CN105656830B - Ofdm signal method for inhibiting peak-to-average ratio based on distributed implementation - Google Patents
Ofdm signal method for inhibiting peak-to-average ratio based on distributed implementation Download PDFInfo
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- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
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- H04L27/2614—Peak power aspects
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/26—Systems using multi-frequency codes
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Abstract
The invention discloses a kind of ofdm signal method for inhibiting peak-to-average ratio based on distributed implementation mainly solves the problems, such as that complexity is high when existing inhibition ofdm system inhibits peak-to-average ratio.The present invention is by the constraint of the ofdm system peak-to-average ratio thresholding, idle sub-carrier power limiting thresholding and OFDM symbol pilot sub-carrier power of application requirements where meeting system in the setting of OFDM wireless system transmitting terminal, then combines original OFDM frequency domain symbol and related initializaing variable establishes non-convex Optimized model；Then the conversion that relaxes is carried out to model, and obtains desired OFDM frequency domain symbol by solving；Finally the desired OFDM frequency domain symbol is successively launched by antenna after variation plus cyclic prefix, D/A conversion and radio frequency amplification by IFFT and going here and there.The present invention restrained effectively ofdm signal peak-to-average ratio, and have lower computation complexity, can be used for the transmission of communications field signal.
Description
Technical field
The invention belongs to field of communication technology, in particular to a kind of ofdm signal method for inhibiting peak-to-average ratio can be used for communicating
The transmission of field signal.
Background technique
Orthogonal frequency division multiplex OFDM technology has the availability of frequency spectrum high, and anti-multipath fading ability is strong, realizes the advantages that simple,
It has been widely used in wireless communication system.As shown in Figure 1.Original OFDM wireless system transmitting terminal mainly includes to be sent
OFDM frequency-region signal, inverse-Fourier transform IFFT module, serial to parallel conversion module, add cyclic prefix module, D/A digital-to-analogue conversion
Module and RF Amplifier Module, are finally sent by antenna.But if directlying adopt the above method, ofdm signal may
There is very high peak-to-average ratio, high peak-to-average ratio can reduce the power efficiency of power amplifier.Therefore one of ofdm signal is main
The disadvantage is that there are higher peak-to-average ratio PAPR for its time-domain signal.This is because when multiple sub-carrier phases are same or similar,
Corresponding time domain waveform will appear instantaneous peak value.When number of sub carrier wave is more, OFDM time-domain signal level value is just approximate is presented Gauss
The probability that the likelihood ratio low level signal that distribution, i.e. high level signal occur occurs is much smaller.If avoiding ofdm signal from occurring
Dynamic range of signals, is limited to the linear work area of power amplifier by non-linear distortion and the high level signal for yielding to probability of occurrence very little
It is interior, it is extremely inefficient to will cause power amplification efficiency.Its operating point is pushed towards into saturation point if power amplification efficiency is guaranteed, then will lead to OFDM
High level signal in signal generates apparent non-linear distortion.This non-linear distortion can not only be destroyed between subcarrier just
Hand over property and deteriorate system error performance, also will form out of band spectrum regeneration and interfere other wireless systems.
The method of classical inhibition ofdm signal PAPR has repetition shearing and filtering RCF, Tone reservation TR etc., but they are all
Better performance can not be obtained in existing ofdm system because of its own the shortcomings that.For example shearing and filtering method RCF is repeated, by
It is that a distortion process will necessarily just generate out-of-band radiation and inband distortion in it, although carrying out repetition shearing and filtering can reduce
Out-of-band radiation and inband distortion, but the effect for the inhibition PAPR being unable to get because regenerating amplitude；Tone reservation TR is pre-
Stay some carrier waves specially to inhibit PAPR, but this method equally reduces channel efficiency.
Currently, having become new research direction using the PAPR that convex optimisation technique reduces ofdm signal.For example, using convex excellent
Change technological improvement filtering, the RCF method optimized, it can reach expected PAPR under seldom the number of iterations
Value.Aggarwal also proposed a kind of Second-order cone programming SOCP model, and the model is in constraint error vector magnitude EVM and free time
Under conditions of carrier power expense FCPO, the peak value of time-domain signal is minimized.Semidefinite Programming SDP model can also be used for PAPR suppression
System: for minimizing EVM, constraint condition is the non-convex optimization model of PAPR and FCPO, can be by it using semidefinite decoding SDR technology
It is converted into the convex optimization problem of SDP, so as to which optimal solution is effectively calculated.
Although being compared with the traditional method, the available better PAPR inhibitory effect of convex optimization method, because of its calculating
Complexity is high and its practical application is made to suffer restraints, and is not able to satisfy the demand of modern wireless communication systems still.
Summary of the invention
It is an object of the invention to overcome the shortcomings of above-mentioned prior art, propose it is a kind of can distributed implementation ofdm signal
Method for inhibiting peak-to-average ratio makes it by the constraint of practical application, not meet modern wireless communication systems to reduce computation complexity
Demand.
