CN106998229B - A kind of mode division multiplexing system Deplexing method based on variable step without constraint FD-LMS - Google Patents
A kind of mode division multiplexing system Deplexing method based on variable step without constraint FD-LMS Download PDFInfo
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- CN106998229B CN106998229B CN201611150443.4A CN201611150443A CN106998229B CN 106998229 B CN106998229 B CN 106998229B CN 201611150443 A CN201611150443 A CN 201611150443A CN 106998229 B CN106998229 B CN 106998229B
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
- H04L25/024—Channel estimation channel estimation algorithms
- H04L25/025—Channel estimation channel estimation algorithms using least-mean-square [LMS] method
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- H—ELECTRICITY
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- H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
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- H04B10/2581—Multimode transmission
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
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- H04J14/00—Optical multiplex systems
- H04J14/04—Mode multiplex systems
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- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
- H04L25/024—Channel estimation channel estimation algorithms
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Abstract
The invention discloses a kind of mode division multiplexing system Deplexing methods based on variable step without constraint FD-LMS, belong to field of communication technology, the first step, electric-wave filter matrix W is set to realize pre- convergence with one section of training sequence, using training sequence as desired signal, second step, output data is obtained with the method directly adjudicated, the balanced device obtained pre- convergent tap vector value being assigned in S2 step, and the signal for obtaining judgement is as desired signal, remaining step is carried out according to the method for the first step, continuous iteration, until the output data bit error rate no longer reduces.Algorithm used in the present invention can change the step value of each frequency cabinet of each data block, to achieve the purpose that fast convergence.The present invention can make up adaptive unconstrained frequency domain least-mean-square error algorithm (Unconstrained FD-LMS) and restrain slow problem, demultiplexing efficiency with higher.
Description
Technical field
The invention belongs to fields of communication technology, are related to a kind of Deplexing method of mode division multiplexing (MDM) system, are walked using becoming
Long unconstrained frequency domain least mean square algorithm realizes the demultiplexing to MDM system.
Background technique
With the continuous propulsion of social informatization process, large-scale data center, Internet of Things, HD video etc. " bandwidth consumption "
Type business is grown rapidly, and is continuously increased to the bandwidth demand of Networks of Fiber Communications.And be time-multiplexed (TDM), wavelength-division multiplex
(WDM), the extensive use of the technologies such as palarization multiplexing (PDM) and higher-dimension high order modulation so that the power system capacity of single mode optical fiber by
Gradually close to shannon limit.For foreseeable " bandwidth crisis ", a kind of new capacity-enlargement technology of coping with optical communication network ----be based on
The mode division multiplexing technology of less fundamental mode optical fibre (FMF) is come into being.MDM technology utilizes the orthogonality in less fundamental mode optical fibre between each mode,
Each mode is subjected to information transmitting as independent channel, to realize high capacity transmission.However, in the mould based on less fundamental mode optical fibre point
In multiplex system, Mode Coupling and differential mode time delay (DMGD) equivalent damage have seriously affected the transmission performance of system.Meanwhile in mould
Under formula coupling and differential mode time delay collective effect, the demultiplexing of mode division multiplexing system also becomes relative complex.
Adaptive filter algorithm can effectively realize demultiplexing.Wherein, lowest mean square (LMS) algorithm is because simple and be easy to
It realizes and is widely applied.LMS algorithm can both be realized in time domain, can also be realized in frequency domain.Compared to Time-Domain algorithm,
Frequency domain lowest mean square (Variable step-size unconstrained FD-LMS) algorithm passes through Fast Fourier Transform (FFT)
(FFT) a large amount of operations are saved.And it is minimum to be further divided into constraint frequency domain according to the presence or absence of time-domain constraints for FD-LMS algorithm
Side's (Constrained FD-LMS) algorithm and unconstrained frequency domain lowest mean square (Unconstrained FD-LMS) algorithm.Wherein
No bounding algorithm has cast out time-domain constraints block, to further save operand, the advantage of this complexity is more in multi input
It is particularly evident in (MIMO) system of output.However it is slower without constraint FD-LMS convergence speed of the algorithm, need more midamble code
Member realizes convergence, to reduce the availability of frequency spectrum.Therefore, further promoted without constraint FD-LMS convergence speed of the algorithm, into
And the demultiplexing efficiency of algorithm is improved, it is a urgent problem to be solved.
