CN114978342A - Optical filtering damage compensation method and system in coherent optical communication digital multi-carrier system - Google Patents
Optical filtering damage compensation method and system in coherent optical communication digital multi-carrier system Download PDFInfo
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Abstract
The invention provides a method and a system for compensating optical filtering damage in a coherent optical communication digital multi-carrier system, which comprises the following steps: step S1: mapping the communication system into a neural network, mapping the linear filter into a convolutional layer of the neural network, and mapping other modules into a static layer in the neural network; step S2: constructing a loss function aiming at a digital multi-carrier system neural network; step S3: converging the neural network through a gradient descent algorithm; step S4: extracting the coefficient of the originating convolutional layer as the coefficient of a system originating pre-equalizer, and pre-compensating the optical filtering damage; step S5: after the sending-end precompensation filter coefficient is configured, the filter coefficient of the receiving-end compensation optical filtering damage is obtained through self-adaptive convergence, and therefore compensation is carried out. The invention is easy to realize, convenient to use, low in realization complexity, free from changing the structure of the existing communication system and capable of overcoming the defects of the prior art.
Description
Technical Field
The invention relates to the technical field of optical filtering damage compensation in a coherent optical communication system, in particular to an optical filtering damage compensation method and system in a coherent optical communication digital multi-carrier system.
Background
Reconfigurable optical add-drop multiplexers (ROADMs) are important optical devices in flexible optical networks, which use WSS to implement both upper and lower service wavelengths. Due to the limited bandwidth of WSS, the optical filtering of the system is impaired, resulting in inter-symbol interference (ISI). Because the size of the filtering damage is in direct proportion to the number of the WSSs, the number of the WSSs is more and more along with the increasing flexibility of the optical network, and the optical filtering damage caused by the WSSs is more and more serious. Meanwhile, as the baud rate and the spectral efficiency of the optical communication system are higher and higher, the carrier guard interval between adjacent channels is continuously reduced, which further aggravates the optical filtering damage introduced by the WSS, so that the optical filtering damage becomes a non-negligible factor affecting the transmission rate.
Patent document CN105827321A (application number: CN201510003764.0) discloses a nonlinear compensation method, apparatus and system in a multi-carrier optical communication system, the method comprising: determining coefficients of a linear filter in nonlinear compensation according to the end-to-end channel linear response of the system; determining taps of the nonlinear compensation filter to be opened and coefficients of the taps according to the hardware compensation capacity of the system and the coefficients of the linear filter; and compensating the nonlinear damage of the system by using the selected coefficient of the nonlinear compensation filter.
At present, the optical filtering damage of a compensation system is mainly the scheme that the spectrum of a pre-equalizer at a transmitting end is scanned through the performance of a receiving end, the scheme is high in complexity and difficult to apply in practice. In addition, the method for deriving the originating pre-equalization expression based on theory is also a scheme, and can obtain certain gain, but the scheme ignores the influence of noise, and has a larger optimization space in performance.
An optimization scheme based on a neural network is an effective scheme for compensating optical filtering damage, and has been verified in a single carrier system before. In a single carrier system, Minimum Mean Square Error (MMSE) can be directly used as a loss function of a neural network in the single carrier system since MMSE and BER are in a one-to-one relationship. However, in the multi-carrier system, the neural network needs to be redesigned to find a new loss function.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method and a system for compensating optical filtering damage in a coherent optical communication digital multi-carrier system.
The optical filtering damage compensation method in the coherent optical communication digital multi-carrier system provided by the invention comprises the following steps:
step S1: mapping the communication system into a neural network, mapping the linear filter into a convolutional layer of the neural network, and mapping other modules into a static layer in the neural network;
step S2: constructing a loss function aiming at a digital multi-carrier system neural network;
step S3: converging the neural network through a gradient descent algorithm;
step S4: extracting the coefficient of the originating convolutional layer as the coefficient of a system originating pre-equalizer, and pre-compensating the optical filtering damage;
step S5: after the sending-end precompensation filter coefficient is configured, the filter coefficient of the receiving-end compensation optical filtering damage is obtained through self-adaptive convergence, and therefore compensation is carried out.