Technical thought of the invention is: being embedded in and inhibits before the inverse-Fourier transform module of original OFDM wireless transmitting system
Ofdm signal peak-to-average ratio module, by set the peak-to-average ratio thresholding of desired ofdm signal, idle sub-carrier clipping thresholding and
Pilot sub-carrier constraint, combine original OFDM frequency domain symbol, by the optimization problem of OFDM symbol be converted into ADMM can solve it is convex
Optimization problem passes through the OFDM frequency domain symbol with ADMM algorithm to the model solution, after being optimized.Using optimization module
OFDM emission system has lower peak-to-average ratio and distorted signals, and the process of solving model has lower algorithm complicated
Degree.Its implementation is as follows:
Technical solution 1: the ofdm signal method for inhibiting peak-to-average ratio based on distributed implementation includes the following steps:
(1) system requirements is set are as follows: peak-to-average ratio threshold value of the time-domain signal peak-to-average ratio no more than the expectation symbol of setting
α, and distorted signals is minimum；
(2) original orthogonal frequency division multiplex OFDM frequency domain symbol c is inputtedo, co∈CN×1, N is sub-carrier number；
(3) initializaing variable is set, comprising: inversefouriertransform rotated factor matrix A ∈ ClN×N, useful sub-carrier selection square
Battle array S ∈ RN×N, data subcarrier selection matrix SD∈RN×N, idle sub-carrier selection matrix SF∈RN×N, pilot sub-carrier select square
Battle array SP∈RN×N, unit matrix I ∈ RN×N, desired frequency domain symbol c ∈ CN×1, and time-domain signal x ∈ C corresponding with clN×1,
Wherein N is OFDM sub-carrier number, and l is oversample factor；
(4) according to system application and purpose, the peak-to-average ratio PAPR threshold value α ∈ of setting expectation symbol [1 ,+∞) and
Idle sub-carrier amplitude peak thresholding Tc；
(5) according to the system requirements set in step (1), the following desired frequency domain symbol c and time-domain signal x of solution is established
Optimized model:
Wherein, | | x | |∞Indicate the Infinite Norm of vector x, | | x | |2Indicate 2 norms of vector x.
Optimization mould<1>is subjected to relaxation conversion and obtains following convex Optimized model<2>:
Wherein, parameter TxByApproximate calculation obtains, to the T in the convex Optimized modelxPass through alternating direction
Multiplier Algorithm iterative solution is updated；
(6) the convex Optimized model that solution procedure (5) obtains obtains desired frequency domain symbol c and time-domain signal x:
(6a) solves above-mentioned convex Optimized model<2>by alternating direction Multiplier Algorithm, obtains the solution table of Optimized model<1>
Up to formula:
Wherein, k indicates kth time iteration, and ρ > 0 is penalty factor, and u is sized Lagrange duality variable,It indicates
Set X=x | | | x | |∞≤TxOn projection operation, FFTl() indicates first directly to do fast Fourier change to lN dimensional vector
It changes, obtains corresponding frequency domain lN dimensional vector, then take the top n component of the vector, scale finally is carried out to obtained N-dimensional vector
Change, i.e., is multiplied with constant 1/lN, IFFTl() indicates to seek the lN point inversefouriertransform of N-dimensional vector；
(6b) is iterated solution until meeting stopping criterion for iteration to above-mentioned solution expression formula<3>, i.e., final is original
Residual volume Ac-x and antithesis remnants variable xcurrent-xoldMeet simultaneously and presets value 10-5, it is desired to obtain Optimized model<1>
Frequency domain symbol c and time-domain signal x；Wherein xcurrentIndicate the value of current x in iterative process, xoldIndicate the value of last time x；
(7) the expectation frequency domain symbol c that step (6) obtains successively is passed through into IFFT conversion module and go here and there variation, plus circulation before
Sew, D A digital-to-analogue conversion and radio frequency amplification after launched by antenna.
Technical solution 2: the ofdm signal method for inhibiting peak-to-average ratio based on distributed implementation includes the following steps:
1) system requirements is set are as follows: the peak-to-average ratio threshold value α of the expectation symbol of time-domain signal peak-to-average ratio no more than setting,
Distorted signals is minimum, and idle sub-carrier peak amplitude is no more than idle sub-carrier amplitude peak thresholding Tc；
2) original orthogonal frequency division multiplex OFDM frequency domain symbol c is inputtedo, co∈CN×1, N is sub-carrier number；
3) initializaing variable is set, comprising: inversefouriertransform rotated factor matrix A ∈ ClN×N, useful sub-carrier selection square
Battle array S ∈ RN×N, data subcarrier selection matrix SD∈RN×N, idle sub-carrier selection matrix SF∈RN×N, pilot sub-carrier select square
Battle array SP∈RN×N, unit matrix I ∈ RN×N, desired frequency domain symbol c ∈ CN×1, and time-domain signal x ∈ C corresponding with clN×1,
Wherein N is OFDM sub-carrier number, and l is oversample factor；
4) according to system application and purpose, the peak-to-average ratio PAPR threshold value α ∈ of setting expectation symbol [1 ,+∞) and it is empty
Not busy subcarrier amplitude peak thresholding Tc；
5) establish the following desired frequency domain symbol c's and time-domain signal x of solution according to the system requirements set in step 1)
Optimized model:
Wherein, | | x | |∞Indicate the Infinite Norm of vector x, | | x | |2Indicate 2 norms of vector x.
Optimization mould<4>is subjected to relaxation conversion and obtains following convex Optimized model<5>:
Wherein, parameter TxByApproximate calculation obtains, to the T in the convex Optimized modelxPass through alternating direction
Multiplier Algorithm iterative solution is updated；
6) solution procedure 5) obtained convex Optimized model, obtain desired frequency domain symbol c and time-domain signal x:
Above-mentioned convex Optimized model<5>6a) is solved by alternating direction Multiplier Algorithm, obtains the solution table of Optimized model<4>
Up to formula:
Wherein, k indicates kth time iteration, and ρ > 0 is penalty factor, and u is sized Lagrange duality variable,It indicates
Set X=x | | | x | |∞≤TxOn projection operation, set C=c | | | SFc||∞≤Tc, FFTl() indicates to tie up lN
Vector first directly does Fast Fourier Transform (FFT), obtains corresponding frequency domain lN dimensional vector, then take the top n component of the vector, finally
It is sized to obtained N-dimensional vector progress, i.e., it is multiplied with constant 1/lN, IFFTl() expression is asked in anti-Fu of lN point of N-dimensional vector
Leaf transformation；
Solution 6b) is iterated until meeting stopping criterion for iteration to above-mentioned solution expression formula<6>, i.e., final is original residual
Surplus Ac-x and antithesis remnants variable xcurrent-xoldMeet simultaneously and presets value 10-5, obtain Optimized model<4>desired frequency
Domain symbol c and time-domain signal x；Wherein xcurrentIndicate the value of current x in iterative process, xoldIndicate the value of last time x；
7) the expectation frequency domain symbol c that step 6) obtains successively is passed through into IFFT conversion module and go here and there variation, plus circulation before
Sew, D A digital-to-analogue conversion and radio frequency amplification after launched by antenna.
