CN109309542A - A kind of orthogonal letter based on time domain oversampling point multiplexing underwater acoustic communication method - Google Patents
A kind of orthogonal letter based on time domain oversampling point multiplexing underwater acoustic communication method Download PDFInfo
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Abstract
The present invention relates to a kind of, and the orthogonal letter based on time domain oversampling point is multiplexed underwater acoustic communication method, by ability of the frequency diversity gain obtained of precoding in OSDM vector in conjunction with the frequency diversity gain that time domain oversampling mutually obtains, compared with traditional symbol rate samples OSDM system, frequency diversity gain is higher in the vector of the system.In this case, each OSDM symbolic vector is equivalently transmitted by multiple pseudo channels.Therefore in receiving end, equilibrium treatment and polynary receive for each vector have similar structure.Numerical Simulation Results can clearly find out that time domain oversampling OSDM system performance proposed by the invention is significantly promoted compared to for traditional OSDM system.In addition, by being decomposed using composite channel matrix, equalization algorithm used in the present invention has the computation complexity of approximately linear, so that the time domain oversampling OSDM system proposed has practical value.
Description
Technical field
The invention belongs to field of underwater acoustic communication, are related to a kind of orthogonal letter based on time domain oversampling point multiplexing underwater sound communication side
Method, and in particular to a kind of orthogonal letter of time domain oversampling suitable for multipath time- variant channel divides multiplexing method.
Background technique
Underwater acoustic channel is acknowledged as most challenging one of wireless communication media at present.The lower transmission rate of sound wave
(1500m/s) can cause prolonged multipath delay spread, and tens underwater sound communication mark spaces are usually crossed in this delay, from
And lead to serious intersymbol interference (Inter-Symbol Interference, ISI).In order to overcome this interference and realize
High rate data transmission, orthogonal frequency division multiplexing (Orthogonal Frequency Division Multiplexing, OFDM) and its
Frequency-domain equalization technology is widely used in field of underwater acoustic communication.
Compared with traditional single carrier wave time domain equilibrium, the frequency domain equalization algorithm of OFDM technology has lower complexity, because
Frequency selective fading channels can be converted to a series of parallel flat channels by it, and be disappeared by simple single tap frequency domain equalization
Except ISI.However, a prominent question of OFDM is its peak-to-average power ratio (Peak-to-Average Power Ratio, PAPR)
It is higher.In contrast, current another single carrier frequency domain equalization (Single-Carrier Frequency-Domain
Equalization, SC-FDE) though technology can be realized lower PAPR, its bandwidth allocation and power distribution are inflexible.
In this regard, orthogonal letter point multiplexing (Orthogonal Signal-Division Multiplexing, OSDM) is
OFDM and SC-FDE it establishes a kind of extensive modulation frame and are unified for two therein by a kind of emerging modulation scheme
Extreme special case.Specifically, in a data block, the symbol that K=MN symbol segmentation is N number of a length of M is sweared for OSDM algorithm
Amount, by by M element carry out N point discrete Fourier in leaf inverse transformation (Inverse Discrete Fourier Transform,
IDFT modulation) is realized.Since the value of M and N can carry out flexible configuration according to the actual situation, OSDM modulator approach is flat
There is higher freedom degree in terms of balance system design requirement.In addition, OSDM can effectively drop compared with traditional OFDM technology
Low PAPR, and multipath diversity gains can be introduced simultaneously.
Existing OSDM research is mainly for frequency selective fading channels, in the case, between symbolic vector still
Orthogonality can be kept, to allow independently to carry out each vector equilibrium treatment to restore initial data in receiving end.However,
When OSDM system introduces Doppler's distortion, the orthogonality between symbolic vector can be destroyed, and be similar to OFDM carrier wave to generate
Between interfere (Inter-Carrier Interference, ICI) vector between interference (Inter-Vector Interference,
IVI), system performance significantly reduces.In addition, part research work shows that carrying out space-frequency coding in OSDM system transmitting terminal can realize
Emission diversity gain.For this purpose, the present invention devises a kind of time domain oversampling OSDM system suitable for multipath time- variant channel,
Wherein each OSDM symbolic vector is equally transmitted on multiple pseudo channels, so as to realize enhancing vector internal frequency point
The effect of collection.Meanwhile the OSDM system performance proposed is assessed by Numerical Simulation, it is demonstrated in multipath
Become the validity in underwater acoustic channel.
