CN114978342B - 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 application provides a method and a system for compensating optical filtering damage in a coherent optical communication digital multi-carrier system, comprising the following steps: step S1: mapping the communication system into a neural network, mapping the linear filter into a convolution 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 neural network of the digital multi-carrier system; step S3: converging the neural network through a gradient descent algorithm; step S4: extracting an originating convolution layer coefficient as a coefficient of a system originating pre-equalizer, and pre-compensating optical filtering damage; step S5: after the pre-compensation filter coefficient of the transmitting end is configured, the filter coefficient of the damage of the optical filtering of the receiving end is obtained through self-adaptive convergence, so that compensation is performed. The application is easy to realize, convenient to use, low in realization complexity, does not need to change the structure of the existing communication system, and can overcome the defects of the prior art.
Description
Technical Field
The application 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 an optical filtering damage compensation 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 that use WSSs to implement both up and down traffic wavelengths. Due to the limited bandwidth of WSS, optical filtering impairments of the system can result, leading to inter-symbol interference (ISI). Since the size of the filtering damage is proportional to the number of the WSS, as the optical network becomes more flexible, the number of the WSS becomes more and more, and the optical filtering damage caused by the WSS becomes more and more serious. Meanwhile, as the baud rate and the spectrum efficiency of the optical communication system are higher and higher, the carrier protection interval between adjacent channels is continuously reduced, which further aggravates the optical filtering damage introduced by the WSS and makes the optical filtering damage a non-negligible factor affecting the transmission rate.
Patent document CN105827321a (application number: CN 201510003764.0) discloses a nonlinear compensation method, apparatus and system in a multicarrier optical communication system, the method comprising: determining coefficients of a linear filter in nonlinear compensation according to an end-to-end channel linear response of the system; determining taps of the nonlinear compensation filter to be opened and coefficients of all the taps according to the hardware compensation capability of the system and the coefficients of the linear filter; and compensating the nonlinear damage of the system by using the coefficients of the selected nonlinear compensation filter.
At present, the optical filtering damage of the compensation system mainly comprises a scheme for scanning the frequency spectrum of the pre-equalizer at the transmitting end through the performance of the receiving end, and the scheme has higher complexity and is difficult to apply in practice. In addition, deriving the originating pre-equalization expression based on theory is also a scheme, a certain gain can be obtained, however, the influence of noise is ignored in the scheme, and a larger optimization space is provided in the aspect of performance.
The neural network-based optimization scheme is an effective scheme for compensating the optical filtering impairments, and has been previously verified in a single carrier system. In a single carrier system, since Minimum Mean Square Error (MMSE) and BER are in a one-to-one relationship, MMSE can be directly used as a loss function of a neural network in the single carrier system. In a multi-carrier system, however, 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 application aims to provide an optical filtering damage compensation method and an optical filtering damage compensation system 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 application comprises the following steps:
step S1: mapping the communication system into a neural network, mapping the linear filter into a convolution 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 neural network of the digital multi-carrier system;
step S3: converging the neural network through a gradient descent algorithm;
step S4: extracting an originating convolution layer coefficient as a coefficient of a system originating pre-equalizer, and pre-compensating optical filtering damage;
step S5: after the pre-compensation filter coefficient of the transmitting end is configured, the filter coefficient of the damage of the optical filtering of the receiving end is obtained through self-adaptive convergence, so that compensation is performed.
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 is 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, represents convolution operation; x is x r (n) represents an in-phase signal in the linear filter input signal; n represents the time instant in the discrete random process; j represents an imaginary part; x is x i (n) represents a quadrature signal in the linear filter input signal; h is a r (n) represents the real part of the tap coefficients of the linear filter; h is a i (n) represents an imaginary part of tap coefficients of the linear filter; y is r (n) represents the real part of the linear filter output signal; y is i (n) represents an imaginary part of the output signal of the linear filter.
