CN113300779B - Pilot-assisted CO-FBMC/OQAM system phase noise compensation method - Google Patents

Abstract

A pilot frequency auxiliary phase noise compensation method in a CO-FBMC/OQAM system is characterized in that a receiving end firstly adopts an Extended Kalman Filter (EKF) algorithm to compensate CPE noise of data on the basis of pilot frequency data, and carries out pre-judgment after compensation is finished; then selecting data in a proper range after the CPE is compensated, recording the position of the data, and using the data after the data is pre-judged as a data estimation value symbol of a transmitting end for the use of the following steps; and then, constructing a DCT basis function, carrying out approximate estimation on the phase noise, establishing a DCT time domain model of the phase noise, solving a DCT coefficient by utilizing LS estimation, and carrying out more accurate compensation on the phase noise in a time domain. The invention ensures that the system has higher tolerance to the phase noise generated by the laser and has lower algorithm calculation complexity.

Description

Pilot-assisted CO-FBMC/OQAM system phase noise compensation method

Technical Field

The invention belongs to the field of optical fiber communication, and particularly relates to a phase noise compensation method in a coherent optical filter bank multi-carrier/offset quadrature amplitude modulation system.

Background

Since the Coherent Optical filter bank multi-carrier/offset Quadrature Amplitude Modulation (CO-FBMC/OQAM Coherent Optical-offset Quadrature Amplitude Modulation-based filter multicarrier) system adopts a prototype filter with excellent time-Frequency focusing characteristics, it does not need to add a cyclic prefix and a guard band, and compared with the conventional multi-carrier Coherent Optical-Orthogonal Frequency Division Multiplexing (OFDM) system, the system has the advantages of low out-band radiation, high spectrum efficiency and the like, and is considered as one of the future development directions of multi-carrier Optical transmission technologies.

A typical CO-FBMC/OQAM system structure is shown in fig. 1, and the whole system can be divided into 5 modules: the system comprises a system transmitting end module 101, an optical modulation module 102, an optical fiber transmission module 103, a photoelectric detection module 104 and a system receiving end module 105. The transceiving process of the system will be described in detail with reference to fig. 1. The data 106 input in series by the CO-FBMC/OQAM system is firstly converted into parallel data by a serial-parallel conversion module 107; 108, carrying out QAM modulation on the parallel data according to different QAM modulation modes to obtain a complex signal; 109, carrying out OQAM preprocessing: respectively taking a real part and an imaginary part of each QAM data to obtain a corresponding in-phase component and a corresponding quadrature component, and then delaying the quadrature component relative to the in-phase component by half symbol period for transmission; the inverse fast fourier transform IFFT module 110 converts the signal from the frequency domain to the time domain; after passing through a polyphase filter bank 111, parallel-to-serial conversion 112 is performed to convert the parallel data into serial data again; the digital-to-analog converter 113 converts the digital signal into an analog signal and passes through a low-pass filter 114. The same-direction component 115 and the orthogonal component 116 are respectively amplified into an I/Q modulator to realize orthogonal modulation; the I/Q modulator consists of 2 Mach-Zehnder modulator (MZM) 119 and 120 with two arms and a modulator 121, the MZM modulator realizes the modulation of signals, and the modulator 121 controls the phase difference of 90 degrees between an in-phase component I and a quadrature component Q of the optical modulation; the transmitting laser 117 is split into two identical lasers by a beam splitter 118 for driving two optical modulators 119 and 120; the two optical modulation output signals are changed into a single optical signal through the beam combiner 122; the signal is then transmitted to a fibre channel for transmission. The generated CO-FBMC/OQAM signals are transmitted after being transmitted by optical fibers, and then are transmitted after being compensated for optical fiber loss by a direct optical-optical amplifier-erbium-doped optical fiber amplifier (EDFA) 124; and then through a band pass filter 125. After optical fiber transmission, the optical domain signal is converted into an electrical domain signal through the photoelectric detection module 104; the CO-FBMC/OQAM receiving end local laser 126 is split into two beams of identical laser light by a beam splitter, 127 denotes a 90 ° phase shifter, 128 and 129 denote two couplers for driving 4 photodiodes 130, 131, 132 and 133; the obtained in-phase component I and quadrature component Q are subjected to analog-to-digital conversion by the analog-to-digital converter 135 after passing through the low-pass filter 134 to convert analog signals into digital signals; converting the single-path signal into a multi-path signal through parallel-serial conversion 136; through a polyphase structure filter bank 137; the fast fourier transform 138 converts the time domain signal to the frequency domain; and then 139 digital signal processing is carried out, 140 real part processing is carried out on the data obtained after 139, OQAM post-processing recovery is carried out to obtain QAM complex symbols, 141QAM demodulation is carried out, and serial data output 143 is obtained through parallel-serial conversion 142.

