CN108631904B - A kind of mode division multiplexing system injury compensation method based on lattice reduction - Google Patents

A kind of mode division multiplexing system injury compensation method based on lattice reduction Download PDF

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CN108631904B
CN108631904B CN201810287801.9A CN201810287801A CN108631904B CN 108631904 B CN108631904 B CN 108631904B CN 201810287801 A CN201810287801 A CN 201810287801A CN 108631904 B CN108631904 B CN 108631904B
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CN108631904A (en
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胡贵军
张天
李莉
李娇
苏丛哲
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Jilin University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J14/00—Optical multiplex systems
    • H04J14/04—Mode multiplex systems
    • 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
    • H04B10/66—Non-coherent receivers, e.g. using direct detection
    • H04B10/69—Electrical arrangements in the receiver
    • H04B10/697—Arrangements for reducing noise and distortion
    • H04B10/6971—Arrangements for reducing noise and distortion using equalisation
    • 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
    • H04B10/25—Arrangements specific to fibre transmission
    • H04B10/2507—Arrangements specific to fibre transmission for the reduction or elimination of distortion or dispersion
    • H04B10/2513—Arrangements specific to fibre transmission for the reduction or elimination of distortion or dispersion due to chromatic dispersion

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Abstract

The mode division multiplexing system injury compensation method based on lattice reduction that the invention discloses a kind of, belong to field of communication technology, the non-orthogonal channel matrix H that method of the invention first obtains least square (LS) estimation carries out specification processing, obtains an almost orthogonal matrixWith a modular matrix T, almost orthogonal matrix is then utilizedIt is obtained to signal progress equilibrium is receivedFinally willPremultiplication modular matrix T after quantization judgement is carried out, is realizedBetween conversion, obtain send signal estimated value.That is, converting the equalization problem of non-orthogonal channel matrix to the signal processing problems of almost orthogonal matrix by lattice reduction, to solve the problems, such as the deterioration of channel matrix orthogonality caused by MDL, the damage compensation performance of equalization algorithm is improved.The present invention carries out carrying out quasi- orthogonalization to channel matrix using lattice algorithm, and the damage caused by MDL has carried out effective compensation, has the characteristics that computation complexity is low, error performance is excellent, has preferable demultiplexing effect.

Description

A kind of mode division multiplexing system injury compensation method based on lattice reduction
Technical field
The invention belongs to fields of communication technology, are related to a kind of damage compensation method of mode division multiplexing (MDM) system, using lattice Base algorithm realizes the demultiplexing to MDM system.
Background technique
With the rapid development of informationized society, global data flow every year to be more than 50% speed explosive growth, Traditional single mode fiber communications power system capacity has moved closer to non-linear shannon limit.As single mode optical fiber capacity bottleneck can be broken through A kind of novel expansion technology, come into being based on the mode division multiplexing technology (MDM) of less fundamental mode optical fibre (FMF).Mode division multiplexing technology Realize that dilatation at double is transmitted by carrying out individual transmission using the orthogonal mode in less fundamental mode optical fibre.In MDM system, there are modes (MC), differential mode time delay (DMGD) are coupled, the peculiar damage such as mode dependent loss (MDL) seriously affects system performance, usually adopts The caused system performance degradation of these damages is solved the problems, such as with the balancing technique based on multiple-input and multiple-output (MIMO), is mainly had MIMO balancing technique based on channel estimation and linear detection algorithm (ZF, MMSE), based on adaptive filter algorithm (LMS, RLS, CMA, MMA) MIMO balancing technique and be based on the MIMO balancing technique of blind source separating (such as ICA), these methods can neglect in MDL It works well in the case of slightly.However, for actual MDM system, since optical fiber, fiber amplifier and optical passive component are to difference The gain or decaying of mode are different, MDL there are inevitable, especially in long range large capacity MDM system, MDL compared with Greatly, the orthogonality of system channel matrix is caused to deteriorate serious, at this point, traditional MIMO equalization algorithm is no longer applicable in.
Summary of the invention
For the prior art can not under effective compensation MDL existence condition MDM system damage compensation problem, the present invention provides A kind of MDM system injury compensation method based on lattice reduction, this method is merely with electrical domain number compared with prior art The compensation of the damage under MDL existence condition can be realized in signal processing technology, and computation complexity is low, and damage compensation effect is excellent, System can be effectively improved to MDL tolerance value, improve transmission matrix orthogonality, the development to long range large capacity optical-fiber network is promoted It is of great significance.
