CN106130643A - A kind of high speed optical communication system electrical dispersion compensation method - Google Patents

Abstract

The invention discloses a kind of high speed optical communication system electrical dispersion compensation method, first carry out the excitation feedback arrangement net structure of phase place multi thresholds according to leggy modulation optical communication system model；Then designed phase multi thresholds excitation function provide the relation of decay factor and flex point in designed phase place multi thresholds excitation function, and illustrate method for solving；And then design brand-new energy function and be used to refer to wire guide network back-to-back running；When finally performing, network only need to not stop feedback until energy function value minimum then exits circulates.Present invention is generally directed to the dispersion compensation occasion that the modulation system that optical communication system used is single modulus value leggy, regardless of whether modulation system constellation point is the most sparse or intensive, the method all can be suitable for.

Description

A kind of high speed optical communication system electrical dispersion compensation method

Technical field

The present invention relates to optic communication coherent signal detection field, particularly a kind of high speed optical communication system electrical dispersion compensation side Method, the modulation system used mainly for optical communication system is the dispersion compensation occasion of single modulus value leggy, regardless of whether adjust Mode constellation point processed is the most sparse or intensive, and the method all can be suitable for.

Background technology

The liftings that technology is transmission capacity such as the complication of coherent detection, modulation classification, palarization multiplexing (DP) have played important Effect.Wherein light coherent reception technology makes transmitting terminal use various dimensions multi-system while improving photoreceiver receiving sensitivity Modulation format is possibly realized, and various dimensions multi-system modulation technique can carry multiple bit information on a symbol, effectively carries Spectral efficient..Difference quadrature phase shift keying (DQPSK) modulation format obtains good application in optical transport technology.In recent years Come, the octal system difference quadrature phase shift keying (8DPSK) received much concern be then on the basis of DQPSK multi-system modulation, it 3 bit informations can be transmitted in one code-element period, there is the chip rate lower compared with DQPSK and the higher availability of frequency spectrum], can With the modulation format densification (such as 8PSK, 16QAM etc.) in anticipated optical communication system.But, Shannon theory determines system Spectrum efficiency the highest, the signal to noise ratio needed for signal error free transmission is the biggest, and excessive signal to noise ratio can directly result in light pass Defeated distance significantly shortens.From the point of view of current main flow equipment manufacturer's test result, have employed dual carrier and 16QAM modulation technique The transmission range of 400Gb/s system only has the 1/4 of 100Gb/s system, the most shorter.Industry achievement in research shows, more than 32QAM High order modulation code can only transmit hundreds of kilometer on the link of single-mode fiber (SMF)+erbium-doped fiber amplifier (EDFA).If can be right In high-speed optical transmission system, chromatic dispersion (CD) and polarization mode dispersion (PMD) carry out effective compensation, then can promote spectrum efficiency While keep signal long-distance transmission, it is possible to make the transmission cable laid in a large number can be reused and carry out System Expansion, Create conditions for following ASON and be that the development of Ultrahigh capacity Optical Fiber Communication Systems is prepared.

Electrical dispersion compensation (EDC) technology uses electronic filtering (equilibrium) technology to compensate optical dispersion, by reception Optical signal be sampled in electrical domain, software optimization and signal restoring, can effectively adjust reception signal waveform, recover due to Optical signal broadening that CD, PMD and nonlinear effect etc. cause, distortion, thus reach the effect compensated.The equilibrium of EDC/go damage Function and polarization demultiplexing function synthesized one, can realize combined optimization and eliminate polarization real-time tracking feedback control link. Additionally, due to electronic technology is ripe, it is integrated to be easy to, electronic equipment adds extremely existing optical communication system and can ensure the optical cable laid Recycling.Therefore, the research worker in optical communication system dispersion compensation field starts to direct attention to how to seek in electrical domain Preferably dispersion compensation method.The main research work of CD, PMD electrical domain comprehensive compensation concentrates on maximum-likelihood sequence estimation at present (MLSE) on method and butterfly constant modulus algorithm (CMA).In general, existing dispersion compensation method all follows the pattern of indirect compensation, In other words, need first to design two wave filter (static and dynamic), then carry out convolution algorithm and obtain output signal.So, If a kind of employing without designing wave filter can be found directly to detect (recovery) source transmission signal, then can avoid designing wave filter Redundancy, reaches the purpose that signal directly recovers.