Summary of the invention
Technical problems to be solved
In order to avoid the shortcomings of the prior art, the present invention proposes a kind of orthogonal letter based on time domain oversampling point multiplexing
Underwater acoustic communication method, reduces the peak-to-average power ratio of transmitting signal, and introduces multipath diversity gains.
Technical solution
A kind of orthogonal letter based on time domain oversampling point multiplexing underwater acoustic communication method, it is characterised in that: be directed to multipath time-varying
Underwater acoustic channel devises time domain oversampling OSDM system model, wherein each OSDM symbolic vector is equally believed in multiple virtual subnets
It is transmitted on road, so as to so that frequency diversity gain is higher in the vector of system；(2) receiving end uses null vector and frequency displacement Chu
Sequence carries out Doppler effect correction and channel estimation, and balanced obtain to transmission symbol is independently carried out to each vector received
Estimation；(3) simultaneously, equalization algorithm is based on composite channel matrix and decomposes realization, computation complexity approximately linear.Steps are as follows:
Step 1, based on when constant channel build time domain oversampling OSDM system model:
The transmitting signal of OSDM system are as follows:
Wherein, FNIndicate N point Fourier transformation unitary matrice, ()HThe Hermitian transposition of representing matrix, IMIndicate M dimension
Unit matrix,Indicate Kronecker product；
It is sent in underwater acoustic channel to signal addition cyclic prefix and after carrying out carrier modulation；
With G/TsSample rate the OSDM signal received is sampled in communication receiver, wherein TsIt is symbol period,
G is oversample factor；Baseband receiving signalsrLength beK=GK, channel impulse response vectorcLength beL=GL, removal
Over-sampling OSDM systems baseband after carrier wave and cyclic prefix receives signalrIt indicates are as follows:
In formula:
Wherein, iG(n) unit matrix I is indicatedGN-th column,sIt indicatesK× 1 dimension transmitting signal terms,nIt indicatesK× 1 dimension noise
,Indicate K × K dimension circulation channel matrix,The first column element be0 K - L -1Indicate that length isK-L- 1
Full null vector；
It is rightrCarry out byMLeaf transformation obtains receiving symbolic blocks in column N point discrete Fourierx, indicate are as follows:
Receive symbolic blocksxN-th are as follows:
In formula
Wherein, fN(n) unitary matrice F is indicatedNN-th column,d n=[d]n M :n M + M -1Indicate that over-sampling OSDM system emits symbol
BlockdN-th,x n=[x]n M :n M + M -1Indicate that over-sampling OSDM system receives symbolic blocksxN-th；
Step 2: according to the common time variation of underwater acoustic channel in practice, considering the influence of IVI, use null vector in receiving end
Carry out Doppler effect correction:
In formula,
Wherein, ∈ is CFO parameter, TsFor the time interval of each OSDM symbol；
The estimation of CFO parameter are as follows:
Wherein:Indicate null vector index；
Step 3, channel equalization: definitionWith
It willWithSubstituting into above-mentioned definition indicates are as follows:
In formula,
It defines M × M and ties up submatrixH n,g=[H n]gM:gM+M-1,gM:gM+M-1, 0≤g≤G-1, formula (13) rewriting are as follows:
In formula,
Above formula shows: each symbolic vector in over-sampling OSDM system is equally corresponding toG it is virtual
Channel, thus to obtain diversity gains more in addition to frequency diversity in the vector in OSDM；Lead between pseudo channel
It is often relevant, therefore diversity order is less than G；
MMSE equilibrium is carried out to over-sampling OSDM system, the estimation to transmitting symbolic blocks d is obtained, indicates are as follows:
In formula,
Wherein, WnIndicate the coefficient matrix of MMSE equilibrium；
Design factor matrix WnIt needs to oversampled channel shock response vectorcWith noise variance σ2Estimated:
It is inserted into U pilot tone vector in each OSDM block equal intervals, and sets UM>L, while defining the index of pilot tone vector
It is expressed asWherein pu=u Δ, Δ=N/U；It is obtained according to formula (7), formula (13) and formula (14):
In formula,
DefinitionAnd U pilot tone vector is superimposed upon
Together, oversampled channel impulse response vector is obtainedcLeast-squares estimation:
It selects frequency displacement Chu sequence as pilot tone vector, indicates are as follows:
Wherein, bMIndicate that length is the Chu sequence of M.In this case,To simplify pair
In oversampled channel impulse response vectorcEstimation, indicate are as follows:
Null vector is inserted into each OSDM block, noise variance uses the average function that vector is accordingly demodulated after Doppler effect correction
Rate is measured, and is indicated are as follows:
Wherein, V indicates the number of null vector.
