Optical Modulator Evaluation Technique Based on Phase Retrieval

Abstract

To provide a system for estimating power-optical response imbalance between an I (in-phase) channel and a Q (quadrature-phase) channel of an optical quadrature amplitude modulator (optical IQ modulator) using a simple device.SOLUTION: A system comprises: a photodetector (PD)3; an analog-digital converter (ADC)5; and an imbalance calculation section 11 for estimating power-optical response imbalance between an I channel and a Q channel of an optical quadrature amplitude modulator (optical IQ modulator). The imbalance calculation section has an input signal information reception section 13 that receives information pertaining to a first modulation signal and a strength information reception section 15 that receives strength information for digitized output signals from the ADC, estimates the power-optical response imbalance between the I channel and the Q channel of the optical IQ modulator using the information pertaining to the first modulation signal and the strength information for the digitized output signals. Thus, the system estimates the power-optical response imbalance between the I channel and the Q channel of the optical IQ modulator.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to an optical modulator evaluation system, and more specifically to a system capable of evaluating the characteristics of an optical modulator using a simple optical detector, and a method for evaluating the characteristics of an optical modulator using the system. [Background technology]

[0002] In the past 20 years, the transmission capacity per fiber in the backbone optical network has improved by nearly 2000 times. In particular, the optical frequency utilization efficiency of the transmitter and receiver has improved by 160 to 640 times, which is a particularly large contribution. This dramatic improvement in spectral efficiency (SE) is due to the adoption of optical multi-level modulation methods such as QAM, polarization multiplexing transmission methods, and optical spectrum shaping such as Nyquist filters, but all of these require high-speed and extremely precise control of the optical field. However, it is known that optical IQ (In-phase and Quadrature, orthogonal amplitude modulation) modulators using nested Mach-Zehnder interferometers, which are widely used for high-speed modulation of optical fields, have signal distortions due to variations in the path length and loss of the optical waveguide, or variations in the RF modulated signal due to high-frequency amplifiers and PCB wiring losses, so-called IQ imbalance, and this problem has become apparent as SE has improved.

[0003] In the future, it will not be economical to ensure further improvements in SE only by improving the characteristics of these optical analog circuits (analog coherent optics) and high-frequency electrical analog circuits, and it will be necessary to compensate for analog imperfections at the optical transmitting and receiving ends using digital signal processing. In addition, for this purpose, monitoring technology that evaluates the degree of imperfection in optical modulation and feeds back the evaluation results to the digital compensation circuit will be important.

[0004] A widely known technique for monitoring optical IQ modulated signals is to use a well-calibrated optical coherent receiver, such as an optical modulation analyzer, but this requires an expensive measurement system to be placed in close proximity to the modulator, and is not suitable for integration into a transponder or for on-service adaptive calibration. A technique has also been proposed for remotely estimating and compensating for the IQ imbalance on the transmitting side by signal processing on the receiver side after transmission, but in this case, it is necessary to simultaneously handle the analog imperfection of the receiver itself, which requires complex signal processing.

[0005] On the other hand, as an approach that is lower cost and can be integrated into the transmitter, a method has been proposed in which the IQ imbalance of an optical IQ modulator is estimated and calibrated based on field intensity information from a photodetector (PD) without using a coherent receiver (Non-Patent Document 1 below). However, this method assumes the advance or simultaneous transmission of a pilot tone or dither signal, making on-service monitoring difficult with the former, and the degradation of signal quality due to the dither signal itself, particularly in high-order multi-level modulation methods, is an issue with the latter.

[0006] Furthermore, in recent years, it has been pointed out that in high-order multi-level modulation, the degree of IQ imbalance varies depending on the input frequency, which is called frequency-dependent IQ imbalance. However, most existing monitoring methods parametrically estimate frequency-nonselective IQ imbalance and cannot be used to estimate frequency-dependent IQ imbalance. [Prior art documents] [Non-patent literature]

[0007] [Non-Patent Document 1] CRS Fludger, T. Duthel, P. Hermann, and T. Kupfer, "Low cost transmitter self-calibration of time delay and frequency response for high baud-rate QAM transceivers," in Optical Fiber Communications Conference and Exhibition (OFC) (2017), Summary of the Invention [Problem to be solved by the invention]

[0008] The present invention aims to provide a system for estimating the imbalance in the electrical-optical response between the I (in-phase) channel and the Q (quadrature-phase) channel of an optical quadrature amplitude modulator (optical IQ modulator) using a simple device. [Means for solving the problem]

[0009] The present invention is basically based on the following concept. The problem of determining the imbalance of the electrical-optical response between the I (in-phase) and Q (quadrature-phase) channels in an optical quadrature amplitude modulator for a known modulation signal input is formulated as a phase retrieval problem, which allows the estimation of the frequency-dependent IQ imbalance and bias misalignment of the modulator even using a single photodetector.