Preferably, for a linear filter, the input is expressed as:
x(n)＝x r (n)+jx i (n)
the linear filter coefficients are expressed as:
h(n)＝h r (n)+jh i (n)
the linear filter output is expressed as:
y(n)＝x(n)*h(n)＝y r (n)+jy i (n)
wherein, y r [n]And y i [n]Expressed as:
y r (n)＝x r (n)*h r (n)-x i (n)*h i (n)
y i (n)＝x r (n)*h i (n)+x i (n)*h r (n)
wherein denotes a convolution operation; x is the number of r (n) represents an in-phase signal in the input signal of the linear filter; n represents the time instant during the discrete random process; j represents an imaginary part; x is the number of i (n) represents the quadrature signal in the linear filter input signal; h is r (n) represents the real part of the linear filter tap coefficients; h is i (n) represents an imaginary part of a tap coefficient of the linear filter; y is r (n) denotes a linear filterA real part in the output signal; y is i (n) represents the imaginary part of the linear filter output signal.
Preferably, for neural network convolutional layers, the expression is:
wherein the input dimension and the output dimension are (N, C) respectively in L) and (N, C) out ，L out ) N is the batch size, C is the number of channels, L is the length of the signal, as the cross-correlation operation; i. j represents the ith batch, the jth output channel;
representing a neural network bias;
representing the number of output channels; k represents the kth input channel;
representing neural network weights.
Preferably, the number of input channels is set to 2, the number of output channels is set to 1, the offset is set to 0, and the convolutional layer input is set to [ x ] 1 (n)，x 2 (n)]Convolution layer weight is [ h 1 (n)，h 2 (n)]Then the output is expressed as:
y＝x 1 (n)⊙h 1 (n)+x 2 (n)⊙h 2 (n)
＝x 1 (n)*h 1 (-n)+x 2 (n)*h 2 (-n)
when the input is [ x ] r (n)；-x i (n)]When the output is y r When the input is [ x ] i (n)；x r (n)]When the output is y i 。
Preferably, for a parameter related to the bit error probability BER and no hard decision exists in the calculation, the generalized mutual information GMI is selected as a neural network loss function, and the calculation formula is as follows:
the first part in the GMI formula represents the information entropy of the signal point of the sending end; the second part in the GMI formula represents the measurement of the influence of channel noise on the information transmission rate; n represents the number of signal points; m is the number of bits required for representing each QAM signal point; b k，i The value of the ith bit corresponding to the kth signal point of the sending end is represented; x, y k Respectively representing signals of a sending end and a receiving end; 2 sigma 2 The average power of complex Gaussian noise in a channel;
respectively representing a set of signal points of which the ith bit of a sending end is 0 or 1; p X (x) Is the probability of the corresponding signal point,
the optical filtering damage compensation system in the coherent optical communication digital multi-carrier system provided by the invention comprises:
module M1: mapping the communication system into a neural network, mapping the linear filter into a convolutional layer of the neural network, and mapping other modules into a static layer in the neural network;
module M2: constructing a loss function aiming at a digital multi-carrier system neural network;
module M3: converging the neural network through a gradient descent algorithm;
module M4: extracting the coefficient of the originating convolutional layer as the coefficient of a system originating pre-equalizer, and pre-compensating the optical filtering damage;
module M5: after the sending end precompensation filter coefficient is configured, the filter coefficient of the receiving end compensation optical filtering damage is obtained through self-adaptive convergence, and therefore compensation is carried out.