Beneficial effect
A kind of orthogonal letter based on time domain oversampling proposed by the present invention point multiplexing underwater acoustic communication method, will be in OSDM vector
Ability of the precoding frequency diversity gain obtained in conjunction with the frequency diversity gain that time domain oversampling mutually obtains is and traditional
Symbol rate sampling OSDM system is compared, and frequency diversity gain is higher in the vector of the system.In this case, each OSDM symbol
Number vector is all equivalently transmitted by multiple pseudo channels.Therefore in receiving end, for each vector equilibrium treatment with
Polynary receive has similar structure.
Numerical Simulation Results can clearly find out compared to for traditional OSDM system, time domain mistake proposed by the invention
Sampling OSDM system performance is significantly promoted.In addition, by being decomposed using composite channel matrix, it is used in the present invention
Equalization algorithm has the computation complexity of approximately linear, so that the time domain oversampling OSDM system proposed has practical value.
Detailed description of the invention
Fig. 1: bit error rate performance of the time domain oversampling OSDM system when channel condition is completely known on constant channel is bent
Line chart
Fig. 2: under the premise of channel condition is completely known, for different Doppler factors value to time domain oversampling
OSDM system carries out error rate analyzer
Fig. 3: under the premise of introducing channel estimation errors, time domain oversampling OSDM system when constant channel on error code
Rate analysis
Fig. 4: under the premise of introducing channel estimation errors, for different Doppler factors value to time domain oversampling
OSDM system carries out error rate analyzer
Specific embodiment
Now in conjunction with embodiment, attached drawing, the invention will be further described:
The specific method of orthogonal letter based on time domain oversampling point multiplexing water sound communication technique is: (1) for multipath time-varying
Underwater acoustic channel devises time domain oversampling OSDM system model, wherein each OSDM symbolic vector is equally believed in multiple virtual subnets
It is transmitted on road, so as to so that the appropriate interior frequency diversity gain of system is higher；(2) receiving end uses null vector and frequency displacement Chu
Sequence carries out Doppler effect correction and channel estimation, and balanced obtain to transmission symbol is independently carried out to each vector received
Estimation；(3) simultaneously, equalization algorithm is based on composite channel matrix and decomposes realization, computation complexity approximately linear.
Method according to the present invention includes the following steps:
Step 1: constant channel build time domain oversampling OSDM system model when being based on.
In OSDM emission system, it is assumed that the symbolic blocks d that one length of transmitting is K=MN, then OSDM modulation generate transmitting
Signal s is represented by
Wherein, FNIndicate N point Fourier transformation unitary matrice, ()HThe Hermitian transposition of representing matrix, IMIndicate M dimension
Unit matrix,Indicate Kronecker product.This signal adds cyclic prefix and is sent in underwater acoustic channel after carrying out carrier modulation.
In communication receiver to the OSDM signal received with G/TsSample rate sampled, wherein TsIt is symbol period,
G is oversample factor.In the case, baseband receiving signalsrLength becomeK=GK, channel impulse response vectorcLength
BecomeL=GL, then the over-sampling OSDM systems baseband after removing carrier wave and cyclic prefix receive signalrIt is represented by
In formula,
Wherein, iG(n) unit matrix I is indicatedGN-th column,sIt indicatesK× 1 dimension transmitting signal terms,nIt indicatesK× 1 dimension noise
,Indicate K × K dimension circulation channel matrix,The first column element beHerein 0 K - L -1Indicate that length isK-L-
1 full null vector.
