WO2023245828A1 - 一种多载波接入网失真信号的补偿方法及非线性均衡器 - Google Patents

一种多载波接入网失真信号的补偿方法及非线性均衡器 Download PDF

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WO2023245828A1
WO2023245828A1 PCT/CN2022/110580 CN2022110580W WO2023245828A1 WO 2023245828 A1 WO2023245828 A1 WO 2023245828A1 CN 2022110580 W CN2022110580 W CN 2022110580W WO 2023245828 A1 WO2023245828 A1 WO 2023245828A1
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signal
filter
frequency domain
difference
order
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French (fr)
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高明义
褚佳敏
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苏州大学
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
    • H04L27/2689—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation
    • H04L27/2695—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation with channel estimation, e.g. determination of delay spread, derivative or peak tracking
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04Q—SELECTING
    • H04Q11/00—Selecting arrangements for multiplex systems
    • H04Q11/0001—Selecting arrangements for multiplex systems using optical switching
    • H04Q11/0062—Network aspects
    • H04Q11/0067—Provisions for optical access or distribution networks, e.g. Gigabit Ethernet Passive Optical Network (GE-PON), ATM-based Passive Optical Network (A-PON), PON-Ring
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Definitions

  • the present invention relates to the field of signal processing technology, and in particular to a compensation method and a nonlinear equalizer for distorted signals in a multi-carrier access network.
  • High data rate access networks are essential to sustain the rapid development of 5G deployment, IoT, edge computing and future high-bandwidth and low-latency services.
  • Passive optical network PON
  • PON Passive optical network
  • higher-speed 50-Gb/s PON is best implemented in the near-zero dispersion O-band.
  • higher fiber losses in the O-band result in reduced optical power budgets. Therefore, the number of access users and the optical fiber range in the O-band are limited.
  • C-band multi-carrier modulation has advantages in low fiber loss and anti-dispersion performance, in which high-speed data is transmitted in multiple parallel low-speed sub-channels.
  • Intensity modulation direct detection (IM/DD) orthogonal frequency division multiplexing (OFDM) has the advantages of high spectral efficiency, strong anti-dispersion performance, and simple implementation, and is very promising in high-speed PON.
  • IM/DD Intensity modulation direct detection
  • OFDM orthogonal frequency division multiplexing
  • One of the MCM technologies However, the cyclic prefix (CP) in the OFDM system will reduce the net bit rate, and the longer the CP sequence, the better the performance against inter-symbol interference (ISI). However, long sequences of CPs will bring inevitable overhead and reduce spectrum efficiency.
  • ISI inter-symbol interference
  • FBMC/OQAM filter bank multicarrier with offset quadrature amplitude modulation
  • FBMC/OQAM signals introduce prototype filters with excellent performance to alleviate ISI and additional CP overhead. Furthermore, lower out-of-band power leakage is beneficial against ICI.
  • the FBMC system can be implemented without the help of Hermitian symmetry, so that more effective data subcarriers can be utilized. Therefore, FBMC systems can increase the data rate by increasing the number of data subcarriers. However, as the number of data subcarriers increases, signal distortion during optical fiber transmission will rapidly increase, causing system performance to deteriorate. At this point, choosing an appropriate equalizer will help reduce the interference of nonlinear distortion.
  • the classic Volterra filter is widely used to deal with nonlinear distortion. The higher the order of the Volterra filter, the better the anti-nonlinear distortion effect, but the higher the order, the complexity of its implementation will increase. Low-complexity second-order Volterra filters cannot handle severely distorted signals.
  • the purpose of the present invention is to provide a compensation method and a nonlinear equalizer for distorted signals in a multi-carrier access network to solve the serious signal distortion problem caused by a large number of data subcarriers in a high-speed multi-carrier optical access network.
  • the present invention provides a compensation method for the distortion signal of a multi-carrier access network, including:
  • the optimal serial signal is:
  • x(t) is the input signal of the n-order Volterra filter, that is, the distortion signal
  • y 1 (t) is the optimal serial signal obtained after filtering by the n-order Volterra filter
  • w 1 is the n-order Volterra filter.
  • the first-order kernel function of , w 2 (l 1 ,l 2 ) is the second-order kernel function of n-order Volterra filter
  • w n (l 1 ,l 2 ,...,l n ) is the n-order Volterra filter
  • the nth order kernel function of the filter, all kernel functions are the optimal tap coefficients of the nth order Volterra filter
  • L is the memory length
  • l i represents the point coordinates of the discrete domain kernel function.
  • the e-th difference value is updated through the NLMS algorithm.
  • processing the optimal serial signal to obtain a frequency domain signal includes:
  • the fast Fourier transform is performed on the parallel signal processed by the matched filter to obtain the frequency domain signal.
  • the frequency domain signal is:
  • Y 1 (k) and F (k) are the frequency domain signals obtained after fast Fourier transform of y 1 (t) and f (t) respectively
  • y 1 (t) is the frequency domain signal obtained after n
  • f(t) is the square root raised cosine function with a roll-off factor of 0.5.
  • performing channel estimation processing on the frequency domain signal to output a compensated signal includes: processing the frequency domain signal using a three-layer complex-valued neural network, and the compensated signal output is:
  • the number of neurons in the output layer is equal to the number of neurons in the input layer.
  • the determination process of the optimal weight values from the input layer to the hidden layer and from the hidden layer to the output layer is:
  • the weight value w jk from the input layer to the hidden layer and the weight value w ij from the hidden layer to the output layer are respectively assigned an initial value between [-0.1-0.1], and the frequency domain signal is processed for the first time. Calculate the first compensated signal Y 1 (k);
  • the filter is a linear filter
  • the filter is a nonlinear filter.
  • the invention also provides a nonlinear equalizer, including:
  • Input port output port for connecting distorted signals
  • Integrated chip Use the steps of the multi-carrier access network distortion signal compensation method as described above to realize distortion signal compensation;
  • Output port used to output the compensation signal processed by the integrated chip.
  • the integrated chip includes:
  • n-order Volterra filter module used to perform n-order Volterra filtering on the distorted signal to generate a serial signal
  • Time domain-frequency domain conversion module used to convert the serial signal into a frequency domain signal
  • Channel estimation module used to perform channel estimation on the frequency domain signal.
  • the multi-carrier access network distortion signal compensation method and nonlinear equalizer provided by the present invention input the distortion signal into an n-order Volterra filter and continuously update the difference between the filtered signal and the reference signal, and then continuously update The tap coefficient of the filter is used to filter the distorted signal using the continuously updated tap coefficient.
  • the e+1th time is output.
  • the serial signal is regarded as the optimal serial signal; by determining the optimal serial signal through multiple filtering, the anti-interference ability of severe distortion can be well achieved even in the case of low-order filters, maximizing the signal without attenuation.
  • the present invention can effectively solve the problem of existing problems with data With the increase in the number of subcarriers, the signal distortion during fiber transmission increases rapidly and causes the system performance to deteriorate. Low-order filters can also well realize the compensation problem of distorted signals and avoid the long calculation time of high-order filters. and computationally complex problems.
  • Figure 1 is a flow chart of a method for compensating distortion signals in a multi-carrier access network provided by the present invention
  • Figure 2 is a specific flow chart of an embodiment of the compensation method for multi-carrier access network distortion signals provided by the present invention
  • Figure 3 is a diagram of the experimental device of the IM/DD FBMC transmission system in the embodiment of the present invention.
  • Figure 4 is an end-to-end channel response diagram measured in the embodiment of the present invention.
  • Figure 5 is a spectrum diagram before and after MZM modulation in the embodiment of the present invention.
  • Figure 6 is the SNR curve of all subcarriers measured in the 12.5/25-GBd FBMC 30-km SSMF transmission system in the embodiment of the present invention
  • Figure 7 is a subcarrier SNR curve at 1th-5th in the embodiment of the present invention.
  • Figure 8 is a subcarrier SNR curve at 210th-310th in the embodiment of the present invention.