Preferably, for a linear filter, the input is represented as:
x(n)＝x r (n)+jx i (n)
the linear filter coefficients are expressed as:
h(n)＝h r (n)+jh i (n)
the linear filter output is expressed as:
y(n)＝x(n)*h(n)＝y r (n)+jy i (n)
wherein, y r [n]And y i [n]Expressed as:
y r (n)＝x r (n)*h r (n)-x i (n)*h i (n)
y i (n)＝x r (n)*h i (n)+x i (n)*h r (n)
wherein denotes a convolution operation; x is the number of r (n) represents an in-phase signal in the input signal of the linear filter; n represents the time of the discrete random process; j represents an imaginary part; x is the number of i (n) represents the quadrature signal in the linear filter input signal; h is r (n) represents the real part of the linear filter tap coefficients; h is i (n) represents the imaginary part of the linear filter tap coefficients; y is r (n) represents the real part of the output signal of the linear filter; y is i (n) represents the imaginary part of the linear filter output signal.
Preferably, for neural network convolutional layers, it is expressed as:
wherein the input dimension and the output dimension are (N, C) respectively in L) and (N, C) out ，L out ) N is the batch size, C is the number of channels, L is the length of the signal, as the cross-correlation operation; i. j represents the ith batch, the jth output channel;
representing nervesNetwork biasing;
representing the number of output channels; k represents the kth input channel;
representing neural network weights.
Preferably, the number of input channels is set to 2, the number of output channels is set to 1, the offset is set to 0, and the convolutional layer input is set to [ x ] 1 (n)，x 2 (n)]Convolution layer weight is [ h 1 (n)，h 2 (n)]Then the output is expressed as:
y＝x 1 (n)⊙h 1 (n)+x 2 (n)⊙h 2 (n)
＝x 1 (n)*h 1 (-n)+x 2 (n)*h 2 (-n)
when the input is [ x ] r (n)；-x i (n)]When the output is y r When the input is [ x ] i (n)；x r (n)]When the output is y i 。
Preferably, for a parameter related to the bit error probability BER and no hard decision exists in the calculation, the generalized mutual information GMI is selected as a neural network loss function, and the calculation formula is as follows:
the first part in the GMI formula represents the information entropy of the signal point of the transmitting end; the second part in the GMI formula represents the measurement of the influence of channel noise on the information transmission rate; n represents the number of signal points; m is the number of bits required for representing each QAM signal point; b is a mixture of k，i The value of the ith bit corresponding to the kth signal point of the sending end is represented; x, y k Respectively representing signals of a sending end and a receiving end; 2 sigma 2 For complex Gaussian noise in channelsThe average power of the sound;
respectively representing a set of signal points of which the ith bit of a sending end is 0 or 1; px (x) is the probability of the corresponding signal point,
compared with the prior art, the invention has the following beneficial effects:
the invention provides a method for compensating optical filtering damage of a digital multi-carrier system based on communication system and neural network mapping, which relates to the field of coherent optical communication application and has the capability of compensating the optical filtering damage of the digital multi-carrier system; the invention designs a neural network structure and a loss function by utilizing the corresponding relation between a communication system and a neural network, and obtains an optimal receiving and transmitting combined equilibrium coefficient by optimizing the neural network; the invention is easy to realize, convenient to use, low in realization complexity, free from changing the structure of the existing communication system and capable of overcoming the defects of the prior art.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a schematic diagram of an equivalent neural network applied to an optical filtering damage compensation scheme of a digital multi-carrier system;
fig. 2 is a schematic diagram of the originating signal processing applied to the optical filtering damage compensation scheme of the digital multi-carrier system according to the present invention;
fig. 3 is a schematic diagram of the originating signal processing applied to the optical filtering impairment compensation scheme of the digital multi-carrier system according to the present invention.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
Example (b):
as shown in fig. 1, the present invention provides a method for compensating optical filtering impairments of a digital multi-carrier system based on a communication system and neural network mapping, which includes:
mapping the communication system into a neural network, using other modules as static layers in the neural network, and searching the corresponding relation between a linear filter in the communication system and a convolutional layer in the neural network.
