CN108712356A - A kind of coherent fiber communication system based on discrete Fresnel transform extension OFDM modulation - Google Patents
A kind of coherent fiber communication system based on discrete Fresnel transform extension OFDM modulation Download PDFInfo
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- CN108712356A CN108712356A CN201810248785.2A CN201810248785A CN108712356A CN 108712356 A CN108712356 A CN 108712356A CN 201810248785 A CN201810248785 A CN 201810248785A CN 108712356 A CN108712356 A CN 108712356A
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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
- 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
- H04L27/2691—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation involving interference determination or cancellation
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- 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
- H04B10/60—Receivers
- H04B10/61—Coherent receivers
- H04B10/613—Coherent receivers including phase diversity, e.g., having in-phase and quadrature branches, as in QPSK coherent receivers
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- 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
- H04B10/60—Receivers
- H04B10/61—Coherent receivers
- H04B10/616—Details of the electronic signal processing in coherent optical receivers
- H04B10/6161—Compensation of chromatic dispersion
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/0413—MIMO systems
- H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
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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
- 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
Abstract
The present invention provides a kind of coherent fiber communication systems modulated based on discrete Fresnel transform extension OFDM (DFnT-S-OFDM), belong to optical-fibre communications field, it is therefore intended that solve the frequency fading problem present in traditional OFDM and the inter-symbol interference problem present in discrete Fourier transform extension OFDM (DFT-S-OFDM).The core of DFnT-S-OFDM systems includes the inverse DFnT modules and channel equalization module in Signal coding module and receiver in transmitter for generating DFnT-S-OFDM.The present invention passes through DFnT precodings, data information is distributed in time-domain and spectrum domain simultaneously, there is stronger anti-frequency decline performance relative to conventional OFDM modulation format, there is the ability of stronger anti-fibre-optical dispersion and wireless multi-path effect relative to DFT-S-OFDM, and can effectively reduce the complexity of encoder.
Description
Technical field
The invention belongs to optical-fibre communications fields, and in particular to the coherent light based on discrete Fresnel transform extension OFDM modulation
Fiber communication system.
Background technology
Orthogonal frequency division multiplexing (OFDM) technology is developed by multi-carrier modulation (MCM), it is a kind of special more
Subcarrier multiplex technology.The it is proposed of OFDM technology has nearly 40 years history, and first practical application is communicated in wireless high-frequency
In, the application in terms of bidirectional wireless data transmission grows up in the past 10 years.OFDM technology is by light-carried wireless earliest
(ROF) researcher of technology is introduced into optical fiber link, later since it is in the availability of frequency spectrum, dispersion tolerance and data speed
The advantage of rate flexibility ratio etc. receives significant attention, and a kind of modulation and frequency domain multiplex techniques has been used as, in conjunction with optical coherence
The technologies such as detection and palarization multiplexing (PDM) are applied to optical communication field.In the electrical multiplexed field with a large amount of subcarriers,
The complexity of OFDM technology is well below Nyquist FDM technology.Due to Bandwidth-Constrained, traditional OFDM is deposited in high-frequency region
In fading effect, the mode of generally use subcarrier zero padding forms frequency guard bands to resist frequency decline, but simultaneously can
The efficiency of analog-digital converter is caused to reduce.In addition, Metropolitan Area Network largely uses wavelength-selective switches, and cascade wavelength-selective switches
(WSSs) stronger optical filter effect can be introduced, the frequency of high-frequency region is caused to decline.
In order to overcome frequency to decline, adaptive carrier loading algorithm (adaptive loading) and channel pre-compensate for algorithm
(pre-emphasis) etc. largely proposed, so improve constant transmissions link parameter (such as fixed transceivers parameters and
Fixed WSSs parameters) under transmission data capacity.But above method needs accurately channel response information, this can promote channel
The complexity of estimation module and whole system.Document (M.Sung, S.Kang, J.Shim；J.Lee and J.Jeong,"DFT-
precoded coherent optical OFDM with Hermitian symmetry for fiber nonlinearity
Mitigation, " J.Lightw. Technol., vol.30, no.17, pp.2757-2763,2012.) propose direct computation of DFT
Leaf transformation extends orthogonal frequency division multiplexing (DFT-S-OFDM) technology, and frequency can be overcome to decline and put down over the whole width
Smooth signal-to-noise ratio curve.But due to being single-carrier modulated, discrete Fourier transform extension OFDM is to remaining code compared with OFDM
Between crosstalk it is more sensitive, so needing longer cyclic prefix (CP).Document (B.Spinnler, " Equalizer design
and complexity for digital coherent receiver,”J.Sel.Top.Quant.,vol.16,no.5,
Pp.1180-1192,2010.) the cycle phase additive process and overlap-save method frequency-domain equalization technology proposed, can reduce cycle
The length of prefix, but higher complexity can be introduced.Therefore how to eliminate present in traditional OFDM frequency decline and from
Intersymbol interference present in scattered Fourier transform expansion OFDM, which is one, to be worth solving the problems, such as.
