CN108023851B - Synchronous signal transmitting and receiving device and method based on super-Nyquist filtering - Google Patents

Synchronous signal transmitting and receiving device and method based on super-Nyquist filtering Download PDF

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CN108023851B
CN108023851B CN201711235721.0A CN201711235721A CN108023851B CN 108023851 B CN108023851 B CN 108023851B CN 201711235721 A CN201711235721 A CN 201711235721A CN 108023851 B CN108023851 B CN 108023851B
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CN108023851A (en
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胡荣
杨超
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Wuhan Research Institute of Posts and Telecommunications Co Ltd
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00Modulated-carrier systems
    • H04L27/26Systems using multi-frequency codes
    • H04L27/2601Multicarrier modulation systems
    • H04L27/2647Arrangements specific to the receiver only
    • H04L27/2655Synchronisation arrangements
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00Baseband systems
    • H04L25/02Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006Arrangements for removing intersymbol interference
    • H04L25/03343Arrangements at the transmitter end

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  • Synchronisation In Digital Transmission Systems (AREA)
  • Optical Communication System (AREA)

Abstract

The invention discloses a synchronous signal transmitting and receiving device and method based on super-Nyquist filtering, the method includes: at a transmitting end, performing super-Nyquist filtering on input multi-channel synchronous signals respectively, and then aggregating the multi-channel filtering signals into a high-speed aggregated signal; amplifying the obtained polymerization signal; modulating the amplified aggregate signal into an optical signal and transmitting the optical signal; at the receiving end: converting the received optical signal into an electric signal to obtain a path of aggregated signal; amplifying the obtained polymerization signal; and decomposing the amplified one-path high-speed aggregated signal into multiple paths, and respectively carrying out super-Nyquist decoding on each path to recover multiple paths of synchronous signals. The invention realizes the sending and receiving of high-speed multi-channel synchronous signals, supports partial overlapping of synchronous signal frequency spectrums of adjacent channels, has high frequency spectrum utilization rate, effectively reduces the inter-channel crosstalk caused by frequency spectrum overlapping by super Nyquist filtering, and has simple realization mode and lower calculation complexity.

Description

Synchronous signal transmitting and receiving device and method based on super-Nyquist filtering
Technical Field
The invention relates to a synchronous signal transmitting and receiving technology, in particular to a synchronous signal transmitting and receiving device and method based on super-Nyquist filtering.
Background
The transmission and reception of high-speed synchronization signals are generally applied in multi-user optical transmission systems. A method for realizing high-speed synchronous signal is to map multi-channel signal to different sub-carriers of OFDM (orthogonal frequency division multiplexing) symbol in frequency domain, then realize the synchronous sending and receiving of multi-channel signal through the optical OFDM signal sending and receiving device based on direct modulation and direct detection; moreover, due to the orthogonality of the OFDM subcarriers, the multipath signals do not need to consider the guard interval when mapping in the frequency domain.
Nevertheless, as transmission rates continue to increase, systems require higher spectrum utilization. In a general way of improving the frequency spectrum utilization rate, in the frequency domain mapping process, the frequency spectrums of two adjacent paths of signals are overlapped to a certain extent; since the crosstalk between channels due to the overlapping frequency spectrums can reduce the transmission performance of the system to some extent, an effective method for eliminating or reducing the crosstalk between channels is needed.
Disclosure of Invention
The invention aims to solve the technical problem that when the frequency spectrum utilization rate is improved by utilizing the frequency spectrum overlapping of two adjacent paths of signals in the frequency domain mapping process, the transmission performance of a system is reduced to a certain extent by the generated inter-channel crosstalk.
In order to solve the above technical problem, an embodiment of the present invention provides a synchronization signal transmitting and receiving apparatus based on super-nyquist filtering, including:
at a sending end:
the aggregation digital signal processing unit is used for respectively carrying out super-Nyquist filtering on the input multi-channel synchronous signals and then aggregating the multi-channel filtering signals into a high-speed aggregation signal;
the first driver is used for amplifying the aggregation signal output by the aggregation digital signal processing unit;
directly modulating the laser, modulating the amplified polymerization signal into an optical signal, and sending the optical signal;
at the receiving end:
the photoelectric detector is used for converting the received optical signal into an electric signal to obtain a path of aggregated signal;
the second driver is used for amplifying the polymerization signal obtained by the photoelectric detector;
and the de-aggregation digital signal processing unit is used for decomposing the aggregation signal amplified by the second driver into multiple paths, and performing super-Nyquist decoding on each path respectively to recover multiple paths of synchronous signals.
