CN108965192A - Alternately FBMC-QAM system mesarcs filter design method - Google Patents
Alternately FBMC-QAM system mesarcs filter design method Download PDFInfo
- Publication number
- CN108965192A CN108965192A CN201810928643.0A CN201810928643A CN108965192A CN 108965192 A CN108965192 A CN 108965192A CN 201810928643 A CN201810928643 A CN 201810928643A CN 108965192 A CN108965192 A CN 108965192A
- Authority
- CN
- China
- Prior art keywords
- filter
- fbmc
- coefficient vector
- qam system
- composite filter
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 73
- 239000002131 composite material Substances 0.000 claims abstract description 44
- 239000013598 vector Substances 0.000 claims abstract description 41
- 238000005457 optimization Methods 0.000 claims abstract description 23
- 239000011159 matrix material Substances 0.000 claims description 23
- 238000012804 iterative process Methods 0.000 claims description 5
- 230000007246 mechanism Effects 0.000 abstract description 2
- 238000010586 diagram Methods 0.000 description 15
- 230000004044 response Effects 0.000 description 15
- 238000005070 sampling Methods 0.000 description 14
- 238000001914 filtration Methods 0.000 description 6
- 230000005540 biological transmission Effects 0.000 description 5
- 230000015572 biosynthetic process Effects 0.000 description 5
- 238000003786 synthesis reaction Methods 0.000 description 5
- 238000001228 spectrum Methods 0.000 description 2
- 239000000969 carrier Substances 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 235000013399 edible fruits Nutrition 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 230000002452 interceptive effect Effects 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 230000000452 restraining effect Effects 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 230000009897 systematic effect Effects 0.000 description 1
Classifications
-
- 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
- H04L27/2626—Arrangements specific to the transmitter only
- H04L27/2627—Modulators
- H04L27/264—Pulse-shaped multi-carrier, i.e. not using rectangular window
-
- 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]
Landscapes
- Engineering & Computer Science (AREA)
- Computer Networks & Wireless Communication (AREA)
- Signal Processing (AREA)
- Power Engineering (AREA)
- Complex Calculations (AREA)
- Digital Transmission Methods That Use Modulated Carrier Waves (AREA)
Abstract
The present invention discloses a kind of alternately FBMC-QAM system mesarcs filter design method, it is first assumed that the composite filter group and analysis filter group of odd even subcarrier are respectively from four different ptototype filter alternate modulations in the FBMC-QAM system surrounded；Secondly, the design of four ptototype filters in system is described as a unconfined convex optimization problem, objective function is the sum of intersymbol interference (ISI), inter-carrier interference (ICI) and the stopband energy of ptototype filter of alternately FBMC-QAM system.Based on resulting target function gradient vector is derived, using double iterator mechanism solving optimization problems, performance more preferably composite filter and analysis filter may finally be obtained in odd even subcarrier.It is compared with the prior art discovery, the stopband energy that the present invention designs resulting FBMC-QAM system Central Plains mode filter is lower, and resulting FBMC-QAM system has preferable performance, can design for large size FBMC-QAM system and provide a kind of effective solution scheme.
Description
Technical field
The present invention relates to technical field of filter design, and in particular to a kind of alternately FBMC-QAM system Central Plains mode filter
Design method.
Background technique
In FBMC system, letter is realized by the composite filter group of transmitting terminal and the analysis filter group of receiving end respectively
Number modulation and demodulation.Difference with OFDM is, FBMC use the filter group with more preferable spectrum containment instead of
IDFT/DFT module in ofdm system.The traditional FBMC system modulated using OQAM, the inter-carrier interference as existing for itself
And intersymbol interference, so cannot directly apply this technology in MIMO.To break through the limitation, researcher is proposed using two
The FBMC-QAM system of a difference ptototype filter transmits qam symbol.
