CN101867549A - Suppression method for OFDM signal peak-to-average power ratio based on positive semi-definite programming technique - Google Patents

Abstract

The invention discloses a suppression method of an OFDM signal peak-to-average power ratio based on a positive semi-definite programming technique, mainly aiming at solving the defect of poor performance of suppressing OFDM system peak-to-average power ratio by the existing method. In the invention, a semi-definite convex optimization model specially designed is solved through setting any one of an OFDM system peak-to-average power ratio threshold, the ratio threshold of free subcarrier power and system total power and error vector amplitude threshold of OFDM signal distortion which meet the requirements of a situation in which the system is located at the transmitting terminal of an OFDM wireless system, and combining original OFDM frequency domain symbols and relevant initial variable quantity, thereby obtaining new OFDM frequency domain symbols, i.e. the expected OFDM frequency domain symbols; and the expected OFDM frequency domain symbols are transmitted out via an antenna after being subject to IFFT, parallel-to-serial change, cyclic prefix adding, D/A conversion and radio frequency amplification. The OFDM domain symbols provided by the invention to the OFDM system can be directly compatible with the existing standard, and effectively inhibits OFDM system peak-to-average power ratio.

Description

Ofdm signal method for inhibiting peak-to-average ratio based on the positive semidefinite planning technology

Technical field

The invention belongs to wireless technical field, relate to orthogonal frequency division multiplexi OFDM, optimize the OFDM frequency domain symbol by using the positive semidefinite planning technology specifically, be used to reduce the peak-to-average ratio of ofdm signal, improve system power efficient.

Background technology

At wireless transmitting system intermediate power amplifier (hereinafter to be referred as power amplifier) is indispensable parts, and its input-output characteristic curve has nonlinear feature.The zone that makes input signal produce very little nonlinear distortion saturation point rollback 2-3dB on the power amplifier input-output characteristic curve is called the linear work zone; Be called the nonlinear operation zone and will approach the zone that saturation point makes input signal produce obvious nonlinear distortion.When power amplifier was operated in nonlinear area, the power amplifier power efficiency was higher but amplifying signal can produce tangible nonlinear distortion; When being operated in the range of linearity, power amplification efficiency is lower but signal distortion is little.Thereby in wireless communications application, improve power efficiency and the distorted signals that reduces to produce owing to the power amplifier nonlinear characteristic, usually show as the contradiction of a pair of difficult mediation.

Because have advantages such as availability of frequency spectrum height, ability of anti-multipath are strong, the OFDM technology is adopted as physical layer core transmission technology by the various wireless communication standard.As shown in Figure 1, original OFDM wireless system transmitting terminal mainly comprises OFDM frequency-region signal to be sent, inverse-Fourier transform IFFT module, and the serial to parallel conversion module is added cyclic prefix module, and D/A modular converter and RF Amplifier Module are finally gone out by antenna transmission.But if directly adopt said method, very high peak-to-average ratio may appear in ofdm signal, and high peak-to-average ratio can reduce the power efficiency of power amplifier.Therefore a major defect of ofdm signal is that its time-domain signal exists higher peak-to-average ratio PAPR.This is that instantaneous peak value can appear in its corresponding time domain waveform because when a plurality of sub-carrier phase are same or similar.The just approximate Gaussian Profile that presents of OFDM time-domain signal level value when number of sub carrier wave is more, i.e. the probability that the likelihood ratio low level signal of high level signal appearance occurs is much smaller.Yield to the very little high level signal of probability of occurrence if avoid ofdm signal nonlinear distortion to occur, dynamic range of signals is limited in the linear work district of power amplifier, can cause power amplification efficiency very low.If guarantee power amplification efficiency its working point is pushed away nearly saturation point, then can cause the high level signal in the ofdm signal to produce tangible nonlinear distortion.This nonlinear distortion not only can be destroyed the orthogonality between the subcarrier and worsen system's error performance, also can form out of band spectrum regeneration and disturb other wireless systems.