Basic principle of the invention is: lattice reduction algorithm estimates obtained non-orthogonal channel to least square (LS) first Matrix H carries out specification processing, obtains an almost orthogonal matrixWith a modular matrix T, almost orthogonal matrix is then utilizedIt is right Signal progress equilibrium is received to obtainFinally willPremultiplication modular matrix T after quantization judgement is carried out, is realizedWithBetween conversion, Obtain sending the estimated value of signal.That is, by lattice reduction, by orthogonal moment subject to the equalization problem conversion of non-orthogonal channel matrix The signal processing problems (as shown in Figure 1) of battle array improve to solve the problems, such as the deterioration of channel matrix orthogonality caused by MDL The damage compensation performance of equalization algorithm.
In practical MDM system, due to Mode Coupling, the presence of Differential Group Delay and mode dependent loss, signal is being passed There are intersymbol interference and channel interference in transmission link, every road output signal is all multiple signals and channel impulse response linear convolution Superposition, the channel matrix H of MDM system is a non-sequency spectrum matrix at this time, and matrix order is with differential mode group delay Increase and increase, this brings certain difficulty to lattice reduction, and reason has two: first is that the object of lattice reduction algorithm must be that column are full Order matrix, the second is channel matrix order is excessive, lattice algorithm is deteriorated to the improvement of channel.To solve this problem, the present invention mentions Gone out matrix transform method, by channel matrix extension and it is right multiply unit circle matrix and be decomposed into H can carry out the more of lattice reduction A low order sequency spectrum matrix Hfk, a series of elementary transformation is then carried out to multiple matrix Hs according to specification conditionfkIt carries out respectively Orthogonalization specification obtainsFinally utilizeEquilibrium is carried out to signal, then by being sent after the anti-transformation such as translation scaling The estimated value of signal.
The present invention is achieved through the following technical solutions:
A kind of damage compensation method of the mode division multiplexing system based on lattice reduction, the specific steps are as follows:
Step 1 is pre-treatment step, covers the sequency spectrum matrix of channel matrix H all elements in order to obtain, needs pair Channel matrix is extended, and solves the problems, such as that Differential Group Delay leads to the non-sequency spectrum of channel matrix, passes through channel matrix extension and the right side Multiply unit circle matrix, lattice can be carried out about for what the high-order channel matrix H of D × D (Q+1) of non-sequency spectrum was converted to D × D The low order non-singular matrix H of processingfk, wherein D is pattern count, and Q is time delay overlay length；
Its detailed process the following steps are included:
S1, first according to difference modes group delay (DMGD) calculate Q value size, Q=τDMGD/Ts, TSFor code-element period, τDMGDFor differential mode group delay total in optical fiber, and the channel matrix H obtained according to estimation, by carrying out piecemeal to transmission data, Channel matrix corresponding to the input and output of each data block is that the channel matrix after extending is denoted asIts concrete form are as follows:
S2, according to mode quantity D and extension length L, (wherein, L is equal to Q/ δ, the value and signal transmission rate of δ, modulation Format is related with matrixing complexity, and taking δ under normal conditions is 0.161), to construct a DL rank unit matrix IDL, a DQ Rank unit matrix IDQWith a full null matrix 0DQ×D(L-Q), a unit circle matrix U is constructed jointly by these three matrixesCP, Form are as follows:
S3, by the channel matrix after extensionThe right side multiplies UCP, obtain the sequency spectrum block circulant matrix He of DL × DL, the matrix packet Containing all elements in channel matrix H；
S4, L rank Fourier transform matrix and D rank unit matrix are subjected to Kronecker product operation, obtain block Fourier Transformation matrix FDL；
S5, the sequency spectrum block circulant matrix He premultiplication block Fourier transform matrix F for obtaining step 3DL, the right side multiplies in anti-Fu of block Leaf transformation matrix finally obtains a block diagonal matrix HF；
S6, to HFThe minor matrix of each D × D on diagonal line is separated, and the matrix H of corresponding D × D is obtainedfk, In, (k=1 ..., L)；