Due in FBMC system composite filter and analysis filter be by one or more ptototype filter tune
System, therefore the design of ptototype filter becomes the key problem of FBMC system design, which determine the globalities of system
Energy.Currently, the algorithm for design of FBMC system Central Plains mode filter mainly has: (1) Direct Method of Design；(2) window function method；
(3) frequency sampling method.Direct Method of Design is by directly optimizing all parameters of filter to it.Although straight
It is preferable to connect the resulting performance of filter of design method design, but as long as the length of ptototype filter is slightly elongated, design complexity
Degree will increased dramatically therewith, be not a kind of efficient design method.Different from Direct Method of Design, frequency sampling method and window
Functional based method is parametrization structure based on wave filter group, converts the design problem of filter group to using structural parameters as variable
Optimization problem.Compared to Direct Method of Design, latter two method has more high efficiency.
If Jeon et al. is in document " Prototype filter design for QAM-based filter bank
Multicarrier system " design problem of ptototype filter is described as to optimization problem (i.e. half set pattern of a belt restraining
The method of drawing).This method is different from Frequency Sampling Method, and even subcarriers ptototype filter, which uses, is based on Semidefinite Programming
The method of (Semi-Definite Program, SDP) designs, and belongs to one of Direct Method of Design.The design method can be with
The pretty good system of performance is obtained, but the solution of its high complexity makes it not be suitable for large-scale F BMC-QAM system.
For another example NAM et al. is in document " A New Filter-Bank Multicarrier System With Two
Prototype Filters for QAM Symbols Transmission and Reception " in mentality of designing be point
It does not realize the FBMC-QAM system of the transmission of qam symbol using two different ptototype filters in odd even subcarrier, uses
Frequency Sampling Method design odd subcarriers ptototype filter, after it is orthogonal with even subcarriers Central Plains mode filter according to odd number
Relationship solves the ptototype filter (i.e. Frequency Sampling Method) of even subcarriers.This method design is relatively simple, but it is maximum
Deficiency is that design freedom is small, limits the design performance of system.
Summary of the invention
The present invention makes it not support traditional MIMO skill for tradition FBMC-OQAM system there are intrinsic intersymbol interference
The problem of art, provides a kind of alternately FBMC-QAM system mesarcs filter design method.
To solve the above problems, the present invention is achieved by the following technical solutions:
Alternately FBMC-QAM system mesarcs filter design method, specifically includes that steps are as follows:
Step 1, the coefficient vector h that composite filter in FBMC-QAM system odd chanel will be replaced0And analysis filter
Coefficient vector h1And in even-numbered channels composite filter coefficient vector g0With the coefficient vector g of analysis filter1Design is asked
Topic is attributed to a unconfined optimization problem, and objective function is the alternately intersymbol interference of FBMC-QAM system, intercarrier
The weighted sum of interference and ptototype filter stopband energy；
Step 2, the objective function for deriving step 1 are converted into the objective function about intermediate variable x and y, and enable mesh
The gradient vector of scalar functions is zero, obtains the optimal solution's expression about intermediate variable x and y, and the expression formula is as required
Majorization of solutions problem:
Wherein, x0To transmit variable x0, y is intermediate variable,
G1(x0)=[A1(x0)B1(x0)C1(x0)]T, G2(y)=[A1(y)B1(y)C2(y)]T,
B=[b0,1,b0]T, b0For0 vector, I1=[I0Z], I2=[Z I0], I0It is
The unit matrix of L × L, Z are 0 matrixes of L × L, and S is the Toeplitz matrix about L × L of ptototype filter stopband energy,
W is the diagonal matrix of L × L, and expression is
EΔkIt is the diagonal matrix of L × L, expression is
GΔnIt is the translation matrix of L × L, expression is
Δ k ∈ [- K, K], K are the near influence symbolic numbers of required consideration, and Δ n ∈ [- t, t], t are that near influence of required consideration carries
Wave number, i=0,1 ..., L-1, L are the length of ptototype filter, and N is the sub-carrier number of composite filter；
The coefficient vector h of composite filter in step 3, given odd chanel0It is with composite filter in even-numbered channels
Number vector g0, and carry it into x0=[h0 g0]TIn, solve transmitting variable x0；
Step 4, with double alternative manners, utilize resulting transmitting variable x0The formula of solution procedure 2 1. optimization problem is gone, is obtained
To the intermediate variable y of current iteration, recycles the intermediate variable y of current iteration to go the formula of solution procedure 2 2. optimization problem, obtain
The intermediate variable x of current iteration；
Step 5, judgement | | x0-x||2Whether≤δ is true, if set up, stops iterative process, the centre of current iteration
Variable x and y is exported as optimal solution, if not, the intermediate variable x of current iteration is then assigned to transmitting variable x0, and return
It returns to step 4 and continues iterative process；Wherein δ is given positive number；
Step 6, the intermediate variable x and y exported using step 5, the coefficient of composite filter in solving system odd chanel
Vector h0With the coefficient vector h of analysis filter1And in even-numbered channels composite filter coefficient vector g0And analysis filter
Coefficient vector g1:
Wherein, I0It is the unit matrix of L × L, Z is the null matrix of L × L, and L is given positive integer；
Step 7, odd chanel final according to calculated by step 7 composite filter coefficient vector h0It is filtered with analysis
The coefficient vector h of wave device1And the coefficient vector g of the composite filter of even-numbered channels0With the coefficient vector g of analysis filter1,
Determine the composite filter and analysis filter of entire alternately FBMC-QAM system odd chanel and even-numbered channels.