Preferably, for the neural network convolutional layer, expressed as:
wherein the input dimension and the output dimension are (N, C) in L) and (N, C) out ，L out ) N is the batch size, C is the channel number, L is the length of the signal, and the allgather is the cross-correlation operation; i. j represents the ith batch and the jth output channel;representing 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 convolution layer input is [ x ] 1 (n)，x 2 (n)]The convolution layer weight is [ h ] 1 (n)，h 2 (n)]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)]At the time, the output is y r When the input is [ x ] i (n)；x r (n)]At the time, the output is y i 。
Preferably, for parameters related to bit error probability BER, and no hard decision exists in the calculation, generalized mutual information GMI is selected as a neural network loss function, and the calculation formula is:
the first part in the GMI formula represents the information entropy of a signal point of a transmitting end; the second part of the GMI formula represents a measure of the effect of channel noise on the information transmission rate; n represents the number of signal points; m is the number of bits required to represent each QAM signal point; b k，i Represents the kth signal point pair of the transmitting endThe value of the corresponding ith bit; x, y k Respectively representing signals of a transmitting end and a receiving end; 2 sigma 2 Average power for complex gaussian noise in the channel;respectively representing a set of signal points with the ith bit of 0 or 1 at a transmitting end; p (P) X (x) Probability for the corresponding signal point, +.>
The application provides an optical filtering damage compensation system in a coherent optical communication digital multi-carrier system, which comprises:
module M1: mapping the communication system into a neural network, mapping the linear filter into a convolution 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 neural network of the digital multi-carrier system;
module M3: converging the neural network through a gradient descent algorithm;
module M4: extracting an originating convolution layer coefficient as a coefficient of a system originating pre-equalizer, and pre-compensating optical filtering damage;
module M5: after the pre-compensation filter coefficient of the transmitting end is configured, the filter coefficient of the damage of the optical filtering of the receiving end is obtained through self-adaptive convergence, so that compensation is performed.
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 is 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, represents convolution operation; x is x r (n) represents an in-phase signal in the linear filter input signal; n represents the time instant in the discrete random process; j represents an imaginary part; x is x i (n) represents a quadrature signal in the linear filter input signal; h is a r (n) represents the real part of the tap coefficients of the linear filter; h is a i (n) represents an imaginary part of tap coefficients of the linear filter; y is r (n) represents the real part of the linear filter output signal; y is i (n) represents an imaginary part of the output signal of the linear filter.
Preferably, for the neural network convolutional layer, expressed as:
wherein the input dimension and the output dimension are (N, C) in L) and (N, C) out ，L out ) N is the batch size, C is the channel number, L is the length of the signal, and the allgather is the cross-correlation operation; i. j represents the ith batch and the jth output channel;representing 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 convolution layer input is [ x ] 1 (n)，x 2 (n)]The convolution layer weight is [ h ] 1 (n)，h 2 (n)]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)]At the time, the output is y r When the input is [ x ] i (n)；x r (n)]At the time, the output is y i 。
Preferably, for parameters related to bit error probability BER, and no hard decision exists in the calculation, generalized mutual information GMI is selected as a neural network loss function, and the calculation formula is:
the first part in the GMI formula represents the information entropy of a signal point of a transmitting end; the second part of the GMI formula represents a measure of the effect of channel noise on the information transmission rate; n represents the number of signal points; m is the number of bits required to represent each QAM signal point; b k，i A value representing an ith bit corresponding to a kth signal point of the transmitting end; x, y k Respectively representing signals of a transmitting end and a receiving end; 2 sigma 2 Average power for complex gaussian noise in the channel;respectively representing a set of signal points with the ith bit of 0 or 1 at a transmitting end; p (P) X (x) Probability for the corresponding signal point, +.>
Compared with the prior art, the application has the following beneficial effects:
the application provides a digital multi-carrier system optical filtering damage compensation method based on a communication system and a neural network mapping, which relates to the field of coherent optical communication application and has the capability of compensating the digital multi-carrier system optical filtering damage; the application designs the neural network structure and the loss function by utilizing the corresponding relation between the communication system and the neural network, and obtains the optimal receiving and transmitting joint equalization coefficient by optimizing the neural network; the application is easy to realize, convenient to use, low in realization complexity, does not need to change the structure of the existing communication system, and can overcome the defects of the prior art.
