JP2006340115A - Waveform deterioration compensation method and apparatus - Google Patents

Abstract

【Task】
Compensation for waveform deterioration of an optical signal whose waveform is degraded depending on the frequency by propagating through the optical transmission line without measuring the dispersion value or converting to the frequency domain.
[Solution]
In order to minimize the time waveform error between the reference waveform corresponding to the modulation signal and the output waveform detected from the modulated wave, the time waveform error is directly used to adjust the compensation characteristic of the waveform deterioration compensation means in the frequency domain. Control. Preferably, the waveform deterioration compensation means is a variable dispersion compensator, and the control of the compensation characteristic is to optimize the control variable of the group delay characteristic. The optimization of the control variable of the waveform deterioration compensation unit is preferably performed by an optimization unit using a gradient.
[Selection]
FIG.

Description

The present invention relates to a waveform deterioration compensation method and apparatus, and more particularly, to a method and apparatus for compensating for waveform deterioration of a modulated wave whose waveform has deteriorated by propagating through a transmission line. In the present invention, in one preferred aspect, the modulated wave is an optical signal modulated by a modulation signal, and the waveform compensating means according to the present invention propagates through an optical transmission line to degrade the waveform depending on the frequency. The optical signal is compensated for deterioration of the optical signal.

In optical communication, chromatic dispersion is one of the factors that give an upper limit to the communication distance and speed. As shown in FIG. 1, chromatic dispersion is a phenomenon in which the speed varies depending on the wavelength of light propagating through a medium. As a result, there is a problem in optical communication that if the light is transmitted over a certain distance, the waveform is distorted and the bit error rate (BER) increases.

This method of compensating for chromatic dispersion is roughly realized by inserting a fiber with a group delay characteristic opposite to that of single mode fiber (SMF), which is currently called dispersion compensation fiber (DCF), into the communication path. ing. However, in all-optical routing, which is expected to be realized in the near future, the transmission route changes from time to time, so it is necessary to perform adaptive dispersion compensation.

Some tunable dispersion compensation devices use FBG, MEMS, or the like. There is a possibility that dispersion compensation can be adaptively performed using this. As one of the methods, there is a method in which the dispersion value of the transmission line is measured by a method such as a phase shift method, and the characteristic of the compensation device is controlled to have the opposite value. However, this control method has a problem that it takes cost and time to accurately measure the dispersion value.

In addition, a method has been proposed in which a waveform of a received signal is Fourier transformed and compensated using an error in the frequency domain (Patent Documents 1 and 2). However, in this case, a computational cost is required for sufficiently accurate Fourier transform. Furthermore, since the Fourier transform spectrum of the waveform is not necessarily directly linked to the original spectrum of the signal light, various devices are required to actually operate effectively.
JP-A-2002-261692 JP2004-80701

An object of the present invention is to perform waveform degradation compensation of a modulated wave whose waveform is degraded depending on the frequency by propagating through a transmission line without measuring a dispersion value or converting to a frequency domain.

In order to solve this object, the first technical means adopted by the present invention compensates the waveform degradation of the modulated wave whose waveform is degraded depending on the frequency by propagating through the transmission line by using the waveform degradation compensation unit. Compensation of the waveform degradation compensation means using the time waveform error directly so that the time waveform error between the reference waveform corresponding to the modulation signal and the output waveform detected from the modulated wave is minimized. The characteristic is controlled in the frequency domain.

The second technical means adopted by the present invention is a waveform degradation compensation device, which compensates the waveform of the modulated wave whose waveform is degraded depending on the frequency by propagating through the transmission line. Means for acquiring an output waveform detected from the modulated wave, means for storing a reference waveform corresponding to the modulation signal, and control means for controlling the compensation characteristic of the waveform deterioration compensation means, The control means controls the compensation characteristic of the waveform deterioration compensation means in the frequency domain by directly using the time waveform error so that the time waveform error between the reference waveform and the output waveform is minimized. It is.