Summary of the invention
For the problem slow without constraint FD-LMS algorithmic statement existing in the prior art, the present invention provides one kind to be based on
Reception signal Deplexing method of the variable step without constraint FD-LMS algorithm, this method have faster convergence rate, lower multiple
Miscellaneous degree, while guaranteeing preferable error performance, there is preferable demultiplexing effect.
Influenced by differential mode time delay and Mode Coupling equivalent damage, the output signal of mode division multiplexing system be input signal with
The convolved mixtures of channel transfer matrices.The principle of the present invention is to estimate channel without constraint FD-LMS algorithm by variable step to pass
The inverse matrix W of defeated matrix H, enables W=H-1, wherein W is M × Metzler matrix, by received time-domain signal u (n)=[u1(n),...,uM
(n)]TThe recovery signal y (n) obtained with electric-wave filter matrix W convolution, is expressed as matrix form are as follows:
The present invention is achieved through the following technical solutions:
A kind of mode division multiplexing system Deplexing method based on variable step without constraint FD-LMS, the specific steps are as follows:
The first step makes electric-wave filter matrix W realize pre- convergence with one section of training sequence, using training sequence as desired signal,
Wherein, W be M × Metzler matrix, detailed process the following steps are included:
S1, to jth (1≤j≤M) the road time domain signal u to be equalized after two times of over-samplings, dispersion compensationsj(n) odd even is carried out
Branch obtains parallel odd circuit-switched dataWith even circuit-switched dataPiecemeal is distinguished to two paths of data, and according to Time Delay of Systems
Obtaining every piece of he number with the relationship of shock response is N, and two successive sub-blocks are put together, sequentially carries out FFT transform and obtains
To kth block odd even road frequency-region signalWherein, diag { } represents diagonal matrix operation, FFT []
Represent Fourier transformation；
S2, the sub- balanced device of odd even for being N to weight vector lengthInitialize installation is carried out, it, will when i and j are unequal
Each weight is set as 0；When i is equal with j, the N/2 weight is set as 1, remaining weight is set as 0, and mends to N number of weight thereafter
Zero；Then FFT transform is carried out again to obtain
S3, the output of the i-th (1≤i≤M) road frequency domain is calculatedFourier's contravariant is carried out to it
It changes (IFFT) and gives up top n value, obtain its kth block time domain output signal yi(k)；
S4, Carrier Phase Noise estimation item φ is addedi(k), kth block desired signal d is utilizedi(k) time domain error e is calculatedi
(k)=(di(k)-yi(k))·exp(jφi(k)) zero padding, is carried out to the N number of value of the front and carries out FFT operation, obtains kth block
Error of frequency domain signal Ei(k)；
S5, in every piece each frequency cabinet variable step:Wherein α is normal
Number,For kth block input signal power, Se,i,m(k)=λ Se,i,m(k-1)+(1-λ)|
Ei(k)|2For kth block error power,For the mutual function of kth block signal error
Rate, wherein λ is forgetting factor；
S6, the tap weights vector for updating balanced deviceWherein []HFor
Conjugate operation is taken,For Step matrix, occurrence is step value obtained in step S5；
S7, judge whether to restrain, if do not restrained, go to step S1, terminates if convergence, obtains pre- convergent tap
Vector
Second step obtains output data with the method directly adjudicated, and obtained pre- convergent tap vector value is assigned to S2
Balanced device in step, and the signal that judgement is obtained, as desired signal, remaining step is carried out according to the method for the first step, no
Disconnected iteration, until the output data bit error rate no longer reduces.
Further, in the step S1, the sub- equaliser operating on signal of odd even is respectively adopted and carries out odd even branch process, it can
So that the sum of balanced output and the down-sampled output phase at half code element interval etc., to eliminate down-sampled process.
Further, in the step S4, carrier phase estimates item φi(k) it is obtained using the algorithm operation of M power,
Step are as follows: on the one hand, take argument to obtain a value time domain error at one moment,；On the other hand, M times of time domain error is taken
Side, enters back into low-pass filter, filters out radio-frequency component, then carries out taking argument to obtained value and except M operation, obtain another
Two value additions are obtained carrier phase estimation item by a value.Carrier phase estimation is carried out in two steps.Wherein the first step is auxiliary in data
The pre- converged state of filter tap is helped, second step is in the decision-feedback stage.