  • Figure 10 shows the measured PSD curve of the 12.5-GBd FBMC 30-km SSMF system without using NLE when the number of data subcarriers is 448 in the embodiment of the present invention
  • Figure 11 shows the measured PSD curve after using NLE in the 12.5-GBd FBMC 30-km SSMF system when the number of data subcarriers is 448 in the embodiment of the present invention
  • Figure 12 shows the measured SNR curve of the 12.5-GBd FBMC 30-km SSMF system without using NLE when the number of data subcarriers is 448 in the embodiment of the present invention
  • Figure 13 shows the measured SNR curve after using NLE in the 12.5-GBd FBMC 30-km SSMF system in the embodiment of the present invention when the number of data subcarriers is 448;
  • Figure 14 shows the measured PSD curve of the 25-GBd FBMC 30-km SSMF system without using NLE when the number of data subcarriers is 352 in the embodiment of the present invention
  • Figure 15 shows the measured PSD curve of NLE used in the 25-GBd FBMC 30-km SSMF system in the embodiment of the present invention when the number of data subcarriers is 352;
  • Figure 16 shows the measured SNR curve of the 25-GBd FBMC 30-km SSMF system without using NLE when the number of data subcarriers is 352 in the embodiment of the present invention
  • Figure 17 shows the measured SNR curve of NLE used in the 25-GBd FBMC 30-km SSMF system when the number of data subcarriers is 352 in the embodiment of the present invention
  • Figure 18 is a graph showing the variation of the measured BER with received optical power of the 12.5-GBd FBMC signal in the embodiment of the present invention.
  • Figure 19 is a constellation diagram of the 12.5-GBd system using LS processing when the number of data subcarriers is 448 in the embodiment of the present invention.
  • Figure 20 is a constellation diagram of the 12.5-GBd system using LE processing when the number of data subcarriers is 448 in the embodiment of the present invention
  • Figure 21 is a constellation diagram of the 12.5-GBd system processed by NLE when the number of data subcarriers is 448 in the embodiment of the present invention
  • Figure 22 is a graph showing the measured BER of the 25-GBd FBMC signal as a function of the received optical power in the embodiment of the present invention.
  • Figure 23 is a constellation diagram of the 25-GBd system using LS processing when the number of data subcarriers is 352 in the embodiment of the present invention.
  • Figure 24 is a constellation diagram of the 25-GBd system using LE processing when the number of data subcarriers is 352 in the embodiment of the present invention
  • Figure 25 is a constellation diagram of the 25-GBd system processed by NLE when the number of data subcarriers is 352 in the embodiment of the present invention.
  • the core of the present invention is to provide a compensation method and a nonlinear equalizer for distortion signals in multi-carrier access networks, which are mainly used to solve the problem of rapid signal distortion caused by existing FBMC systems when increasing the data rate by increasing the number of data subcarriers. Increased problem.
  • the data rate can be increased by increasing the number of data subcarriers.
  • signal distortion during optical fiber transmission will rapidly increase, causing system performance to deteriorate. Therefore, it is necessary to choose an appropriate equalizer to reduce the interference of nonlinear distortion.
  • the present invention constructs a nonlinear equalizer including: an n-order Volterra filter module, used to perform n-order Volterra filter processing on the distorted signal to generate a serial signal; a time domain transformation module, using for converting serial signals into frequency domain signals; and a channel estimation module for performing channel estimation on the frequency domain signals.
  • the present invention introduces an NLE (nonlinear equalizer) at the FBMC receiving end to restore the received distorted signal x(t).
  • the NLE mainly consists of an n-order Volterra filter and a channel estimator. In the embodiment of the present invention, it is mainly composed of a second-order Volterra filter and a three-layer complex-valued neural network (CVNN) channel estimator.
  • CVNN complex-valued neural network
  • Figure 1 is a flow chart of a method for compensating distortion signals in a multi-carrier access network provided by the present invention. the details are as follows:
  • the FBMC transmission system obtains x(t) through channel transmission, which is expressed as:
  • N c and N S are the number of data subcarriers and the number of FBMC symbols respectively.
  • a m,n is the nth QAM data symbol on the mth subcarrier
  • the prototype filter f(t) is a square root raised-cosine (SRRC) function with a roll-off factor of 0.5
  • j represents an imaginary number
  • T is the period.
  • the main process of compensating the distorted signal is: first, the distorted signal x(t) is processed by an n-order Volterra filter to obtain y 1 (t). Then, the serial signal y 1 (t) is converted into a parallel signal, and the This parallel signal is subjected to matched filtering and fast Fourier transform (FFT) to obtain signal Y 2 (k). Finally, Y 2 (k) is processed by the CVNN channel estimator to obtain the output signal Y (k) of the NLE equalizer.
  • FFT fast Fourier transform
  • the Volterra filter can effectively suppress the linear and nonlinear distortion of the system.
  • the n-order Volterra filter is used to process the distortion signal x(t) and the output y 1 (t) can be expressed as:
  • x(t) is the input signal of the n-order Volterra filter, that is, the distortion signal
  • y 1 (t) is the serial signal processed by the n-order Volterra filter
  • w n (l 1 ,l 2 ,... ,l n ) is the n-order tap coefficient
  • L is the memory length.
  • the performance of the Volterra filter depends largely on the filter order. The higher the filter order, the better the ability to restore the distorted signal, but it will also greatly increase the computational complexity. Generally speaking, a second-order Volterra filter is sufficient to equalize signals in an IM/DD transmission system. In this embodiment, a low-complexity second-order Volterra filter is used to process distorted signals.
  • FIG. 2 is a structural diagram of the nonlinear equalizer used in this embodiment.
  • the input x(t) of the second-order Volterra filter is a non-ideal FBMC
  • the distorted signal is processed by linear and nonlinear filtering to obtain the output signal y 1 (t).
  • the error e(t) is obtained by calculating the difference between y 1 (t) and the ideal reference signal, and e(t) is continuously updated through the normalized least mean square (NLMS) algorithm, thus continuously updating Update the linear and nonlinear tap coefficient w n .
  • NLMS normalized least mean square
  • Determination of the optimal tap coefficient input the distorted signal into the n-order Volterra filter and perform the first filtering process according to the first tap coefficient to obtain the first serial signal, and then calculate the difference from the set reference signal to obtain the first error;
  • the normalized least mean square algorithm is used to update the first error for the first time to update the tap coefficients for the first time.
  • the n-order Volterra filter uses the first updated tap coefficients to filter the distorted signal for the second time to obtain the second string. line signal, and the difference from the set reference signal is obtained to obtain the second error;
  • the first updated tap coefficient is the optimal tap coefficient
  • the n-th order Volterra filter uses the e-th updated tap coefficient to correct the distorted signal. Perform the e+1th filtering process to obtain the e+1th serial signal, and calculate the difference from the set reference signal to obtain the e+1th error;
  • the tap coefficient updated for the eth time is the optimal tap coefficient.
  • the output signal y 1 (t) enters the matched filtering and FFT modules. After matched filtering and FFT operation, the frequency domain signal Y 2 (k) can be obtained:
  • Y 1 (k) and F (k) are the frequency domain signals obtained by y 1 (t) and f (t) respectively after fast Fourier transform.
  • the number of neurons in the output layer is equal to the number of neurons in the input layer.
  • the input of the hidden layer is obtained through f 1 ( ⁇ ) processing. Then, multiply the input value of the hidden layer by the weight Then, the output signal Y(k) is obtained through f 1 ( ⁇ ) processing again.
  • the weight value w ij from the input layer to the hidden layer and the weight value w jk from the hidden layer to the output layer are respectively assigned an initial value between [-0.1-0.1]; they are continuously updated iteratively through the L-BFGS algorithm The weight value is adjusted until the final output signal becomes stable to determine the optimal weight value.
  • the specific way to determine the optimal weight value is: assign an initial value between [-0.1-0.1] to the weight value w jk from the input layer to the hidden layer and the weight value w ij from the hidden layer to the output layer. value, perform the first calculation on the frequency domain signal to obtain the first compensated signal Y 1 (k);
  • the sth updated is the optimal weight value from the input layer to the hidden layer
  • after the sth update is the optimal weight value from the hidden layer to the output layer.
  • the linear equalizer (LE) is enough to restore it well.
  • the signal x(t) is first restored by a linear feed-forward equalizer (FFE), and then processed by the matching filter, FFT and CVNN channel estimator.
  • FFE linear feed-forward equalizer
  • the structure of LE is similar to NLE, consisting of FEE, matched filter, FFT, and CVNN channel estimator.
  • the linear filter is FFE.
  • the output of FFE can be expressed as:
  • the implementation principle of FFE is similar to the second-order Volterra filter. It also uses the NLMS algorithm to continuously update the error to obtain the optimal linear filter tap coefficient.
  • X k and Y k are the pilot signals of the transmitting end and the receiving end respectively, is the estimated value that we want to use for the frequency domain channel, in order to obtain the cost function
  • the minimum value of about The reciprocal value of should be 0:
  • the channel estimate value H LS of the pilot signal is:
  • the LS channel estimation algorithm can estimate the channel response in the frequency domain based on the pilot signals at the transmitting and receiving ends, and its computational complexity is low.
  • LS does not consider the impact of noise.