Invention content
The present invention provides a kind of coherent fiber communication system based on discrete Fresnel transform extension OFDM modulation, purposes
It is to solve to deposit in frequency fading problem present in traditional OFDM and discrete Fourier transform extension OFDM (DFT-S-OFDM)
Inter-symbol interference problem.
To achieve the above object, the present invention devises in the transmitter of system for generating discrete Fresnel transform extension
Inverse discrete Fresnel transform (DFnT) module in the Signal coding module and receiver of OFDM (DFnT-S-OFDM) and channel
Balance module.In this way, which can get the diversity gain of frequency domain and time-domain, relative to conventional OFDM modulation lattice
There is formula stronger anti-frequency to decline performance, relative to discrete Fourier transform extension OFDM have stronger anti-fibre-optical dispersion and
Wireless multi-path effect, and effectively reduce the complexity of encoder.
Based on the coherent fiber communication system of discrete Fresnel transform extension OFDM modulation, including transmitter and receiver two
Part.Transmitter section includes that series connection turns parallel module, discrete Fresnel transform extension OFDM coding modules, addition cyclic prefix
Module, parallel connection turn serial module structure, D/A converter module and palarization multiplexing optical modulation module.Receiver section includes analog-to-digital conversion
Module, synchronization module, series connection turn parallel module, remove cyclic prefix module, channel equalization module, inverse discrete Fresnel transform mould
Block and parallel connection turn serial module structure.
The original signal of transmitting terminal first passes through series connection and turns the N number of data carrier of parallel module acquisition, using discrete Fresnel
Transformation extension OFDM coding modules obtain discrete Fresnel transform pre-coded symbols block and then respectively by addition cyclic prefix moulds
Block, parallel connection turn serial module structure, D/A converter module and palarization multiplexing optical modulation module, finally enter erbium-doped fiber amplifier.
After cyclic prefix is added, time-domain signal is by light modulator modulates and is sent in optical fiber.In receiver part head
First pass through analog-to-digital conversion module, synchronization module, series connection turn parallel module and remove to obtain after cyclic prefix module and receive signal r,
It obtains using channel equalization module, inverse discrete Fresnel transform module and restores signal, finally turn serial module structure by parallel connection.
The discrete Fresnel transform extends OFDM coding modules, when L subcarrier and N number of data carrier meet L >=N
When, discrete Fresnel transform matrix is expressed as Θ=Θ1FΘ2, F is N × N-dimensional Discrete Fourier transform, Θ in formula1With
Θ2N × N-dimensional diagonal matrix.When L subcarrier and N number of data carrier meet L=N, discrete Fresnel transform matrix is expressed as
Θ=F Γ FH, Γ is the eigenmatrix of Θ in formula.
In the inverse discrete Fresnel transform module, inverse discrete Fresnel transform matrix can be expressed as ΘH, ΘHFor N
× N-dimensional diagonal matrix.
Advantage possessed by the present invention is：
1. the present invention is to extend the improvement of OFDM modulation formats to traditional OFDM and discrete Fourier transform.It is proposed based on
Discrete Fresnel transform extends the diversity gain of coherent fiber communication the system available frequency domain and time-domain of OFDM modulation, relatively
There is stronger anti-frequency decline performance in OFDM, there is stronger anti-light fibre relative to discrete Fourier transform extension OFDM
Dispersion and wireless multi-path effect.
2. the present invention is compared with OFDM, discrete Fourier transform extension OFDM and Nyquist FDM, encoder complexity is big
Width declines.
Description of the drawings
Fig. 1 is discrete Fresnel transform extension ofdm system frame diagram.