For a linear filter, assume the input is x (n) ═ x r (n)+jx i (n) filter coefficients h (n) h r (n)+jh i (n), then the filter output can be expressed as:
y(n)＝x(n)*h(n)＝y r (n)+jy i (n)…………(1a)
y r (n)＝x r (n)*h r (n)-x i (n)*h i (n)…………(1b)
y i (n)＝x r (n)*h i (n)+x i (n)*h r (n)…………(1c)
where denotes a convolution operation.
For neural network convolutional layers, it can be expressed as:
wherein the input dimension and the output dimension can be (N, C) respectively in L) and (N, C) out ，L out ). N is the batch size, C is the number of channels, L is the length of the signal, as an interrelating operation.
Consider the number of input channels to be 2, the number of output channels to be 1, and the offset to be 0. Let the convolution layer input be [ x ] 1 (n)，x 2 (n)]Convolution layer weight is [ h 1 (n)，h 2 (n)]. The output substituted into equation (2a) can be expressed as:
y＝x 1 (n)⊙h 1 (n)+x 2 (n)⊙h 2 (n)
＝x 1 (n)*h 1 (-n)+x 2 (n)*h 2 (-n)…………(1a)
comparing with formula (1b) and formula (1c), when the input is [ x ] r (n)；-x i (n)]When the output is y r When the input is [ x ] i (n)；x r (n)]When the output is y i I.e., a complex linear filter can be mapped to convolutional layers in a neural network.
For the neural network loss function, since the loss function needs to be related to the bit error probability (BER), the overall performance cannot be guaranteed to be optimal by using the minimum mean square error as the loss function. However, in the step of calculating BER, a decision-taking step is required, which is not conducive, i.e., BER cannot be directly used as a loss function of the neural network.
For parameters related to BER, and for which no hard decision step exists in the calculating step, Generalized Mutual Information (GMI) may be chosen as the neural network loss function. The GMI calculation formula is as follows:
wherein, the first part of formula (4a) represents the information entropy of the signal point at the transmitting end, the second part measures the influence of the channel noise on the information transmission rate, N represents the number of signal points, m represents the number of bits required by each QAM signal point, b k，i A value (0 or 1) of an ith bit corresponding to a kth signal point of the transmitting end is represented; in the formula (4b), x, y k Representing transmit and receive signals, 2 sigma, respectively 2 Is the average power of the complex gaussian noise in the channel,
set of signal points respectively representing ith bit of 0 or 1 at transmitting end，P X (x) Which is the probability of the corresponding signal point, for uniform,
for updating neural network parameters, Adam optimization scheme is used. Adam optimization is a stochastic gradient descent algorithm based on first and second moment estimates.
Since the convergence process of the adaptive filter in the digital signal module at the receiving end of the communication system is also based on the gradient descent algorithm, the second convolution layer of the mapped neural network has the same updating process as the adaptive filter. After the neural network converges, we only need to extract the first convolutional layer coefficient of the neural network as the pre-equalization coefficient of the communication system.
The method for compensating the optical filtering damage needs the joint compensation of the transmitting end and the receiving end. The structure of the present invention applied to the transmission end compensation is shown in fig. 2. It can be seen that, in this case, the module at the transmitting end mainly includes:
a bit mapping module, configured to map a bit sequence to be transmitted into a quadrature amplitude modulation symbol;
the pulse forming module is used for forming the symbol root raised cosine pulse to generate a signal;
the subcarrier multiplexing module is used for aggregating different digital subcarriers to form a signal;
the linear damage compensation module is used for pre-compensating the filtering damage in the system at the transmitting end;
the structure of the compensation system applied to the receiving end of the present invention is shown in fig. 3. It can be seen that, at this time, the modules at the receiving end mainly include:
the dispersion compensation module is used for compensating dispersion accumulated by the optical fiber in the transmission process;
the frequency offset compensation module is used for estimating the frequency offset of the signal and compensating the frequency offset;
a subcarrier demultiplexing module for separating the subcarriers from a signal;
the self-adaptive equalization module is used for equalizing the signal by the minimum mean square error equalizer;
the carrier phase recovery module is used for tracking the phase noise of the symbol and recovering the phase of the symbol;
a digital demodulation module for demapping the symbols into a bit sequence.
