CN105049386B - A kind of active interference clearance method in UFMC systems - Google Patents

A kind of active interference clearance method in UFMC systems Download PDF

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CN105049386B
CN105049386B CN201510274259.XA CN201510274259A CN105049386B CN 105049386 B CN105049386 B CN 105049386B CN 201510274259 A CN201510274259 A CN 201510274259A CN 105049386 B CN105049386 B CN 105049386B
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CN105049386A (en
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张朝阳
王红
王超
张昱
王献斌
罗茜倩
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Zhejiang University ZJU
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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
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • 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
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L25/03821—Inter-carrier interference cancellation [ICI]
    • 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
    • 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
    • H04L25/0212—Channel estimation of impulse response
    • H04L25/0216—Channel estimation of impulse response with estimation of channel length
    • 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
    • H04L27/2602—Signal structure
    • H04L27/2605—Symbol extensions, e.g. Zero Tail, Unique Word [UW]
    • H04L27/2607—Cyclic extensions
    • 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
    • H04L27/2668—Details of algorithms
    • H04L27/2673—Details of algorithms characterised by synchronisation parameters
    • H04L27/2676—Blind, i.e. without using known symbols
    • H04L27/2678—Blind, i.e. without using known symbols using cyclostationarities, e.g. cyclic prefix or postfix

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  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Power Engineering (AREA)
  • Noise Elimination (AREA)

Abstract

The invention discloses the active interference clearance method in a kind of UFMC systems, transmitting terminal utilizes the blank spaces between UFMC system sub-bands, a number of interference cancellation subcarrier is symmetrically inserted in sub-band both sides（First sub-band and last sub-band only operate in side）, using the data of original data message and interference cancellation subcarrier-modulated as new data message, filtering is then modulated by UFMC again and sent；Receiving terminal carries out time-domain windowed pretreatment and serial to parallel conversion first, then the wave filter and FFT by matching with transmitting terminal again, the estimate of new data message is finally obtained using zero forcing equalizer, after removing the data that the interference cancellation subcarrier that each sub-band uses is modulated, original data message is recovered.The present invention is combined by the way that UFMC is eliminated with active interference, not only retains the superperformance of UFMC systems, and interference suppressioning effect is more preferable between making UFMC sub-bands, so as to the error bit ability of strengthening system, raising communication quality.

Description

A kind of active interference clearance method in UFMC systems
Technical field
The present invention relates to wireless communication field, and in particular to the active interference clearance method in a kind of UFMC systems.
Background technology
It is well known that LTE and evolution form and WiFi that it is current are all the basic letters by the use of OFDM as carry data Number form, OFDM is currently the most important ones multi-carrier modulation technology.OFDM is divided into whole channel by N number of subcarrier N number of Subchannel carries out parallel transmission information.It mainly has the advantage that：First, the high availability of frequency spectrum.Between each subchannels of OFDM not But there is no guard band, and the secondary lobe of signal spectrum is overlapped between adjacent channel.In addition, each subchannels of OFDM can be with Using different multi-system modulation schemes, which further improves the spectrum efficiency of system.Second, implementation process is fairly simple. Modulation and demodulation can be realized by the way of based on FFT.3rd, anti-multipath fading ability is strong.By the way that whole channel is divided For many narrow channels, the decline in each subchannel can regard near flat as, often only need single tap per sub-channels Balanced device.Though in this way, OFDM has the shortcomings that very big：First, higher sidelobe level.Due to each subcarrier when Rectangle adding window is carried out on domain, corresponding frequency spectrum is in sinc shapes, and this would generally cause the interference (ICI) of intercarrier and intersymbol Interference (ISI)；Second, ofdm system peak-to-average force ratio is higher, and this can improve the requirement to the amplifier in radio circuit, so as to increase Addition sheet；3rd, OFDM are very sensitive to the positioning calibration on time-frequency, and the small carrier wave frequency deviation in any point can all destroy subcarrier Between orthogonality, cause ICI, systematic entirety is declined.
With developing rapidly for science and technology, following mobile radio system has two big main trends：Internet of Things and with cell Centered on arrive customer-centric transformation, if using strict synchronization mechanism again, will can bring very big signaling consumption And system energy consumption, be applied to actual conditions, can be ten points it is not to one's profit, therefore the trend decides that non-critical synchronization mechanism is not Carry out the main direction of development of radio communication.Only it can just be shown under strict synchronization in view of ofdm system recited above Itself good characteristic, so the demand to face the future, OFDM is no longer dominant technology, and designing new multi-carrier modulation technology is One urgent problem to be solved.Typical technical scheme has following two at present：
(1) FBMC (multi-carrier modulation based on filtering group, Filter Bank based on Multi-Carrier)：Hair Sending end uses OQAM mapping mode, and it divides the spectrum into multiple orthogonal sub-bands, then each subcarrier is filtered Ripple operates.There are following characteristics：A) there is a relatively low sidelobe level, inter-sub-carrier interference is smaller；B) time-frequency efficiency can be realized For 1, but on condition that filter length tends to be infinite, this can bring the problem of new：The rising and falling time of wave filter can make short The efficiency of burst communication is very low, and short burst is particularly significant for the MTC (Machine Type Communication) in future； C) the OQAM mechanism used, it is impossible to directly compatible with all types of mimo systems；D) in theory, FBMC has good spy Property, but when configuration, it is actual infeasible.
(2) UFMC (typically filtering multi-carrier modulation, Universal Filtered Multi-Carrier):It is by frequency spectrum A series of sub-bands for including several subcarriers are divided into, operation then is filtered to each sub-band.There is following spy Point：A) fragmented spectrum communication is supported；B) compared with OFDM, spectral sidelobes level has lacked tens dB, very low；C) for when frequency deviation Move and the interference of intercarrier has higher robustness；D) due to being calibrated using not strict time-frequency, opened so reducing signaling Pin, this also introduces many new selections for access；E) the crucial design for being wave filter, has certain complexity.