In the above-described apparatus, the first and second air-conditioning units,
at a transmitting end, the implementation principle of the aggregation digital signal processing unit is as follows:
performing super-Nyquist filtering on the N paths of synchronous signals respectively; then, after performing serial-to-parallel conversion on each path of filtering signal, performing fast Fourier transform of K points respectively to obtain synchronous frequency domain signals; mapping each path of frequency domain signal to OFDM subcarrier by adopting partial overlapping mapping to obtain a frequency domain OFDM signal; finally, performing inverse fast Fourier transform and parallel-serial conversion of L points on the frequency domain OFDM signal to obtain a high-speed aggregated signal;
wherein K and L are the FFT and IFFT dimensions, respectively, and L > K.
In the above-described apparatus, the first and second air-conditioning units,
at the receiving end, the implementation principle of the deaggregation digital signal processing unit is as follows:
firstly, performing serial-parallel conversion and L-point fast Fourier transform on the aggregated signal to obtain a frequency domain OFDM signal; after the frequency domain OFDM signal is subjected to channel recovery, reverse partial overlapping mapping is carried out on the subcarrier of the frequency domain OFDM signal to obtain N paths of synchronous frequency domain signals; n paths of synchronous frequency domain signals are subjected to K-point inverse fast Fourier transform and parallel-serial conversion to generate N paths of time domain synchronous signals; n paths of time domain synchronous signals are subjected to super-Nyquist decoding respectively, and N paths of synchronous signals sent by a sending end are recovered;
wherein K and L are inverse fast Fourier transform and fast Fourier transform dimensions, respectively, and L > K.
In the device, the aggregate digital signal processing unit performs super-nyquist filtering on each path of synchronous signals, firstly pre-codes the multiple paths of synchronous signals, and then filters the multiple paths of synchronous signals through the digital low-pass filters respectively.
In the above apparatus, the precoding operation principle is:
the input signal at the k-th moment is represented as a (k), and k is a positive integer; the intermediate signal at the k-th moment is represented as b (k), and the initial value of b (k) is 0; b, (k) obtaining a transit signal b (k-1) at the k-1 th moment through the time delay of one symbol period;
adding the transfer signal b (k-1) at the k-1 moment with the input signal a (k) at the k moment, and then performing 'M-mode' operation to obtain a transfer signal b (k) at the k moment;
adding the transfer signal b (k) at the k moment with the transfer signal b (k-1) at the k-1 moment to obtain an output signal c (k) at the current moment as a filtering signal;
the de-aggregation digital signal processing unit only needs to perform 'modulo M' operation when performing super-Nyquist decoding;
where M in the 'modulo M' operation represents the number of levels of the signal.
In the above-described apparatus, the first and second air-conditioning units,
for QPSK signals, M ═ 2;
for a 16-QAM signal, M-4.
In the above apparatus, a cutoff frequency of the digital low-pass filter is lower than a nyquist sampling frequency of the input synchronization signal;
the specific cut-off frequency ranges are: [0.75 × Fs, Fs ], where Fs represents the super-Nyquist sampling frequency of the input signal.
In the above apparatus, the principle that the aggregation digital signal processing unit maps each channel of frequency domain signals to OFDM subcarriers by using partially overlapping mapping is as follows:
each path of the synchronous frequency domain signal obtained through serial-parallel conversion and fast Fourier transform of K points is a channel, and the number of OFDM subcarriers occupied by the channel is K;
in the process of partial overlapping mapping, OFDM subcarriers repeatedly occupied by adjacent channels exist, and for each channel, the number of the OFDM subcarriers repeatedly occupied by the channel is not higher than 25% of the number of the OFDM subcarriers occupied by the channel;
partial overlap mapping is only for positive frequency subcarriers of OFDM; after the partial overlapping mapping is finished, the negative frequency sub-carrier of the OFDM is set to be in a conjugate symmetrical form of the positive frequency sub-carrier of the OFDM so as to generate the real OFDM signal.
