory,

C I_{K}

(

K = I, Q, P

) can represent the correlation degree between original dither signals and the photo-detected dither signals. As shown in Eq. (4), when the bias of parent MZM is set to the optimum value, the dither inter-modulation frequency (

f_{1} \pm f_{2}

) are minimum, so

{| S (t) |}^{2}

and

\sin (2 π f_{1} t + φ_{1}) \sin (2 π f_{2} t + φ_{2})

are uncorrelated and

C I_{P} = 0

. Figure 2(c) shows the

C I_{P}

curve around the optimum point, and in this simulation the

C I_{P}

value is also normalized by the

C I_{P}

when

p = 0.55 π

. Obviously, this curve is linear and monotonous, and the zero point corresponds to the optimum bias point of the parent MZM. Therefore, directional bias adjustment could be easily realized in our scheme. Actually, in the proposed method, only two bias voltage values are required to achieve the optimum point, resulting in the faster convergence rate. However, many bias voltage values need to be scanned and calculated to find out the optimum point in the conventional dither frequency monitoring method.

Considering the orthogonality of trigonometric function, Eq. (5) could be simplified as

\begin{array}{l} C I_{I} = C_{1} \sin (\frac{π V_{b i a s I}}{V_{π}}) + C_{1}^{'} \sin (\frac{π V_{b i a s I}}{2 V_{π}}) \sin (\frac{π V_{b i a s Q}}{2 V_{π}}) \cos (p) \\ C I_{Q} = C_{2} \sin (\frac{π V_{b i a s Q}}{V_{π}}) + C_{2}^{'} \sin (\frac{π V_{b i a s I}}{2 V_{π}}) \sin (\frac{π V_{b i a s Q}}{2 V_{π}}) \cos (p), \\ C I_{P} = C_{3} \sin (\frac{π V_{b i a s I}}{2 V_{π}}) \sin (\frac{π V_{b i a s Q}}{2 V_{π}}) \cos (p) \end{array}

where

C_{n}

and

C_{n}^{'}

(n = 1,2,3) are constant values which are affected by the parameters of the dither signals, such as

A

,

f_{1}

and

f_{2}

.

As we all known, the optimum bias point of an optical IQ modulator means that the bias of two child MZMs are set to be at their null transmission point ( $V_{b i a s I} = V_{π}$ and $V_{b i a s Q} = V_{π}$ ), and the bias of the parent MZM is set to be at its $\pm π / 2$ point. As shown in Eq. (6), it is easy to find out the optimum bias point of the parent MZM just by scanning $V_{b i a s P}$ to make $C I_{P} = 0$ . However, $C I_{I} or C I_{Q} = 0$ doesn’t mean two-child MZMs are at their optimum bias points due to the influence of $\cos (p)$ . To solve this problem, the bias of parent MZM should be adjusted preferentially. Assuming the bias of parent MZM is set to be around the optimum point ( $p \approx π / 2, \cos p \approx 0$ ), Eq. (6) could be rewritten as

\begin{matrix} C I_{I} = C_{1} \sin (\frac{π V_{b i a s I}}{V_{π}}) \\ C I_{Q} = C_{2} \sin (\frac{π V_{b i a s Q}}{V_{π}}) . \\ C I_{P} = C_{3} \cos (p) \end{matrix}