In the step S5, time domain backward error signal is definedIt will step
Tap weights vector renewal equation in rapid S6 brings backward error formula into, and carries out Fourier transformation, it is available it is corresponding after
To error frequency domain formAnd then it is rewritten to obtain each frequency cabinet
μ value representation:Utilize the amplitude coherent side between input signal and error signal
Journey is available:
By Sv,i,m(k) it brings into the step expression tentatively obtained, it can be with
Obtain final step expression:
Compared with prior art, the present invention has the advantage that
The present invention restores mixed signal without constraint FD-LMS algorithm using variable step, with computation complexity
Low, the advantages that availability of frequency spectrum is high, while can guarantee preferable error performance, there is preferable demultiplexing effect.
Detailed description of the invention
Fig. 1 is 6 × 6 mode division multiplexing system structure diagrams based on less fundamental mode optical fibre；
Fig. 2 is 6 × 6 mode division multiplexing system receiver structural schematic diagrams based on less fundamental mode optical fibre；
Fig. 3 is the flow chart of variable step proposed by the invention without constraint FD-LMS algorithm；
Fig. 4 is the functional block diagram of variable step proposed by the invention without constraint FD-LMS algorithm for each output；
Fig. 5 is to carry out equilibrium with algorithm proposed by the invention, at different optical signal to noise ratio (OSNR), the mistake of 6 modes
Code rate (BER) change curve；
Fig. 6 be at different optical signal to noise ratio (OSNR), using have constraint FD-LMS algorithm, without constraint FD-LMS algorithm and
Variable step carries out balanced obtained BER comparison diagram without constraint FD-LMS algorithm；
Fig. 7 is the convergence graph of 6 modes in the case that OSNR is 15dB；
Fig. 8 be in the case that OSNR is 15dB have constraint FD-LMS algorithm, without constraint FD-LMS algorithm and variable step without
The convergence rate comparison diagram of constrained-LMS algorithm.
Specific embodiment
The present invention is described further with reference to the accompanying drawing.
Implement 16 × 6 mode division multiplexing Transmission systems based on less fundamental mode optical fibre to verify method proposed by the present invention.Fig. 1
It shows to verify practical 6 × 6 mode division multiplexing system schematics based on less fundamental mode optical fibre used of method proposed by the invention,
Its composition includes: 4,66 data transmission blocks 1, pattern multiplexer 2,80km less fundamental mode optical fibre 3, pattern demultiplexer phase stem graftings
Receipts machine 5 and off-line data handle mould 6.Wherein the Random Coupling intensity of FMF be -30dB/km, fibre loss 0.2dB/km,
The chromatic dispersion of LP01 mould is 20ps/nm/km, and the chromatic dispersion of LP11 mould is 21ps/km/nm, and differential mode time delay is 27ps/
km.The stiffness of coupling that pattern multiplexer and pattern demultiplexer introduce is -21dB.
In Fig. 1 the QPSK optical signal of 6 56Gbit/s by pattern multiplexer be coupled into FMF 3 modes (LP01,
LP11a and LP11b) and its corresponding polarization mode separated after the transmission of 80km less fundamental mode optical fibre into pattern demultiplexer.
Obtained signal is received using coherent receiver, and output signal is handled by digital signal processing module,
Output signal after being restored.
Data transmission blocks in Fig. 1 increase Dare tune to Mach by the source signal that two independent rates are 28Gbit/s
Device processed is driven, generate a rate be 56Gbit/s QPSK signal, used in light source be wavelength be 1550nm, line
Width is the laser of 100kHz.
The coherent receiver composed structure in Fig. 1 is shown in Fig. 2 comprising: a local oscillator, one 90 ° it is mixed
Frequency device, two pairs of balanced detectors and two low-pass filters.The light of received each mode is sent into together with local oscillator light
90 ° of frequency mixers, the optical signal after mixing obtains electric signal by balanced detector, then two path signal is sent into
In Bessel low-pass filter, two-way output signal is finally obtained.