The feature of the present invention is that “in order to correct a deterioration phenomenon with high frequency dependency (and therefore, correction work normally performed in the frequency domain) is performed using the data in the time domain as it is”. The physical means of compensation is also operation in the frequency domain, but it is not necessary to convert to frequency data for compensation. In the present invention, in one preferred aspect, the modulated wave is an optical signal modulated by a modulation signal, and the transmission path is an optical transmission path. However, the wave and transmission path in the present invention are not limited to light and optical transmission path, and the present invention relates to waveform degradation when various waves such as electric signals, radio waves, X-rays, ultrasonic waves, and sound waves propagate through the transmission path. It can be widely used for compensation.

In one aspect, the control of the compensation characteristic of the waveform degradation compensation means is to optimize the control variable of the waveform degradation compensation means. Optimizing control variables to control compensation characteristics is advantageous for adaptive waveform degradation compensation. In one preferred embodiment, the waveform deterioration compensation means is a variable dispersion compensator, and the control of the compensation characteristic is to optimize a control variable of the group delay characteristic. For example, as a cause of waveform deterioration of an optical signal propagating through an optical transmission line, dispersion, simple attenuation, nonlinear effect, etc. can be considered, but in the case of high-speed communication, the influence of dispersion is generally considered to be dominant. . However, the waveform deterioration compensating means in the present invention is not limited to the dispersion compensating means, and waveform deterioration based on causes other than dispersion may be compensated.

In one preferred embodiment, the optimization of the control variable is performed by an optimization means using a gradient. As the optimization means using the gradient, the steepest descent method is preferably exemplified, but other means such as a conjugate gradient method may be used.

In one aspect, the waveform degradation compensation device is a component of a receiver in an optical transmission system. In another aspect, the waveform deterioration compensation device is a component of a repeater in an optical transmission system.

As the tunable dispersion compensator of the present invention, any device can be used as long as the relationship between the control variable and the group delay is basically known. Specifically, FBG (including chirped-FBG), MEMS (Micro Electro Mechanical Systems) (such as moving a small mirror), VIPA dispersion compensator (using a curved mirror), ring resonator Examples thereof include those used, those using a spatial light modulator and a prism, and the like.

The time waveform error between the reference waveform and the output waveform corresponding to the modulation signal is defined by the norm of the difference between the two time waveforms, and is a square norm in the preferred example. In the time waveform error calculation processing, the output waveform function is a function that represents the output waveform as a function of time, and is a function that represents the output waveform itself, and an outline of the output waveform based on the sampling value of the output waveform. Contains functions. In one aspect, the time waveform error calculation process uses a difference between a finite number of sampled values. That is, the difference between the value obtained by sampling the output waveform (finite number, 3 or 5 points per pulse) and the time value (finite number) corresponding to the ideal waveform (reference waveform) is evaluated. In another aspect, the time waveform error is obtained using the waveform as it is. In that case, the reference waveform is also actually generated by the pulse generator, and is subtracted or squared in analog.

The waveform deterioration compensation according to the present invention directly uses a time waveform error and does not require measurement of a dispersion value or conversion to a frequency domain, so that a reduction in system cost can be expected. In addition, since the present invention does not require measurement of the dispersion value or conversion to the frequency domain, high-speed dispersion compensation is possible, which is advantageous for adaptive dispersion compensation. Furthermore, in the present dispersion compensation system, even higher-order dispersion of the second or higher order, which is difficult to compensate at high speed, can be compensated in a short time in principle.

A preferred embodiment of the present invention will be described. First, a transmission system as a premise of the present invention will be described. The transmission system includes a transmitter, a receiver, and a transmission path that connects the transmitter and the receiver. An input waveform is given to the transmitter as a modulation signal. A reference waveform f _ref corresponding to the modulation signal is acquired. When the modulated wave is a light wave, the reference waveform is an electrical signal obtained when the light wave modulated by the input waveform (modulated wave) is received by a light receiving element such as a photodiode after transmission through an optical fiber of 0 km. Generally, it is different from the modulation signal. The waveform of the modulated wave sent out from the transmitter is called a transmission waveform. The transmission waveform reaches the receiver after propagating through the transmission line, and the waveform is called a reception waveform. In the receiver, the received light wave passes through a compensator, is detected by a photodiode, and outputs an output waveform f _out . The output waveform is an electrical signal. Here, only the information of the reference waveform and output waveform (output waveform detected from the modulated wave) is directly used, and the waveform is obtained by optimizing the group delay characteristics of the tunable dispersion compensator using the steepest descent method. A method for compensating for the waveform deterioration of the deteriorated optical signal will be described. And the effectiveness is confirmed by a simulation experiment.