In view of the advantage of UFMC technologies, the thought that existing active interference eliminates (AIC) is combined again：It is to be based on frequency spectrum Pool technology, suitable for a kind of interference mitigation technology under cognition OFDM environment, spectrum pool is divided into some numbers by cognitive user Purpose subcarrier, the side position of frequency spectrum two of subcarrier is correspondingly being occupied close to primary user's frequency range, placing some and modulate special weighting The subcarrier of the factor, referred to as interference cancellation subcarrier, these subcarriers are modulated by using weighted factor, so that The data subcarrier of cognitive user, that is, the subcarrier of data message modulation is originally sent, with interference cancellation subcarrier in primary user Out-of-band interference is cancelled out each other caused by frequency range, by AF panel to sufficiently small, so as to reach the purpose of protection primary user's communication, I Propose a kind of active interference clearance method in UFMC systems, by UFMC each sub-band as one in cognition OFDM Individual subcarrier, is protected to it, so that interference reaches lower between sub-band.
The content of the invention
The purpose of the present invention is to propose to a kind of innovation scheme, enables UFMC systematic entireties more preferable.This method can not only The advantages of retaining UFMC systems itself, and communication quality can be improved, setting for UFMC median filters is reduced to a certain extent Count complexity.
Active interference clearance method in UFMC systems comprises the following steps that：
1) assume that interference comes from the i-th -1 sub-band and i+1 sub-band to caused by i-th of sub-band, by the I-1, i and i+1 sub-bands are handled as an entirety, and the subcarrier index occupied by three sub-bands is from left to right It is followed successively by：[v3:v4]、[v1:V2] and [v5:v6]；
2) multi-system modulation mapping is carried out to original bit stream
Respectively three sub-bands are uploaded with the original bit stream sent and carries out multi-system modulation mapping, obtains treating to adjust by UFMC The coded bit stream of system is respectively XlI、XiAnd XrI, length is respectively v4-v3+1, v2-v1+1 and v6-v5+1；
3) solution of interference cancellation sub-carrier modulation data
3.1) after to the frequency domain symbol progress IFFT conversion of transmission, corresponding time-domain signal is obtained, then the time domain is believed Number addition cyclic prefix, obtains new time-domain signal, and carry out μ times and rise sampling, obtains the spectral model S of signal, the frequency spectrum mould Type is expressed as the form of the frequency domain symbol and matrix multiple sent, and the matrix is defined as into spectral coefficient matrix QG；
3.2) the i-th -1 sub-band places interference cancellation subcarrier i-th of sub-band both sides
The i-th -1 sub-band respectively places c i-th of sub-band both sides1Individual interference cancellation subcarrier, is estimated by lowest mean square Meter solves the data X of interference cancellation subcarrier-modulated used in the i-th -1 sub-bandlC, make the data of the i-th -1 sub-band The total interference of subcarrier and interference cancellation subcarrier at i-th of sub-band is minimum, and the data subcarrier of the i-th -1 sub-band is made Into interference spectral coefficient matrix QGSubmatrix and XlIProduct representation, the line label where the submatrix is [u*v1:u* V2], arrange marked as [v3:V4], spectral coefficient matrix Q is used in interference caused by interference cancellation subcarrierGSubmatrix and XlCMultiply Product representation, the line label where the submatrix are [u*v1:U*v2], arrange marked as [v1-c1:v1-1,v2+1:v2+c1], by XlI And XlCAs data message X new on the i-th -1 sub-bandi-1, wherein Xi-1=[0 ..., 0, XlI,0,...,0,XlC, 0,...,0]1×N, N is IFFT point number；
3.3) i+1 sub-band places interference cancellation subcarrier i-th of sub-band both sides
It is consistent with the solution procedure of the i-th -1 sub-band, by least mean-square estimate, solve i+1 sub-band institute The data X of the interference cancellation subcarrier-modulated usedrC, by XrIAnd XrCAs data message X new on i+1 sub-bandi+1, Wherein Xi+1=[0 ..., 0, XrC,0,...,0,XrI,0,...,0]1×N；
4) UFMC modulation is sent：
X is obtained by step 2) and step 3)i-1、XiAnd Xi+1Afterwards, two mistakes are converted and filtered successively respectively by IFFT Journey is modulated transmission；
5) processing of receiving terminal：
5.1) receiving terminal carries out time-domain windowed pretreatment and serial to parallel conversion first to the signal received, is believed parallel Number；
5.2) obtained parallel signal is subjected to following operate on corresponding sub-band respectively：First by with transmitting terminal The wave filter to match, FFT is then carried out, finally eliminate ISI using zero forcing equalizer, obtain estimating for new data message Evaluation, after removing the data that the interference cancellation subcarrier that each sub-band uses is modulated, you can recover original data letter Breath.