Technical solution 3: the ofdm signal method for inhibiting peak-to-average ratio based on distributed implementation includes the following steps:
(I) system requirements is set are as follows: peak-to-average ratio threshold value of the time-domain signal peak-to-average ratio no more than the expectation symbol of setting
α, distorted signals is minimum, and idle sub-carrier peak amplitude is no more than idle sub-carrier amplitude peak thresholding Tc, and to guarantee channel
Estimation and signal synchronize and cannot have deviation, that is, require pilot sub-carrier to remain unchanged with original pilots subcarrier；
(II) original orthogonal frequency division multiplex OFDM frequency domain symbol c is inputtedo, co∈CN×1, N is sub-carrier number；
(III) initializaing variable is set, comprising: inversefouriertransform rotated factor matrix A ∈ ClN×N, useful sub-carrier selection
Matrix S ∈ RN×N, data subcarrier selection matrix SD∈RN×N, idle sub-carrier selection matrix SF∈RN×N, pilot sub-carrier selection
Matrix SP∈RN×N, unit matrix I ∈ RN×N, desired frequency domain symbol c ∈ CN×1, and time-domain signal x ∈ C corresponding with clN ×1, wherein N is OFDM sub-carrier number, and l is oversample factor；
(IV) according to system application and purpose, the peak-to-average ratio PAPR threshold value α ∈ of setting expectation symbol [1 ,+∞) and
Idle sub-carrier amplitude peak thresholding Tc；
(V) system requirements set according to step (I) establishes the following desired frequency domain symbol c and time-domain signal x of solution
Optimized model:
Wherein, | | x | |∞Indicate the Infinite Norm of vector x, | | x | |2Indicate 2 norms of vector x.
Optimization mould<7>is subjected to relaxation conversion and obtains following convex Optimized model<8>:
Wherein, parameter TxByApproximate calculation obtains, to the T in the convex Optimized modelxPass through alternating direction
Multiplier Algorithm iterative solution is updated；
(VI) the convex Optimized model that solution procedure (V) obtains obtains desired frequency domain symbol c and time-domain signal x:
(VI a) solves above-mentioned convex Optimized model<8>by alternating direction Multiplier Algorithm, obtains the solution of Optimized model<7>
Expression formula:
Wherein, k indicates kth time iteration, and ρ > 0 is penalty factor, and u is sized Lagrange duality variable,It indicates
Set X=x | | | x | |∞≤TxOn projection operation, set C1=c | | | SFc||∞≤Tc, C2=c | SPC=SPco,
FFTl() indicates first directly to do Fast Fourier Transform (FFT) to lN dimensional vector, obtains corresponding frequency domain lN dimensional vector, then take this to
The top n component of amount, it is finally sized to obtained N-dimensional vector progress, i.e., it is multiplied with constant 1/lN, IFFTlN is sought in () expression
The lN point inversefouriertransform of dimensional vector；
(VI b) is iterated solution until meeting stopping criterion for iteration to above-mentioned solution expression formula<9>, i.e., final is original
Residual volume Ac-x and antithesis remnants variable xcurrent-xoldMeet simultaneously and presets value 10-5, it is desired to obtain Optimized model<7>
Frequency domain symbol c and time-domain signal x；Wherein xcurrentIndicate the value of current x in iterative process, xoldIndicate the value of last time x；
(VII) the expectation frequency domain symbol c that step (VI) obtains successively is passed through into IFFT conversion module and go here and there variation, plus circulation
Prefix, D A digital-to-analogue conversion and radio frequency amplification after launched by antenna.
Compared with the prior art, the present invention has the following advantages:
First, due to present invention introduces various initializaing variables it is all unrelated with receiving end normal work, so without additional
Transmitted sideband information can be directly compatible with to receiving end, therefore using OFDM wireless system of the invention with existing standard.
Second, three models proposed by the present invention can be converted into convex Optimized model alternating side by convex relaxing techniques
It is solved to Multiplier Algorithm, and after solution, each variable all has analytic solutions, iterative process master in iteration each time
It to be completed by FFT twice, reduce computation complexity.
Third, due to FFT transform factor matrix relevant to ofdm signal be it is orthogonal, it is proposed by the present invention several
Model, iterative solution process can by parallel distributed be realized, to improve calculating speed.
Detailed description of the invention
The existing OFDM wireless system transmitting terminal structural block diagram of Fig. 1；
Fig. 2 is equipped with the OFDM wireless system transmitting terminal structural block diagram that the present invention inhibits signal peak-to-average ratio；
The flow chart of Fig. 3 present invention progress ofdm signal peak-to-average ratio inhibition；
Fig. 4 is figure compared with three kinds of methods of the invention carry out the effect of ofdm signal peak-to-average ratio inhibition with three kinds of methods of tradition；
Fig. 5 is compared with three kinds of methods of the invention carry out the bit error rate of ofdm signal peak-to-average ratio inhibition with three kinds of methods of tradition
Figure.
Specific embodiment
Referring to Fig.1, the method for existing OFDM wireless system transmitting terminal transmitting signal, be to original frequency domain symbol directly into
Row inversefouriertransform, obtains time-domain signal, and the time-domain signal is using serial to parallel conversion module and cyclic prefix module is added to become
Complete OFDM time-domain symbol, becomes analog signal for the complete OFDM time-domain symbol from D/A conversion module, finally by penetrating
Frequency amplification module is sent after amplifying the analog signal by antenna.
Referring to Fig. 2, the present invention is added before the inversefouriertransform module of existing OFDM wireless system transmitting end structure
Inhibit ofdm signal peak-to-average ratio module, i.e., by optimizing to OFDM frequency domain symbol, inhibition of the realization to signal peak-to-average ratio will
The OFDM frequency domain symbol of optimization becomes OFDM time-domain signal by IFFT module, the time-domain signal using serial to parallel conversion module and
Add cyclic prefix module to become complete OFDM time-domain symbol, is become the complete OFDM time-domain symbol from D/A conversion module
Analog signal is finally sent after RF Amplifier Module amplifies the analog signal by antenna.