Fig. 2 is that the bit error rate is 10-3When optical signal to noise ratio and transmission range variation relation figure (896 data subcarriers).
Fig. 3 is that the bit error rate is 10-3When optical signal to noise ratio and transmission range variation relation figure (1024 data subcarriers).
Fig. 4 be transmission range be 1040km when signal-to-noise ratio and subcarrier relational graph.
Fig. 5 be transmission range be 1360km when signal-to-noise ratio and subcarrier relational graph.
Fig. 6 be transmission range be 880km when signal-to-noise ratio and subcarrier relational graph.
Fig. 7 be transmission range be 1120km when signal-to-noise ratio and subcarrier relational graph.
The relational graph of required optical signal to noise ratio and transmission range when Fig. 8 is no laser linewidth.
Fig. 9 is the relational graph that laser linewidth is optical signal to noise ratio and transmission range needed for 100-kHz.
Figure 10 be cyclic prefix be 3ns when transmission range and respective distance best bit-error rate relational graph.
Figure 11 be cyclic prefix be 4ns when transmission range and respective distance best bit-error rate relational graph.
Figure 12 is the best bit-error rate of wdm system central channel and the relational graph of transmission range.
Figure 13 is the relational graph of the best bit-error rate and WSS 3-dB bandwidth of wdm system central channel.
Specific implementation mode
Below in conjunction with the accompanying drawings, the present invention is described further：
The original signal of transmitting terminal first passes through series connection and turns the N number of data carrier of parallel module acquisition, using discrete Fresnel
Transformation extension OFDM coding modules obtain discrete Fresnel transform pre-coded symbols block and then respectively by addition cyclic prefix moulds
Block, parallel connection turn serial module structure, D/A converter module and palarization multiplexing optical modulation module, finally enter erbium-doped fiber amplifier,
Detailed process is as follows：
Discrete Fresnel transform extends OFDM coding modules at transmitter, often presses x=[x0,x1,…,xN-1]TDivided
Block, ()TRepresent matrix transposition.Discrete Fresnel transform pre-coded symbols block can be expressed as：
x'=Θ x (1)
Θ is N × N-dimensional discrete Fresnel transform matrix in above formula, can be expressed as：
Θ=Θ1FΘ2 (2)
F is N × N-dimensional Discrete Fourier transform, Θ in above formula1And Θ2N × N-dimensional diagonal matrix.
Assuming that there are L subcarrier and meeting L >=N, it is the vectorial X that length is L by pre-coded symbols DUAL PROBLEMS OF VECTOR MAPPING, then produces
Raw time-domain signal can be expressed as：
In above formula ()HMatrix Conjugate transposition is represented,Inverse discrete Fourier transform matrix is tieed up for L × L.Adjustment process is such as
In Fig. 1 shown in No. 1 encoder.
As L=N, i.e., subcarrier is fully loaded with information.By the characteristic of circular matrix Θ：Θ=F Γ FH, propose as shown in Figure 1
No. 2 encoders, (3) formula can be expressed as again：
Γ is the eigenmatrix of Θ in above formula, whereinK-th of diagonal entry is in Γ：
No. 1 encoder needs two FFT transform, and No. 2 encoders only need a FFT transform, in contrast, Hou Zhefu
Miscellaneous degree is relatively low.
After cyclic prefix is added, time-domain signal is by light modulator modulates and is sent in optical fiber.In receiver part head
First pass through analog-to-digital conversion module, synchronization module, series connection turn parallel module and remove to obtain after cyclic prefix module and receive signal r,
It obtains using channel equalization module, inverse discrete Fresnel transform module and restores signal, finally turn serial module structure by parallel connection, have
Body process is as follows：
Due to polarization mode dispersion, dispersion or noise, signal is damaged, then receiving signal can be expressed as：
N indicates that variance is N in above formula0Length is the Gaussian noise vector of L, and H indicates channel impulse response.Channel it is discrete
Frequency response isThen frequency-domain received signal can be expressed as：
FromModulated sub-carriers in extract N number of data carrier.