However, the orthogonality between the sub-carriers of CO-FBMC/OQAM is only valid in the real number domain, which causes inter-carrier interference and inter-symbol interference in the system, and the transmission symbol is affected by the surrounding symbols, i.e. so-called Intrinsic imaginary interference (IMI) in the FBMC system, so the phase noise compensation method of CO-OFDM system cannot be used in the techniques such as channel equalization, which causes the system transmission performance to be seriously degraded. And because the CO-FBMC/OQAM system has longer symbol length and high peak-to-average power ratio, the phase noise mainly comes from laser linewidth and link nonlinearity, and the CO-FBMC/OQAM system is more easily influenced by the phase noise than the CO-OFDM system, and the rotation and divergence of a QAM modulation constellation diagram at a receiving end are generated, thereby causing the system performance degradation. Therefore, how to compensate the phase noise efficiently is a key problem of the CO-FBMC/OQAM system, wherein the imaginary part interference inherent to the system becomes a difficult problem that must be solved by the phase noise processing algorithm.

The phase noise compensation algorithms of the current CO-FBMC/OQAM system are mainly divided into two categories, namely a blind phase noise compensation algorithm and a pilot frequency-based phase noise compensation algorithm. Among them, a blind phase estimation method that improves spectral efficiency is widely used. For example, trunk-Hien Nguyen et al propose an improved blind phase search (M-BPS) method for FBMC/OQAM systems (document 1, Nguyen T H, Louvaux J, Gorza S P, et al.simple feedback for carrier phase estimation for optical FBMC/OQAM systems [ J ]. IEEE photonics technology drivers, 2016,28(24): 2823-. The method does not need any complex multiplication operation, so the complexity of the algorithm is reduced compared with the common blind phase search algorithm (BPS). The computational complexity and accuracy of the algorithm itself depends on the number of phases tested. However, when the laser linewidth is large, these BPS algorithms are still limited to systems with a small number of subcarriers. A time domain phase noise estimation algorithm based on orthogonal basis spreading is also applied to the FBMC/OQAM system. (document 2, X.Fang, Y.Xu, Z.Chen, et al.time-domain least square channel estimation for polarization-division-multiplexed CO-OFDM/OQAMSYSTEMS [ J ], IEEE J.Lightwave technol.,2016,34(3), pp.891-900, i.e., X.Fang, Y.Xu, Z.Chen, et al. time-domain least mean square channel estimation in FBMC/OQAM systems [ J ]. IEEE lightwave technology, 2016,34(3), pp.891-900). An extended Kalman filtering method is also applied to an FBMC/OQAM system in which the laser linewidth is small (document 3, t.nguyen, f.rottenberg, s.gorza, et al.extended Kalman filter for carrier phase recovery in Optical filter bank multicarrier QAM systems [ C ], in: Proc, Optical Fiber Communication Conference,2017, Paper th4c.3. i.e., t.nguyen, f.rottenberg, s.gorza, et al. Optical FBMC-OQAM system carrier phase recovery [ C ], Fiber optic Conference,2017, Paper th4c.3.). By combining the blind algorithms, although a system with a smaller laser line width obtains a better phase noise compensation effect, a commercial large-line-width laser system cannot well realize the phase noise compensation effect, and the system still has higher complexity and is difficult to apply in real time.

Compared with a blind phase noise compensation algorithm, the complexity of the pilot frequency-based phase noise algorithm is one hundredth or one thousandth of the complexity, and real-time application is easy to realize. In terms of its spectral efficiency, if the pilot algorithm has a 3% to 5% spectral efficiency drop, it is quite acceptable for multi-carrier systems. The Thanh Nguyen proposes a pseudo pilot coding method (document 4, t.h.nguyen, s.t.le, r.nissel, et al.pseudo-pilot coding based phase noise estimation for coherent optical FBMC-OQAM transmissions. journal of light wave Technology,2018,36(14): 2859:. t.h.nguyen, s.t.le, r.nissel, et al. coherent light FBMC-OQAM phase noise estimation based on pseudo pilot coding. light wave Technology,2018,36(14): 2859-. When the filter is fixed, the impulse response of the system is also kept unchanged, namely the influence coefficient of the symbols around the transmission symbol on the impulse response is unchanged, therefore, the method enables the influence of the data symbols around the pilot symbol on the pilot to approach 0 through encoding at the transmitting end, and the imaginary part interference of the pilot symbol approaches 0 during the transmission process, thereby the phase noise value of the current symbol can be estimated through the pilot position. Biyu You et al propose a method of combining an "encoding" method with extended Kalman filtering (document 5, You B, Yang L, Luo F, et al, Pilot-based extended Kalman filter for phase noise estimation in CO-FBMC/OQAM systems [ J ]. Optics Communications,2019,443:116-122. that is, You B, Yang L, Luo F, et al, CO-FBMC/OQAM systems [ J ]. optical communication, 2019,443:116-122 ]) and (patent 1, 201811394725.8). The "coding" of this method differs from document 4 in that it brings the imaginary interference at the pilot close to 0 by setting all 8 symbols around the pilot symbol to 0, but it is clear that this method increases the spectral loss, so only one pilot position is set on each symbol, and finally the result is made more accurate with the extended kalman filter. Although the pilot method has a lower complexity than the blind estimation algorithm and can avoid the inherent problem of fuzzy phase estimation in the blind algorithm, the effect is still not ideal in the large-linewidth laser system. This is because the above pilot algorithm is still limited to estimating only common phase noise (CPE) among phase noise, and neglecting inter-carrier interference (ICI). When the laser line width is smaller, the ICI effect is smaller and therefore negligible, but when the laser line width is increased, the phase noise is increased therewith, the ICI cannot be ignored, and at this time, only compensating the CPE cannot achieve a good phase compensation effect.