[A] Dispersion compensation using the steepest descent method that directly uses the time waveform error [A-1] Direct use chromatic dispersion of the time waveform error is a phenomenon in the frequency domain in which the speed of propagation through the medium differs depending on the wavelength of light. It is. Therefore, in many cases, information in the frequency domain obtained by Fourier transforming a waveform in the time domain is used for the compensation. However, in the current optical communication, only information in the time domain is necessary for information transmission, and it can be said that obtaining information in the frequency domain is an additional work.

と定義し、この値が最小になるように、簡単な近似（誤差関数の偏微分を求める際に、たとえば補償デバイスが持つ特性を、扱いやすい形の曲線で近似することが例示される）を用いて、最急降下法を利用することにより、可変分散補償器を制御する。 Therefore, a method for adaptively controlling the tunable dispersion compensator from only the waveform in the time domain without performing Fourier transform is proposed. Specifically, in the time domain, the time waveform error Er is _calculated from the reference waveform f _ref which is the output waveform when not affected by the actual output waveform f _out and the dispersion of the transmission path.

In order to minimize this value, a simple approximation (when the partial derivative of the error function is obtained, for example, the characteristic of the compensation device is approximated with a curve that is easy to handle) is exemplified. And use the steepest descent method to control the tunable dispersion compensator.

2 and 3 are schematic diagrams of the adaptive variable dispersion compensation system. The coefficient (control variable) of the group delay characteristic of the tunable dispersion compensator is adaptively updated using the steepest descent method. The optical signal modulated by the modulation signal input to the optical modulator is propagated for a certain distance incident on the optical fiber, and its waveform is deteriorated due to the influence of dispersion. The deteriorated signal is output after being compensated for dispersion by the variable dispersion compensator. The optical signal output from the dispersion compensator is converted into an electric signal by the optical detector. At this time, the dispersion compensation control variable is repeatedly updated by the tunable dispersion compensator, and the received optical signal is dispersion compensated. However, the modulation signal, which is the input signal here, is information on the waveform of the bit representing “1” or “0” used in actual transmission. At the receiving end, the modulation signal is the input signal to the optical modulator. The corresponding reference waveform is known. When it is assumed that the transmission path has only the influence of dispersion and the compensation object is only dispersion, it is considered that the output waveform when not affected by dispersion = reference waveform f _ref . The information to be transmitted is a combination of "1" or "0" and does not follow the waveform of each bit, so compensation work is not required in the operating state without the need for a pilot signal. Can be done.

As shown in FIG. 3, the present invention is characterized in that frequency domain compensation is performed without directly converting time domain errors into frequency domains. In the present invention, since there is no need for Fourier transform or direct measurement of dispersion value, it is possible to construct a high-speed and low-cost adaptive dispersion compensation system. At that time, in the present invention, it is necessary to obtain the relationship between the control variable and the control characteristic of the tunable dispersion compensator. However, as shown in the experiment, it is only necessary to obtain the rough tendency, so that compensation can be realized only by simple calculation by approximation. Furthermore, high-speed control can be expected even for devices that require multivariable control that is required to compensate for higher-order dispersion, which is expected to increase as communication speed increases.

[A-2] Steepest Descent Method (SD Method) is one of methods for determining a minimum point in a certain function as shown in FIG. This method can find a local minimum point in a relatively fast and stable manner compared to a full search or a mountain climbing method. Therefore, it plays an important role in many learning methods and adaptive systems including neural networks.