According to practical application scene, OFDM wireless system is equipped with different system requirements, generally includes following three kinds of requirements
Situation:
The first requirement is: time-domain signal peak-to-average ratio is believed no more than the peak-to-average ratio threshold value α for it is expected symbol set
Number the smallest peak-to-average ratio of distortion inhibits；
Second of requirement is: peak-to-average ratio threshold value α of the time-domain signal peak-to-average ratio no more than the expectation symbol of setting, signal
It is distorted the smallest peak-to-average ratio to inhibit, and idle sub-carrier peak amplitude is no more than idle sub-carrier amplitude peak thresholding Tc；
The third requirement is: peak-to-average ratio threshold value α of the time-domain signal peak-to-average ratio no more than the expectation symbol of setting, signal
It is distorted the smallest peak-to-average ratio to inhibit, idle sub-carrier peak amplitude is no more than idle sub-carrier amplitude peak thresholding Tc, and to protect
The estimation and signal for demonstrate,proving channel, which synchronize, cannot deviation, that is, pilot sub-carrier is required to remain unchanged with original pilots subcarrier.
Referring to Fig. 3, the present invention provides the following three kinds of realities for realizing that ofdm signal peak-to-average ratio inhibits according to three kinds of system requirements
Apply example:
Embodiment 1: the peak-to-average ratio of the first corresponding system requirements inhibits.
Step 1, original OFDM symbols are inputted.
The frequency domain symbol of (1a) input is co, co∈CN×1, N is sub-carrier number, takes N=64 in this example；
The time-domain signal x of (1b) inputoIt indicates, xo∈ClN×1, by vector coLN point IFFT convert to obtain, wherein l is
Oversample factor takes l=4 in this example.
Step 2, initializaing variable is set.
(2a) is arranged in anti-Fu to indicate the relationship between frequency domain symbol and time-domain signal with the form of matrix multiple
Leaf transformation rotated factor matrix A ∈ ClN×N；
Useful sub-carrier selection matrix S ∈ R is arranged in order to indicate all kinds of subcarriers in OFDM symbol in (2b)N×N, data
Sub-carrier selection matrix SD∈RN×N, idle sub-carrier selection matrix SF∈RN×N, pilot sub-carrier selection matrix SP∈RN×NAnd
Unit matrix I ∈ RN×N, they are all diagonal matrix, and corresponding diagonal entry is set as 1 or 0, and value is related with subscript；
The symbol c ∈ C of (2c) setting expectation frequency domainN×1, after indicating by inhibiting the optimization of ofdm signal peak-to-average ratio module
OFDM frequency domain symbol, its corresponding time-domain signal be x ∈ ClN×1, wherein x=Ac.
Step 3, system parameter is set.
According to system application, the peak-to-average ratio threshold value α ∈ of setting expectation symbol [1 ,+∞) and idle sub-carrier maximum
Amplitude threshold Tc, it is respectively used to the constraint to peak-to-average ratio PAPR and idle sub-carrier power overhead FCPO.
Step 4, according to the system requirements of the present embodiment, desired frequency domain symbol c and time-domain signal x is calculated.
The system parameter that the initial signal and step 3 that (4a) is arranged according to step 2 are arranged establishes such as drag, and passes through pine
Relaxation conversion and ADMM iteratively solve to obtain desired frequency domain symbol c and time-domain signal x:
Relaxation is converted into convex Optimized model:
Constraint condition | | x | |∞≤Tx, Ac=x
Wherein, parameter TxByApproximate calculation obtains, to the T in the convex Optimized modelxPass through alternating direction
Multiplier Algorithm iterative solution is updated.
It obtains solving expression formula by alternating direction Multiplier Algorithm ADMM:
uk+1=uk+IFFTl(ck+1)-xk+1
Wherein, k indicates kth time iteration, and ρ > 0 is called penalty factor, and u is sized Lagrange duality variable,Table
Show convex set X=x | | | x | |∞≤TxOn projection operation, FFTl() first directly does fast Fourier change to lN dimensional vector
It changes, obtains corresponding frequency domain lN dimensional vector, then take the top n component of the vector, scale finally is carried out to obtained N-dimensional vector
Change, i.e., is multiplied with constant 1/lN.IFFTl() indicates to seek the lN point IFFT of N-dimensional vector.
(4b) is iterated solution until meeting stopping criterion for iteration, i.e., final original residual to above-mentioned solution expression formula
Measure Ac-x and antithesis remnants variable xcurrent-xoldMeet simultaneously and presets value 10-5, obtain Optimized model 1) and desired frequency domain
Symbol c and time-domain signal x；Wherein xcurrentIndicate the value of current x in iterative process, xoldIndicate the value of last time x.
Step 5, frequency domain symbol c obtained above is handled and is emitted.
By original frequency domain symbol coFrequency domain symbol c after step 4 is optimized obtains signal peak-to-average ratio fine
Inhibition；OFDM frequency domain symbol c is passed through IFFT module first again becomes OFDM time-domain symbol；Then the time-domain symbol is passed through
Serial to parallel conversion module and plus cyclic prefix module become complete OFDM time-domain symbol, then by the complete OFDM time-domain symbol
Become analog signal by D/A conversion module, finally sends the analog signal by antenna after RF Amplifier Module.
Embodiment 2: the peak-to-average ratio of corresponding second of system requirements inhibits.
Step 1 inputs original OFDM symbols.
(1.1) frequency domain symbol inputted is co, co∈CN×1, N is sub-carrier number, takes N=64 in this example；
(1.2) the time-domain signal x inputtedoIt indicates, xo∈ClN×1, by vector coLN point IFFT convert to obtain, wherein l
For oversample factor, l=4 is taken in this example.