[0010] The first invention relates to a system for evaluating the characteristics of an optical quadrature amplitude modulator (optical IQ modulator). This system is a system for estimating the imbalance of the electrical-optical response between the I (in-phase) channel and the Q (quadrature-phase) channel of the optical quadrature amplitude modulator.

[0011] The imbalance in electrical-optical response between the I and Q channels of an optical IQ modulator can be, for example, Impulse response and frequency response of I-channel and Q-channel of optical IQ modulator, Frequency dependence of the phase shift between the electro-optical responses of the I and Q channels of an optical IQ modulator, Frequency dependence of the intensity shift between the electro-optical responses of the I and Q channels of an optical IQ modulator, DC bias components of I and Q channels of optical IQ modulator, and The parameter includes any one or more imbalances in the frequency dependence of nonlinear distortion of the I channel and the Q channel of the optical IQ modulator.

[0012] The optical quadrature amplitude modulator characteristic evaluation system 1 includes a photodetector (PD) 3 , an analog-to-digital converter (ADC) 5 , and an imbalance calculation unit 11 .

[0013] The photodetector (PD) 3 is an element for measuring the intensity component of the first output signal from the optical IQ modulator when the first modulated signal is input to the optical IQ modulator.

[0014] The analog-to-digital converter (ADC) 5 is an element for converting the intensity component of the first output signal received by the photodetector (PD) into a digital signal and obtaining intensity information of the digitized output signal.

[0015] The imbalance calculation unit 11 is an element for estimating the imbalance of the electrical-optical response between the I channel and the Q channel of the optical IQ modulator. The imbalance calculation unit 11 is an input signal information receiving unit 13 for receiving information regarding the first modulated signal; and an intensity information receiving unit 15 for receiving the intensity information of the digitized output signal from the analog-to-digital converter (ADC) 5. Then, the imbalance calculation unit estimates an imbalance in the electrical-optical response between the I channel and the Q channel of the optical IQ modulator using information about the first modulated signal and intensity information of the digitized output signal.

[0016] An example of the information about the first modulated signal is information about the time change in intensity and phase of the first modulated signal (E in (t)). The imbalance calculation unit 11 further includes, for example, a phase recovery calculation unit 17 and an imbalance coefficient calculation unit 19 in order to perform the above calculations. The phase recovery calculation unit 17 calculates the intensity information (|E(t)| 2 ) is an element that performs a phase recovery calculation to recover the phase information of the output signal. The imbalance coefficient calculation unit 19 is an element for calculating an imbalance parameter from the phase-recovered output signal (E(t)) and information (s(t)) relating to the first modulated signal. The phase recovery calculation unit 17 estimates the imbalance in the electrical-optical response between the I channel and Q channel of the optical IQ modulator by having the imbalance coefficient calculation unit 19 calculate the imbalance coefficient for the phase-recovered output signal (E(t)) obtained by the phase recovery calculation unit.

[0017] The second invention relates to a method for estimating the imbalance of electrical-optical response between an I (in-phase) channel and a Q (quadrature-phase) channel of an optical quadrature amplitude modulator (optical IQ modulator), the method including the following steps. A first modulated signal is input to the optical IQ modulator. The optical signal input to the optical IQ modulator is IQ modulated by the optical IQ modulator based on the first modulating signal, and a first output signal is output. A photodetector (PD) receives the first output signal and measures an intensity component of the first output signal. An analog-to-digital converter (ADC) converts the intensity component of the first output signal measured by the photodetector (PD) into a digital signal to obtain intensity information of the digitized output signal. An imbalance estimator receives information relating to the first modulated signal. An imbalance estimator receives the magnitude information of the digitized output signal from the ADC. An imbalance estimator estimates an imbalance in the electrical-optical response between the I-channel and the Q-channel of the optical IQ modulator using information about the first modulated signal and intensity information of the digitized output signal. Effect of the Invention

[0018] According to the system and method of the present invention, the problem of determining the imbalance in the electrical-optical response between the I (in-phase) channel and the Q (quadrature-phase) channel of an optical quadrature amplitude modulator (optical IQ modulator) can be treated as a phase retrieval problem, making it possible to estimate the imbalance using a simple device. [Brief description of the drawings]