Summary of the invention

The technical problem to be solved is, not enough for prior art, it is provided that a kind of high speed optical communication system electricity Dispersion compensation method.

For solving above-mentioned technical problem, the technical solution adopted in the present invention is: a kind of high speed optical communication system electricity dispersion Compensation method, comprises the following steps:

1) continuous multi thresholds excitation function f (x, m, θ) of structure mpsk signal:

$f(x,m,\mathrm{\θ})=\[\underset{i=1}{\overset{m}{\Σ}}\frac{2\mathrm{\θ}}{1+e^{-a(x+b_i)}}\]-m\mathrm{\θ}$

In formula: a is the attenuation quotient of cumulative item meta-function, a ＞ 0；b_iIt is the abscissa at each cumulative meta-function center,M is cumulative item sum, and m=M-1, θ=π/M is preferable mpsk signal any two Close on the phase difference value between constellation point；M represents the kind number sum of the i.e. phase place of order of modulation, M=4,8,16...；X is mpsk signal Phasing matrix；

2) one feedback arrangement network with N number of neuron of design, at the random vector s of one a length of N of t T () enters network, s (t) and weight matrix W does matrix multiple computing, then by asking phase bit arithmetic arg () to seek multiplication operation The phase place of result, obtains t mpsk signal phasing matrixAgain willReplace the x in f (x, m, θ) expression formula, obtain t The mpsk signal phasing matrix in+1 momentThen, the output signal to excitation function operatorCarry out's Computing, obtains output signal s (t+1) in t+1 moment, and this output feeds back to the input of feedback arrangement network again after postponing 1 unit End, the most repeatedly.

The solution procedure of the attenuation quotient a of cumulative item meta-function is:

1) order

2) single order of f (x), second order and three order derivative forms are tried to achieve:

$f^{\′}\left(x\right)={\{\[2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}{\mathrm{\σ}}_s(x+b_i)\]-m\mathrm{\θ}\}}^{\′}=2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}{\mathrm{\σ}}_s^{\′}(x+b_i)=2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}{\mathrm{a\σ}}_s^2(x+b_i)\·e^{-a(x+b_i)}$

$f^{\′\′}\left(x\right)=2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}{\mathrm{\σ}}_s^{\′\′}(x+b_i)=2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}\{a^2{\mathrm{\σ}}_s^3(x+b_i)e^{-2a(x+b_i)}-a^2{\mathrm{\σ}}_s^2(x+b_i)e^{-a(x+b_i)}\}$

$f^{\′\′\′}\left(x\right)=2\mathrm{\θ}\underset{i=1}{\overset{N_s}{\Σ}}{\mathrm{\σ}}_s^{\′\′\′}(x+b_i)=2\mathrm{\θ}\underset{i=1}{\overset{N_s}{\Σ}}{a}^3{\mathrm{\σ}}_s^4(x+b_i)\·e^{-a(x+b_i)}\·\left\{e^{-2a(x+b_i)}-4e^{-a(x+b_i)}+1\right\}$

3) for each value in one group of given a value, corresponding x value is calculated respectively；Observe a value and equattion root number Relation, finds minimum a value a comprising required character set_k；The most again at a_kCan not comprise that of required character set previous with it Individual a_k-1Between, take one group of interval smaller sampled point, and obtain this group sampled point corresponding x value, and determine a pair a made new advances_k And a_k-1；And so on, obtain a critical a value.

Weight matrix W=U^HU, U are to receive data matrix X (t) singular value decompositionIn the tenth of the twelve Earthly Branches Battle array, singular value matrixUnusual for obtained by after X (t) singular value decomposition Value, 0 represents null matrix, U_cRepresenting the singular value decomposition matrix corresponding with secondary series 0 matrix size, V is that singular value decomposition obtains Right unitary matrix；Q is oversample factor, L_hIt is the length of optical communication channel equivalence impulse response；Subscript H represents conjugate transpose.