In above-mentioned steps 4, the coefficient of composite filter in odd chanel is given to h0With composite filter in even-numbered channels
Coefficient vector g0Gained is designed by the lowpass prototype filter that 2 given lengths are L respectively.
Compared with prior art, the present invention considers the optimization design of FBMC-QAM system Central Plains mode filter.Firstly, at this
In invention design, in order to improve system design freedom, it is assumed that the synthesis of odd even subcarrier in the FBMC-QAM system surrounded
Respectively from four different ptototype filter alternate modulations, the present invention expects multiple originals for filter group and analysis filter group
The use of mode filter can for system design more freedom degrees are provided, for make obtain have more preferable performance FBMC system at
It is possible.Subsequent emulation experiment also verifies the feasibility of this method, designs resulting ptototype filter and has better stopband
Fade performance；Secondly, performance indicator of the present invention according to alternately FBMC-QAM system, four ptototype filters in system are set
Meter is described as a unconfined convex optimization problem, objective function be the alternately intersymbol interference (ISI) of FBMC-QAM system,
The sum of inter-carrier interference (ICI) and the stopband energy of ptototype filter.Based on resulting target function gradient vector is derived, use
Double iterator mechanism solving optimization problems may finally obtain performance more preferably composite filter and analysis filtering in odd even subcarrier
Device.It is compared with the prior art discovery, the stopband energy that the present invention designs resulting FBMC-QAM system Central Plains mode filter is lower,
Resulting FBMC-QAM system has preferable performance, can design for large size FBMC-QAM system and provide a kind of effective solution side
Case.
Detailed description of the invention
Fig. 1 is alternating FBMC-QAM system block diagram.
Fig. 2 is composite filter and analysis filter in odd even subcarrier in design provided by the invention alternating FBMC-QAM system
The flow chart of wave device.
Fig. 3 is that the FBMC system odd chanel Central Plains mode filter of design gained port number N=64 in example 1 is adopted with frequency
The amplitude response comparison diagram of sample method and Semidefinite Programming method；Wherein (a) is that the prior art and the present invention design resulting odd number and lead to
Road composite filter amplitude response comparison diagram (b) designs resulting odd chanel analysis filter for the prior art and the present invention
Amplitude response comparison diagram.
Fig. 4 is that the FBMC system even-numbered channels Central Plains mode filter of design gained port number N=64 in example 1 is adopted with frequency
The amplitude response comparison diagram of sample method and Semidefinite Programming method；Wherein (a) is that the prior art and the present invention design resulting even number and lead to
Road composite filter amplitude response comparison diagram (b) designs resulting even-numbered channels analysis filter for the prior art and the present invention
Amplitude response comparison diagram.
Fig. 5 is the FBMC system odd chanel Central Plains mode filter and frequency of design gained port number N=256 in example 1
The amplitude response comparison diagram of sampling method and Semidefinite Programming method；Wherein (a) is that the prior art and the present invention design resulting odd number
Channel composite filter amplitude response comparison diagram (b) designs resulting odd chanel analysis filtering for the prior art and the present invention
Device amplitude response comparison diagram.