[0019] [Figure 1] FIG. 1 is a block diagram for explaining a system for evaluating the characteristics of an optical quadrature amplitude modulator (optical IQ modulator). [Diagram 2] FIG. 2 is a block diagram showing the basic configuration of a computer. [Diagram 3] FIG. 3 is a flow chart illustrating an example process for estimating the imbalance of the electro-optical response. [Figure 4] FIG. 4 is a schematic diagram of the optical quadrature amplitude modulator characteristic evaluation system (SP-IQM) of the present invention. [Diagram 5] FIG. 5 is a diagram showing a verification experiment system for verifying the principle of the present invention. [Figure 6] FIG. 6 shows examples of the estimated impulse response, the frequency response calculated from the impulse response, and the received signal points actually observed by a modulation analyzer for three patterns of h'ideal. [Figure 7] FIG. 7 shows the MSE characteristics for each trial when h'ideal is generated independently and randomly 20 times. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] Hereinafter, the embodiments for carrying out the present invention will be described with reference to the drawings. The present invention is not limited to the embodiments described below, and includes appropriate modifications of the embodiments described below within the scope obvious to those skilled in the art.

[0021] FIG. 1 is a block diagram for explaining a system for evaluating the characteristics of an optical quadrature amplitude modulator (optical IQ modulator). This system is a system for estimating the imbalance of the electrical-optical response between the I (in-phase) channel and the Q (quadrature-phase) channel of an optical quadrature amplitude modulator. By estimating the imbalance of the electrical-optical response between the I channel and the Q channel of the optical IQ modulator, this imbalance can be output, the characteristics of the optical IQ modulator can be evaluated, and control taking this imbalance into consideration (for example, adjusting the modulation signal applied to the optical IQ modulator) can be performed. As shown in FIG. 1, this optical quadrature amplitude modulator characteristic evaluation system 1 has a photodetector (PD) 3, an analog-to-digital converter (ADC) 5, and an imbalance calculation unit 11.

[0022] The photodetector (PD) 3 is an element for measuring the intensity component of the first output signal from the optical IQ modulator when the first modulated signal is input to the optical IQ modulator.

[0023] The analog-to-digital converter (ADC) 5 is an element for converting the intensity component of the first output signal received by the photodetector (PD) into a digital signal and obtaining intensity information of the digitized output signal.

[0024] The imbalance calculation unit 11 is an element for estimating the imbalance of the electrical-optical response between the I channel and the Q channel of the optical IQ modulator. The imbalance calculation unit 11 is connected to, for example, a signal source of the first modulated signal and an analog-to-digital converter (ADC) 5 so as to be able to exchange information. The imbalance calculation unit 11 preferably has a control device (computer).

[0025] FIG. 2 is a block diagram showing the basic configuration of a computer. As shown in this figure, the computer has an input unit 21, an output unit 23, a control unit 25, a calculation unit 27, and a storage unit 29, and each element is connected by a bus 31 or the like so as to be able to transmit and receive information. For example, the storage unit may store a control program or various information. When predetermined information is input from the input unit, the control unit reads out the control program stored in the storage unit. Then, the control unit reads out the information stored in the storage unit as appropriate and transmits it to the calculation unit. Also, the control unit transmits the input information as appropriate to the calculation unit. The calculation unit performs calculation processing using the various information received and stores it in the storage unit. The control unit reads out the calculation results stored in the storage unit and outputs them from the output unit. In this manner, various processes are executed.

[0026] The imbalance calculation unit 11 is implemented by the above-mentioned computer. Each unit described below is implemented by each element of the computer and a control program stored in a storage unit. The imbalance calculation unit 11 has an input signal information receiving unit 13 and an intensity information receiving unit 15. The imbalance calculation unit 11 estimates the imbalance of the electrical-optical response between the I channel and the Q channel of the optical IQ modulator using information on the first modulated signal and intensity information on the digitized output signal. To perform the above estimation, the imbalance calculation unit 11 may further have, for example, a phase recovery calculation unit 17 and an imbalance coefficient calculation unit 19.

[0027] The input signal information receiving unit 13 is an element for receiving information about the first modulated signal. The input unit 21 of the control device functions as the input signal information receiving unit 13. The imbalance calculation unit 11 may be electrically connected to, for example, a signal source of the first modulated signal. Therefore, the imbalance calculation unit 11 can receive information about the first modulated signal from the signal source. An example of the information about the first modulated signal is information (s(t)) about the time change in intensity and phase of the first modulated signal. If s(t) is a predetermined sequence, the imbalance calculation unit 11 does not need to receive s(t) from the signal source of the first modulated signal. In this case, the imbalance calculation unit 11 may read information (s(t)) about the time change in intensity and phase of the first modulated signal stored in the storage unit 29 and receive the information about the read first modulated signal.