Therefore, it is important to effectively compensate phase noise including ICI noise in CO-FBMC/OQAM systems using a pilot-aided phase noise compensation algorithm.

Disclosure of Invention

In order to overcome the defects of the prior art, in the CO-FBMC/OQAM system, phase noise can be approximated by discrete cosine transform due to low-pass characteristic, and judgment data obtained after CPE compensation is realized by combining pilot frequency assisted extended Kalman filtering.

The technical scheme adopted by the invention for solving the technical problems is as follows:

a pilot-assisted CO-FBMC/OQAM system phase noise compensation method, comprising the steps of:

(1) and (3) transmitting end signal processing: 4/16/64QAM mapping is carried out on the data respectively to obtain a complex signal X ═ X^I+jX^QThen, the complex symbols are preprocessed by OQAM to obtain PAM symbols a_m,n∈{X^I,X^QWhere M is 0,1, 2., M-1, n is 0,1, 2., Ns-1, M denotes the number of subcarriers, Ns denotes the number of FBMC symbols, where a denotes the number of FBMC symbols_u,n，a_v,nSet as pilot data, u, v are any two sub-carriers, and to avoid adverse effects on the pilot-assisted phase noise compensation algorithm, the data of two sub-carriers adjacent to the two sub-carriers are also set to 0, i.e. a_u+1,n＝a_u-1,n＝0；a_v+1,n＝a_v-1,nWhen the PAM symbol data is 0, the baseband signal s [ k ] of the CO-FBMC/OQAM is obtained after the PAM symbol data is subjected to inverse discrete Fourier transform and a polyphase structure filter bank]Represented by the formula:

wherein

Phase modulation factor psi_m,n＝(m+n)π/2，g[k]Is of length L_gKM, K being an overlap factor, and expressed in the time domain as the number of overlaps of the multicarrier symbol, where K is 4;

(2) baseband signal optical modulation and transmission: the baseband signal is affected by phase noise after being subjected to optical modulation and then affected by Gaussian white noise after being subjected to optical fiber channel modulation;

(3) receiving end time domain signals: the time domain signal at the receiving end is represented as:

wherein

Representing phase noise, w k]Representing white gaussian noise;

(4) the receiving end demodulates the signal: the time domain data at the receiving end is subjected to the filter bank with the multiphase structure and the fast Fourier transform, and the frequency domain data at the receiving end is represented as follows:

the above formula can be approximated as

Wherein

For the purpose of the imaginary part of the interference,

in order to be a noise term, the noise term,

denotes the n-th₀Common phase noise per symbol (CPE);

(5) the EKF algorithm of the extended Kalman filter precompensates phase noise: firstly, compensating a public phase noise value CPE on each symbol through an EKF algorithm;

(6) partial pre-judgment: the method comprises the steps of carrying out partial pre-judgment on data compensated by CPE (customer premise equipment) of an EKF (extended Kalman Filter) algorithm, wherein the step is to select data with higher correct judgment probability from the data compensated by the CPE to carry out judgment for the following ICI phase noise estimation, and if more wrong judgments exist in the data compensated by the CPE, the estimation precision of the ICI phase noise compensation algorithm is greatly influenced, so that a receiving end in the embodiment of the invention carries out optimized selection on a bit error rate through the CPE compensation data by taking 4QAM as an example, as shown in figure 3, the data of an area part in a dotted line frame is regarded as the data with higher wrong judgment probability and should be discarded without participating in the judgment process, and only the data of the area part outside the dotted line frame participates in the judgment process. The optimization result shows that the error rate is not significantly reduced by the partial data discarding, and the range of the dotted frame portion adopted in this embodiment is [ -0.9,0.9 ];

(7) establishing a DCT transformed time domain model: receiving end signal r_n[i]By complex conjugate of the phase noise estimate, i.e.