Fig. 6 is the FBMC system even-numbered channels Central Plains mode filter and frequency of design gained port number N=256 in example 1
The amplitude response comparison diagram of sampling method and Semidefinite Programming method；Wherein (a) is that the prior art and the present invention design resulting even number
Channel composite filter amplitude response comparison diagram (b) designs resulting even-numbered channels analysis filtering for the prior art and the present invention
Device amplitude response comparison diagram.
Specific embodiment
To make the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with specific example, and referring to attached
Figure, the present invention is described in more detail.
Fig. 1 gives the alternating FBMC-QAM system model that the present invention is considered.H in figure0(i)、h1(i)、g0(i)、g1
(i) what is indicated is the ptototype filter that length is L, wherein i=0 ..., L-1, the composite filter group and analysis filtering of system
Device group is respectively from this four prototype alternate modulations.On the basis of above structure, alternating FBMC- proposed by the invention
QAM system mesarcs filter design method, as shown in Fig. 2, it includes the following steps:
Step 1: ak(n) and bk(n) the QAM signal of n-th of input on k-th of odd and even number channel, N generation are respectively represented
Table be composite filter group port number.The base band of FBMC-QAM sends signal and indicates are as follows:
In formula,In the state that transmission channel is completely ideal, i.e., it is believed that alternately
The modulation end signal of FBMC-QAM systems baseband signal is equal to the demodulation end signal of baseband signal, the kth odd number of receiver
With the output signals of kth even-numbered channels byWithIt is collectively denoted as:
To make system Perfect Reconstruction, i.e.,Then ptototype filter has to full
The perfect reconstruction filter bank of foot column:
Wherein, δ (k '-k, n '-n) is impulse function, works as k'=k, when n'=n, δ (k'-k, n'-n)=1, and other situations
It is down 0.As ptototype filter h0(i)、h1(i)、g0(i)、g1(i) be reality and even function when, formula (4a), (4b) can be set up.
Step 2: enablingISI/ICI is respectively indicated to odd subcarriers ak(n) and even subcarriers bk(n)
Interference, interfering energy expression formula respectively indicate are as follows:
In formula (5) and formula (6), E [] indicates expectation, due to qam signal energy normalized, so E [| ak'(n')
|2]=1, E [| bk'(n')|2Therefore (5) formula and (6) formula can be rewritten by]=1:
Particularly, work as k'=k, when n'=n, composite filter h in odd subcarriers0(i) and analysis filter h1(i) with
And even subcarriers composite filter g0(i) and analysis filter g1(i) condition for needing to meet are as follows:
In view of adjacent sub-carrier and adjacent-symbol are maximum to the interference of output signal, therefore Δ n=is only considered in the design
The integer situation of n'-n, Δ n ∈ [- 2,2] and Δ k=k'-k, Δ k ∈ [- 2,2], the influence phase of remaining sub-carriers and symbol
It influences for smaller, does not consider further that herein.If the composite filter and analysis filter of odd subcarriers are respectively h0=
[h0(0),h0(1),…,h0(L-1)]T、h1=[h1(0),h1(1),…,h1(L-1)]T, the composite filter of even subcarriers and
Analysis filter is respectively g0=[g0(0),g0(1),…,g0(L-1)]T、g1=[g1(0),g1(1),…,g1(L-1)]T, b=
[b0,1,b0]T, wherein b0For 1 × 12 0 vector.For convenience of subsequent arithmetic as, (7) and (9) formula can be write to the shape of matrix multiple
Formula are as follows:
Similarly, (8) and (10) formula can also be write as to the form of matrix multiple:
Matrix A (h in formula0)、B(g0)、C(g0) and C (h1) respectively indicate are as follows:
In formula, GΔnIt is the matrix of L × L, EΔkIt is L × L diagonal matrix with W, is specifically defined expression are as follows:
Enabling the synthesis of odd subcarriers and analyzing the frequency response of ptototype filter is respectively H0(ejω)=cT(ω,L)h0
And H1(ejω)=cT(ω,L)h1, the synthesis of even subcarriers and the frequency response for analyzing ptototype filter are respectively G0(ejω)=
cT(ω,L)g0And G1(ejω)=cT(ω,L)g1, wherein c (ω, L)=[1 ..., e-j(L-1)ω]T。h0、h1、g0And g1Stopband energy
Amount is denoted as E respectivelys(h0)、Es(h1)、Es(g0) and Es(g1), it indicates are as follows:
Wherein S is the Toeplitz matrix of L × L.