In the above apparatus, the principle of inverse mapping, in which the deaggregation digital signal processing unit performs partial overlap mapping on subcarriers of the frequency domain OFDM signal after the frequency domain OFDM signal is subjected to channel recovery, is as follows:
extracting OFDM subcarriers of non-overlapping parts of all channels, wherein the number of the subcarriers of the parts is smaller than K, and K is the size of the multichannel synchronous signals for carrying out fast Fourier transform;
and setting the subcarriers of the overlapped part to zero to form a data block with two ends of zero and the length of K, and then carrying out IFFT transformation on the data block.
The title also provides a synchronous signal transmitting and receiving method based on super-Nyquist filtering, which comprises the following steps:
at a sending end:
step S10, performing super-Nyquist filtering on the input multi-channel synchronous signals respectively, and then aggregating the multi-channel filtering signals into a single-channel high-speed aggregation signal;
amplifying the aggregation signal obtained in the step S20 and the step S10;
step S30, modulating the amplified aggregate signal into an optical signal and sending the optical signal;
at the receiving end:
step S40, converting the received optical signal into an electric signal to obtain a path of aggregate signal;
step S50, amplifying the aggregation signal obtained in the step S40;
and S60, decomposing the one path of high-speed aggregated signal amplified in the step S50 into multiple paths, and respectively carrying out super-Nyquist decoding on each path to recover multiple paths of synchronous signals.
The invention realizes the sending and receiving of high-speed multi-channel synchronous signals, supports partial overlapping of synchronous signal frequency spectrums of adjacent channels, has high frequency spectrum utilization rate, effectively reduces the inter-channel crosstalk caused by frequency spectrum overlapping by super Nyquist filtering, and has simple realization mode and lower calculation complexity.
Drawings
Fig. 1 is a block diagram of a transmitting end of a synchronization signal transmitting and receiving apparatus based on super-nyquist filtering according to the present invention;
fig. 2 is a block diagram of a receiving end of a synchronization signal transmitting and receiving apparatus based on super-nyquist filtering according to the present invention;
FIG. 3 is a schematic diagram of an implementation of a sender-side aggregated digital signal processing unit according to the present invention;
FIG. 4 is a schematic diagram of an implementation of a receiver deaggregation digital signal processing unit in accordance with the present invention;
FIG. 5 is a schematic block diagram of precoding in the present invention;
FIG. 6 is a schematic diagram of a partial overlap mapping in accordance with the present invention;
FIG. 7 is a schematic diagram of reverse partial overlap mapping in accordance with the present invention;
fig. 8 is a flowchart of a method for transmitting and receiving a synchronization signal based on super-nyquist filtering according to the present invention.
Detailed Description
The synchronous signal transmitting and receiving device and method based on the super-Nyquist filtering can realize synchronous transmission and reception of multiple paths of signals, support partial overlapping of synchronous signal spectrums of adjacent channels, and effectively reduce crosstalk between channels caused by frequency spectrum overlapping, so that the transmission frequency spectrum efficiency is higher than that of the conventional synchronous signal transmitting and receiving scheme.
The invention is described in detail below with reference to the figures and specific examples.
As shown in fig. 1 and 2, the synchronization signal transmitting and receiving apparatus based on super-nyquist filtering according to the present invention includes:
at a sending end:
the aggregation digital signal processing unit 10 is used for respectively carrying out super-Nyquist filtering on the input multi-channel synchronous signals and aggregating the multi-channel filtering signals into a high-speed aggregation signal;
a first driver 20 for amplifying the aggregate signal output from the aggregate digital signal processing unit 10;
the laser 30 is directly modulated, and the amplified aggregate signal is modulated into an optical signal and transmitted.
At the receiving end:
the photoelectric detector 40 converts the received optical signal into an electrical signal to obtain a path of aggregate signal;
a second driver 50 for amplifying the aggregate signal obtained by the photodetector 40;
the de-aggregation digital signal processing unit 60 decomposes the one path of high-speed aggregated signal amplified by the second driver 50 into multiple paths, and performs super-nyquist decoding on each path respectively to recover multiple paths of synchronous signals.