The method of conventional inhibition ofdm signal PAPR has repetition shearing and filtering RCF, coding Coding, and partial sequence transmission method PTS, selectivity mapping SLM, the Interleaving that interweaves, carrier wave is reserved TR, dynamic constellation extension ACE etc.But conventional method all can't obtain more performance because of the shortcoming of himself in existing ofdm system.Such as repeating shearing and filtering method RCF, because it is that a distortion process just will inevitably produce out-of-band radiation and inband distortion, can reduce out-of-band radiation and inband distortion though carry out the repetition shearing and filtering, because of the effect of the regeneration amplitude inhibition PAPR that can't obtain; Coding Coding often is subjected to the restriction of code efficiency and decoding complex degree, makes range of application be restricted; The shortcoming of partial sequence transmission method PTS and selectivity mapping SLM maximum is to take the special transmitted sideband information of some carrier waves, makes channel efficiency reduce; Carrier wave is reserved TR and is reserved some carrier waves in order to special inhibition PAPR, but this method has reduced channel efficiency equally.Table 1 has been listed the principal character of these methods.

The conventional ofdm signal PAPR of table 1 inhibition method relatively

	Whether need side information	Algorithm complex	Distorted signals	PAPR suppresses effect
					??RCF	Not	Low	Be	Difference
??Coding	Not	High	Not	Good
					??PTS	Be	Higher	Not	In
??SLM	Be	Higher	Not	In
					??Interleaving	Be	Higher	Not	In
??TR	Not	In	Not	In
					??ACE	Not	In	Be	In

By table 1 as seen, though the PAPR problem of ofdm signal is known by industry, and there is multiple solution, but or owing to need extra side information exist can not with the operating such problem, or, still can not satisfy the demand of modern wireless communication systems because algorithm complex limits and only is suitable for the less occasion of sub-carrier number.

Summary of the invention

The objective of the invention is to overcome the deficiency of above-mentioned prior art, a kind of ofdm signal method for inhibiting peak-to-average ratio based on the positive semidefinite planning technology has been proposed, this method does not need transmitted sideband information, can be directly compatible with the prior art standard, and to satisfy the demand of modern wireless communication systems.

Technical scheme of the present invention is: embed OFDM frequency domain symbol optimal module before the inverse-Fourier transform module of original OFDM wireless transmitting system, any two threshold values in the ratio thresholding of peak-to-average ratio thresholding, idle sub-carrier power and system's gross power of the ofdm signal by setting expectation and the Error Vector Magnitude thresholding of OFDM signal distortion, unite original OFDM frequency domain symbol, the optimization problem of OFDM symbol is converted into the protruding Optimization Model of positive semidefinite, by the OFDM frequency domain symbol after this model solution is optimized.Adopt the OFDM emission system of optimal module to have lower peak-to-average ratio and distorted signals.The specific implementation step is as follows:

(1) the original OFDM frequency domain symbol f of input _o,

N is a sub-carrier number;

(2) initializaing variable is set, comprises: the inversefouriertransform rotated factor matrix

The carrier wave selection matrix

Companion matrix

Unit matrix

With

The expectation symbol Expectation symbol peaks p and empirical parameter w, wherein N is the OFDM sub-carrier number, l is an oversample factor;

(3) according to the initial auxiliary variable F=f ' f ' of initial symbol f ' calculating ^H

(4) according to system applies occasion and purpose, set peak-to-average ratio thresholding α ∈ [1 ,+∞), the ratio thresholding β ∈ of idle sub-carrier power and system's gross power [0,1) and the Error Vector Magnitude thresholding ε ∈ of OFDM signal distortion [0 ,+∞);

(5), calculate peak-to-average ratio auxiliary variable G according to above-mentioned each initializaing variable and threshold value _i, idle sub-carrier power and the gross power ratio auxiliary variable G of system _Nl+1, B _Nl+1, peak value auxiliary variable B _i, signal distortion auxiliary variable P _GapWith idle sub-carrier auxiliary variable P _Free, wherein, i=1 ..., lN;

(6) according to system requirements, the relevant auxiliary variable of utilizing step (5) to be calculated calculates expectation symbol f ':

If the ratio of system requirements system peak-to-average ratio and idle sub-carrier power and system's gross power is satisfying under the prerequisite that limits thresholding, the signal distortion minimum is then utilized peak-to-average ratio auxiliary variable G _i, idle sub-carrier power and system's gross power ratio auxiliary variable G _Nl+1And signal distortion auxiliary variable P _Gap, obtain expecting symbol f ' by finding the solution the protruding Optimization Model of following positive semidefinite:

Target function:

Constraints: s.t.Tr (G _iF) 〉=0 i=1 ..., lN+1,1)

$\left[\begin{array}{cc}F& f^{\&prime;}\\ f^{\&prime;\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HSA00000158303400031.png,HSA00000158303400032.png"\; state="\{\{state\}\}">H</figure-callout>}}& 1\end{array}\right]\&GreaterEqual;0$

Tr () representing matrix trace function wherein;

If the ratio of system requirements idle sub-carrier power and system's gross power, and the Error Vector Magnitude of OFDM signal distortion satisfy to limit under the prerequisite of thresholding, the peak value minimum is then utilized the auxiliary variable B of idle sub-carrier power and system's gross power ratio _Nl+1, the OFDM signal distortion Error Vector Magnitude thresholding ε and peak value auxiliary variable B _i, obtain expecting symbol f ' by finding the solution the protruding Optimization Model of following positive semidefinite:

Target function:

Constraints: s.t.Tr (B _iF)≤p i=1 ..., lN

$\mathrm{Tr}\left(\mathrm{SF}\right)-2\mathrm{Re}\left(f_o^H{\mathrm{Sf}}^{\&prime;}\right)\&le;({\mathrm{\&epsiv;}}^2-1){\left|\right|{\mathrm{Sf}}_o\left|\right|}_2^2,---2)$

Tr(B _lN+1F)≤0

$\left[\begin{array}{cc}F& f^{\&prime;}\\ f^{\&prime;\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HSA00000158303400031.png,HSA00000158303400032.png"\; state="\{\{state\}\}">H</figure-callout>}}& 1\end{array}\right]\&GreaterEqual;0$

Wherein real is got in Re () expression;

If the Error Vector Magnitude of system requirements system peak-to-average ratio and OFDM signal distortion is satisfying under the prerequisite that limits thresholding, idle sub-carrier power minimum is then utilized peak-to-average ratio auxiliary variable G _i, the OFDM signal distortion Error Vector Magnitude thresholding ε and idle sub-carrier auxiliary variable P _Free, obtain expecting symbol f ' by finding the solution the protruding Optimization Model of following positive semidefinite:

Target function:

Constraints: s.t.Tr (G _iF) 〉=0 i=1 ..., lN

$\mathrm{Tr}\left(\mathrm{SF}\right)-2\mathrm{Re}\left(f_o^H{\mathrm{Sf}}^{\&prime;}\right)\&le;({\mathrm{\&epsiv;}}^2-1){\left|\right|{\mathrm{Sf}}_o\left|\right|}_2^2;---3)$

$\left[\begin{array}{cc}F& f^{\&prime;}\\ f^{\&prime;\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HSA00000158303400031.png,HSA00000158303400032.png"\; state="\{\{state\}\}">H</figure-callout>}}& 1\end{array}\right]\&GreaterEqual;0$

(7) f ' that step (6) is obtained successively through IFFT, and string change, add Cyclic Prefix, D A conversion and radio frequency amplify the back and launch by antenna.

Because the various initializaing variables that the present invention introduces are all irrelevant with the receiving terminal operate as normal, so just do not need extra transmitted sideband information to give receiving terminal, therefore using OFDM wireless system of the present invention can be directly compatible with existing standard.

Description of drawings

Fig. 1 has OFDM wireless system transmitting terminal structured flowchart now;

Fig. 2 OFDM wireless system of the present invention transmitting terminal structured flowchart;

The flow chart that Fig. 3 the present invention is optimized the OFDM frequency domain symbol of OFDM wireless system transmitting terminal;

Fig. 4 is the flow chart that the OFDM frequency domain symbol is optimized with existing RCF method;

Fig. 5 is by finding the solution the protruding Optimization Model of positive semidefinite of the present invention, repeat shearing and filtering method RCF and Aggarwal method, obtaining the complementation accumulative total density function CCDF emulation comparison diagram of system's peak-to-average ratio of OFDM frequency domain symbol correspondence;

Fig. 6 is by finding the solution the protruding Optimization Model of positive semidefinite of the present invention, repeat shearing and filtering method RCF and Aggarwal method, obtaining the bit error rate BER emulation comparison diagram of OFDM frequency domain symbol correspondence.