Concretely comprising the following steps 3.1), 3.2) He 3.3) in described step 3)：
3.1) defineExpression is d to length2Vector carry out d1Point Fourier transformation, the element in matrix For：0≤m≤d2-1,0≤n≤d1-1
Wherein m, n are element subscript；
To the frequency domain symbol vectors X=[X of transmission0,X1,…XN-1], IFFT conversion is done, the time domain x expression after being converted Formula is：
Wherein, N is IFFT point number, ()*Represent complex conjugate operation,For Fourier transform matrix；
Add cyclic prefix to each UFMC symbols, it is as follows to define C matrixes：
Wherein, 0 is 0 matrix, and I is unit matrix, and NG is the length of cyclic prefix；
After the time-domain signal x of transmission is added into cyclic prefix, the calculation formula for obtaining new time-domain signal x', x' is x' =Cx；
To new time-domain signal x', carry out μ times and rise sampling, the calculation formula for obtaining the spectral model S, S of signal is：
Wherein, μ is to rise decimation factor, FμN×(N+NG)Defined in step 3.1)d1For uN, d2For N+NG, ()T Represent transposition computing；
Define the spectral coefficient matrix that dimension is uN × N
3.2) the i-th -1 sub-band places interference cancellation subcarrier i-th of sub-band both sides
The i-th -1 sub-band is in i-th of sub-band ([v1:V2]) both sides respectively place c1Individual interference cancellation subcarrier, do It is [v1-c to disturb and offset the position of subcarrier1:v1-1,v1:v2,v2+1:v2+c1], the i-th -1 sub- band modulation sends data Subcarrier index is [v3:v4]；
Data subcarrier XlIIt is Q in interference caused by i-th of sub-bandlIXlI T, the data of interference cancellation subcarrier-modulated XlCIt is Q in interference caused by i-th of sub-bandlCXlC T, calculate caused by two sub-carriers and interference, calculation formula be：
Ii-1=| | QlCXlC T+QlIXlI T||2
Wherein, XlI=[Xi-1(v3),Xi-1(v3+1) ... Xi-1(v4)],
XlC=[Xi-1(v1-c1),...Xi-1(v1-1),Xi-1(v2+1),...Xi-1(v2+c1)],
WhereinWith
Subscript represent matrix Q in step 3.1)GRow, the equal representing matrix Q of subscriptGRow, | |·||2Represent the quadratic sum of vector element；X in formulai-1It is new on the i-th -1 sub-band after introducing interference cancellation subcarrier Data message, Xi-1Expression formula be：
Xi-1=[0 ..., 0, XlI,0,...,0,XlC,0,...,0]1×N
=[0 ... 0, Xi-1(v3),Xi-1(v3+1),...Xi-1(v4),0,...0,Xi-1(v1-c1),...Xi-1(v1- 1),Xi-1(v2+1),...Xi-1(v2+c1),0,...0]1×N
Solve XlC, make both interference in frequency range [v1:V2] place is reduced to minimum, that is, meet following formula：
Above formula by least mean-square estimate solve：
XlC=-(QlC HQlC)-1QlC HQlIXlI T
3.3) i+1 sub-band places interference cancellation subcarrier i-th of sub-band both sides
Consistent with the solution procedure in step 3.2), i+1 sub-band is in i-th of sub-band ([v1:V2]) both sides It is each to place c2Individual interference cancellation subcarrier, the position of interference cancellation subcarrier is [v1-c2:v1-1,v1:v2,v2+1:v2+c2], The subcarrier index that the sub- band modulation of i+1 sends data is [v5:v6]；
Data subcarrier XrIIt is Q in interference caused by i-th of sub-bandrIXrI T, interference cancellation subcarrier XrCIn i-th of son Interference is Q caused by frequency bandrCXrC T, caused by both subcarriers and interference is：
Ii+1=| | QrCXrC T+QrIXrI T||2
Wherein, XrI=[Xi+1(v5),Xi+1(v5+1),...Xi+1(v6)],
XrC=[Xi+1(v1-c2),...Xi+1(v1-1),Xi+1(v2+1),...Xi+1(v2+c2)],
WithWhereinWith Subscript represent matrix Q in step 3.1)GRow, the equal representing matrix Q of subscriptGRow, the X in formulai+1To introduce interference cancellation After subcarrier, new data message, X on i+1 sub-bandi+1Expression formula be：
Xi+1=[0 ..., 0, XrC,0,...,0,XrI,0,...,0]1×N
=[0 ... 0, Xi+1(v1-c2),...Xi+1(v1-1),Xi+1(v2+1),...Xi+1(v2+c2),0,...0,Xi+1 (v5),Xi+1(v5+1),...Xi+1(v6),0,...0]1×NBy least mean-square estimate solve：
XrC=-(QrC HQrC)-1QrC HQrIXrI T
Required XrCThe data of interference cancellation subcarrier-modulated as used in i-th of sub-band.
4.1) and 4.2) the concretely comprising the following steps in described step 4)：
4.1) IFFT is converted
Realize that IFFT is converted by Fourier's matrix, Fourier's matrix is defined asExpression be to length d2Vector carry out d1Point IFFT is converted, and the element among Fourier's matrix is as follows：
4.2) filter
For filtering, the linear convolution operation is completed with toeplitz matrix, for different sub-bands need by The centre frequency of wave filter moves to the centre of sub-band；
It is L to set UFMC system mesarcses filter length, and impulse response h expression formula is：H=h [0], h [1] ..., H [L-1] }, corresponding frequency domain response is H；
Calculate the i-th -1 sub- mid-band frequency where subcarrier index be：By ptototype filter Frequency domain response H is translatedIndividual unit, obtain the frequency domain response H of the i-th -1 sub-bandi-1,
The impulse response h of the i-th -1 sub-bandi-1For：hi-1={ hi-1[0],hi-1[1],…,hi-1[L-1] }, wherein,0≤n≤L-1；
Define toeplitz matrix Ti-1For：
Its preceding N row is taken to be designated asWithRealize the filtering of the i-th -1 sub-band；
It is consistent with the solution procedure of i-1 sub-band, for i-th of sub-band, translated on frequency domainIt is individual Unit, obtain frequency domain response HiWith impulse response hi, hiIn element be：0≤n≤L-1；For i-th + 1 sub-band, translate on frequency domainIndividual unit, obtain frequency domain response Hi+1With impulse response hi+1, hi+1In Element be：0≤n≤L-1, by hi-1[n] uses h respectivelyi[n] and hi+1[n] is replaced and obtained i-th The toeplitz matrix of sub-band and i+1 sub-band, its preceding N row is then taken respectively, obtains i-th of sub-band and i+1 Individual sub-band realizes that the toeplitz matrix of filtering is respectivelyWith
By above-mentioned steps 1), step 2), step 3) and step 4), the time-domain signal x that transmitting terminal is senttotalFor：
xtotal=TVX
Wherein,
V=diag { Vi-1,Vi,Vi+1Represent with matrix Vi-1, ViAnd Vi+1The diagonal matrix formed for diagonal element, V, Vi-1、 ViAnd Vi+1Represent to realize Fourier's matrix that IFFT is converted in step 4.1) on three sub-bands respectivelyAnd d1And d2's Value factor band and it is different.