  • the noise increases, the performance of LS channel estimation deteriorates. will get worse. Therefore, when the number of data subcarriers and the baud rate increase, severe signal distortion makes the LS channel estimation algorithm unable to achieve expected performance.
  • Figure 3 is a diagram of the experimental device of the IM/DDFBMC transmission system.
  • PRBS pseudo-random binary sequence
  • IFFT IFFT
  • filtering operation of the SRRC filter bank are performed, and then a pseudo-noise (PN) signal is added to facilitate signal synchronization at the receiving end.
  • PN pseudo-noise
  • this serial real-valued signal is loaded into an arbitrary waveform generator (AWG) with a sampling rate of 50-GSa/s to achieve digital-to-analog (D/A) conversion.
  • AWG arbitrary waveform generator
  • D/A digital-to-analog
  • the bandwidth of AWG is about 10-GHz, and its end-to-end response is shown in Figure 4.
  • the output of the AWG is modulated into a continuous wave (CW) with a wavelength of 1550.116nm by a Mach-Zehnder modulator (MZM).
  • MZM Mach-Zehnder modulator
  • the output power of the MZM modulator is about 5.9dBm.
  • the spectrum diagram before and after MZM modulation is shown in Figure 5.
  • the modulated optical signal enters the noise control section after being transmitted through 30km SSMF.
  • VOA variable optical attenuator
  • EDFA erbium-doped fiber amplifier
  • the noise control part is used to measure BER to simulate various noise levels.
  • the input signal power of EDFA is generally defined as received optical power (ROP).
  • ROP received optical power
  • PD photodetector
  • the PD converts the transmitted optical signal into an electrical signal
  • a real-time oscilloscope with a sampling rate of 50GSa/s collects data for offline DSP processing.
  • the collected digital signals are first inversely concatenated, and the real and imaginary data are recombined into complex numbers for subsequent processing. Then, the original transmitted signal is restored through equalizer, matched filter bank, FFT, channel estimation, and Offset-64QAM demapping in sequence. Finally, the BER of the system is calculated.
  • Figure 6 shows the SNR curves of all subcarriers measured in the 12.5/25-GBd FBMC 30-km SSMF transmission system. It can be seen from Figure 6 The effects of fiber dispersion and beat frequency interference on SNR values are clearly observed. First of all, there is obvious beat frequency interference in both 12.5GBd and 25GBd signals, and the SNR of the first few subcarriers is low, as shown in Figure 7. Since the SNR of the first few subcarriers is relatively low, it is best to avoid them for data Loading, Figure 7 also shows that fiber dispersion has a greater impact on the 25-GBd transmission system than on the 12.5-GBd transmission system.
  • the subcarriers at 210th -310th should be set to empty carriers.
  • Table 1 the allocation strategy of data subcarriers in a baud rate 12.5/25-GBd system is shown in Table 1.
  • the BER curves were measured when the number of data subcarriers was 128, 320 and 448.
  • the data subcarriers In order to avoid beat frequency interference, the data subcarriers should be placed at 193th -320th , 97th -416th and 33th -480th respectively. In the 25GBdIM/DD transmission system, the BER curves were measured when the number of data subcarriers was 128, 256 and 352. In order to avoid power attenuation caused by beat frequency interference and dispersion, the data subcarriers should be placed at 120 th -183 th & 330 th -393th , 56th -183th & 330th -457th and 27th -202th & 311th -486th .
  • the performance of NLE is verified by measuring the SNR, PSD, BER curve and constellation diagram of the 12.5/25-GBd FBMC transmission system. The net bits under different numbers of data subcarriers and baud rates are also calculated. Rate.
  • the BER performance after using NLE is significantly better than the performance without using NLE, as shown in Figure 9 marked by gray solid lines and dotted diamonds. curve shown.
  • the greater the number of data subcarriers the better the effect of NLE.
  • the curves marked by black solid lines and dotted circles in Figure 9 are the BER curves in the 25-GBd FBMC transmission system with and without the NLE scheme. Since the 25-GBd transmission system suffers from severe high-frequency power fading and bandwidth-limited distortion, although the NLE solution can improve BER performance to a certain extent, it cannot achieve the same performance as the 12.5-GBd transmission system.
  • the test measured the PSD and SNR curves in the 12.5/25-GBd FBMC 30-km SSMF transmission system, as shown in Figures 10-17.
  • Figures 10 and 11 are the measured PSD curves without and with NLE, respectively.
  • Figures 12 and 13 are without and with NLE respectively.
  • Significant PSD improvement can be achieved by utilizing the proposed NLE scheme, as shown in Figure 11.
  • the NLE scheme can also compensate for the distorted signal and improve the SNR value, as shown in Figure 13, especially the SNR value improvement at the 33th-144th and 373th-480th is the most obvious.
  • Figures 14 and 15 are the measured PSD curves without and with NLE, respectively.
  • Figures 16 and 17 are without and with NLE, respectively.
  • Measured SNR curve after NLE It can be observed from Figure 15 and Figure 17 that signal distortion is effectively alleviated by using NLE, and both PSD and SNR values are improved.
  • the SNR of the data subcarrier in the severe power attenuation part is still relatively low, the NLE scheme improves the SNR value of the data subcarrier at 27th-105th and 408th-486th, thereby improving the average signal-to-noise ratio. Therefore, in a 25-GBd FBMC transmission system, NLE is essential to achieve good performance.
  • this embodiment In order to verify the feasibility and superior performance of NLE in the 12.5-GBd IM/DD FBMC transmission system, this embodiment also measured the back-to-back (BTB) when the number of data subcarriers is 128, 320 and 448. and the BER curve after 30-km transmission, as shown in Figure 18.
  • BTB back-to-back
  • Figures 19 to 21 show the 64-QAM constellation diagrams processed using the LS, LE and NLE schemes respectively when the number of data subcarriers is 448 and the ROP is -6dBm. From Figure 19 to Figure 21, it can be observed that the constellation diagram is continuously converging, which is consistent with the performance change of BER.
  • FIG. 22 shows the measured BER of the 25-GBd FBMC signal as a function of received optical power when the number of data subcarriers is 128, 256 and 320 respectively.
  • the solid and dashed lines in Figure 22 correspond to the situation after BTB and 30-km SSMF transmission, respectively.
  • the BER curve of the LS algorithm exceeds the HD-FEC threshold, as shown in the curves marked by black and light gray circles in Figure 22. Therefore, the distorted signal cannot be recovered at the receiving end using the LS algorithm.
  • the compensation effect of LE and NLE is much better than that of LS.
  • NLE can achieve approximately 1dB improvement in receiving sensitivity at the HD-FEC threshold.
  • the number of data subcarriers increases to 256 and 352
  • LE cannot recover the distorted signal well, while NLE can still achieve better BER performance.
  • the received optical power is -11dBm and -5dBm respectively, approaching the HD-FEC threshold.
  • the proposed NLE scheme has excellent performance in high data rate FBMC transmission systems with more effective data subcarriers.
  • the excellent channel estimator enhances the performance of the second-order Volterra filter and can better handle severe nonlinear distortion, thereby reducing the BER of the system below the HD-FEC threshold.
  • Figures 23 to 25 are 64-QAM constellation diagrams using the LS, LE and NLE schemes when the number of data subcarriers is 352 and the ROP is -3dBm. Compared with using the LS and LE schemes, the constellation diagram using the NLE scheme has better convergence.
  • the net bit rate of the 12.5/25-GBd FBMC transmission system with different numbers of data subcarriers is calculated, and the results are shown in Table 2.
  • the net bit rate R is calculated by:
  • B and E are the baud rate and information entropy respectively
  • Nc and N are the number of data subcarriers and the total number of carriers respectively.
  • E is 6 bits/symbol
  • B is 12.5/25-GBd
  • N is 512.
  • the calculated net bit rate is shown in Table 2. From Table 2, it can be concluded that by using the NLE scheme, a 12.5-GBd transmission system can achieve a net bit rate of 58.18-Gb/s. The 25-GBd transmission system can achieve a net bit rate of 91.42-Gb/s.
  • the IM/DD FBMC-PON system has great application prospects in high-speed access networks.
  • the net bit rate is highly dependent on the number of data subcarriers used.
  • the greater the number of data subcarriers the more serious the signal distortion.
  • the superiority of the NLE plan in the 12.5/25-GBd IM/DD FBMC 30-km SSMF transmission system is proposed and experimentally verified. NLE can handle severe nonlinear distortion in systems with a large number of data subcarriers and high baud rates.
  • the 12.5-GBd FBMC system achieves a net bit rate of 58.18-Gb/s.
  • the HD-FEC value of the NLE scheme is An approximately 2-dB improvement in receiving sensitivity was achieved.