In the present invention, as shown in fig. 3, at the transmitting end, the aggregation digital signal processing unit 10 implements the following principle:
performing Faster-Than-Nyquist (FTN) filtering on the N paths of synchronous signals; then, after performing serial-to-parallel conversion on each path of filtering signals, performing Fast Fourier Transform (FFT) of K points respectively to obtain synchronous frequency domain signals; mapping each channel of Frequency domain signals to OFDM (Orthogonal Frequency Division Multiplexing) subcarriers by adopting partial overlapping mapping to obtain Frequency domain OFDM signals; and finally, performing Inverse Fast Fourier Transform (IFFT) and parallel-serial conversion on the frequency domain OFDM signal to obtain a time domain OFDM signal, i.e., a high-speed aggregate signal. It is noted here that K and L are FFT and IFFT sizes, respectively, and L > K.
In the present invention, as shown in fig. 4, at the receiving end, the deaggregation digital signal processing unit 60 implements the following principle:
firstly, performing serial-parallel conversion and L-point fast Fourier transform on the aggregated signal to obtain a frequency domain OFDM signal; after the frequency domain OFDM signal is subjected to channel recovery, reverse partial overlapping mapping is carried out on the subcarrier of the frequency domain OFDM signal to obtain N paths of synchronous frequency domain signals; n paths of synchronous frequency domain signals are subjected to K-point inverse fast Fourier transform and parallel-serial conversion to generate N paths of time domain synchronous signals; and the N paths of time domain synchronous signals are subjected to super-Nyquist decoding respectively, and the N paths of synchronous signals sent by the sending end are recovered, wherein K and L are inverse fast Fourier transform and fast Fourier transform sizes respectively, and L is larger than K.
At the transmitting end, the aggregate digital signal processing unit 10 performs super-nyquist filtering on each path of synchronous signals, firstly pre-codes the multiple paths of synchronous signals, and then filters the signals through digital low-pass filters. As shown in fig. 5, the precoding operation principle is as follows:
the input signal at the k-th moment is represented as a (k), and k is a positive integer; the intermediate signal at the k-th moment is represented as b (k), and the initial value of b (k) is 0; b (k) delaying by one symbol period to obtain b (k-1); b (k-1) is added with the input signal a (k) at the current moment and then subjected to 'M' operation to obtain a transfer signal b (k) at the current moment; adding b (k) and b (k-1) to obtain an output signal c (k) at the current moment, namely a filtering signal; note that M in the 'modulo' operation represents the number of levels of the signal, and for a QPSK signal, M is 2; for a 16-QAM signal, M-4. The requirements of the invention on the digital low-pass filter are as follows: the cut-off frequency is lower than the Nyquist sampling frequency of the input signal (each path of synchronous signal), and the specific cut-off frequency range is as follows: [0.75 × Fs, Fs ], where Fs represents the super-Nyquist sampling frequency of the input signal.
At the receiving end, the deaggregation digital signal processing unit 60 performs faster than nyquist decoding (FTN decoding) only by simple 'modulo M' operation; where M in the modulo M operation represents the number of levels of the signal.
In the present invention, as shown in fig. 6, the principle of mapping each channel of frequency domain signals to OFDM subcarriers by using partially overlapping mapping is as follows:
each path of the synchronous frequency domain signal obtained through serial-parallel conversion and fast Fourier transform of K points is a channel, and the number of OFDM subcarriers occupied by the channel is K;
in the process of partial overlapping mapping, OFDM subcarriers repeatedly occupied by adjacent channels exist, and for each channel, the number of the OFDM subcarriers repeatedly occupied by the channel is not higher than 25% of the number of the OFDM subcarriers occupied by the channel;
to generate real OFDM signals (frequency domain OFDM signals), the partial overlap mapping is only for the positive frequency subcarriers of OFDM; after the partial overlapping mapping is finished, the negative frequency sub-carrier of the OFDM is set to be in a conjugate symmetrical form of the positive frequency sub-carrier of the OFDM so as to generate the real OFDM signal.
In the present invention, as shown in fig. 7, after the frequency domain OFDM signal is subjected to channel recovery, the principle of performing reverse partial overlap mapping on its subcarriers is as follows:
extracting OFDM subcarriers of non-overlapping parts of all channels, wherein the number of the subcarriers of the parts is less than K, and K is the size of FFT (fast Fourier transform) of the multi-channel synchronous signals;
and setting the subcarriers of the overlapped part to zero to form a data block with two ends of zero and the length of K, and then carrying out IFFT transformation on the data block.