Figures 3(a) and 3(b) show the simulated correlation integral coefficient curves of one child MZM and the parent MZM versus bias voltage. It could be clearly observed that, when $C I_{I}$ or $C I_{Q}$ is equal to zero, $V_{b i a s I}$ and $V_{b i a s Q}$ is equal to $V_{π}$ or 0. $V_{b i a s I} = V_{π}$ and $V_{b i a s Q} = V_{π}$ correspond to the null transmission point (which is the optimum bias point), $V_{b i a s I} = 0$ and $V_{b i a s Q} = 0$ correspond to the peak transmission point. When $C I_{P}$ is equal to zero, $p = \pm π / 2$ , and both of these two points are the optimum bias points. Therefore, the optimum bias point of the parent MZM could be found out by scanning the bias voltage and monitoring $C I_{P}$ . As same as the averaged optical power curves in the traditional ABC method, it could be clearly shown in Fig. 4(a) that the $C I_{K}$ ( $K = I, Q$ ) curves in the proposed scheme will also be reversed when the modulation index is really high such as in large-driver single carrier QPSK (SC-QPSK) application [16]. However, the zero points of these $C I_{K}$ curves are not changed with different modulation format and modulation index as shown in Figs. 4(a) and 4(b), and the $C I_{P}$ curves are not reversed with different modulation format and modulation index [17, 18] as shown in Figs. 4(c) and 4(d). To avoid this reversion, the modulation index is set to relative low value by turning off RF signal or reducing the gain of RF driver amplifier [16] before the ABC operation. Subsequently, to distinguish the null and the peak transmission point of two child MZMs, a coarse adjustment process [14, 15] which could adjust the bias voltages to around the optimum point ( $Δ < 10 % V_{π}$ ) is adopted in our scheme. In this coarse adjustment, the average optical power at the PD is reduced as much as possible by adjusting BiasI and BiasQ in turn. After that, the gain of the RF driver amplifier could be set to the normal value.

Fig. 3 The simulated correlation integral coefficients $C I_{P}$ (a) and $C I_{I}$ (b) versus bias voltage.

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Fig. 4 Simulated $C I_{I}$ curves with different amplitude SC-QPSK signals (a), $C I_{I}$ curves with different modulation format RF signals ( $V_{p p} = 0.8 V_{π - R F}$ ) (b), $C I_{P}$ curves with different amplitude SC-QPSK signals (c), and $C I_{P}$ curves with different modulation format RF signals ( $V_{p p} = 0.8 V_{π - R F}$ ) (d). $V_{π - R F}$ is the half-wave voltage of two-child MZMs at the RF signal port.

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As mentioned above, the proposed ABC algorithm could be performed with three steps. Firstly, the RF signal is disabled, and the bias voltage of two child MZMs are scanned in turn to find out the minimum average optical power at the input of PD. In the second step, the RF signal is enabled, and the bias voltage of parent MZM is scanned to decrease $C I_{P}$ . Finally, the bias voltage of two child MZMs and parent MZM are all adjusted to decrease $C I_{I}$ , $C I_{Q}$ and $C I_{P}$ as much as possible by an iterative algorithm. To stabilize the bias of optical IQ modulator at the optimum point, an iterative algorithm based on Newton-iterative method is proposed. For example, assuming that $K_{P}$ is the slope of the $C I_{P} - Δ V$ curve near the optimum point, the $(n + 1)$ th iteration of $B i a s P$ can be written as

B i a s P_{n + 1} = B i a s P_{n} - \frac{C I_{P_{n}}}{K_{P}},

where the

C I_{P_{n}}

is the correlation integral coefficient corresponding to

B i a s P_{n}

, and

K_{P}

is calculated in real time to eliminate the interference caused by modulation format or modulation index changing.

C I_{I}

,

C I_{Q}

and

C I_{P}

could be calculated by numerical integration, which are defined as

\begin{matrix} C I_{I} = \int_{0}^{T} {| S (t) |}^{2} \sin (2 π f_{1} t + φ_{1}) d t \\ \approx \sum_{k = 0}^{N - 1} {| S (k Δ t) |}^{2} \sin (2 π f_{1} k Δ t + φ_{1}) \\ C I_{Q} = \int_{0}^{T} {| S (t) |}^{2} \sin (2 π f_{2} t + φ_{2}) d t, \\ \approx \sum_{k = 0}^{N - 1} {| S (k Δ t) |}^{2} \sin (2 π f_{2} k Δ t + φ_{2}) \\ C I_{P} = \int_{0}^{T} {| S (t) |}^{2} \sin (2 π f_{1} t + φ_{1}) \sin (2 π f_{2} t + φ_{2}) d t \\ \approx \sum_{k = 0}^{N - 1} {| S (k Δ t) |}^{2} \sin (2 π f_{1} k Δ t + φ_{1}) \sin (2 π f_{2} k Δ t + φ_{2}) \end{matrix}

where

N

is the sampling points, and

T = N Δ t

. According to Eq. (9), higher sampling frequency means smaller

Δ t

and more samples can be acquired in every dither signal period, so more information of dither signals can be acquired by increasing the sampling frequency. Figure 5 shows the slope of

C I_{P}

curve versus different sampling frequency, and larger slope coefficient means better sensitivity.