Embodiment

With reference to Fig. 2, the present invention adds OFDM frequency domain symbol optimal module before the inverse-Fourier transform module of existing OFDM wireless system transmitting terminal structure, utilize this module that the OFDM frequency domain symbol is optimized, the OFDM frequency domain symbol of optimizing is become the OFDM time-domain symbol by the IFFT module, this time-domain symbol is passed through the serial to parallel conversion module again and added cyclic prefix module becomes complete OFDM time-domain symbol, by the D/A modular converter this complete OFDM time-domain symbol is become analog signal, go out by antenna transmission after the process RF Amplifier Module amplifies this analog signal at last.

With reference to Fig. 3, the step that the present invention is optimized the OFDM frequency domain symbol comprises as follows:

Step 1 is imported original OFDM frequency domain symbol f _o

Step 2 is provided with initializaing variable.

In order to obtain the auxiliary variable of the protruding optimization formula of positive semidefinite, at first following initializaing variable should be set:

The inversefouriertransform rotated factor matrix

The carrier wave selection matrix

And companion matrix

Unit matrix

With

The expectation symbol

And expectation symbol peaks p provides initializaing variable for subsequent step calculates;

Empirical parameter w;

N is the OFDM sub-carrier number, and l is an oversample factor.

Step 3, the expectation symbol f ' according to step 2 provides calculates initial auxiliary variable: F=f ' f ' ^H

Step 4 according to system applies occasion and purpose, is set the ofdm system parameter threshold value of expectation.

Setting peak-to-average ratio thresholding α ∈ [1 ,+∞);

The ratio thresholding β ∈ of setting idle sub-carrier power and system's gross power [0,1);

The Error Vector Magnitude thresholding ε ∈ of setting OFDM signal distortion [0 ,+∞);

In the real system, system's peak-to-average ratio is low more, and system power is just high more, but systematic distortion is also big more, therefore should take all factors into consideration various factors to reach systematic function the best when setting thresholding.

Step 5 according to the threshold value that the initialize signal and the step 4 of step 2 setting are set, is calculated relevant auxiliary variable.

The peak-to-average ratio auxiliary variable of characterization system peak-to-average ratio:

Characterize the idle sub-carrier power and system's gross power ratio auxiliary variable: the G of idle sub-carrier power and system's gross power relation _LN+1=-B _LN+1=(β+1) S-I;

The peak value auxiliary variable of characterization signal peak value: B _i=A ^HT _iA i=1 ..., lN;

Characterize the auxiliary variable of OFDM signal distortion:

Characterize the auxiliary variable of idle sub-carrier: P _Free=Tr[(I-S) F].

Step 6, the relevant auxiliary variable of utilizing step 5 to calculate, the expectation symbol f ' of computing system under difference requires:

If the ratio of system requirements system peak-to-average ratio and idle sub-carrier power and system's gross power is satisfying under the prerequisite that limits thresholding, the signal distortion minimum is then utilized peak-to-average ratio auxiliary variable G _i, idle sub-carrier power and the gross power ratio auxiliary variable G of system _Nl+1And signal distortion auxiliary variable P _Gap, obtain expecting symbol f ' by finding the solution the protruding Optimization Model of following positive semidefinite:

Target function:

Constraints: s.t.Tr (G _iF) 〉=0 i=1 ..., lN+1,1)

$\left[\begin{array}{cc}F& f^{\&prime;}\\ f^{\&prime;\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HSA00000158303400031.png,HSA00000158303400032.png"\; state="\{\{state\}\}">H</figure-callout>}}& 1\end{array}\right]\&GreaterEqual;0$

Tr () representing matrix trace function wherein;

If the ratio of system requirements idle sub-carrier power and system's gross power, and the Error Vector Magnitude of OFDM signal distortion satisfy to limit under the prerequisite of thresholding, the peak value minimum is then utilized the auxiliary variable B of idle sub-carrier power and system's gross power ratio _Nl+1, the OFDM signal distortion Error Vector Magnitude thresholding ε and peak value auxiliary variable B _i, obtain expecting symbol f ' by finding the solution the protruding Optimization Model of following positive semidefinite:

Target function:

Constraints: s.t.Tr (B _iF)≤p i=1 ..., lN

$\mathrm{Tr}\left(\mathrm{SF}\right)-2\mathrm{Re}\left(f_o^H{\mathrm{Sf}}^{\&prime;}\right)\&le;({\mathrm{\&epsiv;}}^2-1){\left|\right|{\mathrm{Sf}}_o\left|\right|}_2^2,---2)$

Tr(B _lN+1F)≤0

$\left[\begin{array}{cc}F& f^{\&prime;}\\ f^{\&prime;\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HSA00000158303400031.png,HSA00000158303400032.png"\; state="\{\{state\}\}">H</figure-callout>}}& 1\end{array}\right]\&GreaterEqual;0$

Wherein real is got in Re () expression;

If the Error Vector Magnitude of system requirements system peak-to-average ratio and OFDM signal distortion is satisfying under the prerequisite that limits thresholding, idle sub-carrier power minimum is then utilized peak-to-average ratio auxiliary variable G _i, the OFDM signal distortion Error Vector Magnitude thresholding ε and idle sub-carrier auxiliary variable P _Free, obtain expecting symbol f ' by finding the solution the protruding Optimization Model of following positive semidefinite:

Target function:

Constraints: s.t.Tr (G _iF) 〉=0 i=1 ..., lN

$\mathrm{Tr}\left(\mathrm{SF}\right)-2\mathrm{Re}\left(f_o^H{\mathrm{Sf}}^{\&prime;}\right)\&le;({\mathrm{\&epsiv;}}^2-1){\left|\right|{\mathrm{Sf}}_o\left|\right|}_2^2;---3)$

$\left[\begin{array}{cc}F& f^{\&prime;}\\ f^{\&prime;\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HSA00000158303400031.png,HSA00000158303400032.png"\; state="\{\{state\}\}">H</figure-callout>}}& 1\end{array}\right]\&GreaterEqual;0$

Step 7 is handled the OFDM frequency domain symbol f ' after optimizing and is launched.

OFDM frequency domain symbol f ' after optimizing is at first become the OFDM time-domain symbol by the IFFT module, secondly this time-domain symbol is passed through serial to parallel conversion module and add cyclic prefix module and become complete OFDM time-domain symbol, then this complete OFDM time-domain symbol is become analog signal by the D/A modular converter, at last this analog signal is gone out by antenna transmission through behind the RF Amplifier Module.

Below by emulation experiment effect of the present invention is described further.

1. emulation experiment content

A. the inventive method is optimized the OFDM frequency domain symbol:

At first, input meets the original OFDM frequency domain symbol f of IEEE802.11a standard _o, modulation system adopts BPSK, sub-carrier number N=64, oversample factor l=4.

Secondly, it is preceding 64 row of IFFT rotated factor matrix that inversefouriertransform rotated factor matrix A is set, the carrier wave selection matrix

Companion matrix

Unit matrix

The expectation symbol

Empirical parameter w=0.01.

It is 3dB that supposing the system requires system's peak-to-average ratio thresholding of expectation, and idle sub-carrier power and system's gross power ratio thresholding are 0.15, then set α=3dB, β=0.15.

So just can substitution inversefouriertransform rotated factor matrix A, peak-to-average ratio thresholding α, idle sub-carrier power and gross power ratio thresholding β of system and companion matrix T _iAnd unit matrix

Calculate the peak-to-average ratio auxiliary variable

Idle sub-carrier power and the gross power ratio auxiliary variable G of system ₂₅₇=(0.15+1) S-I _{64 * 64}With the signal distortion auxiliary variable

At last, utilize auxiliary variable G _iAnd G ₂₅₇, by finding the solution the protruding Optimization Model 1 of positive semidefinite) and obtain expecting that symbol f ', f ' they are exactly to original OFDM frequency domain symbol f _oThe new OFDM frequency domain symbol that obtains after being optimized.