[0028] The intensity information receiving unit 15 is an element for receiving intensity information of the digitized output signal from the analog-digital converter (ADC) 5. The input unit 21 of the control device functions as the intensity information receiving unit 15. The imbalance calculation unit 11 is electrically connected so as to be able to receive information from, for example, the analog-digital converter (ADC) 5. Therefore, the intensity information receiving unit 15 can receive intensity information of the digitized output signal from the analog-digital converter (ADC) 5.

[0029] The phase recovery calculation unit 17 calculates the intensity information (|E(t)| 2 ) is an element for performing a phase recovery calculation to recover the phase information of the output signal.

[0030] The imbalance coefficient calculation unit 19 is an element for calculating an imbalance parameter from the phase-recovered output signal (E(t)) and information (s(t)) relating to the first modulated signal.

[0031] For example, the control unit 25, the calculation unit 27, and the storage unit 29 (and the control program stored in the storage unit 29) of the control device function as the phase recovery calculation unit 17 and the imbalance coefficient calculation unit 19. The phase recovery calculation unit 17 calculates the phase-recovered output signal (E out For (t), the imbalance coefficient calculation unit 19 calculates the imbalance coefficient to estimate the imbalance in electrical-optical response between the I channel and the Q channel of the optical IQ modulator.

[0032] The imbalance calculation unit 11 stores, for example, information on the first modulated signal received by the input signal information receiving unit 13 and intensity information of the digitized output signal received by the intensity information receiving unit 15 in a suitable storage unit. Then, the imbalance calculation unit 11 causes the phase recovery calculation unit 17 and the imbalance coefficient calculation unit 19 to perform a predetermined calculation using the information on the first modulated signal and the intensity information of the digitized output signal from the storage unit, calculates imbalance parameters, and estimates the imbalance of the electrical-optical response between the I channel and the Q channel of the optical IQ modulator. The specific principle of the calculation will be described later.

[0033] The imbalance in electrical-optical response between the I and Q channels of an optical IQ modulator can be, for example, Impulse response and frequency response of I-channel and Q-channel of optical IQ modulator, Frequency dependence of the phase shift between the electro-optical responses of the I and Q channels of an optical IQ modulator, Frequency dependence of the intensity shift between the electro-optical responses of the I and Q channels of an optical IQ modulator, DC bias components of I and Q channels of optical IQ modulator, and The parameter includes any one or more imbalances in the frequency dependence of nonlinear distortion of the I channel and the Q channel of the optical IQ modulator.

[0034] Impulse and frequency responses of I and Q channels of an optical IQ modulator The impulse responses of the I and Q channels are expressed by their common components h + (t) and the error component h -(t). As will be described later, h + (t) and h - By estimating (t), the impulse responses of the I and Q channels can be obtained. In addition, the frequency response of the I and Q channels can be estimated by performing spectral analysis of the impulse response using techniques such as Fourier transform and periodogram method. The frequency response gives the output amplitude and output phase when a sine wave input of a certain frequency is applied to the I or Q channel.

[0035] Frequency Dependence of Intensity Deviation of Electro-Optical Responses of I- and Q-Channels of an Optical IQ Modulator error component h - By performing a spectrum analysis of (t) and calculating the amplitude components of the frequency response, the frequency dependence of the intensity shift of the electrical-optical response of the I channel and Q channel of the optical IQ modulator can be estimated.

[0036] Frequency Dependence of Phase Shift in the Electro-Optical Responses of I- and Q-Channels of an Optical IQ Modulator error component h - By performing a spectrum analysis of (t) and calculating the phase component of the frequency response, the frequency dependence of the intensity shift of the electrical-optical response of the I channel and Q channel of the optical IQ modulator can be estimated.

[0037] DC bias components of I and Q channels of optical IQ modulator The DC bias components of the I and Q channels of the optical IQ modulator are the deviation between the DC component of the modulated signal and the DC component in the optical modulator output. The DC bias components of the I channel and Q channel of the optical IQ modulator can be expressed as δ. As described later, by estimating δ, the DC biases of the I channel and Q channel of the optical IQ modulator can be estimated.

[0038] Nonlinear distortion of I-channel and Q-channel of optical IQ modulator The nonlinear distortion of the I and Q channels of an optical IQ modulator is a response of the I and Q channels of the optical IQ modulator that depends on the amplitude and phase state of the modulated signal and cannot be expressed in the form of a linear system such as an impulse response. By adopting a function that expresses a nonlinear response, such as a Volterra filter, in the imbalance coefficient calculation unit 19, the imbalance calculation unit 11 can cause the phase recovery calculation unit 17 and the imbalance coefficient calculation unit 19 to perform a specified calculation, thereby estimating the nonlinear distortion of the I channel and Q channel of the optical IQ modulator.