The optical filtering damage compensation system in the coherent optical communication digital multi-carrier system provided by the invention comprises: module M1: mapping the communication system into a neural network, mapping the linear filter into a convolutional layer of the neural network, and mapping other modules into a static layer in the neural network; module M2: constructing a loss function aiming at a digital multi-carrier system neural network; module M3: converging the neural network through a gradient descent algorithm; module M4: extracting the coefficient of the originating convolutional layer as the coefficient of a system originating pre-equalizer, and pre-compensating the optical filtering damage; module M5: after the sending-end precompensation filter coefficient is configured, the filter coefficient of the receiving-end compensation optical filtering damage is obtained through self-adaptive convergence.
For a linear filter, the input is represented as: x (n) ═ x r (n)+jx i (n)
The linear filter coefficients are expressed as: h (n) ═ h r (n)+jh i (n)
The linear filter output is expressed as: y (n) ═ x (n) ═ h (n) ═ y r (n)+jy i (n)
Wherein, y r [n]And y i [n]Expressed as: y is r (n)＝x r (n)*h r (n)-x i (n)*h i (n)
y i (n)＝x r (n)*h i (n)+x i (n)*h r (n)
Wherein denotes a convolution operation; x is the number of r (n) represents an in-phase signal in the input signal of the linear filter; n represents the time of the discrete random process; j represents an imaginary part; x is the number of i (n) represents the quadrature signal in the input signal of the linear filter; h is r (n) represents the real part of the linear filter tap coefficients; h is i (n) represents the imaginary part of the linear filter tap coefficients; y is r (n) represents the real part of the output signal of the linear filter; y is i (n) represents the linear filter outputAnd (4) outputting an imaginary part in the signal.
For neural network convolutional layers, it is expressed as:
wherein the input dimension and the output dimension are (N, C) respectively in L) and (N, C) out ，L out ) N is the batch size, C is the number of channels, L is the length of the signal, as the cross-correlation operation; i. j represents the ith batch, the jth output channel;
representing a neural network bias;
representing the number of output channels; k represents the kth input channel;
representing neural network weights.
Setting the number of input channels as 2, the number of output channels as 1, the bias as 0, the input of convolution layer as [ x ] 1 (n)，x 2 (n)]Convolution layer weight is [ h 1 (n)，h 2 (n)]Then the output is expressed as:
y＝x 1 (n)⊙h 1 (n)+x 2 (n)⊙h 2 (n)
＝x 1 (n)*h 1 (-n)+x 2 (n)*h 2 (-n)
when the input is [ x ] r (n)；-x i (n)]When the output is y r When the input is [ x ] i (n)；x r (n)]When the output is y i 。
For parameters related to bit error probability BER and no hard decision exists in calculation, selecting generalized mutual information GMI as a neural network loss function, wherein the calculation formula is as follows:
the first part in the GMI formula represents the information entropy of the signal point of the sending end; the second part in the GMI formula represents the measurement of the influence of channel noise on the information transmission rate; n represents the number of signal points; m is the number of bits required for representing each QAM signal point; b k，i The value of the ith bit corresponding to the kth signal point of the sending end is represented; x, y k Respectively representing signals of a sending end and a receiving end; 2 sigma 2 The average power of complex Gaussian noise in a channel;
respectively representing a set of signal points of which the ith bit of a sending end is 0 or 1; p X (x) Is the probability of the corresponding signal point,
those skilled in the art will appreciate that, in addition to implementing the systems, apparatus, and various modules thereof provided by the present invention in purely computer readable program code, the same procedures can be implemented entirely by logically programming method steps such that the systems, apparatus, and various modules thereof are provided in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Therefore, the system, the device and the modules thereof provided by the present invention can be considered as a hardware component, and the modules included in the system, the device and the modules thereof for implementing various programs can also be considered as structures in the hardware component; modules for performing various functions may also be considered to be both software programs for performing the methods and structures within hardware components.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.