As shown in fig. 8, the method for transmitting and receiving a synchronization signal based on super-nyquist filtering provided by the present invention includes the following steps:
at a sending end:
step S10, performing super-Nyquist filtering on the input multi-channel synchronous signals respectively, and then aggregating the multi-channel filtering signals into a single-channel high-speed aggregation signal;
amplifying the aggregation signal obtained in the step S20 and the step S10;
step S30, modulating the amplified aggregate signal into an optical signal and sending the optical signal;
at the receiving end:
step S40, converting the received optical signal into an electric signal to obtain a path of aggregate signal;
step S50, amplifying the aggregation signal obtained in the step S40;
and S60, decomposing the one path of high-speed aggregated signal amplified in the step S50 into multiple paths, and respectively carrying out super-Nyquist decoding on each path to recover multiple paths of synchronous signals.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (8)

1. A synchronization signal transmitting and receiving apparatus based on super-nyquist filtering, comprising:
at a sending end:
the aggregation digital signal processing unit is used for respectively carrying out super-Nyquist filtering on the input multi-channel synchronous signals and then aggregating the multi-channel filtering signals into a high-speed aggregation signal;
the first driver is used for amplifying the aggregation signal output by the aggregation digital signal processing unit;
directly modulating the laser, modulating the amplified polymerization signal into an optical signal, and sending the optical signal;
at the receiving end:
the photoelectric detector is used for converting the received optical signal into an electric signal to obtain a path of aggregated signal;
the second driver is used for amplifying the polymerization signal obtained by the photoelectric detector;
the de-aggregation digital signal processing unit is used for decomposing the aggregation signal amplified by the second driver into multiple paths, and performing super-Nyquist decoding on each path respectively to recover multiple paths of synchronous signals;
the aggregation digital signal processing unit carries out super-Nyquist filtering on each path of synchronous signals, firstly carries out precoding on a plurality of paths of synchronous signals, and then carries out filtering on the plurality of paths of synchronous signals through digital low-pass filters;
the working principle of the precoding is as follows:
the input signal at the k-th moment is represented as a (k), and k is a positive integer; the intermediate signal at the k-th moment is represented as b (k), and the initial value of b (k) is 0; b, (k) obtaining a transit signal b (k-1) at the k-1 th moment through the time delay of one symbol period;
adding the transfer signal b (k-1) at the k-1 moment with the input signal a (k) at the k moment, and then performing modulo M operation to obtain a transfer signal b (k) at the k moment;
adding the transfer signal b (k) at the k moment with the transfer signal b (k-1) at the k-1 moment to obtain an output signal c (k) at the current moment as a filtering signal;
the de-aggregation digital signal processing unit only needs to perform modulo-M operation when performing super-Nyquist decoding;
wherein M in the modulo M operation represents the number of levels of the signal.
2. The synchronous signal transmitting and receiving apparatus based on super-nyquist filtering as set forth in claim 1,
at a transmitting end, the implementation principle of the aggregation digital signal processing unit is as follows:
performing super-Nyquist filtering on the N paths of synchronous signals respectively; then, after performing serial-to-parallel conversion on each path of filtering signal, performing fast Fourier transform of K points respectively to obtain synchronous frequency domain signals; mapping each path of frequency domain signal to OFDM subcarrier by adopting partial overlapping mapping to obtain a frequency domain OFDM signal; finally, performing inverse fast Fourier transform and parallel-serial conversion of L points on the frequency domain OFDM signal to obtain a high-speed aggregated signal;
wherein K and L are the FFT and IFFT dimensions, respectively, and L > K.
3. The synchronous signal transmitting and receiving apparatus based on super-nyquist filtering as set forth in claim 1,
at the receiving end, the implementation principle of the deaggregation digital signal processing unit is as follows:
firstly, performing serial-parallel conversion and L-point fast Fourier transform on the aggregated signal to obtain a frequency domain OFDM signal; after the frequency domain OFDM signal is subjected to channel recovery, reverse partial overlapping mapping is carried out on the subcarrier of the frequency domain OFDM signal to obtain N paths of synchronous frequency domain signals; n paths of synchronous frequency domain signals are subjected to K-point inverse fast Fourier transform and parallel-serial conversion to generate N paths of time domain synchronous signals; n paths of time domain synchronous signals are subjected to super-Nyquist decoding respectively, and N paths of synchronous signals sent by a sending end are recovered;
wherein K and L are inverse fast Fourier transform and fast Fourier transform dimensions, respectively, and L > K.