The present invention is applied to the wireless communication system under extensive access environment, and supports fragmented spectrum to communicate, system There need not be strict net synchronization capability, this introduces many new selections for access.In addition, compared to FBMC, due to using length The shorter wave filter of degree, this can make system response time shorten, therefore have good applicability for the short burst communication in future.
The present invention is combined by the way that UFMC is eliminated with active interference, can not only retain the superperformance of UFMC systems, And the interference between sub-band can be largely reduced, so as to improve the error bit ability of system, that improves transmission can By property, in addition, when the timing of annoyance level one between UFMC sub-bands, for simple UFMC systems, using the combination Scheme can reduce the design complexities of UFMC median filters to a certain extent.
Brief description of the drawings
Fig. 1 is that the active interference recognized in OFDM eliminates schematic diagram；
Fig. 2 is the schematic diagram that the UFMC of the present invention is combined with AIC；
Fig. 3 is active interference clearance method structured flowchart in UFMC systems of the invention；
Fig. 4 is when cyclic prefix (CP) length is 16, in protection frequency range [15:25] 2 interference cancellations are respectively placed in both sides The fluting that subcarrier is formed；
Fig. 5 is when cyclic prefix (CP) length is 32, in protection frequency range [15:25] 2 interference cancellations are respectively placed in both sides The fluting that subcarrier is formed；
Fig. 6 is that the UFMC of the present invention is combined the normalized power spectral density of left and right sub-band with AIC；
The UFMC that Fig. 7 is the present invention is combined the united normalized power spectral density of left and right sub-band with AIC；
Fig. 8 is the normalized power spectral density of the UFMC of the present invention or so sub-band；
Fig. 9 is the UFMC of the present invention or so the united normalized power spectral density of sub-band；
Figure 10 be the present invention OFDM UFMC the error bit ability curves that are combined with AIC of UFMC.
Embodiment
The present invention is described in further detail with specific embodiment below in conjunction with the accompanying drawings.
AIC introducing background as shown in Figure 1, the schematic diagram that UFMC is combined with AIC as shown in Figure 2, present invention side The transceiver schematic diagram of method is as shown in Figure 3.
Active interference clearance method in a kind of UFMC systems of the present invention, specific implementation step are as follows：
1) setting interference to caused by the 4th sub-band comes from the 3rd sub-band and the 5th sub-band, by the 3rd, 4 and 5 sub-bands are handled as an arrangement, and the subcarrier index occupied by three sub-bands is from left to right followed successively by： [7:18]、[25:36] and [43:54].
2) original bit stream carries out multi-system modulation mapping：
2.1) to the original bit stream [q of the 3rd sub-band transmission1,q2,q3,…,q24] QPSK modulation mappings are carried out, obtain Treat the coded bit stream X modulated by UFMClI=[b1,b2,b3,…,b12]；
2.2) to the original bit stream [w of the 4th sub-band transmission1,w2,w3,…,w24] QPSK modulation mappings are carried out, obtain Treat the coded bit stream X modulated by UFMC4=[a1,a2,a3,…,a12]；
2.3) to the original bit stream [r of the 5th sub-band transmission1,r2,r3,…,r24] QPSK modulation mappings are carried out, obtain Treat the coded bit stream X modulated by UFMCrI=[s1,s2,s3,…,s12]；
3) solution of interference cancellation subcarrier-modulated weighted factor：
Add the basis of cyclic prefix first of all for offer UFMC symbols, the present invention has carried out simulation analysis, as a result such as accompanying drawing 3 Shown in accompanying drawing 4：In accompanying drawing 4, as CP=16, the groove depth of formation is 35db or so, and the energy cost of consumption is 13.48%；In accompanying drawing 5, the groove depth formed as CP=32 is 35db or so, and the energy cost of consumption only has 5.98%. Both of these case, the energy cost consumed are all far below the energy cost without using consumption 30.66% during cyclic prefix.Therefore It can play a part of reducing with outward leakage using CP, so as to reduce the energy of interference cancellation subcarrier consumption, derive meeting below Consideration uses cyclic prefix.