Fig. 5 The slope of $C I_{P}$ versus different sampling frequency.

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It can be easily obtained from Eq. (9) that the computation complexity of correlation integral operation is $O (N)$ . However, in the conventional dither signal monitoring based ABC methods, FFT based frequency spectrum analysis is adopted and the complexity of FFT is $O (N \log_{2} N)$ . Obviously, the proposed scheme has the lower algorithm complexity.

Figure 6 shows the monitored signals as a function of errors of $V_{b i a s I}$ and $V_{b i a s P}$ around the optimum bias point by using dither-free based ABC approach, dither signal monitoring techniques and the proposed ABC method. In all cases, the monitored signal are normalized to the value when we get the biggest error of $V_{b i a s I}$ or $V_{b i a s P}$ , and the value of monitored signal in this simulation can be defined as distinguish ratio. Moreover, in our simulation, SC-16QAM RF signal with $V_{P P} = 1.2 V_{π - R F}$ and white Gaussian noise is used. It could be clearly observed that the proposed ABC method and the FFT-based dither signal monitoring techniques have much higher sensitivity than the dither-free based ABC approach. However, the proposed ABC method outperform the dither-free based ABC approach in the bias control of the parent MZM, especially when the amplitude of dither signals is lower as shown in Fig. 6 [12].

Fig. 6 The monitored signals as a function of errors of $V_{b i a s I}$ (a) and $V_{b i a s P}$ (b) around the optimum bias point by using different ABC method with different dither signal amplitude.

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3. Experimental setup and results

Figure 7 shows the experimental setup of coherent optical back-to-back transmission system to verify the proposed ABC scheme. In our experiment, both single carrier modulation and multicarrier modulation are evaluated. For single carrier modulation, 5 Gbaud QPSK signals are produced by an arbitrary waveform generator (AWG, TekAWG7122C), and the net rate of the generated QPSK signal is 10 Gb/s. For multicarrier modulation, 16QAM-OFDM signal is produced by this AWG operated at 10 GSa/s. The 16QAM-OFDM baseband signal consists of 138 subcarriers, and 10 subcarriers are used to estimate the phase noise. The used inverse fast Fourier transform (IFFT) length is 256, and the cyclic prefix is 10% of the IFFT length. The length of a frame is set to 139, and in each frame 2 training symbols are inserted to implement time synchronization and channel estimation. Thus, the net rate of the generated 16QAM-OFDM signal is 17.9 Gb/s ( $10 G S a / s \times 4 \times 128 / 281 \times 137 / 139$ ). The photograph of the used ABC module which is designed by ourselves are shown in the inset of Fig. 7. This ABC module consists of MPU, ADC and DAC chips, and the frequency of the dither sine wave signals are set to 3.9 kHz and 4.9 kHz in the experiment. The generated baseband signal is used to modulate a 100 kHz-linewidth continuous-wave from an external cavity laser in an optical IQ modulator (Fujitsu FTM7962EP) with a half-wave voltage of 9V at the bias port. At the receiver, the coherent detector and 100 GSa/s digital sampling oscillator (DSO, Tektronix DSA72504DX) is used to capture the QPSK or 16QAM-OFDM signals. At last, offline signal demodulation is performed by a DSP-based receiver. In our experiment, 99520 bits in QPSK case and 267264 bits in 16QAM-OFDM case are calculated for BER counting.

Fig. 7 The experimental setup of coherent optical back-to-back transmission system based on the proposed ABC scheme.