Step 4: the design of alternately FBMC-QAM system Central Plains mode filter is summed up based on the above analysis are as follows:
B=[b in formula0,1,b0]T, b0For 1 × 12 0 vector.From formula (16) we have observed that coming, it is related in optimization problem
The solution of 4 known variables solves extremely difficult.In order to facilitate calculating, former optimization problem can be converted to about vector x
With the optimization problem of two variables of y.Enable x=[h0 g0]T, y=[h1 g1]T, then x and y and h0、h1、g0、g1Relationship are as follows:
Wherein, I0It is the unit matrix of L × L, Z is 0 matrix of L × L.Enable I1=[I0Z], I2=[Z I0], then it can will be former
Optimization problem conversion are as follows:
It is derived by respectively:
Wherein A1(x)、B1(x)、C1(x)、C2(x) it respectively indicates are as follows:
In addition, enablingTherefore have:
Therefore former optimization problem (16) is converted are as follows:
Since objective function (22) are a non-convex biquadratic optimization problem, the optimization problem is being solved using double iteration machines
System is solved, and double iteration alternately solve two variables, and both when optimizing a variable, another variable is fixed and invariable.
The gradient function of x and y are first obtained according to objective function derivation are as follows:
Wherein,S3=S1+S2.Enable gradient vector (23a) and (23b)
It is zero, the optimal solution of x and y can be acquired are as follows:
Step 5: the composite filter of initial odd and even number subcarrier uses Semidefinite Programming method according to design requirement
The lowpass prototype filter design gained h that design length is L0And g0, h0=[h0(0),h0(1),…,h0(L-1)]T, g0=[g0
(0),g0(1),…,g0(L-1)]T；L is given positive integer；Initial x is obtained by formula (17) afterwards, is denoted as x0；
Step 6: the x that the 5th step is obtained0Substitution formula (24a) acquires y, then obtained y is substituted into formula (24b), more
New x and y；
Step 7: judgement | | x0-x||2Whether≤δ (positive number that δ is given very little) is true, if set up, stops iteration
Process, x and y are exported as optimal solution, if not, enable x0=x, and continue iterative process back to the 7th step；
Step 8:, according to formula (17), solving h using the x and y that acquire0、h1、g0、g1。
Step 9: the coefficient vector h of the ptototype filter according to calculated by the 8th step0、h1、g0、g1.By carrier modulation,
The synthesis ptototype filter for obtaining each odd chanel is h0；The analysis filter of odd chanel is h1；The synthesis of even-numbered channels is filtered
Wave device is g0；The analysis filter of even-numbered channels is g1.So that it is determined that the synthetic filtering of entire alternately FBMC-QAM system transmitting terminal
The analysis filter of device and receiving end.
Performance of the invention is further described below by specific simulation example.
Example 1:
Carrier channel number N=64, odd number are designed with Frequency Sampling Method, Semidefinite Programming method method and the method for the present invention respectively
Composite filter and analysis filter length with even subcarriers are the FBMC-QAM system of L=4N-1.It is set in the present invention
In meter method, δ=1 × 10-3.Table 1 provides the performance comparison of each method design gained FBMC-QAM system, and Fig. 3 and Fig. 4 are respectively
The Frequency and Amplitude response diagram of odd and even number subcarrier ptototype filter in the FBMC-QAM system of each method design.Find out from 1
The method of the present invention significantly reduces ptototype filter energy, and gained FBMC-QAM system spectrum detection performance is more preferably.In conjunction with 1 He of table
Fig. 3-Fig. 4, it is known that the method for the present invention design gained system is worse than document " A New Filter-Bank in mean square error performance
Multicarrier System With Two Prototype Filters for QAM Symbols Transmission
And Reception " (i.e. frequency sampling) method, it is better than document " Prototype filter design for QAM-based
Filter bank multicarrier system " (i.e. Semidefinite Programming) method, but it designs resulting odd and even number
The ptototype filter stopband attenuation performance of carrier wave is significantly better than above two method.