The signal that receiver receives carries out two times of over-samplings and dispersion compensation processing first, then to obtained signal
Carry out equilibrium treatment.The present invention is its equalization algorithm, realizes the demultiplexing to mode division multiplexing system.Fig. 3 gives of the invention
Specific flow chart, and Fig. 4 gives the present invention for the functional block diagram of each output.The specific steps of the present invention are as follows:
The first step realizes pre- convergence to filter tap w (n) using data auxiliary law, will originator input data as
Desired signal, takes 1≤i≤6,1≤j≤6, specifically includes the following steps:
S1, to the signal u to be equalized after two times of over-samplings, dispersion compensationsj(n) odd even branch is carried out, it is parallel to obtain two-way
Neat circuit-switched dataWith even circuit-switched dataPiecemeal is distinguished to two-way serial data, according to Time Delay of Systems and shock response
It is 64 that relationship, which obtains every piece of he number, and successive sub-block is put together, sequentially carries out FFT transform and obtains kth block frequency-region signalWherein diag { } represents diagonal matrix operation, and FFT [] represents Fourier transformation；
S2, the filter for being 64 to weight vector lengthInitialize installation is carried out, it, will be each when i and j are unequal
Weight be set as 0, i it is equal with j when, the 32nd weight is set as 1, remaining weight is set as 0, and to mending 64 zeros thereafter, then
FFT transform is carried out to obtain
S3, frequency domain output is calculatedIFFT transformation is carried out to it and gives up first 64
Value, obtains kth block output signal yi(k)；
S4, Carrier Phase Noise estimation item φ is addedi(k), carrier phase estimates item φi(k) the algorithm operation of M power is used
It obtains, the steps include: on the one hand, to take argument to obtain a value time domain error at one moment,；On the other hand, time domain is taken to miss
The M power of difference, enters back into low-pass filter, filters out radio-frequency component, then carries out taking argument to obtained value and removes M operation,
Another value is obtained, two value additions are obtained into carrier phase estimation item.Utilize kth block desired signal di(k) time domain is calculated to miss
Poor ei(k)=(di(k)-yi(k))·exp(jφi(k)) zero padding, is carried out to 64 values of the front and carries out FFT operation, is obtained
Kth block error of frequency domain signal Ei(k)；
S5, in every piece each frequency cabinet variable step:α=0.01, k
Block input signal power,For kth block input signal power, SE, i, m(k)=λ SE, i, m
(k-1)+(1-λ)|Ei(k)|2For kth block error power,For kth
Block signal error cross-power, wherein λ=0.6；
S6, the tap weights vector for updating balanced deviceWhereinFor Step matrix；
S7, judge whether to restrain, if do not restrained, go to step S1, terminates if convergence, obtains pre- convergent pumping
Head vector
Second step is then needed since this system is modulated using QPSK by data decision after equilibrium to (- 1, -1), (-
1,1), (1, -1), on (1,1) four points, and the signal that judgement is obtained is as desired signal, by pre- convergent tap vector value
The balanced device being assigned in S2 step, remaining according to the first step method carry out, when the number of iterations be 10 when to compared with
For accurate output data.
Fig. 5 gives under different OSNR, the BER change curve of 6 modes；And Fig. 6 then gives under different OSNR, has about
Beam FD-LMS algorithm, without constraint the BER comparison diagram of FD-LMS algorithm and variable step without constrained-LMS algorithm；Fig. 5 shows 6 letters
Performance of the road after algorithm proposed by the present invention demultiplexing is essentially identical；When error rate of system reaches 10-3,6 channels reach
It is 15dB to the smallest OSNR needed for target error rate；Fig. 6 then shows that the bit error rate of the identical lower 3 kinds of algorithms of OSNR is suitable, solution
It is almost consistent to be multiplexed effect；The result shows that algorithm proposed by the invention can effectively demultiplex mode division multiplexing system.
In the case that Fig. 7 gives OSNR as 15dB, the convergence curve of 6 modes；And it is 15dB's that Fig. 8, which gives OSNR,
In the case of, there is constraint FD-LMS algorithm, without constraint FD-LMS algorithm and convergence speed of the algorithm comparison diagram proposed by the present invention；
The abscissa of two figures is fft block number, and ordinate is normalized mean squared error (NMSE)；Fig. 7 shows that 6 modes are almost
With the convergence of identical velocity interpolation, and finally converge on the NMSE that numerical value is less than -12dB；Fig. 8 shows, not up to -12dB's
NMSE has constraint FD-LMS algorithm, the number without fft block required for constraint FD-LMS algorithm and algorithm proposed by the present invention
Respectively 65,73 and 45；The result shows that convergence speed of the algorithm proposed by the invention is very fast, it is able to solve without constraint FD-LMS
The slow problem of algorithm the convergence speed.