Here, the

The ith time domain phase noise sample representing the nth CO-FBMC/OQAM symbol has negligible high frequency components in the phase noise, and thus the complex conjugate of the phase noise can be represented as a linear combination of a set of DCT bases and DCT coefficients: phi_n≈τC_nHere, the

C_n＝[C_n(0),C_n(1),....,C_n(L-1)]^TIs a vector of Lx 1 unknown DCT coefficients, here [ ·]^TIs a transposition operation and L is the length of the DCT coefficients. DCT radical L_gElement τ of xL matrix τ_l,kGiven by the following formula,

after the DCT expansion is substituted, the compensated time domain signal is rewritten into,

further frequency-domain compensated signal

As indicated by the general representation of the,

where A is_n,mIs the received symbol after the perfect compensation of the phase noise, PAM symbol a of the sending end_n,mBy the pair A_n,mTaking the real part to obtain xi_n,mIs a noise term, by

Substituted into the above formula, symbol

Is rewritten to be that it is,

here symbol

Satisfies the following formula of symbols,

receiving end symbol A_n,mAs indicated by the general representation of the,

neglecting the noise term xi_n,mCorresponding estimated vector

Is shown as，

Here, the

Is A_n,mEstimated value of (1), M × 1 vector

Is a matrix V_nThe above formula is the time domain model of the DCT transform;

(8) calculating DCT coefficients: taking real parts of two sides of the time domain model equation of the DCT transformation in the step (7), and changing the equation into

Here, the

P_n＝[Re(V_n)-Im(V_n)],

Sending an estimated value of a PAM symbol, wherein Im (·) represents the operation of taking an imaginary part, judging data in a low-judgment error probability area on a constellation diagram after CPE compensation, balancing the algorithm effect and complexity by using an optimization parameter delta, and Z in each symbol_nThe data of the x 1 vector is used to make a pre-decision, where Z_nIs the total number of pre-decision data in the nth FBMC/OQAM symbol, and the pre-estimated transmission data is estimated from the estimated value

Is selected from and expressed as

Here, the

Is Z_nX M permutation matrix, t_z(z＝1,2,…,Z_n) A subcarrier index representing the z-th estimated transmission data,

is an M x 1 vector

Therefore, the real part equation is taken for both sides,

finally, the least-squares solution of the unknown DCT coefficient vector is obtained by:

(9) final phase noise compensation: DCT coefficient vector Q in step (8)_nAfter acquisition, the phase noise includes CPE and ICI by

Obtaining final compensation;

further, in the step (5), the EKF algorithm compensating for the phase noise CPE207 includes the following steps:

5-1 first determine initial conditions, including initial phase noise φ (0) and initial noise covariance P (0):

φ(0)＝0

P(0)＝0

in the algorithm, n | n-1 represents the prior estimation of the current state, n | n represents the posterior estimation of the current state, i.e. the information of the current symbol is estimated by using the information of the previous symbol, and the following two equations are used:

state prediction and covariance prediction can be completed;

5-2 Kalman gain calculation is represented by:

wherein the superscript H represents the conjugate transpose operator, C_nWritten as follows:

5-3, the actually generated measurement error in the calculation is measured by the following formula:

wherein

Pilot data extracted from the data symbols;

5-4, updating the state information and the covariance information using the following two equations:

5-5, CPE phase noise compensation 206:

the technical conception of the invention is as follows: in a CO-FBMC/OQAM system, based on pilot frequency data, an extended Kalman filtering method is adopted to carry out partial pre-judgment on the data on the basis of compensating the noise of a public phase, so that the CPE and the ICI phase noise of the CPE are compensated, and the tolerance of the system to the phase noise generated by the line width of a laser is improved. Specifically, on the basis of pilot frequency data, an Extended Kalman Filter (EKF) algorithm is adopted to compensate CPE noise of the data at a receiving end, and pre-judgment is carried out after compensation is finished; then selecting data in a proper range after the CPE is compensated, recording the position of the data, and using the data after the data is pre-judged as a data estimation value symbol of a transmitting end for the use of the following steps; and then, constructing a DCT basis function, carrying out approximate estimation on the phase noise, establishing a DCT time domain model of the phase noise, solving a DCT coefficient by utilizing LS estimation, and carrying out more accurate compensation on the phase noise in a time domain.

Compared with the existing phase noise estimation algorithm, the method has the following beneficial effects:

compared with the situation that the phase noise compensation of CPE is only considered in most other algorithms in the prior art, the phase noise compensation method of the CO-FBMC/OQAM system compensates the ICI phase noise, so that the system has higher tolerance to the phase noise generated by a laser. Compared with a blind algorithm, the algorithm of the invention has lower calculation complexity, and the application of the pilot frequency data is only reduced by less than 5 percent of the frequency spectrum efficiency, thereby having extremely high application value in practical application.

Drawings

FIG. 1 is a block diagram of a CO-FBMC/OQAM system of the present invention.