Frequency-domain received signalIt can be expressed as again：
In above formulaFor N × N-dimensional diagonal matrix, k-th of diagonal entry is that the channel frequency of subcarrier needed for k-th is rung
It answers.Using zero forcing equalizer：It compensates channel effect, restores signal and be represented by：
Discrete Fresnel transform extension OFDM receiver as shown in Figure 1 is can be obtained,K-th of element can indicate
For：
μ in above formulaZF,KAnd δZF,KDesired signal and noise, Θ are indicated respectivelykK-th of column vector of Θ is expressed, then signal-to-noise ratio
It can be expressed as：
E in above formulaSIndicate that signal power, E () represent mathematic expectaion, GkIndicate k-th of diagonal entry of G.Formula (11)
Illustrate that discrete Fresnel transform extension OFDM can be averaged out the frequency decline of subcarrier, it is bent to obtain flat signal-to-noise ratio
Line.
Finally, more traditional OFDM, discrete Fourier transform extend OFDM, and discrete Fresnel transform extends OFDM, Nai Kui
The complexity of this spy's FDM system plural number multiplier operation.Wherein OFDM needs a FFT computing module, IFFT operations in transmitter
Module and N number of complex multiplier are balanced to complete single tapping channel in receiver.Compared with OFDM, discrete Fourier transform is expanded
Exhibition OFDM is also additionally required an IFFT computing module and N number of complex multiplier in receivers.Discrete Fresnel transform extends
OFDM needs a FFT computing module, IFFT computing modules and 2N complex multiplier in receiver.Due to Nyquist FDM
N number of tap coefficient is needed to be more than 20 parallel matched filters, so the complexity of Nyquist FDM is higher than OFDM.Due to N number of
The parallelism wave filter of big memory length can form rectangle spectral profile, so the complexity of Nyquist FDM is higher than OFDM.No
The computation complexity comparison of homologous ray is as shown in table 1, and M and L respectively represent the size and overlap length of FFT computing modules.
The computation complexity contrast table of 1 different system of table
The effect of the present invention can pass through following emulation explanation：
Simulated conditions and content：
1. discrete Fresnel transform extends ofdm system frame diagram
Fig. 1 is discrete Fresnel transform extension ofdm system frame diagram, including discrete Fresnel transform extension OFDM transmittings
Machine and receiver.
2. the variation relation of optical signal to noise ratio and transmission range is analyzed
Fig. 2 and Fig. 3 ignore laser line width and optical fiber it is non-linear.Fig. 2 is that the bit error rate (BER) is 10-3Time believes
It makes an uproar than the variation relation figure (896 data carriers) with transmission range, data rate is 224-Gb/s at this time.As seen from the figure, from
It is desirable with transmission range similar in OFDM to dissipate fresnel transform extension OFDM, while can be seen that discrete Fourier transform extension
OFDM transmission performance is worst.
Fig. 3 is that the bit error rate is 10-3When optical signal to noise ratio and transmission range variation relation figure (1024 data carriers), at this time
Data rate is 256-Gb/s.As seen from the figure, no matter how transmission range and circulating prefix-length change, relative to tradition
OFDM, discrete Fresnel transform extension OFDM can obtain the promotion more than 1-dB optical signal to noise ratio.
It can be seen that when cyclic prefix abundance by Fig. 2 and Fig. 3, OFDM, discrete Fourier transform extension OFDM and discrete
Fresnel transform extends OFDM and can get stable optical signal to noise ratio.
3. each sub-carrier signal-noise ratio analysis
Fig. 4 be transmission range be 1040km when signal-to-noise ratio and subcarrier relational graph.Data subcarrier is 896 at this time,
Cyclic prefix is 4ns (cyclic prefix is sufficient).As seen from the figure, sufficient cyclic prefix and frequency guard bands can be effective
Fibre-optical dispersion and frequency is avoided to decline, three kinds of adjustment formats can obtain flat signal-to-noise ratio.
Fig. 5 be transmission range be 1360km when signal-to-noise ratio and subcarrier relational graph.Data subcarrier is 896 at this time,
Cyclic prefix is inadequate.Due to there is remaining intersymbol interference, the signal-to-noise ratio curve of three kinds of modulation formats occurs declining phenomenon,
But collapsed position is different.The movement of OFDM medium-high frequencies is most fast, causes signal-to-noise ratio to decline in high-frequency region apparent.Discrete Fourier transform
Extension OFDM is single-frequency modulation format, is influenced by intersymbol interference closer to symbol protection interval is easier so that signal-to-noise ratio
It is apparent declining closer to symbol protection interval.The signal-to-noise ratio collapsed position that discrete Fresnel transform extends OFDM and OFDM is close
This is because high frequency subcarriers are expanded to entire frequency spectrum by discrete Fresnel transform matrix precoder to a certain extent, so
SNR collapsed positions have certain deviation to low frequency region.As seen from the figure, discrete Fourier transform extension OFDM modulation formats are vulnerable to
Dispersive influence causes signal-to-noise ratio to decline most serious in turn, corresponding with Fig. 2.