  • the NLE still has good performance and reaches the HD-FEC threshold at a received optical power of -5dBm, achieving a net bit rate of 91.42-Gb/s.
  • the spectrum-efficient FBMC transmission system proposed by the present invention is beneficial to the capacity upgrade of passive optical networks.
  • a 91.42-Gb/s net bit rate can be achieved in a transmission system with a bandwidth of approximately 10GHz and a 30-km SSMF.
  • the present invention also provides a channel equalizer, including:
  • Input port used to input distortion signals.
  • the output port of the FBMC system is connected;
  • Integrated chip Process the input distortion signal using the steps of the multi-carrier access network distortion signal compensation method as described above;
  • Output port Outputs the signal processed by the integrated chip.
  • the output of the FBMC system is connected through the input port.
  • the FBMC system inputs the signal into the integrated chip, and compensates the input signal of the FBMC system through the n-order Volterra filter module, time domain transformation module, and channel estimation module built into the integrated chip. deal with.
  • integrated chips include:
  • n-order Volterra filter module perform n-order Volterra filtering on the distorted signal to generate a serial signal
  • Time domain transformation module convert serial signals into frequency domain signals
  • Channel estimation module performs channel estimation on frequency domain signals.
  • RAM random access memory
  • ROM read-only memory
  • electrically programmable ROM electrically erasable programmable ROM
  • registers hard disks, removable disks, CD-ROMs, or anywhere in the field of technology. any other known form of storage media.

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Abstract

本发明公开了一种多载波接入网失真信号的补偿方法及非线性均衡器。将失真信号输入到n阶Volterra滤波器中不断更新滤波处理后的信号与参考信号的差值，继而不断更新滤波器的抽头系数，利用更新后的抽头系数再对失真信号进行滤波处理，直至第e+1次差值与第e次差值相差小于第一设定阈值时，输出第e+1次串行信号作为最优串行信号；通过多次滤波确定最优串行信号，使得n阶Volterra滤波器可以更好地抑制线性或非线性失真，低阶的情况下也能很好地实现严重失真信号的抗干扰能力；将n阶Volterra滤波器处理后的串行信号转换成频域信号，并将频域信号输入信道估计器，进一步补偿失真信号；能有效解决现有随着数据子载波数目的增加，光纤传输过程中的信号失真迅速增大的问题。

Description

一种多载波接入网失真信号的补偿方法及非线性均衡器 技术领域
本发明涉及信号处理技术领域，特别是涉及一种多载波接入网失真信号的补偿方法及非线性均衡器。
背景技术
高数据速率接入网对于维持5G部署、物联网、边缘计算和未来高带宽低延迟服务的快速发展是必不可少的。无源光网络(passive optical network，PON)作为一种高能效的光纤接入网络，从第一代2.5Gb/s、下一代10Gb/s升级到未来更高速的50Gb/s以满足大型光纤网络的需求。为了避免使用色散补偿的器件，更高速的50-Gb/s PON最好在接近零色散的O波段中实现。但是，O波段中较高的光纤损耗会导致光功率预算减少。因此，在O波段接入用户的数量和光纤范围都是有限的。
相比之下，C波段的多载波调制(multi-carrier modulation，MCM)在低光纤损耗和抗色散性能方面具有优势，其中高速数据在多个并行的低速子信道中进行传输。强度调制直接检测(intensity modulation direct detection，IM/DD)正交频分复用(orthogonal frequency division multiplexing，OFDM)具有频谱效率高、抗色散性能强、实现简单等优点，是高速PON中很有前景的MCM技术之一。然而OFDM系统中的循环前缀(cyclic prefix，CP)会降低净比特率，而且CP序列越长，抗符号间干扰(inter-symbol interference，ISI)的性能就越好。但是，长序列的CP会带来不可避免的开销，降低频谱效率。此外，每个OFDM子载波之间都必须保持严格的正交同步，这在很大程度上限制了其灵活性。同时，由于子载波旁瓣衰减缓慢，OFDM信号容易出现严重的载波间干扰(inter-carrier interference，ICI)。因此，一种新型的滤波器组多载波/偏移正交幅度调制(filter bank multicarrier with offset quadrature amplitude modulation，FBMC/OQAM)已经被视为替代OFDM的方案。
FBMC/OQAM信号引入了性能优良的原型滤波器来减轻ISI和额外的CP开销。而且，较低的带外功率泄露有利于抵抗ICI。同时，FBMC系统不需要厄米特对称的帮助便可实现，这样更多有效的数据子载波便可利用起来。因此，FBMC系统可以通过增加数据子载波的数量来提高数据速率。然而，随着数据子载波数目的增加，光纤传输过程中的信号失真会迅速增大，致使系统性能恶化。此时，选择合适的均衡器会有助于减轻非线性失真的干扰。经典的沃尔泰拉(Volterra)滤波器被广泛应用于处理非线性失真。Volterra滤波器的阶数越高，抗非线性失真的效果就越好，但是阶数越高，其实现的复杂度就会增加。低复杂度的二阶Volterra滤波器无法处理严重的失真信号。
综上所述，现今必须有效解决在高速多载波光接入网中，大量数据子载波导 致的严重信号失真问题。
发明内容
本发明的目的是提供一种多载波接入网失真信号的补偿方法及非线性均衡器，以解决高速多载波光接入网中，大量数据子载波导致的严重信号失真问题。
为解决上述技术问题，本发明提供一种多载波接入网失真信号的补偿方法，包括：
将失真信号输入n阶Volterra滤波器进行第e次n阶Volterra滤波处理得到第e次串行信号，对所述第e次串行信号与设定参考信号求差得到第e次差值；
当所述第e次差值与第e-1次差值相差不小于第一设定阈值时，更新所述第e次差值，利用更新后的差值对n阶Volterra滤波器的抽头系数进行更新，根据更新后的抽头系数对所述失真信号进行第e+1次n阶Volterra滤波处理，其中，e＝1,2,…,E，E为滤波总次数；
当所述第e次差值与第e-1次差值相差小于第一设定阈值时，输出所述第e次串行信号作为最优串行信号；
对所述最优串行信号进行处理得到频域信号；
对所述频域信号进行信道估计输出补偿后信号，完成对失真信号的补偿。
优选地，所述最优串行信号为：
Figure PCTCN2022110580-appb-000001
式中，x(t)是n阶Volterra滤波器的输入信号即失真信号，y 1(t)为经过n阶Volterra滤波器滤波处理得到的最优串行信号，w 1为n阶Volterra滤波器的第1阶核函数，w 2(l 1,l 2)为n阶Volterra滤波器的第2阶核函数，w n(l 1,l 2,…,l n)是所述n阶Volterra滤波器的第n阶核函数，所有核函数即为n阶Volterra滤波器的最佳抽头系数，L为记忆长度，