Step 2, initializaing variable is set.
(2.1) in order to indicate the relationship between frequency domain symbol and time-domain signal with the form of matrix multiple, anti-Fu is set
In leaf transformation rotated factor matrix A ∈ ClN×N；
(2.2) in order to indicate all kinds of subcarriers in OFDM symbol, useful sub-carrier selection matrix S ∈ R is setN×N, data
Sub-carrier selection matrix SD∈RN×N, idle sub-carrier selection matrix SF∈RN×N, pilot sub-carrier selection matrix SP∈RN×NAnd
Unit matrix I ∈ RN×N, they are all diagonal matrix, and corresponding diagonal entry is set as 1 or 0, and value is related with subscript；
(2.3) the symbol c ∈ C of setting expectation frequency domainN×1, for indicating by inhibiting the optimization of ofdm signal peak-to-average ratio module
OFDM frequency domain symbol afterwards, its corresponding time-domain signal are x ∈ ClN×1, wherein x=Ac.
System parameter is arranged in step 3.
According to system application, the peak-to-average ratio threshold value α ∈ of setting expectation symbol [1 ,+∞) and idle sub-carrier maximum
Amplitude threshold Tc, it is respectively used to the constraint to peak-to-average ratio PAPR and idle sub-carrier power overhead FCPO.
Step 4 calculates desired frequency domain symbol c and time-domain signal x according to the system requirements of the present embodiment.
(4.1) such as drag is established according to the system parameter of the initial signal of step 2 setting and step 3 setting, and led to
It crosses relaxation conversion and ADMM iteratively solves to obtain desired frequency domain symbol c and time-domain signal x:
Relaxation is converted into convex Optimized model:
Constraint condition | | x | |∞≤Tx, | | SFc||∞≤Tc, Ac=x
Wherein, parameter TxByApproximate calculation obtains, to the T in the convex Optimized modelxPass through alternating direction
Multiplier Algorithm iterative solution is updated；
It obtains solving expression formula by alternating direction Multiplier Algorithm ADMM:
uk+1=uk+IFFTl(ck+1)-xk+1
Wherein, k indicates kth time iteration, and ρ > 0 is called penalty factor, and u is sized Lagrange duality variable,Table
Show convex set X=x | | | x | |∞≤TxOn projection operation, set C=c | | | SFc||∞≤Tc, FFTl() ties up lN
Vector first directly does Fast Fourier Transform (FFT), obtains corresponding frequency domain lN dimensional vector, then take the top n component of the vector, finally
It is sized to obtained N-dimensional vector progress, i.e., it is multiplied with constant 1/lN.IFFTl() indicates to seek the lN point IFFT of N-dimensional vector.
(4.2) solution is iterated until meeting stopping criterion for iteration to above-mentioned solution expression formula, i.e., final is original residual
Surplus Ac-x and antithesis remnants variable xcurrent-xoldMeet simultaneously and presets value 10-5, obtain Optimized model 2) and desired frequency
Domain symbol c and time-domain signal x；Wherein xcurrentIndicate the value of current x in iterative process, xoldIndicate the value of last time x；
Frequency domain symbol c obtained above is handled and is emitted by step 5.
By original frequency domain symbol coFrequency domain symbol c after step 4 is optimized obtains signal peak-to-average ratio fine
Inhibition；Frequency domain symbol c is passed through IFFT module first again becomes OFDM time-domain symbol,；Then by the time-domain symbol by going here and there
And conversion module and plus cyclic prefix module become complete OFDM time-domain symbol；Then the complete OFDM time-domain symbol is led to
Crossing D/A conversion module becomes analog signal；Finally the analog signal is sent after RF Amplifier Module by antenna.
Embodiment 3: the peak-to-average ratio of the third corresponding system requirements inhibits.
Step I inputs original OFDM symbols.
I frequency domain symbol a) inputted is co, co∈CN×1, N is sub-carrier number, takes N=64 in this example；
I time-domain signal x b) inputtedoIt indicates, xo∈ClN×1, by vector coLN point IFFT convert to obtain, wherein l is
Oversample factor takes l=4 in this example.
Initializaing variable is arranged in step II.
II, a) in order to indicate the relationship between frequency domain symbol and time-domain signal with the form of matrix multiple, is arranged in anti-Fu
Leaf transformation rotated factor matrix A ∈ ClN×N；
II, b) in order to indicate all kinds of subcarriers in OFDM symbol, is arranged useful sub-carrier selection matrix S ∈ RN×N, data
Sub-carrier selection matrix SD∈RN×N, idle sub-carrier selection matrix SF∈RN×N, pilot sub-carrier selection matrix SP∈RN×NAnd
Unit matrix I ∈ RN×N, they are all diagonal matrix, and corresponding diagonal entry is set as 1 or 0, and value is related with subscript；
II c) is arranged the symbol c ∈ C of expectation frequency domainN×1, after indicating by inhibiting the optimization of ofdm signal peak-to-average ratio module
OFDM frequency domain symbol, its corresponding time-domain signal be x ∈ ClN×1, wherein x=Ac.
Step III, system parameter is set.
According to system application, the peak-to-average ratio threshold value α ∈ of setting expectation symbol [1 ,+∞) and idle sub-carrier maximum
Amplitude threshold Tc, it is respectively used to the constraint to peak-to-average ratio PAPR and idle sub-carrier power overhead FCPO.
Step IV, according to the system requirements of the present embodiment, desired frequency domain symbol c and time-domain signal x is calculated.
IV a) establishes such as drag according to the system parameter that the initial signal of step II setting and step III are arranged, and passes through
Relaxation conversion and ADMM iteratively solve to obtain desired frequency domain symbol c and time-domain signal x:
Relaxation is converted into convex Optimized model:
Constraint condition | | x | |∞≤Tx, | | SFc||∞≤Tc, SPC=SPco, Ac=x
Wherein, parameter TxByApproximate calculation obtains, to the T in the convex Optimized modelxPass through alternating direction
Multiplier Algorithm iterative solution is updated.