Step 2) after, also include:

1) energy function E (t) of design of feedback neutral net:

Wherein,And W (j :) is the jth row vector of W battle array；By elementComposition, s_jT () is the jth element of input signal vector；The corresponding f of f (τ) (x, m, θ),_φjT () is corresponding with x；

2) Feedback Neural Network output signal s (t) is fed back to Feedback Neural Network input as Feedback Neural Network Input signal, until energy function no longer reduces, exit.

Compared with prior art, the had the beneficial effect that present invention of the present invention can be by sparse and intensive polyphase system The dispersion compensation problem of optical communication system includes Unified Algorithm framework in, it is not necessary to design static state and kinetic filter, it is possible to reach color Dissipate the purpose compensated.

Accompanying drawing explanation

Fig. 1 is that the present invention encourages Feedback Neural Network structure for the phase place multi thresholds of signal detection；

When Fig. 2 is a=40 of the present invention, 8PSK phase place multi thresholds excitation function and each rank derived function thereof；

Fig. 3 is 8PSK of the present invention, and signal to noise ratio is 20dB, the energy function curve that data length is designed when being N=500；

Fig. 4 is the graph of a relation of data frame length of the present invention and energy function value；

Fig. 5 is bit error rate (BER) curve in the case of different pieces of information frame length of the present invention, 16PSK, a=20；

Fig. 6 be the phase excitation functional form in the case of difference a value of the present invention and detecting system output signal.

Detailed description of the invention

High speed optical communication system electrical dispersion compensation method based on phase excitation feedback arrangement network, including following several steps Rapid:

(1) according to multiple phase-shift keying signal characteristic Design continuous multi thresholds excitation function

Multiple phase-shift keying (M-ary Quaternary Phase Shift Keying, MPSK), also known as polyphase system. The spectrum efficiency higher because of it and good noiseproof feature, particularly QPSK (QPSK) is at high speed optical communication system Extensively application.In order to obtain bigger transfer rate, phase-shift keying (PSK) (PSK) signal of higher order will be in following optic communication system In system widely used.But, owing to along with the increase of M value, the difference of phasetophase will reduce at double, greatly reduce system can By property, strengthen the bit error rate of receiving terminal, also can be greatly increased the difficulty of dispersion compensation.

In view of neuron as the elementary cell of neutral net, decide the scale of network, complexity and robustness. Multiple valued neuron is owing to having multiple excitation state, and that can play multiple single threshold neuron in engineer applied combines work With, the neuronal quantity of neutral net energy intensifier circuit when realizing equal function can be reduced and process the ability of information.For tool For body application, the design success or not of many-valued excitation function directly decides effectiveness and network parsimony that algorithm realizes. Due to the tradition S-type function that used of binary signal, it is continuously differentiable increasing function, and at linear and Nonlinear Traveling for it Between have preferably balance.It is contemplated that arrive their good differentiability and balance, design realizes the blind Detecting of polyphase system signal Problem, can use S-type excitation function to carry out compound splicing and obtain continuous multi thresholds S-type excitation function.Due to shaking of psk signal Width is respectively positioned on unit circle, and only phase information changes, then can write out constraints is

Y ∈ C={exp (j2 π (m-1)/M), m=1,2 ..., M} (1)

Here: y represents preferable and sends signal, and C represents ideal signal set, and exp (.) represents exponential function, and π is circumference Rate, M represents the kind number sum of the i.e. phase place of order of modulation, and j is imaginary unit.