Drawings
Other features, objects and advantages of the present application will become more apparent upon reading of the detailed description of non-limiting embodiments, given with reference to the accompanying drawings in which:
FIG. 1 is a schematic diagram of an equivalent neural network of the optical filtering impairment compensation scheme of the present application applied to a digital multi-carrier system;
FIG. 2 is a schematic diagram of the processing of an originating signal applied to an optical filtering impairment compensation scheme for a digital multi-carrier system according to the present application;
fig. 3 is a schematic diagram of the processing of an originating signal applied to an optical filtering impairment compensation scheme of a digital multi-carrier system according to the present application.
Detailed Description
The present application will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the present application, but are not intended to limit the application in any way. It should be noted that variations and modifications could be made by those skilled in the art without departing from the inventive concept. These are all within the scope of the present application.
Examples:
as shown in fig. 1, the present application proposes a method for compensating optical filtering impairment of a digital multi-carrier system based on a communication system and a neural network mapping, comprising:
mapping the communication system into a neural network, taking other modules as static layers in the neural network, and searching the corresponding relation between a linear filter in the communication system and a convolution layer in the neural network.
For a linear filter, assume the input is x (n) =x r (n)+jx i (n), the filter coefficient is h (n) =h r (n)+jh i (n), 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 x represents the convolution operation.
For a neural network convolutional layer, it can be expressed as:
wherein the input dimension and the output dimension may be (N, C, respectively in L) and (N, C) out ,L out ). N is the batch size, C is the channel number, L is the length of the signal, and the allgather is the cross-correlation operation.
Consider that the number of input channels is 2, the number of output channels is 1, and the offset is 0. Let the convolutional layer input be [ x ] 1 (n),x 2 (n)]The convolution layer weight is [ h ] 1 (n),h 2 (n)]. Substituting into equation (2 a) the output 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)
as compared with the formulas (1 b) and (1 c), when the input is [ x ] r (n)；-x i (n)]At the time, the output is y r When the input is [ x ] i (n)；x r (n)]At the time, the output is y i I.e. complex linear filters can be mapped to convolutional layers in a neural network.
For the neural network loss function, the minimum mean square error is used as the loss function, so that the overall performance cannot be guaranteed to be optimal because the loss function needs to be related to the bit error probability (BER). However, in the BER calculation step, a decision-making step is required, which is not conductive, i.e., BER cannot be directly used as a loss function of the neural network.
For parameters related to BER and no hard decision step in the calculation step, generalized Mutual Information (GMI) may be chosen as a neural network loss function. The GMI calculation formula is:
wherein, the first part of the formula (4 a) represents the information entropy of the signal point of the transmitting end, the second part measures the influence of the channel noise on the information transmission rate, N represents the number of the signal points, m represents the number of bits needed by each QAM signal point, b k，i A value (0 or 1) representing the ith bit corresponding to the kth signal point of the transmitting end; in formula (4 b), x, y k Representing the signal at the transmitting end and the signal at the receiving end respectively, 2σ 2 Is the average power of the complex gaussian noise in the channel,representing the set of signal points with the ith bit of 0 or 1 at the transmitting end, P X (x) For the probability of the corresponding signal point, for uniform +.>
For updating the neural network parameters, adam optimization scheme is used. Adam optimization is a stochastic gradient descent algorithm based on first and second moment estimates.
Because the adaptive filter convergence process in the receiving end digital signal module of the communication system is also based on a gradient descent algorithm, the second convolution layer of the mapped neural network is the same as the adaptive filter updating process. After the neural network converges, only the first convolution layer coefficient of the neural network is extracted to be used as a pre-equalization coefficient of the communication system.