[0039] The imbalance calculation unit 11 may receive information about the optical signal input to the optical IQ modulator (e.g., information about changes in the intensity and phase of the optical signal over time). In this case, for example, a light source of the optical signal may be connected to the imbalance calculation unit 11. Also, before the optical signal is input to the optical IQ modulator, the optical signal may be split, one of the split optical signals may be detected by an optical detector, and the intensity of the detected optical signal may be converted into a digital signal, which the imbalance calculation unit 11 receives. Furthermore, information about the optical signal input to the optical IQ modulator (e.g., information about changes in the intensity and phase of the optical signal over time) may be stored in the storage unit 29, and the information may be read out from the storage unit 29.

[0040] The imbalance in electrical-optical response between the I and Q channels of an optical IQ modulator can be, for example, Impulse response and frequency response of I-channel and Q-channel of optical IQ modulator, Frequency dependence of the phase shift between the electro-optical responses of the I and Q channels of an optical IQ modulator, Frequency dependence of the intensity shift between the electro-optical responses of the I and Q channels of an optical IQ modulator, DC bias components of I and Q channels of optical IQ modulator, and The parameter includes any one or more imbalances in the frequency dependence of nonlinear distortion of the I channel and the Q channel of the optical IQ modulator.

[0041] The second invention relates to a method for estimating the imbalance of the electrical-optical response between the I (in-phase) and Q (quadrature-phase) channels of an optical quadrature amplitude modulator (optical IQ modulator). 3 is a flow chart showing an example of a process for estimating the imbalance of electrical-optical response. As shown in FIG. 3, the method includes the following steps: S denotes a step. A first modulated signal is input to the optical IQ modulator (S101). The optical signal input to the optical IQ modulator is IQ modulated by the optical IQ modulator based on the first modulating signal, and a first output signal is output (S102). A photodetector (PD) receives the first output signal and measures the intensity component of the first output signal (S103). An analog-to-digital converter (ADC) converts the intensity component of the first output signal measured by the photodetector (PD) into a digital signal, and obtains intensity information of the digitized output signal (S104). An imbalance estimator receives information relating to the first modulated signal (S105). The imbalance estimator receives the digitized output signal strength information from the ADC (S106). An imbalance estimator estimates an imbalance in the electrical-optical response between the I-channel and the Q-channel of the optical IQ modulator using information about the first modulated signal and the intensity information of the digitized output signal (S107).

[0042] The principle of the present invention will now be described.

[0043] 4 is a schematic diagram of the system for evaluating the characteristics of an optical quadrature amplitude modulator (SP-IQM) of the present invention. The SP-IQM is composed of a photodetector (PD), an analog-to-digital converter (ADC), and a calculation unit.

[0044] Assuming that the optical IQ modulator is driven in the linear region, the complex envelope amplitude E(t) of the optical electric field at the IQ modulator output in the presence of frequency-dependent IQ imbalance can be described by the following wide-sense linear (WL) model, as shown, for example, in L. Anttila, M. Valkama, and M. Renfors, "Frequency-Selective I / Q Mismatch Calibration of Wideband Direct-Conversion Transmitters," IEEE Trans. Circuits Syst. Express Briefs 55(4), 359-363 (2008).

[0045]

number

[0046] where E0 is the optical carrier input to the modulator, s(t) is the modulating signal, * denotes linear convolution, and (·) * denotes the complex conjugate.

[0047] Impulse response h + (t) and h - (t) can be related to the response of individual circuits within the optical IQ modulator, for example, as follows:

[0048]

number

[0049] g I (t) and g Q (t) represents the impulse response of the I channel and the Q channel caused by the modulation signal input electrical circuits such as the DAC, RF amplifier, and printed circuit board trace wiring, and ε and θ represent the intensity and phase shift in the optical quadrature amplitude modulation. δ represents the optical bias component in the modulator output. In the case of an ideal optical IQ modulator with no imbalance, s(t) and E(t) are proportional.

[0050] A coherent receiver is generally used to estimate the modulator IQ imbalance. In this case, the modulator output electric field E(t) can be observed including its phase information, so according to the WL model, h + (t), h - It is possible to directly estimate (t) and δ. Such imbalance estimation methods are known as modulation analyzers. Modulator analyzers consist of a highly accurate coherent receiver that is well calibrated, which poses problems in terms of cost and integration into the modulator circuit.

[0051] On the other hand, the IQ imbalance estimation method using only PD is low cost and can be integrated into the modulator circuit. However, the direct detection by PD does not provide the intensity information |E(t)| of the modulator output electric field E(t). 2 Only the phase information can be detected, and the phase information is lost. For this reason, in conventional imbalance estimation methods using only PD, such as JCM Diniz, F. Da Ros, EP da Silva, RT Jones, and D. Zibar, "Optimization of DP-M-QAM Transmitter Using Cooperative Coevolutionary Genetic Algorithm," J. Lightwave Technol. 36(12), 2450-2462 (2018), a special reference signal such as a dither signal or a tone signal is used as s(t) to estimate |E(t)| 2 In this method, only ε and θ, which are independent of frequency, can be estimated, and there are problems such as the difficulty of evaluating the imbalance during data transmission, and degradation of signal quality due to the superimposed reference signal.