First task is the excitation function of structure neuron, it is considered to the feature of mpsk signal, M-PSK (M can be constructed =4,8,16...) the continuous multi thresholds excitation function of signal is as follows

$f(x,m,\mathrm{\θ})=\[\underset{i=1}{\overset{m}{\Σ}}\frac{2\mathrm{\θ}}{1+e^{-a(x+b_i)}}\]-m\mathrm{\θ}---\left(2\right)$

In formula: a is the attenuation quotient of cumulative item meta-function, and a ＞ 0, its value size directly affects the flex point of excitation function Number；b_iIt is the abscissa at each cumulative meta-function center,M is cumulative item sum, M=M-1,2 θ, θ=π/M are the phase difference value that preferable mpsk signal any two closes between constellation point.This excitation function is applicable to appoint Meaning high-order mpsk signal.Pointing out, this excitation function does not exist can the inverse function form of Analytical Expression.

(2) scope of attenuation quotient a in designed phase multi thresholds excitation function is determined

Owing in multi thresholds excitation function, the scope of attenuation quotient a directly decides designed excitation function the most singly Adjust；And excitation function monotonicity directly decides neural network feedback number of times.Following task is to ask for the scope of a value.

First-selection determines asks a and the relation of flex point in formula (2), need to first seek the second order derived function (Fig. 1) of this function.Solve this letter The process of the second order derived function of number is as follows.

When m and θ fixes, it is known that (2) formula is only the function of variable x, is designated as f (x), makes meta-functionThen have:

$f\left(x\right)=\[\underset{i=1}{\overset{m}{\Σ}}\frac{2\mathrm{\θ}}{1+e^{-a(x+b_i)}}\]-m\mathrm{\θ}=2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}{\mathrm{\σ}}_s-m\mathrm{\θ}---\left(3\right)$

The single order of f (x), second order and three order derivative forms can be tried to achieve as follows:

$f^{\′}\left(x\right)={\{\[2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}{\mathrm{\σ}}_s(x+b_i)\]-m\mathrm{\θ}\}}^{\′}=2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}{\mathrm{\σ}}_s^{\′}(x+b_i)=2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}{\mathrm{a\σ}}_s^2(x+b_i)\·e^{-a(x+b_i)}---\left(4\right)$

$f^{\′\′}\left(x\right)=2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}{\mathrm{\σ}}_s^{\′\′}(x+b_i)=2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}\{a^2{\mathrm{\σ}}_s^3(x+b_i)e^{-2a(x+b_i)}-a^2{\mathrm{\σ}}_s^2(x+b_i)e^{-a(x+b_i)}\}---\left(5\right)$

$f^{\′\′\′}\left(x\right)=2\mathrm{\θ}\underset{i=1}{\overset{N_s}{\Σ}}{\mathrm{\σ}}_s^{\′\′\′}(x+b_i)=2\mathrm{\θ}\underset{i=1}{\overset{N_s}{\Σ}}{a}^3{\mathrm{\σ}}_s^4(x+b_i)\·e^{-a(x+b_i)}\·\left\{e^{-2a(x+b_i)}-4e^{-a(x+b_i)}+1\right\}---\left(6\right)$

According to mathematical knowledge, the value of a is by f with the relation of flex point " (x)=0 and f " ' (x) ≠ 0 together decides on 's.Observe its second order derived function to understand: this function is the equation of nonlinearity.The equation is by numerical solution, for one group The given each value in a value, calculates corresponding x value respectively；Observe the relation of a value and equattion root number, find needed for comprising That minimum a value (such as a of character set_k)；The most again at a_kThat a that can not comprise required character set previous with it_k-1It Between, then take one group of interval smaller sampled point, and obtain this group sampled point corresponding x value, and determine a pair a made new advances_kWith a_k-1；And so on, the critical a value of an available approximation.

(3) planned network connection weight matrix

Optical communication link receiving terminal uses fractional sampling technology thus obtains multiple signals；And assume that optical signal passes through photoelectricity Converting unit becomes analog electrical signal, and analog electrical signal is converted to digital electric signal by analog converter, and system perfection realizes Carrier phase synchronization, symbol accurate timing, Frame meets block fading characteristic.Without loss of generality, when ignoring noise, optic communication connects Receipts system receives equation, Digital Signal Processing equation can be expressed as follows