Figure PCTCN2022110580-appb-000002
为第t-l i点坐标的x序列的n次方，l i表示离散域核函数的点坐标。
优选地，所述第e次差值通过NLMS算法进行更新。
优选地，所述对所述最优串行信号进行处理得到频域信号包括：
将所述最优串行信号转换成并行信号；
对所述并行信号进行匹配滤波处理；
对匹配滤波处理后的并行信号进行快速傅里叶变换，得到频域信号。
优选地，所述频域信号为：
Figure PCTCN2022110580-appb-000003
式中，
Figure PCTCN2022110580-appb-000004
为循环卷积算子，Y 1(k)和F(k)分别是y 1(t)和f(t)经快速傅里叶变 换后得到的频域信号，y 1(t)为经过n阶Volterra滤波器处理得到的串行信号，f(t)为滚降因子为0.5的平方根升余弦函数。
优选地，所述对所述频域信号进行信道估计处理输出补偿后信号包括：将所述频域信号采用三层复数值神经网络进行处理输出的补偿后信号为：
Figure PCTCN2022110580-appb-000005
式中，f 1(·)是tanh激活函数，
Figure PCTCN2022110580-appb-000006
和
Figure PCTCN2022110580-appb-000007
分别代表输入层到隐含层和隐含层到输出层的最优权重值，i＝1,2,...,m，m为输入层神经元的个数，j＝1,2,…,p，p代表隐含层神经元的个数，k＝1,2,...,m，输出层的神经元个数与输入层的神经元个数相等。
优选地，所述输入层到隐含层和隐含层到输出层的最优权重值的确定过程为：
分别对输入层到隐含层的权重值w jk和隐含层到输出层的权重值w ij赋予一个在[-0.1-0.1]之间的初始值，对所述频域信号进行第一次计算得到第一次补偿后信号Y 1(k)；
采用L-BFGS算法对输入层到隐含层的权重值w jk和隐含层到输出层的权重值w jk进行第s次(s＝1,2,…,S)次更新，并利用第s次更新后的
Figure PCTCN2022110580-appb-000008
和
Figure PCTCN2022110580-appb-000009
对所述频域信号进行第s+1次计算，得到第s+1次补偿后信号Y l+1(k)，直至第s+1次补偿信号Y s+1(k)与第s次补偿后信号Y l(k)的差值小于第二设定阈值时，第s次更新后的
Figure PCTCN2022110580-appb-000010
为输入层到隐含层的最优权重值，第s次更新后的
Figure PCTCN2022110580-appb-000011
为隐含层到输出层的最优权重值。
优选地，所述n阶Volterra滤波器的阶数为1时，该滤波器为线性滤波器；
所述n阶Volterra滤波器的阶数大于1时，该滤波器为非线性滤波器。
本发明还提供一种非线性均衡器，包括：
输入端口：用于连接失真信号的输出端
集成芯片：采用如上所述的多载波接入网失真信号的补偿方法的步骤实现失真信号补偿；
输出端口：用于输出所述集成芯片处理得到的补偿信号。
优选地，所述集成芯片包括：
n阶Volterra滤波模组：用于对所述失真信号进行n阶Volterra滤波处理，生成串行信号；
时域-频域变换模组：用于将所述串行信号转变成频域信号；
信道估计模组：用于对所述频域信号进行信道估计。
本发明所提供的多载波接入网失真信号的补偿方法及非线性均衡器，将失真信号输入到n阶Volterra滤波器中通过不断更新滤波处理后的信号与参考信号的差值，继而不断更新滤波器的抽头系数，利用不断更新后的抽头系数再对失真信 号进行滤波处理，直至第e+1次差值与第e次差值相差小于第一设定阈值时，输出第e+1次串行信号作为最优串行信号；通过多次滤波确定最优串行信号，可以在低阶滤波器的情况下也能很好地实现严重失真的抗干扰能力，最大化地使信号无衰减；将n阶Volterra滤波器处理后的最优串行信号转换成频域信号，对频域信号进行信道估计处理进一步补偿失真信号，使得信号衰减进一步减少；本发明能有效解决现有随着数据子载波数目的增加，光纤传输过程中的信号失真迅速增大，且致使系统性能恶化的问题，在低阶滤波器也能够很好地实现失真信号的补偿问题，避免高阶滤波器计算时间长及计算复杂的问题。
附图说明
为了更清楚的说明本发明实施例或现有技术的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单的介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。
图1为本发明所提供的多载波接入网失真信号的补偿方法的流程图；
图2为本发明所提供的多载波接入网失真信号的补偿方法的一种实施例的具体流程图；
图3为本发明实施例中的IM/DD FBMC传输系统的实验装置图；
图4为本发明实施例中测量的端到端信道响应图；
图5为本发明实施例中MZM调制前后的光谱图；
图6为本发明实施例中12.5/25-GBd FBMC 30-km SSMF传输系统中测量的所有子载波的SNR曲线图；
图7为本发明实施例中1th-5th处的子载波SNR曲线图；
图8为本发明实施例中210th-310th处的子载波SNR曲线图；
图9为本发明实施例中ROP＝-10dBm时，12.5/25-GBd FBMC 30-km SSMF系统中实测BER随着数据子载波数目变化图；
图10为本发明实施例中数据子载波数目为448时，12.5-GBd FBMC 30-km SSMF系统中没使用NLE的实测PSD曲线图；
图11为本发明实施例中数据子载波数目为448时，12.5-GBd FBMC 30-km SSMF系统中使用过NLE后的实测PSD曲线图；
图12为本发明实施例中数据子载波数目为448时，12.5-GBd FBMC 30-km SSMF系统中没使用NLE的实测SNR曲线图；
图13为本发明实施例中数据子载波数目为448时，12.5-GBd FBMC 30-km SSMF系统中使用过NLE后的实测SNR曲线图；
图14为本发明实施例中数据子载波数目为352时，25-GBd FBMC 30-km SSMF系统中没使用NLE的实测PSD曲线图；
图15为本发明实施例中数据子载波数目为352时，25-GBd FBMC 30-km SSMF系统中使用过NLE的实测PSD曲线图；
图16为本发明实施例中数据子载波数目为352时，25-GBd FBMC 30-km SSMF系统中没使用NLE的实测SNR曲线图；
图17为本发明实施例中数据子载波数目为352时，25-GBd FBMC 30-km SSMF系统中使用过NLE的实测SNR曲线图；
图18为本发明实施例中12.5-GBd FBMC信号的实测BER随接收光功率变化图；
图19为本发明实施例中数据子载波数目为448时，12.5-GBd系统使用LS处理后的星座图；
图20为本发明实施例中数据子载波数目为448时，12.5-GBd系统使用LE处理后的星座图；
图21为本发明实施例中数据子载波数目为448时，12.5-GBd系统使用NLE处理后的星座图；
图22为本发明实施例中25-GBd FBMC信号的实测BER随接收光功率变化图；
图23为本发明实施例中数据子载波数目为352时，25-GBd系统使用LS处理后的星座图；
图24为本发明实施例中数据子载波数目为352时，25-GBd系统使用LE处理后的星座图；
图25为本发明实施例中数据子载波数目为352时，25-GBd系统使用NLE处理后的星座图。
具体实施方式
本发明的核心是提供一种多载波接入网失真信号的补偿方法及非线性均衡器，主要用于解决现有的FBMC系统通过增加数据子载波的数量来提高数据速率时导致的信号失真迅速增大的问题。
为了使本技术领域的人员更好地理解本发明方案，下面结合附图和具体实施方式对本发明作进一步的详细说明。显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。
针对现有的FBMC系统可以通过增加数据子载波的数量来提高数据速率。然而，随着数据子载波数目的增加，光纤传输过程中的信号失真会迅速增大，致使系统性能恶化。因此需要选择合适的均衡器减轻非线性失真的干扰。
本发明为了实现失真信号的补偿，构建了一种非线性均衡器包括：n阶Volterra滤波模组，用于对失真信号进行n阶Volterra滤波处理，生成串行信号；时域变换模组，用于将串行信号转变成频域信号；信道估计模组，用于对所述频域信号进行信道估计。
在IM/DD FBMC传输系统中，当数据子载波数目和波特率增加时，ICI(载波间干扰)和ISI(抗符号间干扰)会变得非常严重。严重的非线性失阻碍了接 收到的FBMC信号的正确恢复。为解决这一问题，本发明在FBMC接收端引入NLE(非线性均衡器)对接收到的失真信号x(t)进行恢复，NLE主要由n阶Volterra滤波器和信道估计器组成。本发明实施例中主要是采用二阶Volterra滤波器和三层复数值神经网络(complex-valued neural network，CVNN)信道估计器组成。作为其他实施方式，Volterra滤波器的阶数和复数值神经网络的层数可以根据实际信号的失真情况确定。
请参考图1，图1为本发明提供的多载波接入网失真信号的补偿方法的流程图；具体如下：
FBMC传输系统通过信道传输得到x(t)，表示为：