3.1) FFT points Ns are set as 128, circulating prefix-length NG is 32, and up-sampling multiple μ is 2, spectral coefficient matrix QGExpression formula is：
Wherein,0 represents 0 matrix, and I represents unit matrix,
Element in F is：0≤n≤255,0≤m≤159,
Element in F* is：0≤h≤127,0≤g≤127；
3.2) the 3rd sub-band places interference cancellation subcarrier the 4th sub-band both sides
3rd sub-band is in the 4th sub-band ([25:36]) 2 interference cancellation subcarriers, interference cancellation are respectively placed in both sides The position of subcarrier is [23:24,25:36,37:38], the subcarrier index that the 3rd sub- band modulation sends data is [7: 18]；
Data subcarrier XlIIt is Q in interference caused by the 4th sub-bandlIXlI T, the data of interference cancellation subcarrier-modulated XlCIt is Q in interference caused by the 4th sub-bandlCXlC T, caused by both subcarriers and interference is：
I3=| | QlCXlC T+QlIXlI T||2
Wherein, XlI=[b1,b2,…,b12]=[X3(7),X3(8),...X3(18)],
XlC=[X3(23),X3(24),X3(25),...X3(38)],
WithThe equal representing matrix Q of subscriptGRow, the equal representing matrix Q of subscriptG Row, | | | |2Represent the quadratic sum of vector element；
After introducing interference cancellation subcarrier, new data message X on the 3rd sub-band3Dimension is 128, and expression formula is：
X3=[0 ..., 0, XlI,0,...,0,XlC,0,...,0]1×128
=[0 ... 0, X3(7),X3(8),...X3(18),0,...0,X3(23),X3(24),X3(25),...X3(38), 0,...0]1×128
According to the basic thought of interference cancellation, X is solvedlCMake both interference in frequency range [25:36] place is reduced to minimum, i.e., Meet following formula：
Above formula by least mean-square estimate can solve：
XlC=-(QlC HQlC)-1QlC HQlIXlI T
3.3) the 5th sub-band places interference cancellation subcarrier the 4th sub-band both sides
5th sub-band is in the 4th sub-band ([25:36]) 2 interference cancellation subcarriers, interference cancellation are respectively placed in both sides The position of subcarrier is [23:24,25:36,37:38], the subcarrier index that the 5th sub- band modulation sends data is [43: 54]；
Data subcarrier XrIIt is Q in interference caused by the 4th sub-bandrIXrI T, the data of interference cancellation subcarrier-modulated XrCIt is Q in interference caused by the 4th sub-bandrCXrC T, caused by both subcarriers and interference is：
I5=| | QrCXrC T+QrIXrI T||2
Wherein, XrI=[s1,s2,…,s12]=[X5(43),X5(44),...X5(54)],
XrC=[X5(23),X5(24),X5(25),...X5(38)],
Subscript representing matrix QGRow, subscript representing matrix QG's Row, | | | |2Represent the quadratic sum of vector element；
After introducing interference cancellation subcarrier, new data message X on the 5th sub-band5Dimension is 128, and expression formula is：
X5=[0 ..., 0, XrC,0,...,0,XrI,0,...,0]1×128
=[0 ... 0, X5(23),X5(24),X5(25),...X5(38),0,...0,X5(43),X5(44),...X5 (54),0,...0]1×128Similarly, by least mean-square estimate solve to obtain：
XrC=-(QrC HQrC)-1QrC HQrIXrI T
4) UFMC modulation is sent：
By step 1), step 2) and step 3), X is obtained3、X4And X5, then convert and filter by IFFT successively respectively Two processes are modulated transmission；
4.1) IFFT is converted
We are the data message X to each sub-band3、X4And X5, 128 point IFFT conversion is all carried out, three sub-bands are made Fourier's matrix V3、V4And V5It is:V128×128, the element in matrix is：
4.2) filter
For filtering, the linear convolution operation is completed with toeplitz matrix, for different sub-bands need by The centre frequency of wave filter moves to the centre of sub-band, other if it is 16 that ptototype filter used in UFMC systems, which is length, Valve decays to 40dB Chebyshev filter, and its impulse response coefficient is：H={ h [0], h [1] ..., h [15] }, it is corresponding Frequency domain response is H；
Subcarrier index where calculating the 3rd sub- mid-band frequency is：12.5, by the frequency domain response of ptototype filter H is translatedIndividual unit, obtain the frequency domain response H of the 3rd sub-band3,
Impulse response h3For：h3={ h3[0],h3[1],…,h3[15] }, wherein,0≤n≤ 15, toeplitz matrix is：
Its preceding 128 row is taken to be designated asWithRealize the filtering of the 3rd sub-band；
For the 4th sub-band, translated on frequency domainIndividual unit, obtain frequency domain response H4And impulse response h4, h4In element be：0≤n≤15；For the 5th sub-band, translated on frequency domain Individual unit, obtain frequency domain response H5With impulse response h5, h5In element be：0≤n≤15, by h3 [n] uses h respectively4[n] and h5[n] is replaced and is obtained the toeplitz matrix of the 4th sub-band and the 5th sub-band, before then taking it 128, obtain the 4th sub-band and the 5th sub-band realizes filteringWith
By above-mentioned steps 1), step 2), step 3) and step 4), the time-domain signal that transmitting terminal is sent is：
xtotal=TVX
Wherein,
V=diag { V3,V4,V5Represent with matrix V3, V4And V5The diagonal matrix V, V formed for diagonal element3, V4And V5Point Fourier's matrix V that IFFT is converted in step 4) Biao Shi not be realized on three sub-bands128×128；
After AIC and UFMC processing, corresponding signal spectrum is for 3rd sub-band and the 4th sub-band：
It is convenient following for narration, the 3rd sub-band, the 4th sub-band and the 5th sub-band are referred to as left son frequency Band, middle sub-band and right sub-band.By drawing out spectrogram corresponding to above-mentioned equation, use just can be intuitively found out very much After AIC, interference suppressioning effect that the sub-band of left and right two is brought to middle sub-band, as shown in explanation accompanying drawing 6 and accompanying drawing 7, it It is in middle sub-band [25:36] 2 interference cancellation subcarriers are respectively placed in both sides, and the adjacent sub-band of left and right two is in centre The interference suppressioning effect obtained at sub-band, it can be clearly seen that：Groove depth of the left sub-band at middle sub-band is averaged Substantially：85dB, right sub-band decay substantially：70dB or so, right son is also protected while protecting middle sub-band Frequency band；Joint groove depth of the sub-band of left and right two at middle sub-band is averagely substantially：170dB or so.Right sub-band Effect it is consistent with left sub-band.
For the preferably prominent interference suppressioning effect brought using AIC, we are not to using the frequencies of AIC UFMC systems Spectrogram have also been made simulation analysis, as illustrated in Figure 8 and 9 reference.It can be seen that：In UFMC systems, left sub-band is in middle son Groove depth at frequency band is averagely substantially：70dB, right sub-band decay substantially：75dB or so, protect middle son frequency Also right sub-band is protected while band；Joint groove depth of the sub-band of left and right two at middle sub-band is averagely substantially For：140dB or so.The effect of right sub-band is consistent with left sub-band.
Accompanying drawing 6, accompanying drawing 7 and accompanying drawing 8, accompanying drawing 9 are contrasted, can be obtained：For AIC schemes are not used, use AIC UFMC systems achieve preferable interference suppressioning effect at middle sub-band, moreover, the son frequency among protection While band, moreover it is possible to another sub-band is formed and protected.