Fig. 2 is a flow chart of the phase noise compensation method of the pilot-assisted CO-FBMC/OQAM system of the present invention.

FIG. 3 is a diagram illustrating selection of transmit-end data estimate symbols after P-EKF compensation according to an embodiment of the present invention.

FIG. 4 is a graph comparing the performance of P-EKF-DCT algorithm and P-EFK-overlapped algorithm at 256,512 and 1024 sub-carriers respectively at different DCT coefficient lengths in the embodiment of the present invention.

FIG. 5 is a graph of the performance variation of the P-EKF algorithm with different pilot power ratios for 4QAM,16QAM and 64QAM modulation, respectively.

FIG. 6 is a graph showing the performance variation of the P-EKF-DCT algorithm according to the embodiment of the present invention under different lengths of rectangular regions not participating in decision making.

FIG. 7 is a graph comparing the performance of the P-EKF-DCT algorithm and the M-BPS algorithm at different numbers of subcarriers for 4QAM,16QAM and 64QAM, respectively, in the embodiment of the present invention.

FIG. 8 is a graph comparing the performance of the P-EKF-DCT algorithm and the M-BPS algorithm of the present invention at 4QAM,16QAM and 64QAM, respectively, when 256 subcarriers are used in the embodiment of the present invention.

FIG. 9 is a graph comparing the performance of the P-EKF-DCT algorithm and the M-BPS algorithm at 4QAM,16QAM and 64QAM, respectively, when 512 subcarriers are used in the embodiment of the present invention.

FIG. 10 is a graph comparing the performance of the P-EKF-DCT algorithm P-EKF-overlapped algorithm and the M-BPS algorithm of the present invention in 4QAM,16QAM, and 64QAM, respectively, when 1024 subcarriers are used in the embodiment of the present invention.

Detailed Description

The present invention will be described in further detail with reference to the following examples and accompanying drawings.

With reference to fig. 1 to 10, a method for compensating phase noise of a CO-FBMC/OQAM system with pilot assistance, the method comprising the following steps:

(1) and (3) transmitting end signal processing: 4/16/64QAM mapping is carried out on the data respectively to obtain a complex signal X ═ X^I+jX^QThen, the complex symbols are preprocessed by OQAM to obtain PAM symbols a_m,n∈{X^I,X^QWhere M is 0,1, 2.., M-1, n is 0,1, 2.., Ns-1, M representsThe number of subcarriers, Ns denotes the number of symbols of the FBMC, where a_u,n，a_v,nSet as pilot data, u, v are any two sub-carriers, and to avoid adverse effects on the pilot-assisted phase noise compensation algorithm, the data of two sub-carriers adjacent to the two sub-carriers are also set to 0, i.e. a_u+1,n＝a_u-1,n＝0；a_v+1,n＝a_v-1,nWhen the PAM symbol data is 0, the baseband signal s [ k ] of the CO-FBMC/OQAM is obtained after the PAM symbol data is subjected to inverse discrete Fourier transform and a polyphase structure filter bank]Represented by the formula:

wherein

Phase modulation factor psi_m,n＝(m+n)π/2，g[k]Is of length L_gKM, K being an overlap factor, and expressed in the time domain as the number of overlaps of the multicarrier symbol, where K is 4;

(2) baseband signal optical modulation and transmission: the baseband signal is affected by phase noise after being subjected to optical modulation and then affected by Gaussian white noise after being subjected to optical fiber channel modulation;

(3) receiving end time domain signals: the time domain signal at the receiving end is represented as:

wherein

Representing phase noise, w k]Representing white gaussian noise;

(4) the receiving end demodulates the signal: after the time domain data at the receiving end passes through the polyphase structure filter bank 202 and the fast fourier transform 203, the frequency domain data at the receiving end is represented as follows:

the above formula can be approximated as

Wherein

For the purpose of the imaginary part of the interference,

in order to be a noise term, the noise term,

denotes the n-th₀Common phase noise per symbol (CPE);

(5) the extended kalman filter EKF algorithm pre-compensates for phase noise 207: firstly, compensating a public phase noise value CPE on each symbol through an EKF algorithm;

(6) partial pre-decision 208: partial pre-decision is carried out on data compensated by CPE in EKF algorithm, the step is to select data with higher correct decision probability from the data compensated by CPE for decision for the following ICI phase noise estimation, if there are many wrong decisions in the compensated data of the CPE, the estimation accuracy of the ICI phase noise compensation algorithm will be greatly affected, therefore, taking 4QAM as an example, the receiving end in the embodiment of the present invention performs optimal selection for the bit error rate through CPE compensation data, as shown in fig. 3, the data in the area part within the dashed line frame is regarded as the data with a higher probability of false determination, and should be discarded without participating in the determination process, only partial data in the area outside the dashed line frame participates in the decision process, and the optimization result shows that the error rate of the partial data is not remarkably reduced by discarding the partial data, wherein the range of the dashed line frame adopted in the embodiment is [ -0.9,0.9 ];

(7) establishing a time domain model 209 of the DCT transformation: receiving end signal r_n[i]By complex conjugate of the phase noise estimate, i.e.