Figure PCTCN2022110580-appb-000012
其中，N c和N S分别是数据子载波数目和FBMC符号数。a m,n是第m个子载波上的第n个QAM数据符号，原型滤波器f(t)是滚降因子为0.5的平方根升余弦(square root raised-cosine，SRRC)函数，j代表虚数，T是周期。
对失真信号的补偿过程主要是：首先，失真信号x(t)被n阶Volterra滤波器处理后得到y 1(t)，然后，将串行信号y 1(t)转换为并行信号，并对此并行信号进行匹配滤波和快速傅里叶变换(fast Fourier transform，FFT)后得到信号Y 2(k)。最后,Y 2(k)被CVNN信道估计器处理后得到NLE均衡器的输出信号Y(k)。
其中，Volterra滤波器可以有效抑制系统的线性和非线性失真，利用n阶Volterra滤波器对失真信号x(t)进行处理输出的y 1(t)可以表示为：
Figure PCTCN2022110580-appb-000013
式中，x(t)是n阶Volterra滤波器的输入信号，即失真信号，y 1(t)为经过n阶Volterra滤波器处理得到的串行信号，w n(l 1,l 2,…,l n)是n阶抽头系数，L为记忆长度。当n＝1时，该滤波器即为一个传统的线性滤波器，可以用于失真程度较小的信号处理；而当n>1时，该滤波器是一个非线性滤波器。
Volterra滤波器的性能很大程度上取决于滤波器阶数，滤波器的阶数越高，恢复失真信号的能力越好，但同时也会使计算复杂度大大增加。一般来说，二阶Volterra滤波器足以均衡IM/DD传输系统中的信号，本实施例中使用的是低复杂度的二阶Volterra滤波器来处理失真信号。
二阶Volterra滤波器的结构如图2中所示，图2为本实施例中采用的非线性均衡器的结构图，首先，二阶Volterra滤波器的输入x(t)是一个非理想的FBMC失真信号，经过线性和非线性滤波处理后得到输出信号y 1(t)。
其中，通过计算y 1(t)与理想参考信号之间的差值得到误差e(t)，通过归一化最小均方算法(normalized least mean square,NLMS)不断更新e(t)，从而不断更新线性和非线性抽头系数w n，当e(t)值趋于稳定时，确定此时的w n即为最佳抽头系 数。
最优串行信号：将失真信号输入n阶Volterra滤波器进行e(e＝1,2,…,E)次滤波处理得到第e次串行信号，将第e串信号与设定参考信号求差得到第e次差值；当第e+1次差值与第e次差值相差小于第一设定阈值时，输出第e+1次串行信号作为最优串行信号；
最优抽头系数的确定：将失真信号输入n阶Volterra滤波器根据第一抽头系数进行第一次滤波处理得到第一串行信号，与设定参考信号求差得到第一误差；
利用归一化最小均方算法第一次更新第一误差从而第一次更新抽头系数，n阶Volterra滤波器利用第一次更新抽头系数对所述失真信号进行第二次滤波处理得到第二串行信号，并与设定参考信号求差得到第二误差；
当第二误差与第一误差相差小于设定阈值时，第一次更新的抽头系数为最优抽头系数；
否则利用归一化最小均方算法更新第e误差(e＝2,3,…,E)，从而第e次更新抽头系数，n阶Volterra滤波器利用第e次更新抽头系数对所述失真信号进行第e+1次滤波处理得到第e+1串行信号，并与设定参考信号求差得到第e+1误差；
直至第e+1误差与第e误差相差小于设定阈值，此时第e次更新的抽头系数为最优抽头系数。
然后，输出信号y 1(t)进入到匹配滤波和FFT模块。经过匹配滤波和FFT运算，可以得到频域信号Y 2(k)：
Figure PCTCN2022110580-appb-000014
式中，
Figure PCTCN2022110580-appb-000015
代表循环卷积算子，Y 1(k)和F(k)分别是y 1(t)和f(t)经快速傅里叶变换后得到的频域信号。
最后，CVNN信道估计器对Y 2(k)进行处理。采用简单的三层CVNN结构。最终，均衡后的输出信号Y(k)表示如下：
Figure PCTCN2022110580-appb-000016
式中，f 1(·)是tanh激活函数，
Figure PCTCN2022110580-appb-000017
和
Figure PCTCN2022110580-appb-000018
分别代表输入层到隐含层和隐含层到输出层的最优权重值，i＝1,2,...,m，m为输入层神经元的个数，j＝1,2,…,p，p代表隐含层神经元的个数，k＝1,2,...,m，输出层的神经元个数与输入层的神经元个数相等。
Y 2(k)乘以权重
Figure PCTCN2022110580-appb-000019
后经过f 1(·)处理得到隐含层的输入。然后，将隐含层的输入值乘以权重
Figure PCTCN2022110580-appb-000020
后再次经过f 1(·)处理得到输出信号Y(k)。其中，分别对输入层到隐含层的权重值w ij和隐含层到输出层的权重值w jk赋予一个在[-0.1-0.1]之间的初始值；通过L-BFGS算法不断迭代更新权重值，直至最终输出信号趋于稳定，以此确定最优权重值。
其中，最优权重值的具体确定方式为：分别对输入层到隐含层的权重值w jk和隐含层到输出层的权重值w ij赋予一个在[-0.1-0.1]之间的初始值，对所述频域信号进行第一次计算得到第一次补偿后信号Y 1(k)；
采用L-BFGS算法对输入层到隐含层的权重值w jk和隐含层到输出层的权重值w jx进行第s次(s＝1,2,…,S)次更新，并利用第s次更新后的
Figure PCTCN2022110580-appb-000021
和
Figure PCTCN2022110580-appb-000022
对所述频域信号进行第s+1次计算，得到第s+1次补偿后信号Y s+1(k)，直至第s+1次补偿信号Y s+1(k)与第s次补偿后信号Y s(k)的差值小于第二设定阈值时，第s次更新后的
Figure PCTCN2022110580-appb-000023
为输入层到隐含层的最优权重值，第s次更新后的
Figure PCTCN2022110580-appb-000024
为隐含层到输出层的最优权重值。
此外，如果信号失真不是很严重，可以直接使用线性均衡器，线性均衡器(LE)足以将其很好地恢复出来。在LE中，信号x(t)首先有线性前馈均衡器(feed-forward equalizer,FFE)恢复，然后再匹配滤波器、FFT和CVNN信道估计器处理。LE的结构与NLE类似，由FEE、匹配滤波器、FFT、CVNN信道估计器组成，线性滤波器即为FFE，FFE的输出可以表示为：
Figure PCTCN2022110580-appb-000025
其中，FFE的实现原理类似于二阶Volterra滤波器，也是通过NLMS算法不断更新误差从而得到最优的线性滤波器抽头系数。
而在多载波传输系统中，当数据子载波数目少的时候，系统的非线性失真并不会很严重，此时，简单的LS信道估计器就可以很好地恢复处失真信号，LS算法的估计准则是最小化的代价函数：
Figure PCTCN2022110580-appb-000026
其中，X k、Y k分别是发射端和接收端的导频信号，
Figure PCTCN2022110580-appb-000027
是频域信道想用的估计值，为了获得代价函数
Figure PCTCN2022110580-appb-000028
的最小值，
Figure PCTCN2022110580-appb-000029
关于
Figure PCTCN2022110580-appb-000030
的倒数值应该为0：
Figure PCTCN2022110580-appb-000031
因此，导频信号的信道估计值H LS为：
Figure PCTCN2022110580-appb-000032
显然，LS信道估计算法可以根据发送和接收端的导频信号估计频域中的信道响应，并且其计算复杂度低，但是LS没有考虑到噪声的影响，当噪声增加时，LS信道估计的性能就会变差。因此，当数据子载波的数量和波特率增加时，严重的信号失真使得LS信道估计算法无法达到预期性能。
为了进一步说明本发明提出的NLE能够很好地实现失真信号的补偿，利用下述试验进行详细说明。
请参考图3，图3是IM/DDFBMC传输系统的实验装置图。从图中可以看出，在发射端的DSP中，首先伪随机二进制序列(pseudo-random binary sequence， PRBS)被映射为Offset-64 QAM信号。然后，进行IFFT运算和SRRC滤波器组的滤波操作，接着添加伪噪声(pseudo-noise，PN)信号以便于接收端进行信号同步。最后，将此复数信号X(t)的实部和虚部并置得到串行实值信号。之后，将此串行实值信号加载到采样率为50-GSa/s的任意波形发生器(arbitrary waveform generator,AWG)中来实现数模(digital-to-analog,D/A)转换。其中，AWG的带宽约为10-GHz，其端到端响应如图4所示。然后，AWG的输出被马赫-曾德尔(Mach-Zehnder modulator，MZM)调制器调制成波长为1550.116nm的连续波(continuous wave，CW)。MZM调制器的输出功率约为5.9dBm，经过MZM调制前后的光谱图如图5所示。调制后的光信号通过30km SSMF的传输后进入噪声控制部分。它由可变光衰减器(variable optical attenuator，VOA)和掺铒光纤放大器(erbium-doped fiber amplifier，EDFA)组成。噪声控制部分是用来测量BER来模拟各种噪声电平，一般将EDFA的输入信号功率定义为接收光功率(received optical power，ROP)。另一个VOA是用来调整带宽约为10GHz的光电探测器(photo detector，PD)的输入功率。最后，PD将传输的光信号转换为电信号，采样率为50GSa/s的实时示波器采集数据供离线DSP处理。在接收端的DSP中，首先对采集到的数字信号进行逆并置，将实部和虚部数据重新组合成复数形式进行后续处理。然后，依次通过均衡器、匹配滤波器组、FFT、信道估计、Offset-64QAM解映射恢复出原始的发送信号。最后，对系统的BER进行计算。