5) processing of receiving terminal：
Consider additive Gaussian noise channels, the unit that frequency response H=I, the I representation dimension of channel is N+L-1=143 to Amount, now receiving terminal need not do zero forcing equalization, randomly generate the multiple Gauss variable that length is N+L-1=143 and made an uproar as Gauss Sound.
5.1) receiving terminal carries out time-domain windowed pretreatment and serial to parallel conversion first to the signal received；
5.2) obtained parallel signal is subjected to following operate on corresponding sub-band respectively：First by with transmitting terminal The wave filter to match, FFT is then carried out, obtain the estimate of new data message, finally removing each sub-band makes The data that interference cancellation subcarrier is modulated, you can recover original data message.
Concrete operations are as follows：
The time-domain signal that step 1 receives：
Step 2 receiving terminal matched filtering：T-1Y=VX+T-1z；
Step 3FFT is converted:
Step 4 estimates the estimate of the new data message of transmitting terminal by above three step Then The data message for going the interference cancellation subcarrier that sub-band uses unless each to be modulated, obtains the estimate of original data messageDemodulated again by QPSK, recover three sub-bands successively and upload the original bit stream sent
, can be with the errored bit of quantitative analysis the inventive method by using the above-mentioned whole process for including modulation and demodulation Can, and can be by being contrasted with OFDM, UFMC scheme, the advantages of making the inventive method, is more prominent, strengthens confidence level.
Accompanying drawing 10 is the simulation result of the active interference clearance method example in above-mentioned UFMC systems, and contains OFDM The error bit ability curve of scheme and UFMC schemes, the simulation parameter of three kinds of schemes are set as shown in table 1.
Table 1OFDM UFMC the simulation parameters that are combined with AIC of UFMC set
Simulation result is observed, it is apparent that：OFDM error bit abilities are relatively worst, and UFMC takes second place, present invention side Method is optimal, and the UFMC for employing AIC has good error bit ability compared to UFMC, and the two is under same SNR, by mistake Bit rate gap is very big.
The inventive method is respectively from normalized power spectral density and bit error rate angle, by this method and UFMC schemes Carry out contrast simulation, it can be clearly seen that：The inventive method is better than the latter in both cases, has absolutely proved this hair Bright method is reasonable.

Claims (3)

1. the active interference clearance method in a kind of UFMC systems, UFMC is general filtering multi-carrier modulation, it is characterised in that should Method comprises the following steps that：
1) assume that interference comes from the i-th -1 sub-band and i+1 sub-band to caused by i-th of sub-band, by i-th -1, i Handled with i+1 sub-band as an entirety, the subcarrier index occupied by three sub-bands is from left to right successively For：[v3:v4]、[v1:V2] and [v5:v6]；
2) multi-system modulation mapping is carried out to original bit stream
Respectively three sub-bands are uploaded with the original bit stream sent and carries out multi-system modulation mapping, obtains treating by UFMC modulation Coded bit stream is respectively XlI、XiAnd XrI, length is respectively v4-v3+1, v2-v1+1 and v6-v5+1；
3) solution of interference cancellation sub-carrier modulation data
3.1) after to the frequency domain symbol progress IFFT conversion of transmission, corresponding time-domain signal is obtained, then the time-domain signal is added Add cyclic prefix, obtain new time-domain signal, and carry out μ times and rise sampling, obtain the spectral model S of signal, the spectral model table The form of the frequency domain symbol and matrix multiple sent is shown as, the matrix is defined as spectral coefficient matrix QG；
3.2) the i-th -1 sub-band places interference cancellation subcarrier i-th of sub-band both sides
The i-th -1 sub-band respectively places c i-th of sub-band both sides1Individual interference cancellation subcarrier, is asked by least mean-square estimate Solve the data X of interference cancellation subcarrier-modulated used in the i-th -1 sub-bandlC, carry data of the i-th -1 sub-band The total interference of ripple and interference cancellation subcarrier at i-th of sub-band is minimum, caused by the data subcarrier of the i-th -1 sub-band Spectral coefficient matrix Q is used in interferenceGSubmatrix and XlIProduct representation, the line label where the submatrix is [u*v1:U*v2], Row are marked as [v3:V4], spectral coefficient matrix Q is used in interference caused by interference cancellation subcarrierGSubmatrix and XlCProduct table Show, the line label where the submatrix is [u*v1:U*v2], arrange marked as [v1-c1:v1-1,v2+1:v2+c1], by XlIAnd XlC As data message X new on the i-th -1 sub-bandi-1, wherein Xi-1=[0 ..., 0, XlI,0,...,0,XlC,0,..., 0]1×N, N is IFFT point number；
3.3) i+1 sub-band places interference cancellation subcarrier i-th of sub-band both sides
It is consistent with the solution procedure of the i-th -1 sub-band, by least mean-square estimate, solve i+1 sub-band and used Interference cancellation subcarrier-modulated data XrC, by XrIAnd XrCAs data message X new on i+1 sub-bandi+1, wherein Xi+1=[0 ..., 0, XrC,0,...,0,XrI,0,...,0]1×N；
4) UFMC modulation is sent
X is obtained by step 2) and step 3)i-1、XiAnd Xi+1Afterwards, two processes are converted and filter by IFFT successively respectively to carry out Modulation is sent；
5) processing of receiving terminal
5.1) receiving terminal carries out time-domain windowed pretreatment and serial to parallel conversion first to the signal received, obtains parallel signal；
5.2) obtained parallel signal is subjected to following operate on corresponding sub-band respectively：First by with transmitting terminal phase The wave filter matched somebody with somebody, FFT is then carried out, finally eliminate intersymbol interference using zero forcing equalizer, obtain new data letter The estimate of breath, after removing the data that the interference cancellation subcarrier that each sub-band uses is modulated, you can recover original Data message.