Over-sampling OSDM Demodulation Systems be by carry out byMArrange leaf transformation (Discrete Fourier in N point discrete Fourier
Transform, DFT) it obtains receiving symbolic blocksx, it is represented by
At this point, the decoupling processing between each vector of over-sampling OSDM system still may be implemented, because
In formula,
Wherein, fN(n) unitary matrice F is indicatedNN-th column,d n=[d]n M :n M + M -1Indicate that over-sampling OSDM system emits symbol
BlockdN-th,x n=[x]n M :n M + M -1Indicate that over-sampling OSDM system receives symbolic blocksxN-th.
Step 2: considering the common time variation of underwater acoustic channel in practice, consider the influence of IVI, receiving end using zero to
Amount carries out Doppler effect correction.
The present invention slows down the influence of IVI using two step Doppler Compensation Methods.Assuming that in an OSDM block, Suo Youxin
Time change in path can be modeled by a common Doppler factor, carry out front end weight first in the model
Doppler's distortion is converted to narrowband carrier frequency deviation (carrier frequency offset, CFO) by sampling, then carries out CFO
Compensation.Meanwhile the present invention uses two linear frequency modulation (linear frequency-modulated, LFM) sections to Doppler's ruler
It spends the factor and carries out rough estimate, and minimize total IVI energy by some null vectors being previously inserted to obtain CFO estimation.
Specifically on the basis of formula (5), defines Doppler effect correction vector and be expressed as
In formula,
Wherein, ∈ is CFO parameter, TsFor the time interval of each OSDM symbol.Meanwhile it definingIndicate null vector rope
Draw.Therefore, the CFO estimation of over-sampling OSDM system can be expressed as
After carrying out Doppler effect correction, channel constant channel when can be seen as can be achieved between each vector of OSDM at this time
Decoupling processing.DefinitionWithBased on formula (5) and formula (6), can obtain
It arrives
In formula,
Secondly, defining M × M ties up submatrixH n,g=[H n]gM:gM+M-1,gM:gM+M-1, 0≤g≤G-1, formula (13) can be rewritten as
In formula,
By formula (15) it can be seen that each symbolic vector in over-sampling OSDM system is equally corresponding to
G pseudo channel on transmit, it is possible thereby to obtain more diversity gains in addition to frequency diversity in the vector in OSDM.So
And, it should be noted that it is usually relevant between pseudo channel, therefore diversity order is less than G.
Step 3: channel equalization.
Based on above-mentioned conclusion, MMSE equilibrium is carried out to over-sampling OSDM system, obtains the estimation to transmitting symbolic blocks d, table
It is shown as
In formula,
Wherein, WnIndicate the coefficient matrix of MMSE equilibrium.Obviously, as G=1, formula (16) is that character rate samples OSDM
The balanced expression formula of system.Furthermore it is noted thatH n,gIt is entirely diagonal, therefore to each symbol in formula (16)
It is approximately linear that vector, which carries out balanced computation complexity,.
In practice, design factor matrix WnIt needs to oversampled channel shock response vectorcWith noise variance σ2Estimated
Meter.For this purpose, the present invention is inserted into U pilot tone vector in each OSDM block equal intervals, and assume UM>L, while define pilot tone to
The index of amount is expressed asWherein pu=u Δ, Δ=N/U.According to formula (7), formula (13) and formula (14)
It can obtain
In formula,
In addition, definitionAnd U pilot tone vector is folded
It is added together, available oversampled channel impulse response vectorcLeast-squares estimation
In order to be further simplified calculation amount, the present invention selects frequency displacement Chu sequence as pilot tone vector, is expressed as
Wherein, bMIndicate that length is the Chu sequence of M.In this case,To simplify pair
In oversampled channel impulse response vectorcEstimation, be expressed as
In addition, in order to estimate σ2, the present invention is inserted into null vector in each OSDM block.Doppler can be used in noise variance
The mean power of vector is demodulated after compensation accordingly to measure, be expressed mathematically as
Wherein, V indicates the number of null vector.