Here, the

The ith time domain phase noise sample representing the nth CO-FBMC/OQAM symbol has negligible high frequency components in the phase noise, so the complex conjugate of the phase noise is represented as a linear combination of a set of DCT bases and DCT coefficients: phi_n≈τC_nHere, the

C_n＝[C_n(0),C_n(1),....,C_n(L-1)]^TIs a vector of Lx 1 unknown DCT coefficients, here [ ·]^TIs a transposition operation, L is the length of the DCT coefficient, the DCT base L_gElement τ of xL matrix τ_l,kIs given by the following formula;

after the DCT expansion is substituted, the compensated time domain signal is rewritten into,

further frequency-domain compensated signal

As indicated by the general representation of the,

where A is_n,mIs the received symbol after the perfect compensation of the phase noise, PAM symbol a of the sending end_n,mCan pass through the pair A_n,mTaking the real part to obtain xi_n,mIs the noise term. By mixing

Substituted into the above formula, symbol

Is rewritten to be that it is,

here symbol

Satisfies the following formula of symbols,

receiving end symbol A_n,mAs indicated by the general representation of the,

neglecting the noise term xi_n,mCorresponding estimated vector

As indicated by the general representation of the,

here, the

Is A_n,mEstimated value of (1), M × 1 vector

Is a matrix V_nOne column of (c). The above formula is a time domain model of DCT transformation;

(8) calculating the DCT coefficients 210: taking real parts of two sides of the time domain model equation of the DCT transformation in the step (7), and changing the equation into

Here, the

P_n＝[Re(V_n)-Im(V_n)],

Sending an estimated value of a PAM symbol, wherein Im (·) represents the operation of taking an imaginary part, judging data of a low-judgment error probability area on a constellation diagram after CPE compensation as shown in step (6), and balancing the algorithm effect and complexity by using an optimization parameter delta, wherein Z in each symbol_nThe data of the x 1 vector is used to make a pre-decision, where Z_nIs the total number of pre-decision data in the nth FBMC/OQAM symbol, and the pre-estimated transmission data is estimated from the estimated value

Is selected from and expressed as

Here, the

Is Z_nX M permutation matrix, t_z(z＝1,2,…,Z_n) A subcarrier index representing the z-th estimated transmission data,

is an M x 1 vector

Therefore, the real part equation is taken for both sides,

finally, the least-squares solution of the unknown DCT coefficient vector is obtained by:

(9) final phase noise compensation 211: DCT coefficient vector Q in step (8)_nAfter acquisition, the phase noise includes CPE and ICI by

Resulting in a final compensation 211.

In the step (5), the EKF algorithm compensating the phase noise CPE207 includes the following steps:

5-1 first determine initial conditions, including initial phase noise φ (0) and initial noise covariance P (0):

φ(0)＝0

P(0)＝0

in the algorithm, n | n-1 represents the prior estimation of the current state, n | n represents the posterior estimation of the current state, i.e. the information of the current symbol is estimated by using the information of the previous symbol, and the following two equations are used:

state prediction and covariance prediction can be completed;

5-2 Kalman gain calculation is represented by:

wherein the superscript H represents the conjugate transpose operator, C_nWritten as follows:

5-3, the actually generated measurement error in the calculation is measured by the following formula:

wherein

Is pilot data 204 extracted from the data symbols;

5-4, updating the state information and the covariance information using the following two equations:

5-5, CPE phase noise compensation 206:

the invention verifies the performance of the method through simulation. In a CO-FBMC/OQAM actual transmission system, a plurality of interferences exist, and in order to pay attention to the verification of the performance of a phase noise compensation algorithm, the invention builds a CO-FBMC/OQAM back-to-back transmission system with the speed of 30 Gbaud. The original data binary sequence is respectively modulated by 4QAM,16QAM and 64QAM, and each QAM modulation also adopts 256,512 and 1024 sub-carriers for transmission.

FIG. 4 shows P-EKF-DCT algorithm and P-EFK-overlap at 256,512 and 1024 sub-carriers respectively in the embodiment of the present inventiond comparing the performance of the algorithm at different DCT coefficient lengths L. Generally speaking, a larger L is selected to obtain a higher approximation degree in DCT transformation, however, as L increases, the P-EKF-DCT algorithm does not have better phase compensation effect, because of the matrix S_nP_nOr

And the phase noise estimation precision of the least square estimation is poor due to non-column full rank. And taking account of the algorithm effect and complexity, and selecting L as 2. However, for the P-EKF-overlapped algorithm, the matrix S_nP_nOr

The column full rank is approached, so as L is increased, the phase noise estimation precision is higher, and the phase noise compensation effect is better. And the L value is selected to be 7 by comprehensively considering the phase noise compensation effect and the algorithm complexity.