The method for compensating the optical filtering damage requires the transceiver to jointly compensate. The structure of the application applied to the transmitting end compensation is shown in fig. 2. It can be seen that the module at the transmitting end at this time mainly comprises:
a bit mapping module, configured to map a bit sequence to be sent into a quadrature amplitude modulation symbol;
the pulse shaping module is used for shaping 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 filtering damage in the system at the originating end;
the structure of the application applied to the receiving end compensation system is shown in fig. 3. It can be seen that the modules at the receiving end at this time mainly include:
the dispersion compensation module is used for compensating the accumulated dispersion of 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 subcarriers from a signal;
the self-adaptive equalization module is used for equalizing signals by the minimum mean square error equalizer;
the carrier phase recovery module is used for tracking the phase noise of the symbol and carrying out phase recovery on the symbol;
and the digital demodulation module is used for demapping the symbols into bit sequences.
The application provides an optical filtering damage compensation system in a coherent optical communication digital multi-carrier system, which comprises: module M1: mapping the communication system into a neural network, mapping the linear filter into a convolution 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 neural network of the digital multi-carrier system; module M3: converging the neural network through a gradient descent algorithm; module M4: extracting an originating convolution layer coefficient as a coefficient of a system originating pre-equalizer, and pre-compensating optical filtering damage; module M5: after the pre-compensation filter coefficient of the transmitting end is configured, the filter coefficient of the damage of the optical filtering of the receiving end is obtained through self-adaptive convergence.
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 is 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, represents convolution operation; x is x r (n) represents an in-phase signal in the linear filter input signal; n represents the time instant in the discrete random process; j represents an imaginary part; x is x i (n) represents a quadrature signal in the linear filter input signal; h is a r (n) represents the real part of the tap coefficients of the linear filter; h is a i (n) represents an imaginary part of tap coefficients of the linear filter; y is r (n) represents the real part of the linear filter output signal; y is i (n) represents an imaginary part of the output signal of the linear filter.
For the neural network convolutional layer, expressed as:
wherein the input dimension and the output dimension are (N, C) 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 signalDegree, as indicated by the term "cross-correlation; i. j represents the ith batch and the jth output channel;representing 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, offset as 0, and the input of convolution layer as [ x ] 1 (n)，x 2 (n)]The convolution layer weight is [ h ] 1 (n)，h 2 (n)]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)]At the time, the output is y r When the input is [ x ] i (n)；x r (n)]At the time, the output is y i 。
For parameters related to bit error probability BER, and no hard decision exists in the calculation, 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 a signal point of a transmitting end; the second part of the GMI formula represents a measure of the effect of channel noise on the information transmission rate; n represents the number of signal points; m represents each QThe number of bits required for the AM signal point; b k，i A value representing an ith bit corresponding to a kth signal point of the transmitting end; x, y k Respectively representing signals of a transmitting end and a receiving end; 2 sigma 2 Average power for complex gaussian noise in the channel;respectively representing a set of signal points with the ith bit of 0 or 1 at a transmitting end; p (P) X (x) Probability for the corresponding signal point, +.>
Those skilled in the art will appreciate that the systems, apparatus, and their respective modules provided herein may be implemented entirely by logic programming of method steps such that the systems, apparatus, and their respective modules are implemented as logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers, etc., in addition to the systems, apparatus, and their respective modules being implemented as pure computer readable program code. Therefore, the system, the apparatus, and the respective modules thereof provided by the present application may be regarded as one hardware component, and the modules included therein for implementing various programs may also be regarded as structures within the hardware component; modules for implementing various functions may also be regarded as being either software programs for implementing the methods or structures within hardware components.
The foregoing describes specific embodiments of the present application. It is to be understood that the application is not limited to the particular embodiments described above, and that various changes or modifications may be made by those skilled in the art within the scope of the appended claims without affecting the spirit of the application. The embodiments of the application and the features of the embodiments may be combined with each other arbitrarily without conflict.