Over-sampling OSDM error rate of system performance is analyzed by Numerical Simulation Results.Consider underwater sound communication scene,
Given OSDM data block length K=1024 carries out information transmission, mark space T using QPSKs=0.25ms, an OSDM block
Duration T=KTs=256ms, CP length Kg=128, centre carrier frequency fc=6kHz, channel memory length L=80,
Maximum multipath time delay τmax=78Ts=19.5ms.
It is forthright that Fig. 1 illustrates error code of the time domain oversampling OSDM system when channel condition is completely known on constant channel
Energy.Obviously, in vector length M=1, OSDM system is effectively equivalent to ofdm system.In addition, working as oversample factor G=1
When, over-sampling system is reduced to conventional symbol rate sampling system.It is 1 as benchmark using the value of M and G, it can be seen that served as
When the value of decimation factor G is fixed, system performance is promoted with the increase of vector length M.This is because the increasing of vector length M
Adding can be such that the frequency diversity in vector increases.On the other hand, as shown in formula (26), when the value of oversample factor G is larger
When, the diversity of frequency in vector can also be provided.Therefore, in the case where fixed vector length M, by increase over-sampling because
The value of sub- G can obtain better system performance.It is important to note, however, that being relevant between pseudo channel, therefore obtained
Linear relationship will not be presented with the change of oversample factor G in the diversity order obtained.As proof, in Fig. 1 when over-sampling because
The value of sub- G from 2 become 4 when, bit error rate performance slope of a curve is held essentially constant.Therefore, in practical applications, need to consider
The problem of computation complexity brought by diversity gain and time domain oversampling is compromised.
Fig. 2, which is illustrated, introduces Doppler's distortion in the case where channel condition is completely known to time domain oversampling OSDM system
Influence.The value of vector length M and oversample factor G are fixed when carrying out numerical simulation, take M=16, G=2 herein.Together
When, channel Doppler effect is introduced by changing the value of Doppler factor α.In addition, also by when constant channel (α=0)
The case where take into account.Simulation result shown in Fig. 2 can be with it is clear to see that in the case where no Doppler effect correction, OSDM
System almost can not work normally.When carrying out Doppler effect correction using method proposed by the invention, OSDM system performance can
To be obviously improved.However, be completely counterbalanced by since the non-homogeneous Doppler frequency shift of broadband OSDM signal cannot be compensated by narrowband CFO,
Residual doppler effect becomes can not ignore with the increase of Doppler factor value, correspondingly so as to cause OSDM system performance
It reduces.
In addition, considering channel estimation errors in figs. 3 and 4.It is identical as the simulation parameter configuration of Fig. 1 and Fig. 2, uniquely
Difference be using frequency pilot sign become 128.Obviously, the observed result and Fig. 1 obtained after channel estimation errors is introduced
It is similar with Fig. 2, but ber curve slightly rises.
Claims (1)
1. a kind of orthogonal letter based on time domain oversampling point multiplexing underwater acoustic communication method, it is characterised in that steps are as follows:
Step 1, based on when constant channel build time domain oversampling OSDM system model:
The transmitting signal of OSDM system are as follows:
Wherein, FNIndicate N point Fourier transformation unitary matrice, ()HThe Hermitian transposition of representing matrix, IMIndicate that M ties up unit
Matrix,Indicate Kronecker product；
It is sent in underwater acoustic channel to signal addition cyclic prefix and after carrying out carrier modulation；
With G/TsSample rate the OSDM signal received is sampled in communication receiver, wherein TsIt is symbol period, G is
Oversample factor；Baseband receiving signalsrLength beK=GK, channel impulse response vectorcLength beL=GL removes carrier wave
Signal is received with the over-sampling OSDM systems baseband after cyclic prefixrIt indicates are as follows:
In formula:
Wherein, iG(n) unit matrix I is indicatedGN-th column,sIt indicatesK× 1 dimension transmitting signal terms,nIt indicatesK× 1 dimension noise item,
Indicate K × K dimension circulation channel matrix,The first column element be0 K - L -1Indicate that length isK-LComplete the zero of -1
Vector；
It is rightrCarry out byMLeaf transformation obtains receiving symbolic blocks in column N point discrete Fourierx, indicate are as follows:
Receive symbolic blocksxN-th are as follows:
In formula
H n=diag [H n,H N+n,...,H ( M -1)N+n]T} (7)
Wherein, fN(n) unitary matrice F is indicatedNN-th column,d n=[d]n M :n M + M -1Indicate that over-sampling OSDM system emits symbolic blocksd's
N-th, x n =[x]n M :n M + M -1Indicate that over-sampling OSDM system receives symbolic blocksxN-th；
Step 2: according to the common time variation of underwater acoustic channel in practice, considering the influence of IVI, carried out in receiving end using null vector
Doppler effect correction:
In formula,
Wherein, ∈ is CFO parameter, TsFor the time interval of each OSDM symbol；
The estimation of CFO parameter are as follows:
Wherein: SzIndicate null vector index；
Step 3, channel equalization: definitionWith
It willWithSubstituting into above-mentioned definition indicates are as follows:
In formula,
It defines M × M and ties up submatrixH n,g=[H n]gM:gM+M-1,gM:gM+M-1, 0≤g≤G-1, formula (13) rewriting are as follows:
In formula,
Above formula shows: each symbolic vector in over-sampling OSDM system is equally corresponding toG pseudo channel
Upper transmission, thus to obtain diversity gains more in addition to frequency diversity in the vector in OSDM；It is usually between pseudo channel
It is relevant, therefore diversity order is less than G；
MMSE equilibrium is carried out to over-sampling OSDM system, the estimation to transmitting symbolic blocks d is obtained, indicates are as follows:
In formula,
Wherein, WnIndicate the coefficient matrix of MMSE equilibrium；
Design factor matrix WnIt needs to oversampled channel shock response vectorcWith noise variance σ2Estimated:
It is inserted into U pilot tone vector in each OSDM block equal intervals, and sets UM>L, while the index for defining pilot tone vector indicates
For Sp={ p0,p1,...,pU-1, wherein pu=u Δ, Δ=N/U；It is obtained according to formula (7), formula (13) and formula (14):
In formula,
DefinitionAnd U pilot tone vector is superimposed,
Obtain oversampled channel impulse response vectorcLeast-squares estimation:
It selects frequency displacement Chu sequence as pilot tone vector, indicates are as follows:
Wherein, bMIndicate that length is the Chu sequence of M.In this case,It is adopted to simplify for crossing
Sample channel impulse response vectorcEstimation, indicate are as follows:
Null vector is inserted into each OSDM block, noise variance is come using the mean power for accordingly demodulating vector after Doppler effect correction
Measurement indicates are as follows:
Wherein, V indicates the number of null vector.
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| CN110233688A (en) * | 2019-05-23 | 2019-09-13 | 西安交通大学 | Inhibit the extensive antenna orthogonal Space Time Coding launching technique of Beam Domain based on Doppler |
| CN110691048A (en) * | 2019-10-02 | 2020-01-14 | 西北工业大学 | Orthogonal signal division multiplexing equalization method based on diagonal block banded matrix enhancement |
| CN110691048B (en) * | 2019-10-02 | 2021-09-14 | 西北工业大学 | Orthogonal signal division multiplexing equalization method based on diagonal block banded matrix enhancement |
| CN111147157A (en) * | 2019-12-30 | 2020-05-12 | 浙江大学 | Soft interference elimination Turbo equalization method for orthogonal signal division multiplexing on underwater acoustic channel |
| CN111147157B (en) * | 2019-12-30 | 2021-04-23 | 浙江大学 | Soft interference elimination Turbo equalization method for orthogonal signal division multiplexing on underwater acoustic channel |
| CN113271196A (en) * | 2021-04-07 | 2021-08-17 | 北京邮电大学 | Short guard interval orthogonal frequency division multiplexing wireless transmission method |
| CN115361259A (en) * | 2022-08-24 | 2022-11-18 | 西安理工大学 | Channel equalization method based on space delay diversity |
| CN115361259B (en) * | 2022-08-24 | 2023-03-31 | 西安理工大学 | Channel equalization method based on space delay diversity |
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