FIG. 5 is a graph of the performance variation of the P-EKF algorithm with different pilot power ratios for 4QAM,16QAM and 64QAM modulation, respectively. Under the conditions of proper line width delay product and optical signal-to-noise ratio, when the power ratio of the pilot data signal is 17, the QAM modulation with several different orders can obtain better CPE phase noise effect, so that the power ratio is selected to be 17.

FIG. 6 is a graph showing the performance variation of the P-EKF-DCT algorithm according to the embodiment of the present invention under different lengths of rectangular regions not participating in decision making. It can be seen from the figure that, as the length δ of the rectangular region not participating in the decision changes from 0 to 1.9, the actions of the decision error in the discarded data and the negation generated by the decision correctness cancel each other out, and the error rate performance does not change greatly. When δ is changed from 1.9 to 2, data is greatly deteriorated in 64QAM modulation due to a serious reduction in data participating in decision, and therefore, the length δ of a rectangular region not participating in decision is selected to be 1.9.

FIG. 7 is a graph comparing the performance of the P-EKF-DCT algorithm and the M-BPS algorithm at different numbers of subcarriers for 4QAM,16QAM and 64QAM, respectively, in the embodiment of the present invention. Because the P-EKF-DCT algorithm compensates not only CPE phase noise but also ICI phase noise, and the M-BPS only compensates the CPE phase noise, the performance of the P-EKF-DCT algorithm is improved by nearly one order of magnitude compared with the M-BPS when QAM modulation and subcarrier number are the same.

Fig. 8, 9, and 10 show the relationship diagrams of normalized line width and OSNR penalty of the P-EKF-DCT algorithm, the P-EFK-overlapped algorithm, and the M-BPS algorithm of the present invention at 4QAM,16QAM, and 64QAM, respectively, when 256/512/1024 subcarriers are used, and points in the diagrams all represent OSNR penalty when hard-decision forward error correction error rate of 3.8e-3 is reached under the current normalized line width. As shown in FIG. 8, for the 4/16/64-QAM 32G baud rate system, when 256 subcarriers are used, the M-BPS algorithm is applied with Δ ν T_SThe tolerance of 0.0655, 0.01209 and 0.0023 is obtained; for the P-EKF-DCT algorithm, Δ v.T_SThe tolerance of 0.1044, 0.01669 and 0.00188 is obtained. In general, the effect of the P-EKF-DCT algorithm is obviously better than that of the M-BPS algorithm. Note that as the QAM modulation order increases, such as 64QAM modulation, the Δ ν T of both algorithms_STolerance differences are reduced. The main reason is that the pilot signal occupies a larger power during high-order modulation, so that the difference of 1dB OSNR of the pilot algorithm is reduced compared with the blind algorithm. Δ ν T of M-BPS and P-EKF-DCT at 2dB OSNR at 64QAM and 256 subcarriers_S0.00403 and 0.00489 respectively, the difference between the two algorithms is obviously increased, and the result shows that the P-EKF-DCT algorithm can still obtain better phase noise compensation effect.

The blind phase noise compensation method (BD-PNC) in the CO-FBMC/OQAM system described above is introduced in detail, and the above description of the example is only used to help understanding the method and its core idea, but not to limit the same, and any other changes, modifications, substitutions, combinations, simplifications that do not depart from the spirit and principle of the present invention should be regarded as equivalent substitutions and all fall within the protection scope of the present invention.

Claims (2)

1. A method for compensating phase noise of a CO-FBMC/OQAM system with pilot assistance, said method comprising the steps of:

(1) and (3) transmitting end signal processing: for data respectively4/16/64QAM mapping is carried out to obtain a complex signal X ═ X^I+jX^QThen, the complex symbols are preprocessed by OQAM to obtain PAM symbols a_m,n∈{X^I,X^QWhere M is 0,1, 2., M-1, n is 0,1, 2., Ns-1, M denotes the number of subcarriers, Ns denotes the number of FBMC symbols, where a denotes the number of FBMC symbols_u,n，a_v,nSetting the data as pilot frequency data, wherein u and v are any two subcarriers; to avoid adverse effects on the pilot-assisted phase noise compensation algorithm, the data of two subcarriers adjacent to the two subcarriers are also set to 0, i.e., a_u+1,n＝a_u-1,n＝0；a_v+1,n＝a_v-1,nWhen the PAM symbol data is 0, the baseband signal s [ k ] of the CO-FBMC/OQAM is obtained after the PAM symbol data is subjected to inverse discrete Fourier transform and a polyphase structure filter bank]Represented by the formula:

wherein

Phase modulation factor psi_m,n＝(m+n)π/2，g[k]Is of length L_gKM for a prototype filter, K being an overlap factor, expressed in the time domain as the number of overlaps of a multicarrier symbol;