次に、傾きの計算のためにEr (x₁,x₂,…,x_N)をx_iについて偏微分し、

g₁,g₂,…,g_Nを得る。この値を利用して(x₁,x₂,…,x_N)の値をeが適当な十分小さい定数として、

と更新する。ここで、この更新によってEr (x₁,x₂,…,x_N)が増加したり、大きく変化したりしなくなるまで以上の過程を繰り返し行い、極小値を決定する。 In the steepest descent algorithm, an initial value is appropriately given, a direction in which a function value is reduced is determined with reference to the gradient of the function, and calculation is repeatedly performed based on a local search. This algorithm can also be extended to multivariable cases. When a certain multivariable function is Er (x ₁ , x ₂ ,..., X _N ), an initial value is given appropriately.

Next, Er (x ₁ , x ₂ , ..., x _N ) is partially differentiated with respect to x _i for the calculation of the slope,

g ₁ , g ₂ , ..., g _N are obtained. Using this value, let (x ₁ , x ₂ , ..., x _N ) be a constant that is small enough for e to be

And update. Here, the above process is repeated until Er (x ₁ , x ₂ ,..., X _N ) does not increase or change significantly by this update, and the minimum value is determined.

In this method, there is a problem that the convergence value changes depending on how the initial value is obtained in a function having a plurality of minimum values as shown in FIG. This may be a serious problem when considering the minimum value of a function by the gradient method. However, the minimum value can be obtained with a certain high probability by appropriately setting e.

Using this algorithm, the optimal compensation profile can be found more quickly and adaptively than the full search or downhill method by obtaining the minimum value of the time waveform error Er shown in Eq. (1). It becomes possible.

[A-3] Adaptive Dispersion Compensation System FIG. 5 shows a schematic diagram of an adaptive dispersion compensation system using the steepest descent method that directly uses the time waveform error according to the present invention. An optical communication system to which an adaptive dispersion compensation system is applied includes a transmitter 1 and a transmitter 2 each including a semiconductor laser and an optical modulator, and an optical transmission path 1 through which an optical signal emitted from the optical transmitter 1 propagates. (Route 1), an optical transmission path 2 (route 2) through which the optical signal emitted from the transmitter 2 propagates, an EDFA (erbium-added amplifier) provided in each transmission path, the optical transmission path 1 and the light An OXC (optical cross-connect device) that connects the transmission path 2 and a receiving device that receives an optical signal transmitted via the OXC are included. The receiving device includes a variable dispersion compensator that compensates for waveform deterioration of an optical signal transmitted via OXC, a light receiving element including a photodiode, and an amplifier circuit. The dispersion compensation is performed by the variable dispersion compensator. The optical signal thus converted is converted into an electric signal by the light receiving element (detection), and is amplified by an amplifier circuit to become an output signal. The output signal is sent to a demodulation circuit (determination circuit), and a bit of “1” or “0” is generated. (In reality, many receiving paths and many OXCs are intricately complicated, and the receiving device receives signals that have passed through various paths that change from moment to moment.)

The transmission waveform modulated by the optical modulator passes through one route arbitrarily selected from a plurality of routes (two routes are shown in FIG. 5) as a modulated optical signal. Affected by dispersion. This deteriorated signal enters the variable dispersion compensator, is dispersion compensated, is detected, and becomes an output signal. The compensation characteristic of the tunable dispersion compensator is the time waveform error Er obtained from the output waveform f _out and the reference waveform f _ref that is stored in advance and is not affected by the dispersion of the transmission path. Is controlled using the steepest descent method so that is minimized. At this time, since the selected route is sequentially changed, the control of the tunable dispersion compensator is repeatedly performed.

これは、信号をサンプリングして、その差の2乗の和を計算したA,B,C,D,Eの関数である。この値が小さくなるように最急降下法によってA,B,C,D,Eを決定することにより、適応的な分散補償が可能となる。
(iii) 傾きの計算
Erを可変分散補償器の制御変数で偏微分する。

ここで、基準波形f_refの半値幅をT₀,出力波形f_outの最大値をMとしたとき、出力信号f_outの偏微分は、

と近似できる。ただし、Tは時間、cは光速である。また、同様の方法で他の制御変数B,C,D,Eについても計算できる。
(iv) 制御変数の更新
式（９）にしたがって、制御変数を更新する。