[0052] Unlike conventional imbalance estimation methods that use tone signals, the SP-IQM of the present invention uses phase recovery technology to estimate |E(t)| 2 From the random signal sequence s(t), h + (t), h -In this way, we can realize imbalance estimation that does not require an expensive coherent receiver, can be integrated into the modulation circuit, and can be used during data transmission.

[0053] Assuming that the PD and ADC responses are ideal, the WL model in the discrete time domain after the ADC is

[0054]

number

[0055] Here, the L×1 real vector r is the received signal strength information in the discrete time domain, and the L×1 complex vector h + and h - is the discrete time domain h + (t) and h - (t), s is the L×1 signal vector consisting of s(t). L is the impulse response in the discrete time domain h + (t) and h - represents the memory length of (t). L×1 vector 1 represents a vector whose elements are all 1, and (·) T indicates transposition.

[0056] As shown in Y. Yoshida, T. Umezawa, A. Kanno, and N. Yamamoto, "A Phase-Retrieving Coherent Receiver Based on Two-Dimensional Photodetector Array," J. Lightwave Technol. 38(1), 90-100 (2020). k When K independent signal blocks are transmitted, the response of the IQ modulator is h + ,h - The estimation problem of , and δ is given by the following formula:

[0057]

number

[0058] Here,

[0059]

number

[0060] This problem is mathematically equivalent to a problem known as the phase retrieval problem in many fields such as crystallography and diffraction imaging. Therefore, we can apply the mathematical knowledge of the phase retrieval field to the problem of estimating IQ imbalance using PD.

[0061] For example, as introduced in Y. Shechtman, YC Eldar, O. Cohen, HN Chapman, J. Miao, and M. Segev, "Phase Retrieval with Application to Optical Imaging: A contemporary overview," IEEE Signal Process. Mag. 32(3), 87-109 (2015), there has been a great deal of prior research in the field of phase retrieval on necessary and sufficient conditions for unique retrieval and phase retrieval algorithms.

[0062] First, regarding the uniqueness of phase retrieval, AS Bandeira, J. Cahill, DG Mixon, and AA Nelson, "Saving phase: Injectivity and stability for phase retrieval," Appl. Comput. Harmon. Anal. 37(1), 106-125 (2014), presented the 4N-4 conjecture. In other words, to uniquely determine the phase of N unknown variables, 4N-4 pieces of intensity information are sufficient, and these pieces of intensity information can be obtained based on a random observation process. In the above IQ imbalance estimation problem, this random observation process is mathematically expressed as follows: k(k=1,...,K), and the above prediction means that if K is sufficiently large (e.g., K>8L) relative to the number of elements of the unknown variable vector h' to be estimated, it is possible to uniquely estimate h' including its phase. k Since can be a random sequence, it can be a transmission data sequence as long as it is known in the calculation part of the SP-IQM, and imbalance estimation during data transmission is also possible.

[0063] Next, regarding the phase retrieval algorithm, since the IQ imbalance estimation problem is a general form of phase retrieval, many existing phase retrieval algorithms can be applied. For example, it may be an Alternative Projection method such as the Gerchberg-Saxton method, or it may be based on convex optimization methods such as PhaseLift, PhaseMax, and PhaseCut, or it may be a Stochastic Gradient Descent method such as Wirtinger Flow, or it may be a phase retrieval algorithm based on the Approximate Message Passing method or the Augmented Lagrangian method such as the Alternating Direction Method of Multipliers (ADMM).

[0064] In this embodiment, we use the phase retrieval algorithm PhareADMM, which is based on the ADMM shown in J. Liang, P. Stoica, Y. Jing, and J. Li, "Phase Retrieval via the Alternating Direction Method of Multipliers," IEEE Signal Process. Lett. 25(1), 5-9 (2018). PhareADMM solves the phase retrieval problem as follows:

[0065]

number

[0066] h' is estimated by minimizing the loss function based on the amplitude error given by:

[0067] In the above explanation, the imbalance of the optical IQ modulator is formulated by the WL model, but in the SP-IQM of the present invention, any IQ imbalance model may be used as long as it can be finally expressed in the form of the phase recovery problem. For example, it may be a model in which the real part and the imaginary part of the complex equivalent low-pass expression are treated as vectors individually, or it may include a nonlinear response that can be expressed in the form of vector operation such as a Volterra filter. EXAMPLES