It obtains solving expression formula by alternating direction Multiplier Algorithm ADMM:
uk+1=uk+IFFTl(ck+1)-xk+1
Wherein, k indicates kth time iteration, and ρ > 0 is called penalty factor, and u is sized Lagrange duality variable,Table
Show convex set X=x | | | x | |∞≤TxOn projection operation,Indicate the projection operation on set C, set C=C1∩
C2, set C1=c | | | SFc||∞≤Tc, C2=c | SPC=SPco, FFTl() is first directly in quick Fu lN dimensional vector
Leaf transformation obtains corresponding frequency domain lN dimensional vector, then takes the top n component of the vector, finally carries out ruler to obtained N-dimensional vector
Degreeization is multiplied with constant 1/lN.IFFTl() indicates to seek the lN point IFFT of N-dimensional vector.
IV b) is iterated solution until meeting stopping criterion for iteration, i.e., final original residual to above-mentioned solution expression formula
Measure Ac-x and antithesis remnants variable xcurrent-xoldMeet simultaneously and presets value 10-5, obtain Optimized model 3) and desired frequency domain
Symbol c and time-domain signal x；Wherein xcurrentIndicate the value of current x in iterative process, xoldIndicate the value of last time x；
Step V, frequency domain symbol c obtained above is handled and is emitted.
By original frequency domain symbol coFrequency domain symbol c after step 4 is optimized obtains signal peak-to-average ratio fine
Inhibition, then frequency domain symbol c passed through into IFFT module first become OFDM time-domain symbol；Then by the time-domain symbol by going here and there simultaneously
Conversion module and plus cyclic prefix module become complete OFDM time-domain symbol；Then the complete OFDM time-domain symbol is passed through
D/A conversion module becomes analog signal；Finally the analog signal is sent after RF Amplifier Module by antenna.
Effect of the invention is described further below by emulation experiment:
1. simulated conditions
Matlab 7.11.0 simulation software is used, 5000 ofdm signals are emulated, transmission channel is to add
Property Gaussian white noise channel；Input is ofdm signal as defined in IEEE802.11a standard, and the sub-carrier number of these signals takes N
=64, wherein useful sub-carrier number is 52, including 48 data subcarriers and 4 pilot sub-carriers；Idle sub-carrier number is 12,
The content and its distribution situation that wherein each subcarrier carries are as shown in table 1；The modulation system of ofdm signal is binary phase
BPSK modulation, oversample factor take l=4；The peak-to-average ratio thresholding α of system is set as 3dB, the amplitude peak thresholding of idle sub-carrier
TcIt is set as 0, the back-off of nonlinear amplifier is set as 3.5dB.
1 ofdm signal subcarrier distribution schematic diagram of table
| Subcarrier serial number | Subcarrier carries content |
| - 32 ... -27,26 ... 31 | Idle sub-carrier, zero-signal |
| - 26 ... -22,22 ... 25 | Data-signal |
| - 21,21 | Pilot signal |
| - 20 ... -8,8 ... 20 | Data-signal |
| - 7,7 | Pilot signal |
| - 6 ... 0,1 ... 6 | Data-signal |
2. emulation content
Emulation 1: three kinds of method for inhibiting peak-to-average ratio of the invention and traditional three kinds of method for inhibiting peak-to-average ratio are imitated respectively
Fruit emulation obtains complementary accumulative density function CCDF curve, as a result as shown in Figure 4.Wherein, ADMM1, ADMM2 and ADMM3 distinguish
Indicate that three kinds of method for inhibiting peak-to-average ratio of the invention, RCF, TR and SOCP respectively indicate three kinds of traditional method for inhibiting peak-to-average ratio.
Emulation 2: progressive is distinguished to three kinds of method for inhibiting peak-to-average ratio of three kinds of method for inhibiting peak-to-average ratio of the invention and tradition
It can emulate, the emulation for obtaining bit error rate BER performance curve is compared, as a result as shown in Figure 5.Wherein, ADMM1, ADMM2 and
ADMM3 respectively indicates three kinds of method for inhibiting peak-to-average ratio of the invention, and RCF, TR and SOCP respectively indicate three kinds of traditional peak-to-average ratios
Suppressing method.
3. simulation result
Relative to original ofdm system it can be seen from the simulation result of Fig. 4, although three kinds of methods of the invention and tradition
Three kinds of methods all inhibit ofdm system peak-to-average ratio, still, the amplitude that three kinds of methods of the invention reduce peak-to-average ratio is maximum, and
And it can satisfy pre-set PAPR thresholding constraint, and system peak-to-average ratio is inhibited a very little model near PAPR threshold value
In enclosing, so that system peak-to-average ratio is stable and has controllability.
By the simulation result of Fig. 5 it is found that by nonlinear power amplifier, and believed by identical additive white Gaussian noise
Road, under the conditions of identical signal-to-noise ratio, the bit error rate of the ofdm signal after the present invention is handled is minimum, and error performance is most for receiving end
It is good, illustrate that the present invention can be while reducing system peak-to-average ratio by distorted signals minimum.
Table 2 gives the various method iterative solution primary required times for inhibiting peak-to-average ratio.As can be seen from Table 2, originally
Compared with other inhibit peak-to-average ratio convex optimization method, an iteration is short the time required to calculating for invention, illustrates that invention achieves elder generations
The effect of the reduction complexity of preceding anticipation, this is also exactly sharpest edges place of the invention.