整个实验过程中，子载波和符号的总数分别为512和64，图6、图展示了12.5/25-GBd FBMC 30-km SSMF传输系统中测量的所有子载波的SNR曲线，从图6中可以明显的观察到光纤色散和拍频干扰对SNR值的影响。首先12.5GBd和25GBd信号都存在明显的拍频干扰，前几个子载波的SNR都偏低，如图7中所示，由于前几个子载波的SNR相对较低，因此最好避免它们用于数据加载，图7也可以看出光纤色散对25-GBd传输系统的影响比对12.5-GBd传输系统的影响更大。参考图8，在25-GBd传输系统中，由光纤色散引起的严重功率衰落发生在210 th-310 th处数据子载波处，导致SNR曲线波动较大。所以为了产生所需的BER性能，210 th-310 th处的子载波应该被设置为空载波。综上所述，在波特率为12.5/25-GBd系统中数据子载波的分配策略如表1中所示。在12.5GBd IM/DD FBMC传输系统中，本实施例中分别测量了数据子载波数目为128、320和448时的BER曲线。为了避免拍频干扰，数据子载波应该分别放置在193 th-320 th、97 th-416 th和33 th-480 th处。在25GBdIM/DD传输系统中，分别测量了数据子载波数目为128、256和352时的BER曲线，为了避免拍频干扰和色散引起的功率衰减，数据子载波应该放置在120 th-183 th&330 th-393 th、56 th-183 th&330 th-457 th和27 th-202 th&311 th-486 th处。
表1：
Figure PCTCN2022110580-appb-000033
Figure PCTCN2022110580-appb-000034
此外，本实施例中还通过测量12.5/25-GBd FBMC传输系统的SNR、PSD、BER曲线和星座图来验证NLE的性能，还计算了不同数目的数据子载波和波特率下的净比特率。
(1)12.5/25-GBd FBMC系统中SNR和PSD分析；
请参考图9，图9是当ROP＝-10dBm时，12.5/25-GBd FBMC 30-km SSMF系统中实测BER随着数据子载波数目变化图。在12.5-GBd传输系统中，随着数据子载波数目从128增加到448时，使用NLE后的BER性能明显要优于没有使用过NLE的性能，如图9中灰色实线和虚线菱形标记的曲线所示。此外，由于ICI、ISI和非线性失真的影响，数据子载波的数目越多，NLE的效果越好。图9中黑色实线和虚线圆圈标记的曲线是25-GBd FBMC传输系统中使用和未使用NLE方案后的BER曲线。由于25-GBd传输系统遭受严重的高频功率衰落和带宽受限失真，NLE方案虽然可以在一定程度上提高BER的性能，但是无法达到与12.5-GBd传输系统相同的性能。
本实施例中该试验测量了12.5/25-GBd FBMC 30-km SSMF传输系统中的PSD和SNR曲线，如图10-图17所示。首先，在12.5-GBd系统中，当数据子载波数目为448时，图10和图11分别是没使用和使用过NLE后的实测PSD曲线，图12和图13分别是没使用和使用过NLE后的实测SNR曲线。通过利用所提出的NLE方案可以实现明显的PSD提升，如图11所示。同时，NLE方案也可以补偿失真信号并提高SNR的值，如图13所示，尤其是第33th-144th和373th-480th处的SNR值改善最为明显。类似地，在25-GBd传输系统中，当数据子载波数目为352时，图14和图15分别是没使用和使用过NLE后的实测PSD曲线，图16和图17分别是没使用和使用过NLE后的实测SNR曲线。从图15和图17可以观察到，信号失真通过利用NLE都得到了有效缓解，PSD和SNR值都得到了改善。虽然在功率衰减严重部分的数据子载波SNR仍然相对较低，但NLE方案提高了数据子载波在27th-105th和408th-486th处的SNR值，从而提高了平均信噪比。因此，在25-GBd FBMC传输系统中，为了达到良好的性能，NLE是必不可少的。
(2)12.5-GBd FBMC系统中BER分析；
一般来说，随着数据子载波数目的增加，IM/DD FBMC传输系统的ICI和ISI会越来越严重。因此，传统的LS信道估计算法无法正确恢复出原始传输信号。而且，LE只能抑制线性失真，而不能减轻非线性失真的影响。因此，需要使用NLE来缓解系统中的非线性失真。为了验证NLE在12.5-GBd IM/DD FBMC传输系统中的可行性和优越性能，本实施例还测量了在数据子载波数目为128、320 和448时经背靠背(back-to-back，BTB)和30-km传输后的BER曲线，如图18所示。
当数据子载波数目从128增加到448时，NLE的性能始终优于LE和LS，如图18中黑色、灰色和浅灰色方形标记曲线所示。当数据子载波数为128时，即全部子载波的四分之一用于加载数据，此时信号失真小，LS就足以缓解这些失真，LE和NLE的改进并不大。LS、LE和NLE这三种方案分别在ROP为-19dBm、-20dBm和-21dBm时达到HD-FEC门限值，如图18中黑色圆圈、上三角标记和方形标记的曲线所示。然而，当数据子载波数目增加到320时，LS算法需要更高的ROP以产生低于HD-FEC的BER值。相反，LE和NLE仍然有很好的性能，并且相比于LE，NLE方案在HD-FEC值为3.810-3时实现了大约2-dB的接收灵敏度提升。当数据子载波数目增加到448时，与LE相比，NLE仍可在HD-FEC门限值时实现大约2-dB的性能提升。同时，图18中的实线和虚线分别对应于BTB和30-kmSSMF传输后的情况，可以明显的看到，和BTB传输相比，经过30-km光纤传输后造成的损失很小，几乎可以忽略不计。
图19-图21是当数据子载波数目为448和ROP为-6dBm时，分别使用LS、LE和NLE方案处理后的64-QAM星座图。由图19到图21,可以观察到星座图在不断收敛，这与BER的性能变化是一致的。
(3)25-GBd FBMC系统中BER分析；
本实施例进一步验证NLE方案在25-GBd IM/DD FBMC传输系统上的性能。随着波特率的增加，系统的高频功率衰减、带宽受限和非线性失真变得越来越严重。因此，NLE在25-GBd传输系统中起着至关重要的作用。图22是数据子载波数目分别为128、256和320时，25-GBd FBMC信号的实测BER随接收光功率变化图。图22中的实线和虚线分别对应于BTB和30-km SSMF传输后的情况。当数据子载波数目从128增加到352时，由于非线性失真严重，LS算法的BER曲线超出了HD-FEC门限值，如图22中黑色和浅灰色圆圈标记的曲线所示。因此，使用LS算法无法在接收端恢复出失真信号。LE和NLE的补偿效果要远远好于LS。当数据子载波数目为128时，与LE方案相比，NLE在HD-FEC门限值时可实现大约1dB的接收灵敏度提升。当数据子载波的数目增加到256和352时，LE无法很好的恢复出失真信号，而NLE仍然可以实现更好的BER性能。特别地，当数据子载波数目为256和352时，分别在接收光功率为-11dBm和-5dBm处接近HD-FEC门限值。
综上所述，所提出的NLE方案在更多有效数据子载波的高数据速率FBMC传输系统中具有出色的性能。性能优良的信道估计器增强了二阶Volterra滤波器的性能，能够更好的处理严重的非线性失真，从而使系统的BER降低到HD-FEC门限值之下。图23-图25是数据子载波数目为352，ROP为-3dBm时分别采用LS、LE和NLE方案的64-QAM星座图。与使用LS和LE方案相比，采用NLE方案的星座图有更好的收敛性。
(4)12.5/25-GBd FBMC系统的净比特率分析；
进一步，计算具有不同数据子载波数目的12.5/25-GBd FBMC传输系统的净比特率，得到结果如表2所示。去除二阶Volterra滤波器1.5％的训练序列和CVNN信道估计器10％的训练序列所带来的冗余，净比特率R通过下式计算：
Figure PCTCN2022110580-appb-000035
其中，B和E分别是波特率和信息熵，N c和N分别是数据子载波数和总载波数。对于IM/DD FBMC 64-QAM传输系统来说，E为6比特/符号，B为12.5/25-GBd，N为512。在不同数据子载波数目和波特率的情况下，计算得到的净比特率如表2所示。从表2中可以得出结论，通过使用NLE方案，12.5-GBd传输系统可以实现58.18-Gb/s的净比特率。25-GBd传输系统可以实现91.42-Gb/s的净比特率。
表2：
Figure PCTCN2022110580-appb-000036