4. The synchronous signal transmitting and receiving apparatus based on super-nyquist filtering as set forth in claim 1,
for QPSK signals, M ═ 2;
for a 16-QAM signal, M-4.
5. The synchronous signal transmitting and receiving apparatus based on super-nyquist filtering as set forth in claim 1, wherein a cutoff frequency of the digital low-pass filter is lower than a super-nyquist sampling frequency of the input synchronous signal;
the specific cut-off frequency ranges are: [0.75 × Fs, Fs ], where Fs represents the super-Nyquist sampling frequency of the input signal.
6. The synchronous signal transmitting and receiving apparatus based on super-nyquist filtering as claimed in claim 2, wherein said aggregated digital signal processing unit employs partial overlap mapping, and the principle of mapping each path of frequency domain signal to OFDM subcarriers is:
each path of the synchronous frequency domain signal obtained through serial-parallel conversion and fast Fourier transform of K points is a channel, and the number of OFDM subcarriers occupied by the channel is K;
in the process of partial overlapping mapping, OFDM subcarriers repeatedly occupied by adjacent channels exist, and for each channel, the number of the OFDM subcarriers repeatedly occupied by the channel is not higher than 25% of the number of the OFDM subcarriers occupied by the channel;
partial overlap mapping is only for positive frequency subcarriers of OFDM; after the partial overlapping mapping is finished, the negative frequency sub-carrier of the OFDM is set to be in a conjugate symmetrical form of the positive frequency sub-carrier of the OFDM so as to generate the real OFDM signal.
7. The synchronous signal transmitting and receiving apparatus based on nyquist filtering as set forth in claim 3, wherein said deaggregation digital signal processing unit performs inverse mapping of partial overlapping mapping with respect to its subcarriers after channel-recovering the frequency domain OFDM signal by a principle of:
extracting OFDM subcarriers of non-overlapping parts of all channels, wherein the number of the subcarriers of the parts is smaller than K, and K is the size of the multichannel synchronous signals for carrying out fast Fourier transform;
and setting the subcarriers of the overlapped part to zero to form a data block with zero at two ends and a length of K, and then carrying out IFFT transformation on the data block.
8. A synchronous signal transmitting and receiving method based on super-Nyquist filtering is characterized by comprising the following steps:
at a sending end:
step S10, performing super-Nyquist filtering on the input multi-channel synchronous signals respectively, and then aggregating the multi-channel filtering signals into a single-channel high-speed aggregation signal;
step S20, amplifying the aggregation signal obtained in the step S10;
step S30, modulating the amplified aggregate signal into an optical signal and sending the optical signal;
at the receiving end:
step S40, converting the received optical signal into an electric signal to obtain a path of aggregate signal;
step S50, amplifying the aggregation signal obtained in the step S40;
s60, decomposing the one-path high-speed aggregated signal amplified in the S50 into multiple paths, and respectively carrying out super-Nyquist decoding on each path to recover multiple paths of synchronous signals;
performing super-Nyquist filtering on each path of synchronous signals, firstly pre-coding the multiple paths of synchronous signals, and filtering the multiple paths of synchronous signals through a digital low-pass filter;
the working principle of the precoding is as follows:
the input signal at the k-th moment is represented as a (k), and k is a positive integer; the intermediate signal at the k-th moment is represented as b (k), and the initial value of b (k) is 0; b, (k) obtaining a transit signal b (k-1) at the k-1 th moment through the time delay of one symbol period;
adding the transfer signal b (k-1) at the k-1 moment with the input signal a (k) at the k moment, and then performing modulo M operation to obtain a transfer signal b (k) at the k moment;
adding the transfer signal b (k) at the k moment with the transfer signal b (k-1) at the k-1 moment to obtain an output signal c (k) at the current moment as a filtering signal;
the super-Nyquist decoding only needs to be carried out by modulo-M operation;
wherein M in the modulo M operation represents the number of levels of the signal.
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