The performance comparison of the method for the present invention and frequency sampling method, Semidefinite Programming method in 1 example 1 of table
Example 2:
Carrier channel number N=256 is designed, the composite filter and analysis filter length of odd and even number subcarrier are
The FBMC-QAM system of L=4N-1.Fig. 5 and Fig. 6 is respectively the odd and even number subcarrier ptototype filter of FBMC-QAM system
Frequency and Amplitude respond comparison diagram.Document " Prototype filter design for QAM-based as can be seen from Figure 6
Filter bank multicarrier system " to design resulting even number logical for (i.e. Semidefinite Programming method) and the method for the present invention
Channel filter reconstruction property is than document " A New Filter-Bank Multicarrier System With Two
Prototype Filters for QAM Symbols Transmission and Reception " (i.e. frequency sampling method)
Difference.But the performance comparison of each algorithm is provided from table 2.Know the prototype filtering in the odd and even number channel of the method for the present invention design
The Stopband Performance of the filter of device, especially even-numbered channels is significantly better than frequency sampling method and Semidefinite Programming method.Emulation knot
Fruit shows that design gained systematic entirety can be the compromise performance of frequency sampling method and Semidefinite Programming method, and designers can
It is selected to be applicable in scheme according to system actual demand.
The performance comparison of the method for the present invention and frequency sampling method, Semidefinite Programming method in 2 example 2 of table
On the one hand, the FBMC-QAM modulated structure that the present invention considers, receiving end in odd subcarriers and even subcarriers
Four different ptototype filters are used with the composite filter of transmitting terminal and analysis filter, improve traditional FBMC-QAM
The design freedom of modulated structure.Subsequent emulation has confirmed this structure and has had preferable overall performance.On the other hand, this hair
It is bright that the design problem of ptototype filter is attributed to unconstrained optimization problem, two intermediate variables are rationally set, by original about four
The optimization problem of a known variables is converted into the solution about two intermediate variables, reduces computation complexity；Using double iteration machines
Solve problems processed.Compared to existing method, the method for the present invention not only has more preferably performance, but also solving complexity is much lower.
It should be noted that although the above embodiment of the present invention be it is illustrative, this be not be to the present invention
Limitation, therefore the invention is not limited in above-mentioned specific embodiment.Without departing from the principles of the present invention, all
The other embodiment that those skilled in the art obtain under the inspiration of the present invention is accordingly to be regarded as within protection of the invention.
Claims (2)
1. replacing FBMC-QAM system mesarcs filter design method, characterized in that specifically include that steps are as follows:
Step 1, the coefficient vector h that composite filter in FBMC-QAM system odd chanel will be replaced0With the coefficient of analysis filter
Vector h1And in even-numbered channels composite filter coefficient vector g0With the coefficient vector g of analysis filter1Design problem is returned
Become a unconfined optimization problem, objective function be the alternately intersymbol interference of FBMC-QAM system, inter-carrier interference and
The weighted sum of ptototype filter stopband energy；
Step 2, the objective function for deriving step 1 are converted into the objective function about intermediate variable x and y, and enable target letter
Several gradient vectors is zero, obtains the optimal solution's expression about intermediate variable x and y, which solves needed for being
Optimization problem:
Wherein, x0To transmit variable x0, y is intermediate variable,
G1(x0)=[A1(x0) B1(x0) C1(x0)]T, G2(y)=[A1(y) B1(y) C2(y)]T,
B=[b0,1,b0]T, b0For0 vector, I1=[I0Z], I2=[Z I0], I0It is L × L
Unit matrix, Z is 0 matrix of L × L, and S is the Toeplitz matrix about L × L of ptototype filter stopband energy,