Fig. 6 be transmission range be 880km when signal-to-noise ratio and subcarrier relational graph.Data subcarrier is 1024 at this time,
And circulating prefix-length is sufficient.Because sufficient frequency guard bands, the signal-to-noise ratio curve of OFDM do not show low pass
Filtering characteristic has low signal-to-noise ratio in high-frequency region.Discrete Fresnel transform extends OFDM and discrete Fourier transform extension
The signal-to-noise ratio curve of OFDM is very flat over the whole width, has preferably anti-frequency decline performance compared with OFDM.
Fig. 7 be transmission range be 1120km when signal-to-noise ratio and subcarrier relational graph.Data subcarrier is 1024 at this time,
But circulating prefix-length is inadequate.As seen from the figure, when not having sufficient cyclic prefix and frequency guard bands, with OFDM and
Discrete Fourier transform extension OFDM is best compared to discrete Fresnel transform extension OFDM performances, illustrates that discrete Fresnel transform expands
Exhibition OFDM can preferably resist frequency and decline and eliminate intersymbol interference.
4. the relationship analysis of required optical signal to noise ratio and transmission range when various lasers line width
When Fig. 8 is no laser linewidth, it is 10 to obtain the bit error rate-3Required optical signal to noise ratio and transmission range relational graph.
Fig. 9 be laser linewidth be 100-kHz when, obtain the bit error rate be 10-3Required optical signal to noise ratio and transmission range
Relational graph.
It is 4ns that Fig. 8 and Fig. 9, which is respectively provided with cyclic prefix, and compares the property of 512 point FFT and 1024 point FFT modulating systems
Energy.Two figures are compared it can be found that relative to the modulating system using 512 point FFT, 1024 point FFT modulating systems are in short distance
Transmission performance difference but available longer transmission range.This is because being easier by laser using larger FFT modulating systems
The influence of phase noise, but there is higher tolerance to dispersion.
5. the performance evaluation of best transmission power at different distance
Figure 10 be cyclic prefix be 3ns when transmission range and respective distance best bit-error rate relational graph.As seen from the figure,
It is best that discrete Fresnel transform extends OFDM performances.
Figure 11 be cyclic prefix be 4ns when transmission range and respective distance best bit-error rate relational graph.As seen from the figure,
Discrete Fresnel transform extends OFDM and discrete Fourier transform extension OFDM performances are similar but all better than OFDM.
Figure 10 and Figure 11 considers nonlinear effect, and it is 100-kHz that laser linewidth, which is arranged, and forward error correction is sentenced firmly
Certainly the limit is 3.8 × 10-3.As can be seen that no matter whether cyclic prefix is sufficient, the performance that discrete Fresnel transform extends OFDM is equal
It is best.
6.WDM system performance analysis
Wdm system is made of 7 channels that channel spacing is 50-GHz.Figure 12 is the best mistake of wdm system central channel
The relational graph of code check and transmission range.Cyclic prefix is 3ns at this time, and discrete Fresnel transform extends OFDM and discrete fourier becomes
It is similar to change extension OFDM performances, but better than OFDM.
Figure 13 is the relational graph of the best bit-error rate and WSS 3-dB bandwidth of wdm system central channel.WSS has fixed
50-GHz bandwidth.As seen from the figure, three systems can aggravate frequency decline and intersymbol interference, but discrete Fresnel to a certain extent
Transformation extension OFDM also can express out best performance in the case of strong optically filtering.