2. the active interference clearance method in UFMC systems as claimed in claim 1, it is characterised in that：In described step 3) Step 3.1), step 3.2) and step 3.3) concretely comprise the following steps：
3.1) it is d to length that definition, which represents,2Vector carry out d1Point Fourier transformation, the element in matrix are： <mrow> <msub> <mi>F</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> <mo>=</mo> <msup> <mi>e</mi> <mfrac> <mrow> <mo>-</mo> <mi>j</mi> <mn>2</mn> <mi>&amp;pi;</mi> <mi>n</mi> <mi>m</mi> </mrow> <msub> <mi>d</mi> <mn>1</mn> </msub> </mfrac> </msup> <mo>,</mo> <mn>0</mn> <mo>&amp;le;</mo> <mi>m</mi> <mo>&amp;le;</mo> <msub> <mi>d</mi> <mn>2</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>&amp;le;</mo> <mi>n</mi> <mo>&amp;le;</mo> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>1</mn> </mrow>
Wherein m, n are element subscript；
To the frequency domain symbol vectors X=[X of transmission0,X1,…XN-1], IFFT conversion is done, the time domain x expression formulas after being converted are： <mrow> <mi>x</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <msub> <msup> <mi>F</mi> <mo>*</mo> </msup> <mrow> <mi>N</mi> <mo>&amp;times;</mo> <mi>N</mi> </mrow> </msub> <msup> <mi>X</mi> <mi>T</mi> </msup> </mrow>
Wherein, N is IFFT point number, ()*Represent complex conjugate operation,For Fourier transform matrix；
Add cyclic prefix to each UFMC symbols, it is as follows to define C matrixes：
<mrow> <mi>C</mi> <mo>=</mo> <msub> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mi>N</mi> <mi>G</mi> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mi>N</mi> <mi>G</mi> <mo>)</mo> </mrow> </mrow> </msub> </mtd> <mtd> <msub> <mi>I</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>I</mi> <mrow> <mi>N</mi> <mo>-</mo> <mi>N</mi> <mi>G</mi> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mi>N</mi> <mi>G</mi> <mo>)</mo> <mo>&amp;times;</mo> <mi>N</mi> <mi>G</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mi>N</mi> <mi>G</mi> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mi>N</mi> <mi>G</mi> <mo>)</mo> </mrow> </mrow> </msub> </mtd> <mtd> <msub> <mi>I</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mrow> <mo>(</mo> <mi>N</mi> <mo>+</mo> <mi>N</mi> <mi>G</mi> <mo>)</mo> <mo>&amp;times;</mo> <mi>N</mi> </mrow> </msub> </mrow>
Wherein, 0 is 0 matrix, and I is unit matrix, and NG is the length of cyclic prefix；
After the time-domain signal x of transmission is added into cyclic prefix, the calculation formula for obtaining new time-domain signal x', x' is x'= Cx；
To new time-domain signal x', carry out μ times and rise sampling, the calculation formula for obtaining the spectral model S, S of signal is：
<mrow> <mi>S</mi> <mo>=</mo> <msub> <mi>F</mi> <mrow> <mi>&amp;mu;</mi> <mi>N</mi> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <mi>N</mi> <mo>+</mo> <mi>N</mi> <mi>G</mi> <mo>)</mo> </mrow> </mrow> </msub> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <msub> <mi>F</mi> <mrow> <mi>&amp;mu;</mi> <mi>N</mi> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <mi>N</mi> <mo>+</mo> <mi>N</mi> <mi>G</mi> <mo>)</mo> </mrow> </mrow> </msub> <mi>C</mi> <mi>x</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <msub> <mi>F</mi> <mrow> <mi>&amp;mu;</mi> <mi>N</mi> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <mi>N</mi> <mo>+</mo> <mi>N</mi> <mi>G</mi> <mo>)</mo> </mrow> </mrow> </msub> <msub> <msup> <mi>CF</mi> <mo>*</mo> </msup> <mrow> <mi>N</mi> <mo>&amp;times;</mo> <mi>N</mi> </mrow> </msub> <msup> <mi>X</mi> <mi>T</mi> </msup> </mrow>
Wherein, μ is to rise decimation factor, FμN×(N+NG)Defined in step 3.1)d1For uN, d2For N+NG, ()TRepresent Transposition computing；
Define the spectral coefficient matrix that dimension is uN × N
3.2) the i-th -1 sub-band places interference cancellation subcarrier i-th of sub-band both sides
The i-th -1 sub-band is in i-th of sub-band ([v1:V2]) both sides respectively place c1Individual interference cancellation subcarrier, interference cancellation The position of subcarrier is [v1-c1:v1-1,v1:v2,v2+1:v2+c1], the i-th -1 sub- band modulation sends the subcarrier of data Marked as [v3:v4]；
Data subcarrier XlIIt is Q in interference caused by i-th of sub-bandlIXlI T, the data X of interference cancellation subcarrier-modulatedlC Interference is Q caused by i-th of sub-bandlCXlC T, calculate caused by two sub-carriers and interference, calculation formula be：
Ii-1=| | QlCXlC T+QlIXlI T||2
Wherein, XlI=[Xi-1(v3),Xi-1(v3+1) ... Xi-1(v4)],
XlC=[Xi-1(v1-c1),...Xi-1(v1-1),Xi-1(v2+1),...Xi-1(v2+c1)],
WhereinWithSubscript Represent matrix Q in step 3.1)GRow, the equal representing matrix Q of subscriptGRow, | | | |2Represent the quadratic sum of vector element；Formula In Xi-1After introducing interference cancellation subcarrier, new data message, X on the i-th -1 sub-bandi-1Expression formula be：
Xi-1=[0 ..., 0, XlI,0,...,0,XlC,0,...,0]1×N
=[0 ... 0, Xi-1(v3),Xi-1(v3+1),...Xi-1(v4),0,...0,Xi-1(v1-c1),...Xi-1(v1-1), Xi-1(v2+1),...Xi-1(v2+c1),0,...0]1×N