[0068] FIG. 5 shows a demonstration experiment system for verifying the principle of the present invention. A 63.25 Gbaud polarization multiplexed optical 16QAM modulated signal is generated using an optical IQ modulator using a Mach-Zehnder interferometer (MZI), a 92 GSa / s arbitrary RF waveform generator (AWG) to drive the modulator, and a 1550 nm narrow linewidth light source. The signal sequence is a random sequence assuming a data sequence, and about 80,000 symbols of the random sequence are used as a pilot signal for imbalance estimation. The optical signal is amplified by an erbium-doped fiber amplifier (EDFA) and then split into two by a power splitter. One of the signals is separated into only the X-polarized component by a polarization beam splitter (PBS), and then input to the SP-IQM. The SP-IQM consists of a 3 dB bandwidth 70 GHz PD and a 160 GSa / s real-time sampling oscilloscope (DSO), and the calculation section for phase recovery and imbalance estimation is implemented on a workstation as offline processing. The phase recovery algorithm uses the PhareADMM described above. In this proof-of-principle experiment, a wideband measurement system is used to ignore the effects of the bandwidth limitations of the PD and DSO, and the effective sampling rate in the phase recovery process is 4.2GSa / s. The other power splitter output is input to an optical modulation analyzer using a coherent receiver. The coherent receiver consists of a four-channel 80GSa / s DSO, a narrow linewidth light source, and an optical hybrid circuit, and the calculation processing in the modulation analyzer is implemented offline, as in the SP-IQM. In the case of coherent reception, the frequency offset (CFO) of the transmitter and receiver light sources becomes a problem, but this was compensated for by performing signal spectrum analysis prior to imbalance estimation. For imbalance estimation in the modulation analyzer, we used minimum mean square error estimation (WL-MMSE) using the WL model shown in T. Adali, PJ Schreier, and LL Scharf, "Complex-Valued Signal Processing: The Proper Way to Deal With Impropriety," IEEE Trans. Signal Process. 59(11), 5101-5125 (2011). In addition, the frequency response deviation caused by the analog circuitry of the SP-IQM and the modulator analyzer is compensated for by a fixed linear equalizer.In an actual IQ modulator, it is not easy to strictly control the IQ imbalance, especially its frequency dependency, so in this demonstration experiment, the imbalance was simulated by a digital filter based on a discrete-time WL model in the transmitter AWG. In the following, the impulse response of this digital filter is called h'. ideal , the estimation result by SP-IQM is h' PR ,The estimated result of the modulation analyzer using a coherent receiver is h' coh Let the average estimation error be

[0069]

number

[0070] Defined in.

[0071] Figure 6 shows three patterns of h' ideal This figure shows an example of the estimated impulse response, the frequency response calculated from the impulse response, and the received signal points actually observed by the modulation analyzer for h'. Note that for convenience of graphical display, only the amplitude components of the impulse response and frequency response are shown, but as mentioned above, the estimation is performed including the phase. From Figure 6, h' ideal ,h' PR ,h' coh There is a good agreement between the three patterns. The average MSE characteristics of these three patterns are MSE(h' PR )=2.2×10 -3 ,MSE(h' coh )=3.5×10 -3 In principle, coherent reception has superior sensitivity compared to direct detection, so although the modulation analyzer is more accurate than the SP-IQM, the SP-IQM can achieve sufficient estimation accuracy with its simple configuration. ideal It is calculated based on h' ideal does not include the IQ disparity in the actual experimental system, while h' cohIt should be noted that the MSE characteristics have a certain error floor because it includes not only the IQ modulator but also the IQ imbalance in the coherent receiver.

[0072] Next, Figure 7 shows h' ideal This figure shows the MSE characteristics for each trial when generating 20 independent and random trials. Although there is variation in the estimation accuracy due to the difference in the degree of IQ imbalance for each trial, the average MSE characteristics are MSE(h' PR )=8.2×10 -3 ,MSE(h' coh )=1.2×10 -2 In terms of average performance, the SP-IQM outperformed the modulation analyzer. As shown in F. Horlin and A. Bourdoux, Digital compensation for analog front-ends: A new approach to wireless transceiver design (John Wiley & Sons, 2008), IQ imbalance is known to have a negative effect on the accuracy of CFO compensation in coherent reception. In the random trials, the accuracy of CFO compensation in the modulation analyzer decreased in the characteristic samples, which resulted in a decrease in the accuracy of estimating the imbalance parameters.