Claims (3)
1. a kind of coherent fiber communication system based on discrete Fresnel transform extension OFDM modulation, it is characterised in that：Including hair
Penetrate machine and receiver two parts；Transmitter section includes that series connection turns parallel module, discrete Fresnel transform extension OFDM coding moulds
Block, addition cyclic prefix module, parallel connection turn serial module structure, D/A converter module and palarization multiplexing optical modulation module；Receiver
Part includes that analog-to-digital conversion module, synchronization module, series connection turn parallel module, remove cyclic prefix module, is channel equalization module, inverse
Discrete Fresnel transform module and parallel connection turn serial module structure；
In transmitter section, the original signal of transmitting terminal, which first passes through series connection and turns parallel module, obtains N number of data carrier, using from
Fresnel transform extension OFDM coding modules are dissipated to obtain discrete Fresnel transform pre-coded symbols block and then follow by addition respectively
Ring prefix module, parallel connection turn serial module structure, D/A converter module and palarization multiplexing optical modulation module, finally enter Er-doped fiber
Amplifier is ready for sending；
After cyclic prefix is added, time-domain signal is by light modulator modulates and is sent in optical fiber, is passed through first in receiver part
Cross analog-to-digital conversion module, synchronization module, series connection turn parallel module and remove to obtain after cyclic prefix module and receive signal r, then pass through
Channel equalization module, inverse discrete Fresnel transform module acquisition recovery signal are crossed, finally turns serial module structure by parallel connection and obtains most
Whole signal.
2. a kind of coherent fiber communication system based on discrete Fresnel transform extension OFDM modulation according to claim 1
System, it is characterised in that：The described discrete Fresnel transform extension OFDM coding modules obtain discrete Fresnel transform and prelist code symbol
Number block process is as follows：
Discrete Fresnel transform extends OFDM coding modules at transmitter, often presses x=[x0,x1,…,xN-1]TPiecemeal is carried out,
(·)TMatrix transposition is represented, discrete Fresnel transform pre-coded symbols block can be expressed as：
x'=Θ x (1)
Θ is N × N-dimensional discrete Fresnel transform matrix in above formula, can be expressed as：
Θ=Θ1FΘ2 (2)
F is N × N-dimensional Discrete Fourier transform, Θ in above formula1And Θ2N × N-dimensional diagonal matrix,
Assuming that there are L subcarrier and meeting L >=N, it is the vectorial X that length is L by pre-coded symbols DUAL PROBLEMS OF VECTOR MAPPING, then generates
Time-domain signal can be expressed as：
In above formula ()HMatrix Conjugate transposition is represented,Inverse discrete Fourier transform matrix is tieed up for L × L,
As L=N, i.e., subcarrier is fully loaded with information, by the characteristic of circular matrix Θ：Θ=F Γ FH, (3) formula can indicate again
For：
Γ is the eigenmatrix of Θ in above formula, and k-th of diagonal entry is in Γ：
Wherein
3. a kind of coherent fiber communication system based on discrete Fresnel transform extension OFDM modulation according to claim 1
System, it is characterised in that：The reception signal r is obtained by channel equalization module, inverse discrete Fresnel transform module and is restored letter
Number process it is as follows：
Due to polarization mode dispersion, dispersion or noise, signal is damaged, then receiving signal can be expressed as：
N indicates that variance is N in above formula0Length is the Gaussian noise vector of L, and H indicates channel impulse response, the discrete frequency of channel
Response isThen frequency-domain received signal can be expressed as：
FromModulated sub-carriers in extract N number of data carrier,
Frequency-domain received signalIt can be expressed as again：
In above formulaFor N × N-dimensional diagonal matrix, k-th of diagonal entry is the channel frequency response of subcarrier needed for k-th, is answered
Use zero forcing equalizer：It compensates channel effect, restores signal and be represented by：
K-th of element can be expressed as：
μ in above formulaZF,KAnd δZF,KDesired signal and noise, Θ are indicated respectivelykK-th of column vector of Θ is expressed, then signal-to-noise ratio can be with
It is expressed as：
E in above formulaSIndicate that signal power, E () represent mathematic expectaion, GkIndicate k-th of diagonal entry of G.
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Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| US20140010328A1 (en) * | 2003-03-25 | 2014-01-09 | Teliasonera Ab | Position adjusted guard time interval for ofdm-communications system |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US20140010328A1 (en) * | 2003-03-25 | 2014-01-09 | Teliasonera Ab | Position adjusted guard time interval for ofdm-communications system |
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| Title |
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| YUKUI YU等: "Discrete Fresnel Transform Spread OFDM for Coherent Optical Fiber Communication", 《IEEE PHOTONICS TECHNOLOGY LETTERS》 * |
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