Claims (10)
1. An optical filtering damage compensation method in a coherent optical communication digital multi-carrier system is characterized by comprising the following steps:
step S1: mapping the communication system into a neural network, mapping the linear filter into a convolutional layer of the neural network, and mapping other modules into a static layer in the neural network;
step S2: constructing a loss function aiming at a digital multi-carrier system neural network;
step S3: converging the neural network through a gradient descent algorithm;
step S4: extracting the coefficient of the originating convolutional layer as the coefficient of a system originating pre-equalizer, and pre-compensating the optical filtering damage;
step S5: after the sending-end precompensation filter coefficient is configured, the filter coefficient of the receiving-end compensation optical filtering damage is obtained through self-adaptive convergence, and therefore compensation is carried out.
2. The optical filtering impairment compensation method in a digital multi-carrier system for coherent optical communications according to claim 1, wherein for the linear filter, the input is represented as:
x(n)＝x r (n)+jx i (n)
the linear filter coefficients are expressed as:
h(n)＝h r (n)+jh i (n)
the linear filter output is expressed as:
y(n)＝x(n)*h(n)＝y r (n)+jy i (n)
wherein, y r [n]And y i [n]Expressed as:
y r (n)＝x r (n)*h r (n)-x i (n)*h i (n)
y i (n)＝x r (n)*h i (n)+x i (n)*h r (n)
wherein denotes a convolution operation; x is the number of r (n) represents an in-phase signal in the input signal of the linear filter; n represents the time of the discrete random process; j represents an imaginary part; x is the number of i (n) represents the quadrature signal in the linear filter input signal; h is r (n) represents the real part of the linear filter tap coefficients; h is a total of i (n) represents an imaginary part of a tap coefficient of the linear filter; y is r (n) represents the real part of the output signal of the linear filter; y is i (n) represents the imaginary part of the linear filter output signal.
3. The optical filtering damage compensation method in the coherent optical communication digital multi-carrier system according to claim 2, wherein for the neural network convolution layer, the following expression is given:
wherein the input dimension and the output dimension are (N, C) respectively in L) and (N, C) out ，L out ) N is the batch size, C is the number of channels, L is the length of the signal, and I is the cross-correlation operation; i. j represents the ith batch, the jth output channel;
representing a neural network bias;
representing the number of output channels; k represents the kth input channel;
representing neural network weights.
4. The optical filtering damage compensation method in coherent optical communication digital multi-carrier system according to claim 3, wherein the number of input channels is set to 2, the number of output channels is set to 1, the offset is set to 0,the convolutional layer input is [ x ] 1 (n)，x 2 (n)]Convolution layer weight is [ h 1 (n)，h 2 (n)]Then the output is expressed as:
y＝x 1 (n)⊙h 1 (n)+x 2 (n)⊙h 2 (n)
＝x 1 (n)*h 1 (-n)+x 2 (n)*h 2 (-n)
when the input is [ x ] r (n)；-x i (n)]When the output is y r When the input is [ x ] i (n)；x r (n)]When the output is y i 。
5. The optical filtering damage compensation method in the digital multi-carrier system for coherent optical communication according to claim 4, wherein for the parameter related to the bit error probability BER and no hard decision exists in the calculation, the generalized mutual information GMI is selected as the neural network loss function, and the calculation formula is:
the first part in the GMI formula represents the information entropy of the signal point of the sending end; the second part in the GMI formula represents the measurement of the influence of channel noise on the information transmission rate; n represents the number of signal points; m is the number of bits required for representing each QAM signal point; b is a mixture of k，i The value of the ith bit corresponding to the kth signal point of the sending end is represented; x, y k Respectively representing signals of a transmitting end and a receiving end; 2 sigma 2 The average power of complex Gaussian noise in a channel;
respectively representing a set of signal points of which the ith bit of a sending end is 0 or 1; p X (x) Is the probability of the corresponding signal point,
6. an optical filtering damage compensation system in a coherent optical communication digital multi-carrier system, comprising:
module M1: mapping the communication system into a neural network, mapping the linear filter into a convolutional layer of the neural network, and mapping other modules into a static layer in the neural network;
module M2: constructing a loss function aiming at a digital multi-carrier system neural network;
module M3: converging the neural network through a gradient descent algorithm;
module M4: extracting the coefficient of the originating convolutional layer as the coefficient of a system originating pre-equalizer, and pre-compensating the optical filtering damage;
module M5: after the sending end precompensation filter coefficient is configured, the filter coefficient of the receiving end compensation optical filtering damage is obtained through self-adaptive convergence, and therefore compensation is carried out.