Step 2, the H to obtained D × Dfk(k=1 ..., L) a channel matrix carries out lattice and about subtracts, and according to MDM system System characteristic, after determining specification condition and about subtractingSignal is detected, detailed process the following steps are included:
S7, to receive signal x (t)=[x1(t)…xD(t)]T∈CD×1, (t=kTS, k=1 ..., L) carry out translation contracting It puts, the equivalent signal s that will send is mapped on continuous integral number domain, then has:Wherein, IDFor D rank unit Battle array, α and β respectively represent zooming parameter and translation parameters, the two value be not it is unique, it is true by the modulation format of signal It is fixed, it is equivalent to receive signal are as follows:
S8, the k channel matrix H to obtained D × DfkCarry out amplitude about subtracts, and makes its specification matrixMeetWherein,Representing matrixIn m column vector, in matrixIn if any ColumnIt is unsatisfactory for this condition, then by matrixN-th columnIt is added on m column again, wherein μ is Schimidt orthogonalization Coefficient, andSymbol round () indicates to be rounded, meanwhile, to unit matrix IDSame operation is carried out to obtain Modular matrix T；
S9, using Matrix condition number as the standard of measurement system MDL: under the conditions of OSNR is 18dB, use in MDM system ZF algorithm carries out channel equalization, and (i.e. the bit error rate is less than 10- in the case where ensuring compliance with communication standard3When) MDL tolerance value, i.e., The specification condition of algorithm:
S10, to matrixColumn vector carry out elementary transformation, realize gradually about subtracting to column vector length: firstly, meter It calculatesEach column vector length of matrix, and willAscending order arrangement is carried out, the smallest most short amount of column vector modulus value is obtained, is set Change to matrixThe 1st column, be denoted asThen, it enables1 < m≤D, i.e., by matrixThe 1st column -1 times It is added separately on remaining D-1 column, realization about subtracts length of remaining each column vector on standard column vector opposite direction, to about subtracting AfterwardsMatrix is determined according to the specification condition determined in S9, and S11 is executed when meeting specification condition, otherwise executes S8, Identical elementary transformation is carried out to T matrix obtained in S8 simultaneously to be updated；
S11, it obtains lattice and about subtracts rear matrixWith modular matrix T, useTo receive signal carry out it is balanced successively with LTSReception signal phasor in period after L translation scaling(t=kTS, k= 1 ..., L) ZF equilibrium treatment is carried out, byWhereinIt is equivalent transmission signal, base In the balanced matrix of the ZF detection algorithm of lattice reduction are as follows:Reception signal after then balanced can be with It indicates are as follows:
S12, since lattice algorithm carried out on continuous integral number domain, by the equipollent vectors after equilibriumIt is taken Integral quantization adjudicates to obtainPremultiplication modular matrix T recovers source signal i.e. afterwards
S13, S12 output signal is subjected to anti-translation scaling, recovers source signal
Compared with prior art, the present invention has the advantage that
The present invention carries out carrying out quasi- orthogonalization to channel matrix using lattice algorithm, and damaging caused by MDL is had Effect compensation, has the characteristics that computation complexity is low, error performance is excellent, has preferable demultiplexing effect.
Detailed description of the invention
Fig. 1 is the schematic diagram of lattice reduction；
Fig. 2 is 6 × 6 mode division multiplexing system structure diagrams of the invention based on less fundamental mode optical fibre；
Fig. 3 is the flow chart of the mode division multiplexing system Deplexing method of the invention based on lattice reduction；
Fig. 4 is number off-lined signal processing module flow chart used in the present invention；
Fig. 5 is in MDM system, using the corresponding relationship of bit error rate when linear zero forcing algorithm and MDL；
Fig. 6 is algorithm proposed by the invention and existing FD-LMS, FD-ICA algorithm performance pair when MDL is 5dB Than figure；
Fig. 7 is algorithm proposed by the invention and existing FD-LMS, FD-ICA algorithm performance when MDL is 10dB Comparison diagram；
Fig. 8 is algorithm proposed by the invention and existing FD-LMS, FD-ICA algorithm performance when MDL is 15dB Comparison diagram；
Fig. 9 is MDL when being 10dB, at different optical signal to noise ratio (OSNR), using having zero forcing algorithm (ZF), lattice to assist compeling Zero algorithm and ML algorithm carry out balanced obtained BER comparison diagram；
Specific embodiment
The present invention is described further with reference to the accompanying drawing.