ただし、eは十分に小さい正の値とする。
(v) 判定
値の更新によってErが、大きく変化しなくなったら、そのときのA,B,C,D,Eが最適な制御変数となる。それ以外の場合には(ii)に戻り、同様のプロセスを繰り返す。また、分散状況が時々刻々と変化するような場合には、繰り返しを続ける。 When the group delay characteristic of the tunable dispersion compensator is t (l) and this tunable dispersion compensator has five control variables A to E, a specific procedure by the steepest descent method is shown below.
(i) Setting the initial value of the tunable dispersion compensator
Set (A, B, C, D, E) = (A ₀ , B ₀ , C ₀ , D ₀ , E ₀ ), and set the initial value to an appropriate value. In one aspect, the initial value is set to zero.
(ii) Time waveform error calculation
Calculate Er according to equation (1). In the adaptive dispersion compensation system, when the time waveform of the received current pulse of the reference signal and output waveform is f _ref (t) and f _out (t, A, B, C, D, E), one pulse In the case of performing digital processing by sampling at time t _i (i = 1, 2,...), An error function E is first obtained as follows.

This is a function of A, B, C, D, E that samples the signal and calculates the sum of the squares of the differences. By determining A, B, C, D, and E by the steepest descent method so that this value becomes small, adaptive dispersion compensation can be performed.
(iii) Inclination calculation
Er is partially differentiated with the control variable of the variable dispersion compensator.

Here, when the half width of the reference waveform f _ref is T ₀ and the maximum value of the output waveform f _out is M, the partial differentiation of the output signal f _out is

Can be approximated. Where T is time and c is the speed of light. In addition, other control variables B, C, D, and E can be calculated in the same manner.
(iv) The control variable is updated according to the control variable update formula (9).

However, e is a sufficiently small positive value.
(v) If Er does not change significantly by updating the judgment value, A, B, C, D, and E at that time become optimal control variables. Otherwise, return to (ii) and repeat the same process. Moreover, when the dispersion state changes from moment to moment, the repetition is continued.

[B] Verification by simulation [B-1] Conditions for the simulation In order to confirm the effectiveness of the proposed adaptive dispersion compensation method, a numerical simulation was performed. In this simulation, in order to simplify the problem, the influence of the optical signal due to the transmission is only dispersion, and other effects such as self-phase modulation are not considered. In addition, it was assumed that the change in amplitude due to loss was recovered by an optical amplifier or AGC (Auto Gain Control).

The input waveform was a Gaussian waveform as shown in FIG. 6, and the center wavelength was 1550 [nm]. The transmission rate was verified for 10 [Gb / s] and 40 [Gb / s]. For the transmission line, SMF and dispersion shifted fiber (DSF) having dispersion characteristics as shown in FIG. 7 were considered.

一方、分散補償デバイスの特性もこれと類似に表されるものとし、式（１０）で表し、補償変数A,B,C,D,Eを最適化によって求める。尚、FBGやMEMS等を利用した一般の可変分散補償器を使用する場合は、そのデバイスの補償変数を(10)式の変数に変換することにより、本方法を有効に利用することが可能である。ここで、 A,B,C,D,Eの初期値は全て0とした。また、基準波形は、図６に示したガウス波形である。 [B-2] The group delay characteristic of a simulated optical fiber using a five-term Selmeier equation is expressed by equation (10) by a five-term Selmeier equation that is a general approximate equation. Specific A, B, C, D, and E are determined depending on the type and length of the fiber.

On the other hand, it is assumed that the characteristics of the dispersion compensation device are also expressed in a similar manner, and are expressed by Expression (10), and compensation variables A, B, C, D, and E are obtained by optimization. When using a general tunable dispersion compensator using FBG, MEMS, etc., it is possible to effectively use this method by converting the compensation variable of the device into the variable of equation (10). is there. Here, the initial values of A, B, C, D, and E are all 0. The reference waveform is the Gaussian waveform shown in FIG.