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Figures 8(a)-8(c) show the measured correlation integral coefficient versus different bias voltages in the experiment. In the test, each correlation integral coefficient curve is measured when two other bias voltage is set to the optimum point value. It could be clearly observed that, the measured curves are accordance with the Eq. (7) and Fig. 3. The measured half-wave voltage of the child MZM and the parent MZM are not strictly equal, and the deviation is about 0.5V. Figure 9(a) presents the measured BER performance of 17.9 Gb/s optical 16QAM-OFDM signal as a function of optical signal noise rate (OSNR) when different modulation depth (MD) of dither signal is used, and the results by using manual bias control method are also plotted for comparison. Negligible power penalty is observed between the proposed ABC method and manual bias control method. The MD of dither signal is defined by $M D = A / V_{π}$ , where $A$ is the amplitude of the dither signal. Obviously, MD has significant influence on auto bias control. Figure 9(b) shows the measured $C I_{I}$ curves as a function of the deviation of the current bias voltage and the optimum bias voltage when different MD are used, and Fig. 10 shows the distinguish ratio curves of $C I_{I}$ in different MD value. It could be clearly observed that smaller MD lead to higher sensitivity and better ABC performance in child MZM’s adjusting. However, too small MD will significantly reduce the distinguish ratio of $C I_{P}$ as shown in Fig. 6(b), so that MD is set to be 6.6% in our experiment.

Fig. 8 The measured correlation integral coefficient $C I_{I}$ (a), $C I_{Q}$ (b), and $C I_{P}$ (c) versus different bias voltages.

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Fig. 9 The measured BER vs OSNR curves (a) and the $C I_{I}$ versus $Δ V$ curves (b) with different dither amplitudes.

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Fig. 10 The distinguish ratio curves of $C I_{I}$ in different MD value.

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Figure 11 shows the measured BER performance of both 10 Gb/s optical QPSK signal and 17.9 Gb/s optical 16QAM-OFDM signal as a function of OSNR when the proposed ABC scheme and the manual bias control method are used. MD is set to $6.6 % V_{π}$ in the test. It could be clearly observed that the proposed ABC scheme is modulation format free and has no power penalty compared to the manual bias control method. The constellation of the received optical QPSK signal and optical 16QAM-OFDM signal are both plotted in the insets of Fig. 11. Furthermore, to evaluate the long-term and stable performance of the proposed scheme, both the error vector magnitude (EVM) performance of 17.9 Gb/s optical 16QAM-OFDM signal and the corresponding environment temperature of the optical IQ modulator are measured and shown in Fig. 12. The OSNR is maintained as 20.69 dB, and a hot air blower is used to vary the temperature of the optical IQ modulator indirectly. In the test, not only the temperature is varied but also mechanical vibration is induced by the wind, and this mechanical vibration will cause optical signal polarization jitter, resulting in the fluctuation of the measured EVM performance. Therefore, it could be clearly observed that when the air blower is set to strong wind mode (between 5th and 15th minutes), EVM performance become litter worse in ABC-on case. However, when the temperature changes within 20 to 36°C, the measured EVM performance fluctuates wildly if no ABC is adopted, and the measured EVM performance remains basically below 10% when the proposed ABC method is used.

Fig. 11 The measured BER vs OSNR curves by using different modulation formats.

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Fig. 12 The measured EVM performance under temperature-varying conditions.

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4. Conclusions

In this paper, we propose a novel ABC method for coherent optical communication system based on two different low frequency sine wave dither signals and dither-correlation detection. The theoretical analysis shows that no FFT-based frequency spectral analysis is needed, and the directional bias adjustment could be easily realized, resulting in the lower algorithm complexity and faster convergence rate. This ABC scheme is proved to have other advantages such as higher sensitivity and modulation format independence. The experimental results show that the power penalty caused by the proposed ABC is negligible for both single carrier modulation and optical orthogonal frequency division multiplexing modulation, which make the proposed scheme very suitable for high speed coherent optical communication systems.

Funding

National “863” Program of China (No. 2015AA016904); National Natural Science Foundation of China (NSFC) (Nos. 61675083, 61307091, 61575071 and 61331010).

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Modulation-format-free and automatic bias control for optical IQ modulators based on dither-correlation detection

Abstract

1. Introduction

2. Principle of the proposed ABC method

3. Experimental setup and results

4. Conclusions

Funding

References and links

Cited By

Figures (12)

Equations (9)

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