And X_N=S Γ^H, wherein, subscript H table Showing that conjugate transpose, s (t) are received signal vector, q is oversample factor, L_hIt is the length of optical communication channel equivalence impulse response, Γ=Γ_L(H_j) it is (H_j, j=0,1 ..., P) smoothing matrix of Toeplitz form that constitutes, P is equalizer length,It is the impulse response of communication channel, X (t)=[x (t) ..., x (t+N-1)]^TIt is to receive data matrix, N table Show that data length, subscript T represent transposition computing, and send signal battle array and be

Tectonic network connection weight matrix

W=U^HU (7)

Here U is to receive data matrix X (t) singular value decompositionIn unitary matrix, singular value matrixFor singular value, 0 represents null matrix, U_cRepresent big with secondary series 0 matrix The singular value decomposition matrix of little correspondence, V is the right unitary matrix that singular value decomposition obtains.

(4) structure phase place multi thresholds excitation feedback arrangement network

Owing to data length is N, then need to design a feedback arrangement network with N number of neuron, in t Network input signal enters network, does matrix multiple computing with weight matrix W, then by asking phase bit arithmetic arg () to ask it Phase place, obtains as mpsk signal phasing matrixAgain willEnter phase excitation function operators f ()；Then, excitation letter Obtaining output signal s (t+1) in t+1 moment after figuring output signal entrance exponential function exp (.) computing of son, this output is prolonged Input is fed back to again, the most repeatedly after slow 1 unit.Phase place multi thresholds excitation feedback arrangement network is shown in Fig. 2.(f () in this figure For phase excitation function operators, arg () for seeking phase bit arithmetic,For psk signal phasing matrix, s (t+1) represents that signal is defeated Go out, t express time.Wherein W is network connection weight matrix, W=U^HU, wherein: U is to receive signal matrix X_NSingular value decomposition obtains Unitary matrix, subscript H represents conjugation means computing.)

The feedback arrangement network of design, the network input signal in t enters network, does matrix phase with weight matrix W Multiplication, then seeks its phase place by arg (), obtains as psk signal phasing matrixAgain willEnter phase excitation Function operators f ()；Then, the output signal of excitation function operator obtains the t+1 moment after entering exponential function exp (.) computing Output signal s (t+1), this output postpones to feed back to after 1 unit input, the most repeatedly again.

(5) design energy function instructs network-feedback to run

Designed phase place multi thresholds excitation feedback arrangement network needs energy function to instruct whether network-feedback operation ties Bundle, otherwise network goes possibly among unlimited feedback, causes network paralysis.Ensuing task seeks to design an energy Function.

Firstly the need of the performance function and the network equilibrium condition that provide and prove network.Make t, net during network-feedback The phasing matrix of network output signal point is designated asBy elementComposition.Remember againInverse function for designed excitation function f ().

The multi thresholds excitation Feedback Neural Network being made up of N number of neuron, when weight matrix meets W=W^T, diagonal element w_ii＞- μ, here μ ＞ 0, i=1,2 ... N, thenBe designed instead The energy function of feedback neutral net.(hereAnd W (j :) is the jth row vector of W battle array.)

(6) network does not stop feedback until energy function value minimum then exits

Designed network structure is very simple, and algorithm flow is the most extremely simple, the most repeatedly by network input feedback to net Network inputs, until energy function no longer reduces.Corresponding algorithm performance is shown in Fig. 3-6.Fig. 3 gives 8PSK of the present invention, signal to noise ratio For 20dB, the energy function curve that data length is designed when being N=500；Fig. 4 gives data frame length and energy function value Graph of a relation；Fig. 5 gives bit error rate (BER) curve in the case of different pieces of information frame length, 16PSK, a=20；Fig. 6 is to be given Phase excitation functional form in the case of different a values and detecting system output signal.