W is the diagonal matrix of L × L, and expression is
EΔkIt is the diagonal matrix of L × L, expression is
GΔnIt is the translation matrix of L × L, expression is0≤k, l≤L-1, Δ k ∈
[- K, K], K are the near influence symbolic numbers of required consideration, and Δ n ∈ [- t, t], t are the near influence sub-carrier numbers of required consideration,
I=0,1 ..., L-1, L are the length of ptototype filter, and N is the sub-carrier number of composite filter；
The coefficient vector h of composite filter in step 3, given odd chanel0With the coefficient vector of composite filter in even-numbered channels
g0, and carry it into x0=[h0 g0]TIn, solve transmitting variable x0；
Step 4, with double alternative manners, utilize resulting transmitting variable x0The formula of solution procedure 2 1. optimization problem is gone, this is obtained
The intermediate variable y of secondary iteration recycles the intermediate variable y of current iteration to go the formula of solution procedure 2 2. optimization problem, obtains this
The intermediate variable x of iteration；
Step 5, judgement | | x0-x||2Whether≤δ is true, if set up, stops iterative process, the intermediate variable x of current iteration
It is exported with y as optimal solution, if not, the intermediate variable x of current iteration is then assigned to transmitting variable x0, and return to step
Rapid 4 continue iterative process；Wherein δ is given positive number；
Step 6, the intermediate variable x and y exported using step 5, the coefficient vector h of composite filter in solving system odd chanel0
With the coefficient vector h of analysis filter1And in even-numbered channels composite filter coefficient vector g0With the coefficient of analysis filter
Vector g1:
Wherein, I0It is the unit matrix of L × L, Z is the null matrix of L × L, and L is given positive integer；
Step 7, odd chanel final according to calculated by step 7 composite filter coefficient vector h0And analysis filter
Coefficient vector h1And the coefficient vector g of the composite filter of even-numbered channels0With the coefficient vector g of analysis filter1, determine
The composite filter and analysis filter of entire alternately FBMC-QAM system odd chanel and even-numbered channels.
2. alternately FBMC-QAM system mesarcs filter design method according to claim 1, characterized in that step 4
In, the coefficient of composite filter in odd chanel is given to h0With the coefficient vector g of composite filter in even-numbered channels0Respectively by 2
The lowpass prototype filter that a given length is L designs gained.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810928643.0A CN108965192B (en) | 2018-08-15 | 2018-08-15 | Prototype filter design method in alternating FBMC-QAM system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810928643.0A CN108965192B (en) | 2018-08-15 | 2018-08-15 | Prototype filter design method in alternating FBMC-QAM system |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108965192A true CN108965192A (en) | 2018-12-07 |
| CN108965192B CN108965192B (en) | 2021-03-19 |
Family
ID=64470204
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810928643.0A Active CN108965192B (en) | 2018-08-15 | 2018-08-15 | Prototype filter design method in alternating FBMC-QAM system |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108965192B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109818890A (en) * | 2019-03-12 | 2019-05-28 | 北京科技大学 | A kind of ptototype filter determines method and determining device |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106302300A (en) * | 2015-06-24 | 2017-01-04 | 北京三星通信技术研究有限公司 | The method and device that a kind of signal based on filter bank multi-carrier system sends and receives |
| CN107222184A (en) * | 2017-05-31 | 2017-09-29 | 桂林电子科技大学 | A kind of design method of pair of prototype FBMC system median filter |
| US20180109410A1 (en) * | 2015-02-24 | 2018-04-19 | Senior Engineer of Samsung Electroics Co., Ltd. | Synchronization method and apparatus in mobile communication system |
| CN107959648A (en) * | 2017-11-22 | 2018-04-24 | 桂林电子科技大学 | The design method of double prototype FBMC-OQAM systems Central Plains mode filter |
| CN108123909A (en) * | 2017-12-21 | 2018-06-05 | 北京交通大学 | A kind of ptototype filter implementation method in FBMC-OQAM systems |
-
2018