[0073] As a result, the SP-IQM of the present invention can estimate the impulse response of at least the I channel and Q channel of the optical IQ modulator (here, these are estimated collectively as h'), including the phase response, and can estimate the frequency dependence of the intensity and phase shift between the channels (h - ) can be evaluated. [Industrial Applicability]

[0074] The present invention can be used, for example, in the information and communications industry. [Explanation of symbols]

[0075] 1. Optical quadrature amplitude modulator characterization system 3 Photodetector (PD) 5 Analog-to-Digital Converter 11 Imbalance operation section 13 Input signal information receiving section 15 Strength information receiving unit 17 Phase recovery calculation section 19 Imbalance coefficient calculation section

Claims

1. 1. A system for estimating electro-optical response imbalance between an I (in-phase) channel and a Q (quadrature-phase) channel of an optical quadrature amplitude modulator (optical IQ modulator), comprising: a photodetector (PD) for measuring an intensity component of a first output signal from an optical IQ modulator when a first modulated signal is input to the optical IQ modulator; an analog-to-digital converter (ADC) for converting the intensity component of the first output signal received by the photodetector (PD) into a digital signal to obtain intensity information of the digitized output signal; an imbalance calculation unit for estimating an imbalance in electrical-optical response between an I channel and a Q channel of the optical IQ modulator, an input signal information receiver for receiving information regarding a first modulated signal; an intensity information receiving unit that receives intensity information of the digitized output signal from the ADC; using information about a first modulated signal and intensity information of the digitized output signal to estimate an imbalance in electrical-optical response between an I channel and a Q channel of the optical IQ modulator; A system having The information about the first modulated signal is information (s(t)) about the time change of the intensity and phase of the first modulated signal, The imbalance in electrical-optical response between the I channel and the Q channel of the optical IQ modulator is The impulse response and frequency response of the I and Q channels of the optical IQ modulator; The frequency dependence of the phase shift of the electro-optical responses of the I and Q channels of the optical IQ modulator; Frequency dependence of the intensity shift of the electro-optical response of the I-channel and Q-channel of the optical IQ modulator; DC bias components of the I channel and Q channel of the optical IQ modulator; and A parameter related to one or more imbalances in the frequency dependence of nonlinear distortion of the I channel and the Q channel of the optical IQ modulator, The imbalance calculation unit includes: Based on the information (s(t)) on the first modulated signal, the intensity information (|E(t)| ２ a phase recovery calculation unit that performs a phase recovery calculation to recover phase information of the output signal from the an imbalance coefficient calculation unit that calculates a parameter of the imbalance from the phase-recovered output signal (E(t)) and information about a first modulated signal (s(t)); Further comprising: An imbalance coefficient calculation unit calculates an imbalance coefficient for the phase-recovered output signal (E(t)) obtained by the phase recovery calculation unit, thereby estimating an imbalance in the electrical-optical response between the I channel and the Q channel of the optical IQ modulator. system.

2. 1. A method for estimating electro-optical response imbalance between an I (in-phase) channel and a Q (quadrature-phase) channel of an optical quadrature amplitude modulator (optical IQ modulator), comprising: inputting a first modulated signal into an optical IQ modulator; a step of IQ modulating the optical signal input to the optical IQ modulator based on a first modulation signal by the optical IQ modulator, and outputting a first output signal; a photodetector (PD) receiving the first output signal and measuring an intensity component of the first output signal; An analog-to-digital converter (ADC) converts the intensity component of the first output signal measured by the photodetector (PD) into a digital signal to obtain intensity information of the digitized output signal; an imbalance estimator receiving information relating to a first modulated signal; the imbalance estimator receiving magnitude information of the digitized output signal from the ADC; said imbalance estimator estimating an imbalance in electrical-optical response between an I channel and a Q channel of said optical IQ modulator using information about a first modulated signal and intensity information of said digitized output signal; A method comprising: The imbalance in electrical-optical response between the I channel and the Q channel of the optical IQ modulator is The impulse response and frequency response of the I and Q channels of the optical IQ modulator; The frequency dependence of the phase shift of the electro-optical responses of the I and Q channels of the optical IQ modulator; Frequency dependence of the intensity shift of the electro-optical response of the I-channel and Q-channel of the optical IQ modulator; The frequency dependence of the DC bias components of the I channel and Q channel of the optical IQ modulator; and A parameter related to one or more imbalances in the frequency dependence of nonlinear distortion of the I channel and the Q channel of the optical IQ modulator, estimating an imbalance in electrical-optical response between an I channel and a Q channel of the optical IQ modulator, Based on the information (s(t)) on the first modulated signal, the intensity information (|E(t)| ２ performing a phase recovery operation to recover phase information of the output signal from the calculating a parameter of said imbalance from said phase recovered output signal (E(t)) and information about a first modulated signal (s(t)); Including, method.

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