综上所述，由于优越的抗色散性能，IM/DD FBMC-PON系统在高速接入网络中有很大的应用前景。净比特率高度依赖于所用的数据子载波数目。然而，数据子载波数目越多，信号失真越严重。本实施例中提出并实验验证了12.5/25-GBd IM/DD FBMC 30-km SSMF传输系统中NLE计划的优越性。NLE能在数据子载波数目多并且高波特率的系统下处理严重的非线性失真。在NLE的辅助下，当数据子载波数目增加到448时，12.5-GBd FBMC系统实现了58.18-Gb/s的净比特率。并且，与LE相比，NLE方案在HD-FEC值为
Figure PCTCN2022110580-appb-000037
时实现了大约2-dB的接收灵敏度提升。在25-GBd FBMC传输系统中，当数据子载波数目增加到352时，LS和LE均无法恢复出失真信号。但NLE仍能拥有良好的性能，并且在接收光功率为-5dBm时达到HD-FEC门限值，从而实现91.42-Gb/s的净比特率。因此，本发明所提出的频谱高效的FBMC传输系统有利于无源光网络的容量升级。最终，在提出的NLE方案的辅助下，可以在带宽约为10GHz，30公里SSMF的传输系统中实现91.42-Gb/s的净比特率。
本发明还提供了一种信道均衡器，包括：
输入端口：用于输入失真信号，本实施例中连接有FBMC系统的输出端；
集成芯片：采用如上所述的多载波接入网失真信号的补偿方法的步骤对输入的失真信号进行处理；
输出端口：将集成芯片处理完的信号输出。
通过输入端口连接FBMC系统的输出端，FBMC系统将信号输入至集成芯 片中，通过集成芯片内置的n阶Volterra滤波模组、时域变换模组、信道估计模组对FBMC系统输入的信号进行补偿处理。
其中，集成芯片包括：
n阶Volterra滤波模组：对所述失真信号进行n阶Volterra滤波处理，生成串行信号；
时域变换模组：将串行信号转变成频域信号；
信道估计模组：对频域信号进行信道估计。
本说明书中各个实施例采用递进的方式描述，每个实施例重点说明的都是与其它实施例的不同之处，各个实施例之间相同或相似部分互相参见即可。对于实施例公开的装置而言，由于其与实施例公开的方法相对应，所以描述的比较简单，相关之处参见方法部分说明即可。
专业人员还可以进一步意识到，结合本文中所公开的实施例描述的各示例的单元及算法步骤，能够以电子硬件、计算机软件或者二者的结合来实现，为了清楚地说明硬件和软件的可互换性，在上述说明中已经按照功能一般性地描述了各示例的组成及步骤。这些功能究竟以硬件还是软件方式来执行，取决于技术方案的特定应用和设计约束条件。专业技术人员可以对每个特定的应用来使用不同方法来实现所描述的功能，但是这种实现不应认为超出本发明的范围。
结合本文中所公开的实施例描述的方法或算法的步骤可以直接用硬件、处理器执行的软件模块，或者二者的结合来实施。软件模块可以置于随机存储器(RAM)、内存、只读存储器(ROM)、电可编程ROM、电可擦除可编程ROM、寄存器、硬盘、可移动磁盘、CD-ROM、或技术领域内所公知的任意其它形式的存储介质中。
以上对本发明所提供的多载波接入网失真信号的补偿方法及非线性均衡器进行了详细介绍。本文中应用了具体个例对本发明的原理及实施方式进行了阐述，以上实施例的说明只是用于帮助理解本发明的方法及其核心思想。应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以对本发明进行若干改进和修饰，这些改进和修饰也落入本发明权利要求的保护范围内。

Claims (10)

  1. 一种多载波接入网失真信号的补偿方法，其特征在于，包括：
    将失真信号输入n阶Volterra滤波器进行第e次n阶Volterra滤波处理得到第e次串行信号，对所述第e次串行信号与设定参考信号求差得到第e次差值；
    当所述第e次差值与第e-1次差值相差不小于第一设定阈值时，更新所述第e次差值，利用更新后的差值对n阶Volterra滤波器的抽头系数进行更新，根据更新后的抽头系数对所述失真信号进行第e+1次n阶Volterra滤波处理，其中，e＝1,2,…,E，E为滤波总次数；
    当所述第e次差值与第e-1次差值相差小于第一设定阈值时，输出所述第e次串行信号作为最优串行信号；
    对所述最优串行信号进行处理得到频域信号；
    对所述频域信号进行信道估计输出补偿后信号，完成对失真信号的补偿。
  2. 根据权利要求1所述的多载波接入网失真信号的补偿方法，其特征在于，所述最优串行信号为：
    Figure PCTCN2022110580-appb-100001
    式中，x(t)是n阶Volterra滤波器的输入信号即失真信号，y 1(t)为经过n阶Volterra滤波器滤波处理得到的最优串行信号，w 1为n阶Volterra滤波器的第1阶核函数，w 2(l 1,l 2)为n阶Volterra滤波器的第2阶核函数，w n(l 1,l 2,…,l n)是所述n阶Volterra滤波器的第n阶核函数，所有核函数即为n阶Volterra滤波器的最佳抽头系数，L为记忆长度，
    Figure PCTCN2022110580-appb-100002
    为第t-l i点坐标的x序列的n次方，l i表示离散域核函数的点坐标。
  3. 根据权利要求1所述的多载波接入网失真信号的补偿方法，其特征在于，所述第e次差值通过NLMS算法进行更新。
  4. 根据权利要求1所述的多载波接入网失真信号的补偿方法，其特征在于，所述对所述最优串行信号进行处理得到频域信号包括：
    将所述最优串行信号转换成并行信号；
    对所述并行信号进行匹配滤波处理；
    对匹配滤波处理后的并行信号进行快速傅里叶变换，得到频域信号。
  5. 根据权利要求4所述的多载波接入网失真信号的补偿方法，其特征在于，所述频域信号为：
    Figure PCTCN2022110580-appb-100003
    式中，
    Figure PCTCN2022110580-appb-100004
    为循环卷积算子，Y 1(k)和F(k)分别是y 1(t)和f(t)经快速傅里叶变 换后得到的频域信号，y 1(t)为经过n阶Volterra滤波器处理得到的串行信号，f(t)为滚降因子为0.5的平方根升余弦函数。
  6. 根据权利要求1所述的多载波接入网失真信号的补偿方法，其特征在于，所述对所述频域信号进行信道估计处理输出补偿后信号包括：将所述频域信号采用三层复数值神经网络进行处理输出的补偿后信号为：
    Figure PCTCN2022110580-appb-100005
    式中，f 1(·)是tanh激活函数，
    Figure PCTCN2022110580-appb-100006
    和
    Figure PCTCN2022110580-appb-100007
    分别代表输入层到隐含层和隐含层到输出层的最优权重值，i＝1,2,...,m，m为输入层神经元的个数，j＝1,2,…,p，p代表隐含层神经元的个数，k＝1,2,...,m，输出层的神经元个数与输入层的神经元个数相等。
  7. 根据权利要求6所述的多载波接入网失真信号的补偿方法，其特征在于，所述输入层到隐含层和隐含层到输出层的最优权重值的确定过程为：
    分别对输入层到隐含层的权重值w jk和隐含层到输出层的权重值w ij赋予一个在[-0.1-0.1]之间的初始值，对所述频域信号进行第一次计算得到第一次补偿后信号Y 1(k)；
    采用L-BFGS算法对输入层到隐含层的权重值w jk和隐含层到输出层的权重值w jk进行第s次(s＝1,2,…,S)次更新，并利用第s次更新后的
    Figure PCTCN2022110580-appb-100008
    和
    Figure PCTCN2022110580-appb-100009
    对所述频域信号进行第s+1次计算，得到第s+1次补偿后信号Y l+1(k)，直至第s+1次补偿信号Y s+1(k)与第s次补偿后信号Y l(k)的差值小于第二设定阈值时，第s次更新后的
    Figure PCTCN2022110580-appb-100010
    为输入层到隐含层的最优权重值，第s次更新后的
    Figure PCTCN2022110580-appb-100011
    为隐含层到输出层的最优权重值。
  8. 根据权利要求1所述的多载波接入网失真信号的补偿方法，其特征在于，所述n阶Volterra滤波器的阶数为1时，该滤波器为线性滤波器；
    所述n阶Volterra滤波器的阶数大于1时，该滤波器为非线性滤波器。
  9. 一种非线性均衡器，其特征在于，包括：
    输入端口：用于连接失真信号的输出端；
    集成算法芯片：采用如上述权利要求1-8任一项所述的多载波接入网失真信号的补偿方法的步骤实现失真信号补偿；
    输出端口：用于输出所述集成芯片处理得到的补偿信号。
  10. 根据权利要求9所述的非线性均衡器，其特征在于，所述集成芯片包括：
    n阶Volterra滤波模组：用于对所述失真信号进行n阶Volterra滤波处理，生成串行信号；
    时域-频域变换模组：用于将所述串行信号转变成频域信号；
    信道估计模组：用于对所述频域信号进行信道估计。
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