(2) baseband signal optical modulation and transmission: the baseband signal is affected by phase noise after being subjected to optical modulation and then affected by Gaussian white noise after being subjected to optical fiber channel modulation;

(3) receiving end time domain signals: the time domain signal at the receiving end is represented as:

wherein

Representing phase noise, w k]Representing white gaussian noise;

(4) the receiving end demodulates the signal: the time domain data at the receiving end is subjected to the filter bank with the multiphase structure and the fast Fourier transform, and the frequency domain data at the receiving end is represented as follows:

the above formula can be approximated as

Wherein

For the purpose of the imaginary part of the interference,

in order to be a noise term, the noise term,

denotes the n-th₀Common phase noise per symbol CPE;

(5) the EKF algorithm of the extended Kalman filter precompensates phase noise: firstly, compensating a public phase noise value CPE on each symbol through an EKF algorithm;

(6) partial pre-judgment: the method comprises the steps of carrying out partial pre-judgment on data compensated by CPE of an EKF algorithm, wherein the step is to select data with higher correct judgment probability from the data compensated by the CPE for judgment and use the data for the following ICI phase noise estimation, and if more wrong judgments exist in the data compensated by the CPE, the estimation precision of the ICI phase noise compensation algorithm is greatly influenced;

(7) establishing a DCT transformed time domain model: receiving end signal r_n[i]By complex conjugate of the phase noise estimate, i.e.

Here, the

The ith time domain phase noise sample representing the nth CO-FBMC/OQAM symbol has negligible high frequency components in the phase noise, so the complex conjugate of the phase noise is represented as a linear combination of a set of DCT bases and DCT coefficients: phi_n≈τC_nHere, the

C_n＝[C_n(0),C_n(1),....,C_n(L-1)]^TIs a vector of Lx 1 unknown DCT coefficients, here [ ·]^TIs a transposition operation, L is the length of the DCT coefficient, the DCT base L_gElement τ of xL matrix τ_l,kGiven by the following formula,

after the DCT expansion is substituted, the compensated time domain signal is rewritten into,

further frequency-domain compensated signal

As indicated by the general representation of the,

where A is_n,mIs the received symbol after the perfect compensation of the phase noise, PAM symbol a of the sending end_n,mBy the pair A_n,mTaking the real part to obtain xi_n,mIs a noise term, by

Substituted into the above formula, symbol

Is rewritten to be that it is,

here symbol

Satisfies the following formula of symbols,

receiving end symbol A_n,mAs indicated by the general representation of the,

neglecting the noise term xi_n,mCorresponding estimated vector

As indicated by the general representation of the,

here, the

Is A_n,mEstimated value of (1), M × 1 vector

Is a matrix V_nThe above formula is the time domain model of the DCT transform;

(8) calculating DCT coefficients: for DCT transformation in step (7)The real part is taken from both sides of the time domain model equation, and the equation becomes

Here, the

P_n＝[Re(V_n)-Im(V_n)],

Sending an estimated value of a PAM symbol, wherein Im (·) represents the operation of taking an imaginary part, judging data in a low-judgment error probability area on a constellation diagram after CPE compensation, balancing the algorithm effect and complexity by using an optimization parameter delta, and Z in each symbol_nThe data of the x 1 vector is used to make a pre-decision, where Z_nIs the total number of pre-decision data in the nth FBMC/OQAM symbol, and the pre-estimated transmission data is estimated from the estimated value

Is selected from and expressed as

Here, the

Is Z_nX M permutation matrix, t_z(z＝1,2,…,Z_n) A subcarrier index representing the z-th estimated transmission data,

is an M x 1 vector

Therefore, the real part equation is taken for both sides,

finally, the least-squares solution of the unknown DCT coefficient vector is obtained by:

(9) final phase noise compensation: DCT coefficient vector Q in step (8)_nAfter acquisition, the phase noise includes CPE and ICI by

And obtaining the final compensation.

2. The pilot-assisted CO-FBMC/OQAM system phase noise compensation method of claim 1, wherein said step (5) comprises the steps of:

5-1 first determine initial conditions, including initial phase noise φ (0) and initial noise covariance P (0):

φ(0)＝0

P(0)＝0

in the algorithm, n | n-1 represents the prior estimation of the current state, n | n represents the posterior estimation of the current state, i.e. the information of the current symbol is estimated by using the information of the previous symbol, and the following two equations are used:

state prediction and covariance prediction can be completed;

5-2 Kalman gain calculation is represented by:

wherein the superscript H represents the conjugate transpose operator, C_nWritten as follows:

5-3, the actually generated measurement error in the calculation is measured by the following formula:

wherein

Pilot data extracted from the data symbols;

5-4, updating the state information and the covariance information using the following two equations:

and 5-5, finally performing CPE phase noise compensation:

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