Claims (2)
1. The optical filtering damage compensation method in the 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 convolution 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 neural network of the digital multi-carrier system;
step S3: converging the neural network through a gradient descent algorithm;
step S4: extracting an originating convolution layer coefficient as a coefficient of a system originating pre-equalizer, and pre-compensating optical filtering damage;
step S5: after the pre-compensation filter coefficient of the transmitting end is configured, the filter coefficient of the damage of the optical filtering of the receiving end is obtained through self-adaptive convergence, so that compensation is performed;
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 is 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, represents convolution operation; x is x r (n) represents an in-phase signal in the linear filter input signal; n represents the time instant in the discrete random process; j represents an imaginary part; x is x i (n) represents a quadrature signal in the linear filter input signal; h is a r (n) represents the real part of the tap coefficients of the linear filter; h is a i (n) represents an imaginary part of tap coefficients of the linear filter; y is r (n) represents the real part of the linear filter output signal; y is i (n) represents an imaginary part in the linear filter output signal;
for the neural network convolutional layer, expressed as:
wherein the input dimension and the output dimension are (N, C) in L) and (N, C) out ，L out ) N is the batch size, C is the channel number, L is the length of the signal, and the allgather is the cross-correlation operation; i. j represents the ith batch and the jth output channel;representing 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, offset as 0, and the input of convolution layer as [ x ] 1 (n)，x 2 (n)]The convolution layer weight is [ h ] 1 (n)，h 2 (n)]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)]At the time, the output is y r When the input is [ x ] i (n)；x r (n)]At the time, the output is y i ；
For parameters related to bit error probability BER, and no hard decision exists in the calculation, 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 a signal point of a transmitting end; the second part of the GMI formula represents a measure of the effect of channel noise on the information transmission rate; n represents the number of signal points; m is the number of bits required to represent each QAM signal point; b k，i A value representing an ith bit corresponding to a kth signal point of the transmitting end; x, y k Respectively representing signals of a transmitting end and a receiving end; 2 sigma 2 Average power for complex gaussian noise in the channel;respectively representing a set of signal points with the ith bit of 0 or 1 at a transmitting end; p (P) X (x) Probability for the corresponding signal point, +.>
2. An optical filtering impairment 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 convolution 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 neural network of the digital multi-carrier system;
module M3: converging the neural network through a gradient descent algorithm;
module M4: extracting an originating convolution layer coefficient as a coefficient of a system originating pre-equalizer, and pre-compensating optical filtering damage;
module M5: after the pre-compensation filter coefficient of the transmitting end is configured, the filter coefficient of the damage of the optical filtering of the receiving end is obtained through self-adaptive convergence, so that compensation is performed;
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 is 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, represents convolution operation; x is x r (n) represents an in-phase signal in the linear filter input signal; n represents the time instant in the discrete random process; j represents an imaginary part; x is x i (n) represents a quadrature signal in the linear filter input signal; h is a r (n) represents the real part of the tap coefficients of the linear filter; h is a i (n) represents an imaginary part of tap coefficients of the linear filter; y is r (n) represents the real part of the linear filter output signal; y is i (n) represents an imaginary part in the linear filter output signal;
for the neural network convolutional layer, expressed as:
wherein the input dimension and the output dimension are (N, C) in L) and (N, C) out ，L out ) N is the batch size, C is the channel number, L is the length of the signal, and the allgather is the cross-correlation operation; i. j represents the ith batch and the jth output channel;representing 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, offset as 0, and the input of convolution layer as [ x ] 1 (n)，x 2 (n)]The convolution layer weight is [ h ] 1 (n)，h 2 (n)]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)]At the time, the output is y r When the input is [ x ] i (n)；x r (n)]At the time, the output is y i ；
For parameters related to bit error probability BER, and no hard decision exists in the calculation, 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 a signal point of a transmitting end; the second part of the GMI formula represents a measure of the effect of channel noise on the information transmission rate; n represents the number of signal points; m is the number of bits required to represent each QAM signal point; b k，i A value representing an ith bit corresponding to a kth signal point of the transmitting end; x, y k Respectively representing signals of a transmitting end and a receiving end; 2 sigma 2 Average power for complex gaussian noise in the channel;respectively representing a set of signal points with the ith bit of 0 or 1 at a transmitting end; p (P) X (x) Probability for the corresponding signal point, +.>
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