Mode division multiplexing system described in examples detailed above based on less fundamental mode optical fibre is it is known in the art, being obtained by known approach
?.
The terms such as step-length used, weight vector describe and explain the present invention just to more convenient in the present invention, not can be used as
Its additional limitation.
Claims (2)
1. a kind of mode division multiplexing system Deplexing method based on variable step without constraint FD-LMS, which is characterized in that specific steps
It is as follows:
The first step makes electric-wave filter matrix W realize pre- convergence, using training sequence as desired signal with one section of training sequence, wherein
W be M × Metzler matrix, detailed process the following steps are included:
S1, to two times of over-samplings, the road dispersion compensation Houj time domain signal u to be equalizedj(n) odd even branch is carried out, wherein 1≤j
≤ M obtains parallel odd circuit-switched dataWith even circuit-switched dataTo two paths of data distinguish piecemeal, and according to Time Delay of Systems with
It is N that the relationship of shock response, which obtains every piece of he number, and two successive sub-blocks are put together, sequentially carries out FFT transform and obtains
Kth block odd even road frequency-region signalWherein, diag { } represents diagonal matrix operation, and FFT [] is represented
Fourier transformation；
S2, the sub- balanced device of odd even for being N to weight vector lengthInitialize installation is carried out, it, will be each when i and j are unequal
Weight is set as 0；When i is equal with j, the N/2 weight is set as 1, remaining weight is set as 0, and to N number of weight zero padding thereafter；
Then FFT transform is carried out again to obtain
S3, the output of the i-th road frequency domain is calculatedWherein, 1≤i≤M carries out Fourier's contravariant to it
It changes (IFFT) and gives up top n value, obtain its kth block time domain output signal yi(k)；
S4, Carrier Phase Noise estimation item φ is addedi(k), kth block desired signal d is utilizedi(k) time domain error e is calculatedi(k)=
(di(k)-yi(k))·exp(jφi(k)) zero padding, is carried out to the N number of value of the front and carries out FFT operation, obtains kth block frequency domain mistake
Difference signal Ei(k)；
S5, in every piece each frequency cabinet variable step:Wherein α is constant,For kth block input signal power, Se,i,m(k)=λ Se,i,m(k-1)+(1-λ)|Ei
(k)|2For kth block error power,For kth block signal error cross-power,
Wherein λ is forgetting factor；
S6, the tap weights vector for updating balanced deviceWherein []HTo take altogether
Yoke operation,For Step matrix, occurrence is step value obtained in step S5；
S7, judge whether to restrain, if do not restrained, go to step S1, terminates if convergence, obtains pre- convergent tap vector
Second step obtains output data with the method directly adjudicated, and obtained pre- convergent tap vector value is assigned to S2 step
In balanced device, and will the obtained signal of judgement as desired signal, remaining step is carried out according to the method for the first step, is constantly changed
Generation, until the output data bit error rate no longer reduces.
2. a kind of mode division multiplexing system Deplexing method based on variable step without constraint FD-LMS as described in claim 1,
It is characterized in that, in the step S4, Carrier Phase Noise estimates item φi(k) it is obtained using the algorithm operation of M power, step
Are as follows: on the one hand, take argument to obtain a value time domain error at one moment；On the other hand, the M power of time domain error is taken, then
Into low-pass filter, radio-frequency component is filtered out, then obtained value is carried out taking argument and except M operation, obtains another value,
Two value additions are obtained into Carrier Phase Noise estimation item.
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| CN110474662B (en) * | 2019-07-31 | 2021-11-09 | 同济大学 | MIMO wireless communication demodulation receiving method and system |
| CN113067662A (en) * | 2021-03-17 | 2021-07-02 | 吉林大学 | Demultiplexing algorithm of FBMC-OQAM mode division multiplexing system based on lattice reduction |
| CN114337840B (en) * | 2022-01-10 | 2023-10-31 | 天津师范大学 | Dispersion compensation method for modulated signal 6PolSK-QPSK |
| CN115473774B (en) * | 2022-09-13 | 2023-07-04 | 北京理工大学 | Channel equalization method for mode division multiplexing communication system |
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