The time required to the various method an iterations of table 2
Claims (6)
1. the ofdm signal method for inhibiting peak-to-average ratio based on distributed implementation, includes the following steps:
(1) system requirements is set are as follows: the peak-to-average ratio threshold value α of the expectation symbol of time-domain signal peak-to-average ratio no more than setting, and
Distorted signals is minimum；
(2) original orthogonal frequency division multiplex OFDM frequency domain symbol c is inputtedo, co∈CN×1, N is sub-carrier number, and C indicates complex field set；
(3) initializaing variable is set, comprising: inversefouriertransform rotated factor matrix A ∈ ClN×N, useful sub-carrier selection matrix S
∈RN×N, data subcarrier selection matrix SD∈RN×N, idle sub-carrier selection matrix SF∈RN×N, pilot sub-carrier selection matrix
SP∈RN×N, unit matrix I ∈ RN×N, desired frequency domain symbol c ∈ CN×1And frequency domain symbol coCorresponding time-domain signal xo∈ClN ×1, and time-domain signal x ∈ C corresponding with desired frequency domain symbol clN×1, wherein N be OFDM sub-carrier number, l be over-sampling because
Son, R indicate real number field set, and C indicates complex field set；
(4) according to system application and purpose, the peak-to-average ratio PAPR threshold value α ∈ of setting expectation symbol [1 ,+∞) and it is idle
Subcarrier amplitude peak thresholding Tc；
(5) according to the system requirements set in step (1), the excellent of the following desired frequency domain symbol c and time-domain signal x of solution is established
Change model:
Wherein, | | x | |∞Indicate the Infinite Norm of vector x, | | x | |2Indicate 2 norms of vector x；
Optimized model<1>is subjected to relaxation conversion and obtains following convex Optimized model<2>:
Wherein, parameter TxByApproximate calculation obtains, to the T in the convex Optimized modelxPass through alternating direction multiplier
Algorithm iteration solution is updated；
(6) the convex Optimized model that solution procedure (5) obtains obtains desired frequency domain symbol c and time-domain signal x:
(6a) solves above-mentioned convex Optimized model<2>by alternating direction Multiplier Algorithm, obtains the solution expression of Optimized model<1>
Formula:
Wherein, k indicates kth time iteration, and ρ > 0 is penalty factor, and u is sized Lagrange duality variable,Expression is collecting
Conjunction X=x | | | x | |∞≤TxOn projection operation, FFTl() indicates first directly to do Fast Fourier Transform (FFT) to lN dimensional vector,
Corresponding frequency domain lN dimensional vector is obtained, then takes the top n component of the vector, it is finally sized to obtained N-dimensional vector progress, i.e.,
It is multiplied with constant 1/lN, IFFTl() indicates to seek the lN point inversefouriertransform of N-dimensional vector；
(6b) is iterated solution until meeting stopping criterion for iteration, i.e., final original residual to above-mentioned solution expression formula<3>
Measure Ac-x and antithesis remnants variable xcurrent-xoldMeet simultaneously and presets value 10-5, obtain Optimized model<1>desired frequency domain
Symbol c and time-domain signal x；Wherein xcurrentIndicate the value of current x in iterative process, xoldIndicate the value of last time x；
(7) the expectation frequency domain symbol c that step (6) obtains successively is passed through into IFFT conversion module and go here and there variation, plus cyclic prefix,
D A digital-to-analogue conversion and radio frequency amplification after launched by antenna.
2. according to the method described in claim 1, carrying out the conversion that relaxes to Optimized model<1>in its step (5), as follows
It carries out:
(5a) is by objective functionIt is reduced to
(5b) is by non-convex constraintRelaxation is that convex clipping constrains | | x | |∞≤Tx；
(5c) finally obtains the convex Optimized model<2>after relaxation conversion.
3. the ofdm signal method for inhibiting peak-to-average ratio based on distributed implementation, includes the following steps:
1) system requirements is set are as follows: peak-to-average ratio threshold value α of the time-domain signal peak-to-average ratio no more than the expectation symbol of setting, signal
Distortion is minimum, and idle sub-carrier peak amplitude is no more than idle sub-carrier amplitude peak thresholding Tc；
2) original orthogonal frequency division multiplex OFDM frequency domain symbol c is inputtedo, co∈CN×1, N is sub-carrier number, and C indicates complex field set；
3) initializaing variable is set, comprising: inversefouriertransform rotated factor matrix A ∈ ClN×N, useful sub-carrier selection matrix S ∈
RN×N, data subcarrier selection matrix SD∈RN×N, idle sub-carrier selection matrix SF∈RN×N, pilot sub-carrier selection matrix SP
∈RN×N, unit matrix I ∈ RN×N, desired frequency domain symbol c ∈ CN×1, with frequency domain symbol coCorresponding time-domain signal xo∈ClN×1、
And time-domain signal x ∈ C corresponding with desired frequency domain symbol clN×1, wherein N is OFDM sub-carrier number, and l is oversample factor,
R indicates real number field set, and C indicates complex field set；
4) according to system application and purpose, the peak-to-average ratio PAPR threshold value α ∈ of setting expectation symbol [1 ,+∞) and the free time it is sub
Carrier wave amplitude peak thresholding Tc；
5) the following optimization for solving desired frequency domain symbol c and time-domain signal x is established according to the system requirements set in step 1)
Model:
Wherein, | | x | |∞Indicate the Infinite Norm of vector x, | | x | |2Indicate 2 norms of vector x；
Optimized model<4>is subjected to relaxation conversion and obtains following convex Optimized model<5>:
Wherein, parameter TxByApproximate calculation obtains, to the T in the convex Optimized modelxPass through alternating direction multiplier
Algorithm iteration solution is updated；
6) solution procedure 5) obtained convex Optimized model, obtain desired frequency domain symbol c and time-domain signal x:
Above-mentioned convex Optimized model<5>6a) is solved by alternating direction Multiplier Algorithm, obtains the solution expression formula of Optimized model<4>:
Wherein, k indicates kth time iteration, and ρ > 0 is penalty factor, and u is sized Lagrange duality variable,Expression is collecting
Conjunction X=x | | | x | |∞≤TxOn projection operation,It indicates in set C1On projection operation, set C1=c | | | SF||c|
|∞≤Tc, FFTl() indicates first directly to do Fast Fourier Transform (FFT) to lN dimensional vector, obtains corresponding frequency domain lN dimensional vector, then
The top n component of the vector is taken, it is finally sized to obtained N-dimensional vector progress, i.e., it is multiplied with constant 1/lN, IFFTl(·)
The lN point inversefouriertransform of N-dimensional vector is sought in expression；
Solution 6b) is iterated until meeting stopping criterion for iteration, i.e., final original residual amount to above-mentioned solution expression formula<6>
Ac-x and antithesis remnants variable xcurrent-xoldMeet simultaneously and presets value 10-5, obtain the desired frequency domain symbol of Optimized model<4>
Number c and time-domain signal x；Wherein xcurrentIndicate the value of current x in iterative process, xoldIndicate the value of last time x；
7) the expectation frequency domain symbol c that step 6) obtains successively is passed through into IFFT conversion module and go here and there variation, plus cyclic prefix, D A
Launched after digital-to-analogue conversion and radio frequency amplification by antenna.