Claims (4)

1. a high speed optical communication system electrical dispersion compensation method, it is characterised in that comprise the following steps:

1) continuous multi thresholds excitation function f (x, m, θ) of structure mpsk signal:

$f(x,m,\mathrm{\θ})=\[\underset{i=1}{\overset{m}{\Σ}}\frac{2\mathrm{\θ}}{1+e^{-a(x+b_i)}}\]-m\mathrm{\θ}$

In formula: a is the attenuation quotient of cumulative item meta-function, a ＞ 0；b_iIt is the abscissa at each cumulative meta-function center,M is cumulative item sum, and m=M-1, θ=π/M is preferable mpsk signal any two Close on the phase difference value between constellation point；M represents the kind number sum of the i.e. phase place of order of modulation, M=4,8,16...；X is mpsk signal Phasing matrix；

2) one feedback arrangement network with N number of neuron of design, random vector s (t) at one a length of N of t enters Entering network, s (t) and weight matrix W does matrix multiple computing, then by asking phase bit arithmetic arg () to seek multiplication operation result Phase place, obtain t mpsk signal phasing matrixAgain willReplace the x in f (x, m, θ) expression formula, when obtaining t+1 The mpsk signal phasing matrix carvedThen, the output signal to excitation function operatorCarry outFortune Calculating, obtain output signal s (t+1) in t+1 moment, this output feeds back to feedback arrangement network input after postponing 1 unit again, The most repeatedly.

High speed optical communication system electrical dispersion compensation method the most according to claim 1, it is characterised in that cumulative item meta-function The solution procedure of attenuation quotient a be:

1) order

2) single order of f (x), second order and three order derivative forms are tried to achieve:

$f^{\′}\left(x\right)={\{\[2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}{\mathrm{\σ}}_s(x+b_i)\]-m\mathrm{\θ}\}}^{\′}=2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}{\mathrm{\σ}}_s^{\′}(x+b_i)=2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}{\mathrm{a\σ}}_s^2(x+b_i)\·e^{-a(x+b_1)}$

$f^{\′\′}\left(x\right)=2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}{\mathrm{\σ}}_s^{\′\′}(x+b_i)=2\mathrm{\θ}\underset{i=1}{\overset{m}{\Σ}}\{a^2{\mathrm{\σ}}_s^3(x+b_i)e^{-2a(x+b_i)}-a^2{\mathrm{\σ}}_s^2(x+b_i)e^{-a(x+b_i)}\}$

$f^{\′\′\′}\left(x\right)=2\mathrm{\θ}\underset{i=1}{\overset{N_s}{\Σ}}{\mathrm{\σ}}_s^{\′\′\′}(x+b_i)=2\mathrm{\θ}\underset{i=1}{\overset{N_s}{\Σ}}{a}^3{\mathrm{\σ}}_s^4(x+b_i)\·e^{-a(x+b_i)}\·\{e^{-2a(x+b_i)}-4e^{-a(x+b_i)}+1\}$

3) for each value in one group of given a value, corresponding x value is calculated respectively；Observe the pass of a value and equattion root number System, finds minimum a value a comprising required character set_k；The most again at a_kCan not comprise that of required character set previous with it a_k-1Between, take one group of interval smaller sampled point, and obtain this group sampled point corresponding x value, and determine a pair a made new advances_kWith a_k-1；And so on, obtain a critical a value.

High speed optical communication system electrical dispersion compensation method the most according to claim 1, it is characterised in that weight matrix W= U^HU, U are to receive data matrix X (t) singular value decompositionIn unitary matrix, singular value matrixσ₁...,For singular value obtained after X (t) singular value decomposition, 0 represents null matrix, U_cRepresenting the singular value decomposition matrix corresponding with secondary series 0 matrix size, V is the right unitary matrix that singular value decomposition obtains；Q was to adopt Like factor, L_hIt is the length of optical communication channel equivalence impulse response；Subscript H represents conjugate transpose.

High speed optical communication system electrical dispersion compensation method the most according to claim 3, it is characterised in that step 2) after, Also include:

4) energy function E (t) of design of feedback neutral net:

Wherein,And W (j :) is the jth row vector of W battle array；By elementJ=1,2 ... N forms, s_jT () is the jth element of input signal vector；The corresponding f (x, m, θ) of f (τ), φ_jT () is corresponding with x；

5) Feedback Neural Network output signal s (t) is fed back to defeated as Feedback Neural Network of Feedback Neural Network input Enter signal, until energy function no longer reduces, exit.