7. The optical filter impairment compensation system of claim 6, wherein for a linear filter, the inputs are expressed as:
x(n)＝x r (n)+jx i (n)
the linear filter coefficients are expressed as:
h(n)＝h r (n)+jh i (n)
the linear filter output is expressed as:
y(n)＝x(n)*h(n)＝y r (n)+jy i (n)
wherein, y r [n]And y i [n]Expressed as:
y r (n)＝x r (n)*h r (n)-x i (n)*h i (n)
y i (n)＝x r (n)*h i (n)+x i (n)*h r (n)
wherein, tablePerforming convolution operation; x is the number of r (n) represents an in-phase signal in the input signal of the linear filter; n represents the time instant during the discrete random process; j represents an imaginary part; x is a radical of a fluorine atom i (n) represents the quadrature signal in the linear filter input signal; h is r (n) represents the real part of the linear filter tap coefficients; h is i (n) represents the imaginary part of the linear filter tap coefficients; y is r (n) represents the real part of the output signal of the linear filter; y is i (n) represents the imaginary part of the linear filter output signal.
8. The optical filter damage compensation system in a coherent optical communication digital multi-carrier system according to claim 7, wherein for the neural network convolutional layer, the following is expressed:
wherein the input dimension and the output dimension are (N, C) respectively in L) and (N, C) out ，L out ) N is the batch size, C is the number of channels, L is the length of the signal, as the cross-correlation operation; i. j represents the ith batch, the jth output channel;
representing a neural network bias;
representing the number of output channels; k represents the kth input channel;
representing neural network weights.
9. The system of claim 8, wherein the number of input channels is 2, the number of output channels is 1, the offset is 0, and the convolutional layer input is [ x [ ] 1 (n)，x 2 (n)]Convolution layer weight is [ h 1 (n)，h 2 (n)]Then the output is expressed as:
y＝x 1 (n)⊙h 1 (n)+x 2 (n)⊙h 2 (n)
＝x 1 (n)*h 1 (-n)+x 2 (n)*h 2 (-n)
when the input is [ x ] r (n)；-x i (n)]When the output is y r When the input is [ x ] i (n)；x r (n)]When the output is y i 。
10. The optical filter impairment compensation system of claim 9, wherein for parameters related to bit error probability BER and no hard decision exists in the calculation, the generalized mutual information GMI is selected as the neural network loss function, and the calculation formula is:
the first part in the GMI formula represents the information entropy of the signal point of the transmitting end; the second part in the GMI formula represents the measurement of the influence of channel noise on the information transmission rate; n represents the number of signal points; m is the number of bits required for representing each QAM signal point; b k，i The value of the ith bit corresponding to the kth signal point of the sending end is represented; x, y k Respectively representing signals of a sending end and a receiving end; 2 sigma 2 The average power of complex Gaussian noise in a channel;
respectively representing a set of signal points of which the ith bit of a sending end is 0 or 1; p X (x) Is the probability of the corresponding signal point,
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