- 2018-08-15 CN CN201810928643.0A patent/CN108965192B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20180109410A1 (en) * | 2015-02-24 | 2018-04-19 | Senior Engineer of Samsung Electroics Co., Ltd. | Synchronization method and apparatus in mobile communication system |
| CN106302300A (en) * | 2015-06-24 | 2017-01-04 | 北京三星通信技术研究有限公司 | The method and device that a kind of signal based on filter bank multi-carrier system sends and receives |
| CN107222184A (en) * | 2017-05-31 | 2017-09-29 | 桂林电子科技大学 | A kind of design method of pair of prototype FBMC system median filter |
| CN107959648A (en) * | 2017-11-22 | 2018-04-24 | 桂林电子科技大学 | The design method of double prototype FBMC-OQAM systems Central Plains mode filter |
| CN108123909A (en) * | 2017-12-21 | 2018-06-05 | 北京交通大学 | A kind of ptototype filter implementation method in FBMC-OQAM systems |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109818890A (en) * | 2019-03-12 | 2019-05-28 | 北京科技大学 | A kind of ptototype filter determines method and determining device |
| CN109818890B (en) * | 2019-03-12 | 2020-04-10 | 北京科技大学 | Prototype filter determining method and device |
Also Published As
| Publication number | Publication date |
|---|---|
| CN108965192B (en) | 2021-03-19 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Yang et al. | Analysis of low-complexity windowed DFT-based MMSE channel estimator for OFDM systems | |
| CN101904114B (en) | Method and apparatus for IFDMA receiver architecture | |
| CN103733516B (en) | Receiver, emitter and the method for digital multiple sub-band processing | |
| CN107370704A (en) | Wireless communication apparatus and wireless signal generating method | |
| CN103650445B (en) | Any sample rate conversion for communication system | |
| CN105723672B (en) | The receiving/transmission method and device of modulated signal transmission in filter bank multi-carrier communication system | |
| CN103283201B (en) | Butterfly filter coefficient setting method and device, receiver and method of reseptance | |
| CN106130946A (en) | A kind of biorthogonal frequency-division multiplex multi-carrier modulation/demodulation methods and system | |
| Aminjavaheri et al. | Prototype filter design for FBMC in massive MIMO channels | |
| CN104883238A (en) | Multi-carrier time division multiplexing modulation/demodulation method and system | |
| TWI703842B (en) | Filter bank multicarrier communication system based on discrete hartley transform | |
| CN104917712B (en) | Signal processing method and device | |
| CN106656899A (en) | Method for realizing multicarrier VDE system modulation and demodulation of ship VDES system | |
| CN108270713A (en) | It is a kind of to use scene signals multiple access method and system more | |
| CN107395544B (en) | Real number orthogonal pilot frequency sequence sending method based on MIMO-FBMC | |
| CN109462443B (en) | 5G multi-carrier underwater acoustic communication method | |
| CN107070836A (en) | The design method of FBMC receive-transmit systems based on FRM technologies in a kind of 5G systems | |
| CN110212927A (en) | Signal transmitting method, signal transmitter, storage medium | |
| CN106341362B (en) | Pilot frequency sending method, pilot frequency receiving method and device thereof | |
| CN108965192A (en) | Alternately FBMC-QAM system mesarcs filter design method | |
| CN108809880A (en) | A kind of the MIMO-FBMC system datas receiving/transmission method and device of low complex degree | |
| CN105515711B (en) | Joint compressed sensing and the rangefinder Interference Suppression System for receiving diversity | |
| CN107959648B (en) | Design method of prototype filter in double-prototype FBMC-OQAM system | |
| CN109525290A (en) | Real number feedback iteration channel estimation methods based on MIMO-FBMC system | |
| CN110061941A (en) | A kind of channel equalization method in 5G multi-carrier communications systems |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| EE01 | Entry into force of recordation of patent licensing contract |
Application publication date: 20181207 Assignee: Guangxi wisdom Valley Technology Co.,Ltd. Assignor: GUILIN University OF ELECTRONIC TECHNOLOGY Contract record no.: X2023980046615 Denomination of invention: Design Method of Prototype Filter in Alternating FBMC-QAM System Granted publication date: 20210319 License type: Common License Record date: 20231108 |
|
| EE01 | Entry into force of recordation of patent licensing contract |