4. according to the method described in claim 3, carrying out the conversion that relaxes to Optimized model<4>in its step 5), as follows
It carries out:
5a) by objective functionIt is reduced to
5b) by non-convex constraintRelaxation is that convex clipping constrains | | x | |∞≤Tx；
Convex Optimized model<5>after 5c) finally obtaining relaxation conversion.
5. the ofdm signal method for inhibiting peak-to-average ratio based on distributed implementation, includes the following steps:
(I) system requirements is set are as follows: peak-to-average ratio threshold value α of the time-domain signal peak-to-average ratio no more than the expectation symbol of setting, letter
Number distortion is minimum, and idle sub-carrier peak amplitude is no more than idle sub-carrier amplitude peak thresholding Tc, and to guarantee estimating for channel
Meter and signal, which synchronize, cannot deviation, that is, pilot sub-carrier is required to remain unchanged with original pilots subcarrier；
(II) original orthogonal frequency division multiplex OFDM frequency domain symbol c is inputtedo, co∈CN×1, N is sub-carrier number, and C indicates complex field collection
It closes；
(III) initializaing variable is set, comprising: inversefouriertransform rotated factor matrix A ∈ ClN×N, useful sub-carrier selection matrix S
∈RN×N, data subcarrier selection matrix SD∈RN×N, idle sub-carrier selection matrix SF∈RN×N, pilot sub-carrier selection matrix
SP∈RN×N, unit matrix I ∈ RN×N, desired frequency domain symbol c ∈ CN×1, with frequency domain symbol coCorresponding time-domain signal xo∈ClN ×1And time-domain signal x ∈ C corresponding with desired frequency domain symbol clN×1, wherein N be OFDM sub-carrier number, l be over-sampling because
Son, R indicate real number field set, and C indicates complex field set；
(IV) according to system application and purpose, the peak-to-average ratio PAPR threshold value α ∈ of setting expectation symbol [1 ,+∞) and it is idle
Subcarrier amplitude peak thresholding Tc；
(V) system requirements set according to step (I) establishes the excellent of the following desired frequency domain symbol c and time-domain signal x of solution
Change model:
Wherein, | | x | |∞Indicate the Infinite Norm of vector x, | | x | |2Indicate 2 norms of vector x；
Optimized model<7>is subjected to relaxation conversion and obtains following convex Optimized model<8>:
Wherein, parameter TxByApproximate calculation obtains, to the T in the convex Optimized modelxPass through alternating direction multiplier
Algorithm iteration solution is updated；
(VI) the convex Optimized model that solution procedure (V) obtains obtains desired frequency domain symbol c and time-domain signal x:
(VI a) solves above-mentioned convex Optimized model<8>by alternating direction Multiplier Algorithm, obtains the solution expression of Optimized model<7>
Formula:
Wherein, k indicates kth time iteration, and ρ > 0 is penalty factor, and u is sized Lagrange duality variable,Expression is collecting
Conjunction X=x | | | x | |∞≤TxOn projection operation,It indicates in set C2On projection operation, set C2=C1∩C2, set
C1=c | | | SFc||∞≤Tc, C2=c | SPC=SPco, FFTl() indicates first directly to do fast Fourier to lN dimensional vector
Transformation, obtains corresponding frequency domain lN dimensional vector, then take the top n component of the vector, finally carries out scale to obtained N-dimensional vector
Change, i.e., is multiplied with constant 1/lN, IFFTl() indicates to seek the lN point inversefouriertransform of N-dimensional vector；
(VI b) is iterated solution until meeting stopping criterion for iteration, i.e., final original residual to above-mentioned solution expression formula<9>
Measure Ac-x and antithesis remnants variable xcurrent-xoldMeet simultaneously and presets value 10-5, obtain Optimized model<7>desired frequency domain
Symbol c and time-domain signal x；Wherein xcurrentIndicate the value of current x in iterative process, xoldIndicate the value of last time x；
(VII) the expectation frequency domain symbol c that step (VI) obtains successively is passed through into IFFT conversion module and go here and there variation, plus circulation before
Sew, D A digital-to-analogue conversion and radio frequency amplification after launched by antenna.
It is right in step (V) 6. the ofdm signal method for inhibiting peak-to-average ratio based on distributed implementation according to claim 5
Optimized model<7>carries out the conversion that relaxes, and carries out as follows:
(V a) is by objective functionIt is reduced to
(V b) is by non-convex constraintRelaxation is that convex clipping constrains | | x | |∞≤Tx；
(V c) finally obtains the convex Optimized model<8>after relaxation conversion.
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| CN110210094B (en) * | 2019-05-23 | 2021-02-12 | 浙江大学 | FBMC signal PAPR reduction method based on punishment concave-convex process |
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| CN113315732B (en) * | 2021-05-28 | 2022-11-25 | 江苏科技大学 | Low-complexity method suitable for reducing peak-to-average power ratio of MIMO-OFDM system |
| CN114124637B (en) * | 2021-11-25 | 2024-02-27 | 江苏科技大学 | Low-complexity method suitable for reducing peak-to-average ratio of OFDM (orthogonal frequency division multiplexing) system |
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