8 and 9 show the results of the simulation experiment. FIG. 8 shows the result when SMF is transmitted at 100 [km] at a transmission rate of 10 [Gb / s], and FIG. 9 shows the result when DSF is transmitted at 50 [km] at a transmission rate of 40 [Gb / s]. is there. From the above results, assuming that the group delay characteristic of the tunable dispersion compensator is a five-term celmayer type, that is, a variable compensator with no dispersion value limitation, adaptive dispersion compensation is possible by using the present invention. It shows that there is. At this time, the calculation times from this extreme initial value were 0.188 [s] and 0.156 [s], confirming that high-speed compensation was achieved.

The present invention can be used in a high-speed optical fiber communication network system, particularly in a metro network in which transmission paths frequently change.

It is a figure which shows the dispersion characteristic of an optical fiber. It is a schematic diagram of an adaptive variable dispersion compensation system. It is a schematic diagram of an adaptive variable dispersion compensation system. It is a schematic diagram of the steepest descent method. It is a figure which shows the adaptive dispersion compensation system using the steepest descent method. It is a figure which shows a reference | standard waveform. It is a figure which shows the dispersion | distribution characteristic of SMF and DSF. It is a figure which shows the transmission simulation result of 10 [Gb / s], SMF, and 100 [km]. It is a figure which shows the transmission simulation result of 40 [Gb / s], DSF, and 50 [km].

Claims (14)

A modulated wave whose waveform has deteriorated depending on the frequency by propagating through a transmission line is a method of compensating for the waveform deterioration using a waveform deterioration compensation means,
In order to minimize the time waveform error between the reference waveform corresponding to the modulation signal and the output waveform detected from the modulated wave, the time waveform error is directly used to adjust the compensation characteristic of the waveform deterioration compensation means in the frequency domain. A waveform deterioration compensation method characterized by controlling. The waveform degradation compensation method according to claim 1, wherein the modulated wave is an optical signal modulated by a modulation signal, and the transmission path is an optical transmission path. The waveform degradation compensation method according to claim 1, wherein the control of the compensation characteristic of the waveform degradation compensation unit is to optimize a control variable of the waveform degradation compensation unit. The waveform degradation compensation method according to claim 1, wherein the waveform degradation compensation unit is a tunable dispersion compensator, and the control of the compensation characteristic is to optimize a control variable of a group delay characteristic. 5. The waveform deterioration compensation method according to claim 3, wherein the optimization of the control variable of the waveform deterioration compensation unit is performed by an optimization unit using a gradient. 6. The waveform deterioration compensation method according to claim 5, wherein the optimization means using the gradient is a steepest descent method. Waveform degradation compensation means for compensating the waveform of the modulated wave whose waveform is degraded depending on the frequency by propagating through the transmission line;
Means for obtaining an output waveform detected from the modulated wave;
Means for storing a reference waveform corresponding to the modulation signal;
Control means for controlling the compensation characteristics of the waveform deterioration compensation means,
The control means controls the compensation characteristic of the waveform deterioration compensation means in the frequency domain by directly using the time waveform error so that the time waveform error between the reference waveform and the output waveform is minimized. Waveform deterioration compensation device. The waveform degradation compensation device according to claim 7, wherein the modulated wave is an optical signal modulated by a modulation signal, and the transmission path is an optical transmission path. 9. The waveform deterioration compensation device according to claim 7, wherein the control of the compensation characteristic of the waveform deterioration compensation means is to optimize a control variable of the waveform deterioration compensation means. 10. The waveform degradation compensation device according to claim 7, wherein the waveform degradation compensation means is a tunable dispersion compensator, and the compensation characteristic is controlled by optimizing a control variable of a group delay characteristic. The waveform deterioration compensating apparatus according to claim 9, wherein the control unit includes an optimization unit using a gradient. The waveform deterioration compensation apparatus according to claim 11, wherein the optimization means using the gradient is a steepest descent method. The waveform degradation compensation apparatus according to claim 7, wherein the waveform degradation compensation apparatus is a component of a receiver in an optical transmission system. The waveform degradation compensation device according to claim 7, wherein the waveform degradation compensation device is a component of a repeater in an optical transmission system.

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