To 6 × 6 mode division multiplexing Transmission systems based on less fundamental mode optical fibre to the validity of equalization algorithm proposed by the present invention into Row detection.Fig. 2 shows 6 × 6 mode division multiplexing system schematics of less fundamental mode optical fibre of the present invention.Wherein include: 6 numbers According to sending module 1, pattern multiplexer 2, less fundamental mode optical fibre transmission link module (80km less fundamental mode optical fibre, erbium-doped fiber amplifier (EDFA), mode scrambler (MS)) 3,4,6 coherent receivers 5 of pattern demultiplexer and off-line data processing module.
6 data transmission blocks modulation in Fig. 2 generates 6 road QPSK optical signals, is loaded into 6 different modes respectively (LP01、LP11a、LP11b、LP21a、LP21bWith LP02) on, by pattern multiplexer be coupled into 6 modes in FMF carry out it is defeated, It is recycled in optical fiber transmission module 15 times and enters pattern demultiplexer progress Signal separator after carrying out 1200km transmission, and in number Signal processing module compensates transmission impairment.Wherein laser linewidth 100kHz, operation wavelength 1550nm, every road symbol Rate is 28GBaud, and less fundamental mode optical fibre stiffness of coupling is -20dB/km, and each mode fiber loss is 0.22dB/km, when difference modes group Prolong as 9ps/km.
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 that the damage to mode division multiplexing system compensates.Fig. 3 gives the present invention Specific flow chart, Fig. 4 gives processed offline module flow diagram of the invention digital, and Fig. 5 gives should at signal-to-noise ratio 18dB Using linear squeeze theorem in MDM system, the tolerance value of MDL when meeting communication system requirements at this time, and using this tolerance value as lattice Former channel matrix is carried out specification processing by a series of elementary transformation and recovers source signal by base specification condition.The present invention Specific step is as follows:
The first step is pre-treatment step, covers the sequency spectrum matrix of channel matrix H all elements in order to obtain, needs pair Channel matrix is extended, and multiplies unit circle matrix by channel matrix extension and the right side, solving Differential Group Delay leads to channel square Battle array non-sequency spectrum problem, the high-order channel matrix H of non-sequency spectrum, which is converted to 6 × 6, can carry out the low of lattice reduction processing Rank non-singular matrix Hfk.Its detailed process the following steps are included:
S1, first according to difference modes group delay (DMGD) calculate τDMGDFor differential mode group delay τ total in optical fiberDMGD=τ × Wherein τ is difference modes group delay to l, and τ=9ps/km, l are transmission range 1200km, τDMGD=τ × l=10800ps, symbol speed Rate Rc=28Gbaud=1/Ts, Q=τDMGD/Ts=302.4, be that take Q be 330 for convenience of calculation our approximations, and set δ value as 0.161.According to channel matrix H, by carrying out piecemeal, channel matrix corresponding to the input and output of each data block to transmission data Channel matrix after as extending is denoted asChannel matrix after extending at this timeConcrete form it is as follows:
S2, it determines that extension length L is approximately 2048, constructs 6 × 2048 rank unit matrix I12288, 6 × 330 rank Unit matrix I1980With a full null matrix 01980×12288, a unit circle matrix U is constructed jointly by these three matrixesCP, tool Body form is as follows:
S3, by the channel matrix after extensionThe right side multiplies UCP, sequency spectrum block circulant matrix He is obtained, form is
S4,4096 rank Fourier transform matrix and 6 rank unit matrixs are subjected to Kronecker product operation, obtained in block Fu Leaf transformation matrix F24576, concrete form is as follows:
S5, the block circulant matrix He premultiplication block Fourier transform matrix for obtaining step 3, the right side multiplies block inversefouriertransform square Battle array finally obtains the diagonal equivalent matrix H of a blockF, form are as follows:
WhereinIt is 6 × 6 matrixes；
S6, to obtained HF6 × 6 minor matrix is separated each of on diagonal line, obtains corresponding 2048 6 × 6 Matrix Hfk(k=1 ..., 2048)；
Second step, to 6 × 6 obtained Hfk(k=1 ..., 2048) a channel matrix carries out lattice and about subtracts, according to error code The corresponding relationship of rate and MDL determine specification condition, and obtain corresponding about subtracting matrix by a series of elementary transformationsFinally Restore source signal, detailed process the following steps are included:
S7, to receive signal x (t)=[x1(t)…x6(t)]T∈C6×1, (t=kTS, k=1 ..., 2048) it is translated Scaling, the equivalent signal s that will send are mapped on continuous integral number domain, then have:When taking QPSK to modulate When, it is equivalent to receive signal are as follows:
S8, channel matrix H is obtained to estimationfkCarry out amplitude about subtracts, and makes its specification matrixMeetWhereinRepresenting matrixIn m column vector, in matrixIn if any columnIt is unsatisfactory for this condition, then by matrixN-th columnIt is added on m column again, wherein μ is Schimidt orthogonalization system Number, andSymbol round () indicates to be rounded, meanwhile, to unit matrix IDIt carries out same operation and obtains mould Matrix T；
The corresponding relationship of error rate of system and MDL in S9, foundation Fig. 5, when determining that signal-to-noise ratio is 18dB, when MDL is less than 7dB Existing ZF algorithm can achieve communication requirement, it is thus determined that specification condition are as follows: MDL≤7dB；
S10, to matrixColumn vector carry out elementary transformation.Firstly, calculatingEach column vector length of matrix, and willAscending order arrangement is carried out, the smallest most short amount of column vector modulus value is obtained, is replaced matrixThe 1st column, be denoted as Then, it enablesI.e. by matrixThe 1st column -1 times be added separately to remaining 5 column on, realize pair Length of remaining each column vector on standard column vector opposite direction about subtracts.After about subtractingMatrix according to specification condition into Row determines, executes S11 when meeting the specification condition determined in S9, otherwise executes S8.T matrix obtained in S8 is carried out simultaneously Identical elementary transformation is updated；
S11, it obtains lattice and about subtracts rear matrixWith modular matrix T, useTo receive signal carry out it is balanced successively with LTSReception signal phasor in period after L translation scaling(t=kTS, k= 1 ..., L) ZF equilibrium treatment is carried out, byWhereinIt is equivalent transmission signal, base In the balanced matrix of the ZF detection algorithm of lattice reduction technology are as follows:The then reception signal after equilibrium It can indicate are as follows:
S12, since lattice algorithm carried out on continuous integral number domain, by the equipollent vectors after equilibriumIt is taken Integral quantization adjudicates to obtainPremultiplication modular matrix T recovers source signal i.e. afterwards
S13, S12 output signal is subjected to anti-translation scaling, recovers source signal
In the case of Fig. 6 gives MDL=5dB, algorithm (LR-ZF) proposed by the present invention and existing frequency domain least mean square algorithm (FD-LMS), the BER comparison diagram of frequency domain independent composition analysis algorithm (FD-ICA), Fig. 7,8 show increase with MDL, algorithm solution It is multiplexed effect to be deteriorated, when MDL reaches 10dB, FD-LMS and FD-ICA algorithm are no longer applicable in, and LR-ZF proposed by the present invention is calculated Method still has preferable demultiplexing effect.
Fig. 9 gives in MDL=10dB, traditional squeeze theorem (ZF), lattice assist squeeze theorem (LR-ZF) with Three kinds of algorithms of Maximum Likelihood Detection (ML) demultiplex Contrast on effect under the conditions of different signal-to-noise ratio, the results showed that, lattice auxiliary is compeled Zero detection algorithm can compensate for MDL bring channel degradation, and approach the performance of maximum-likelihood detec-tion algorithm.
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 ?.

Claims (3)

1. a kind of damage compensation method of the mode division multiplexing system based on lattice reduction, which is characterized in that specific step is as follows:
Step 1 is pre-treatment step: by multiplying unit circle matrix to channel matrix extension and the right side, by D × D of non-sequency spectrum (Q+1) high-order channel matrix H is converted to the low order non-singular matrix H that can be carried out lattice and about handle of D × Dfk；
Step 2, the H to obtained D × DfkA channel matrix carries out lattice and about subtracts, wherein k=1 ..., L, and according to MDM system System characteristic, after determining specification condition and about subtractingSignal is detected, wherein Q is time delay overlay length, and D is pattern count Amount, L is extension length.