Solve XlC, make both interference in frequency range [v1:V2] place is reduced to minimum, that is, meet following formula：
<mrow> <msub> <mi>X</mi> <mrow> <mi>l</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <munder> <mi>argmin</mi> <msub> <mi>X</mi> <mrow> <mi>l</mi> <mi>C</mi> </mrow> </msub> </munder> <mo>|</mo> <mo>|</mo> <msub> <mi>Q</mi> <mrow> <mi>l</mi> <mi>C</mi> </mrow> </msub> <msup> <msub> <mi>X</mi> <mrow> <mi>l</mi> <mi>C</mi> </mrow> </msub> <mi>T</mi> </msup> <mo>+</mo> <msub> <mi>Q</mi> <mrow> <mi>l</mi> <mi>I</mi> </mrow> </msub> <msup> <msub> <mi>X</mi> <mrow> <mi>l</mi> <mi>I</mi> </mrow> </msub> <mi>T</mi> </msup> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow>
Above formula by least mean-square estimate solve：
XlC=-(QlC HQlC)-1QlC HQlIXlI T
3.3) i+1 sub-band places interference cancellation subcarrier i-th of sub-band both sides
Consistent with the solution procedure in step 3.2), i+1 sub-band is in i-th of sub-band ([v1:V2]) both sides respectively put Put c2Individual interference cancellation subcarrier, the position of interference cancellation subcarrier is [v1-c2:v1-1,v1:v2,v2+1:v2+c2], i+1 The subcarrier index that individual sub- band modulation sends data is [v5:v6]；
Data subcarrier XrIIt is Q in interference caused by i-th of sub-bandrIXrI T, interference cancellation subcarrier XrCIn i-th of sub-band Caused interference is QrCXrC T, caused by both subcarriers and interference is：
Ii+1=| | QrCXrC T+QrIXrI T||2
Wherein, XrI=[Xi+1(v5),Xi+1(v5+1),...Xi+1(v6)],
XrC=[Xi+1(v1-c2),...Xi+1(v1-1),Xi+1(v2+1),...Xi+1(v2+c2)],
WithWhereinWithIt is upper Mark represents matrix Q in step 3.1)GRow, the equal representing matrix Q of subscriptGRow, the X in formulai+1Carried to introduce interference cancellation After ripple, new data message, X on i+1 sub-bandi+1Expression formula be：
Xi+1=[0 ..., 0, XrC,0,...,0,XrI,0,...,0]1×N
=[0 ... 0, Xi+1(v1-c2),...Xi+1(v1-1),Xi+1(v2+1),...Xi+1(v2+c2),0,...0,Xi+1 (v5),Xi+1(v5+1),...Xi+1(v6),0,...0]1×N
By least mean-square estimate solve：
XrC=-(QrC HQrC)-1QrC HQrIXrI T
Required XrCThe data of interference cancellation subcarrier-modulated as used in i-th of sub-band.
3. the active interference clearance method in UFMC systems as claimed in claim 1, it is characterised in that：Described step 4) tool Body step is：
4.1) IFFT is converted
Realize that IFFT is converted by Fourier's matrix, Fourier's matrix is defined asExpression is d to length2's Vector carries out d1Point IFFT is converted, and the element among Fourier's matrix is as follows：
<mrow> <msub> <mi>V</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <msub> <mi>d</mi> <mn>1</mn> </msub> </msqrt> </mfrac> <msup> <mi>e</mi> <mfrac> <mrow> <mi>j</mi> <mn>2</mn> <mi>&amp;pi;</mi> <mi>n</mi> <mi>m</mi> </mrow> <msub> <mi>d</mi> <mn>1</mn> </msub> </mfrac> </msup> <mo>,</mo> <mn>0</mn> <mo>&amp;le;</mo> <mi>m</mi> <mo>&amp;le;</mo> <msub> <mi>d</mi> <mn>2</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>&amp;le;</mo> <mi>n</mi> <mo>&amp;le;</mo> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>1</mn> </mrow>
4.2) filter
For filtering, linear convolution operation is completed with toeplitz matrix, is needed for different sub-bands by wave filter Centre frequency move to the centre of sub-band；
It is L to set UFMC system mesarcses filter length, and impulse response h expression formula is：H=h [0], h [1] ..., h [L- 1] }, corresponding frequency domain response is H；
Calculate the i-th -1 sub- mid-band frequency where subcarrier index be：By the frequency domain of ptototype filter Respond H translationsIndividual unit, obtain the frequency domain response H of the i-th -1 sub-bandi-1,
The impulse response h of the i-th -1 sub-bandi-1For：hi-1={ hi-1[0],hi-1[1],…,hi-1[L-1] }, wherein,
Define toeplitz matrix Ti-1For：
Its preceding N row is taken to be designated asWithRealize the filtering of the i-th -1 sub-band；
It is consistent with the solution procedure of i-1 sub-band, for i-th of sub-band, translated on frequency domainIndividual unit, Obtain frequency domain response HiWith impulse response hi, hiIn element be：For i+1 Sub-band, translate on frequency domainIndividual unit, obtain frequency domain response Hi+1With impulse response hi+1, hi+1In member Element is：By hi-1[n] uses h respectivelyi[n] and hi+1[n], which is replaced, obtains i-th of son frequency The toeplitz matrix of band and i+1 sub-band, its preceding N row is then taken respectively, obtains i-th of sub-band and i+1 height Frequency band realizes that the toeplitz matrix of filtering is respectivelyWith
By above-mentioned steps 1), step 2), step 3) and step 4), the time-domain signal x that transmitting terminal is senttotalFor：
xtotal=TVX
Wherein,V=diag { Vi-1,Vi,Vi+1Represent with matrix Vi-1, ViAnd Vi+1The diagonal matrix formed for diagonal element, V, Vi-1、ViAnd Vi+1Represent to realize step on three sub-bands respectively 4.1) Fourier's matrix that IFFT is converted inAnd d1And d2Value factor band and it is different.
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