2. a kind of damage compensation method of the mode division multiplexing system based on lattice reduction as described in claim 1, feature exist In detailed process is as follows for the step 1:
S1, first according to difference modes group delay (DMGD) calculate Q value size, Q=τDMGD/Ts, TSFor code-element period, τDMGDFor light Total differential mode group delay in fibre, and the channel matrix H obtained according to estimation, by carrying out piecemeal, each data to transmission data Channel matrix corresponding to the input and output of block is that the channel matrix after extending is denoted asIts concrete form are as follows:
S2, it is equal to Q/ δ, δ 0.161 according to mode quantity D and extension length L, L, constructs a DL rank unit matrix IDL, one DQ rank unit matrix IDQWith a full null matrix 0DQ×D(L-Q), a unit circle matrix U is constructed jointly by these three matrixesCP, Its form are as follows:
S3, by the channel matrix after extensionThe right side multiplies UCP, the sequency spectrum block circulant matrix He of DL × DL is obtained, which includes letter All elements in road matrix H；
S4, L rank Fourier transform matrix and D rank unit matrix are subjected to Kronecker product operation, obtain block Fourier transformation Matrix FDL；
S5, the sequency spectrum block circulant matrix He premultiplication block Fourier transform matrix F for obtaining step 3DL, the right side multiplies the anti-Fourier of block and becomes Matrix is changed, a block diagonal matrix H is finally obtainedF；
S6, to HFThe minor matrix of each D × D on diagonal line is separated, and the matrix H of corresponding D × D is obtainedfk, wherein k =1 ..., L；
3. a kind of damage compensation method of the mode division multiplexing system based on lattice reduction as described in claim 1, feature exist In detailed process is as follows for the step 2:
S7, to receive signal x (t)=[x1(t)…xD(t)]T∈CD×1Carry out translation scaling, wherein t=kTS, k=1 ..., L, The equivalent signal s that will send is mapped on continuous integral number domain, then is had:s∈S；Wherein, IDFor D rank unit matrix, α Zooming parameter and translation parameters are respectively represented with β, the two value is determined by the modulation format of signal, and it is equivalent to receive signal are as follows:
S8, the k channel matrix H to obtained D × DfkCarry out amplitude about subtracts, and makes its specification matrixMeetWherein,Representing matrixIn m column vector, in matrixIn if any ColumnIt is unsatisfactory for this condition, then by matrixN-th columnIt is added on m column again, wherein μ is Schimidt orthogonalization Coefficient, andSymbol round () indicates to be rounded, meanwhile, to unit matrix IDSame operation is carried out to obtain Modular matrix T；
S9, using Matrix condition number as the standard of measurement system MDL: under the conditions of OSNR is 18dB, ZF is used in MDM system (zero forcing algorithm) algorithm carries out channel equalization, and in the case where ensuring compliance with communication standard, i.e., the bit error rate is less than 10-3When, the appearance of MDL Limit value, i.e. the specification condition of algorithm:
S10, to matrixColumn vector carry out elementary transformation, realize gradually about subtracting to column vector length: firstly, calculate Each column vector length of matrix, and willAscending order arrangement is carried out, the smallest most short amount of column vector modulus value is obtained, is replaced MatrixThe 1st column, be denoted asThen, it enables1 < m≤D, i.e., by matrixThe 1st column -1 times point It is not added on remaining D-1 column, realization about subtracts length of remaining each column vector on standard column vector opposite direction, after about subtracting 'sMatrix is determined according to the specification condition determined in S9, and S11 is executed when meeting specification condition, otherwise executes S8, together When identical elementary transformation carried out to T matrix obtained in S8 be updated；
S11, it obtains lattice and about subtracts rear matrixWith modular matrix T, useTo receive signal carry out it is balanced successively with LTSWhen Between reception signal phasor in section after L translation scalingCarry out ZF equilibrium treatment, wherein T=kTS, k=1 ..., L, byWhereinIt is equivalent transmission signal, is based on lattice The balanced matrix of the ZF detection algorithm of specification are as follows:Then the reception signal after equilibrium can indicate Are as follows:
S12, since lattice algorithm carried out on continuous integral number domain, by the equipollent vectors after equilibriumCarry out rounding quantization Judgement obtainsPremultiplication modular matrix T recovers source signal i.e. afterwards
S13, S12 output signal is subjected to anti-translation scaling, recovers source signal
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