B. repeat shearing and filtering method RCF and optimize the OFDM frequency domain symbol:

With reference to Fig. 4, adopt repetition shearing and filtering method RCF to optimize above-mentioned original OFDM frequency domain symbol f _o, modulation system adopts BPSK, and sub-carrier number N=64, oversample factor l=4, peak-to-average ratio thresholding also are 3dB.Original OFDM frequency domain symbol f _o1. become OFDM time-domain symbol x through the IFFT module ₁This time-domain symbol x ₁2. become limitation signal by the amplitude limit module

3. it be transformed into frequency domain symbol again through the FFT module

Carry out frequency domain filtering and obtain frequency domain symbol f after 4. ₁Finish once circulation to this.Quality for the frequency domain symbol that guarantees to obtain skips to module 2 and enters next iteration.The frequency domain symbol f of circulation like this through obtaining after 10 iteration ₁₀Be exactly correspondence and f _oOptimization after the OFDM frequency domain symbol, be designated as f.

The protruding optimization that c.Aggarwal proposes is optimized the OFDM frequency domain symbol:

The protruding optimization that adopts Aggarwal to propose is optimized above-mentioned original OFDM frequency domain symbol f _o, modulation system adopts BPSK, sub-carrier number N=64, and oversample factor l=4, mistake vector magnitude thresholding is-15dB that other setting is identical with the present invention.His protruding optimization formula of being proposed of iterative computation finally obtains correspondence and f _oOptimization after OFDM frequency domain symbol f _A

According to formula

Calculate 5000 original OFDM frequency domain symbol f respectively _oWith OFDM frequency domain symbol f ', f and the f after the optimization that obtains by said process _AMistake vector magnitude root mean square, outcome record in table 2, K=5000 wherein.Complementation according to system's peak-to-average ratio adds up the definition of density function CCDF respectively to original OFDM frequency domain symbol f _oWith new OFDM frequency domain symbol f ', f and f _AThe complementation accumulative total density function of system's peak-to-average ratio carry out emulation, as shown in Figure 5.According to the definition of bit error rate BER to new OFDM frequency domain symbol f ', f and f _ACorresponding BER carries out emulation, as shown in Figure 6.

Table 2 with signal mistake vector magnitude root mean square under the peak-to-average ratio relatively

Can get from table 2, when system's peak-to-average ratio is identical, use the distortion minimum of ofdm system of the present invention, that is to say, the present invention also drops to distortion minimum when reducing system's peak-to-average ratio, has improved receiving terminal and has correctly reduced the probability of primary signal.

As seen from Figure 5, with respect to original ofdm system, though the present invention, RCF method and Aggarwal method have all suppressed the ofdm system peak-to-average ratio,, the present invention is suppressed at a very little fixed value place with system's peak-to-average ratio, makes that system's peak-to-average ratio is stable and has controllability.

As seen from Figure 6, when peak-to-average ratio all was 3dB, bit error rate was about 10 in system ^-3The time, using system signal noise ratio Eb/N0 of the present invention is 8dB, and the signal to noise ratio of Aggarwal method and RCF method is about 9dB.Show that application the present invention can be with the distorted signals minimum when reducing system's peak-to-average ratio.

Top combination model 1) specific embodiments of the invention are had been described in detail, but the present invention is not limited to above-mentioned example, as also can be in conjunction with positive semidefinite Optimization Model 2) and 3) carry out the optimization of OFDM symbol.Therefore under the situation that does not break away from claim scope of the present invention, those skilled in the art can make various modifications or remodeling, but these are all at the row of protection scope of the present invention.

Claims (6)

1. the ofdm signal method for inhibiting peak-to-average ratio based on the positive semidefinite planning technology comprises the steps:

(1) the original OFDM frequency domain symbol f of input _o,

N is a sub-carrier number;

(2) initializaing variable is set, comprises: the inversefouriertransform rotated factor matrix

The carrier wave selection matrix

Companion matrix

Unit matrix

With The expectation symbol

Expectation symbol peaks p and empirical parameter w, wherein N is the OFDM sub-carrier number, l is an oversample factor;

(3) according to the initial auxiliary variable F=f ' f ' of initial symbol f ' calculating ^H

(4) according to system applies occasion and purpose, set peak-to-average ratio thresholding α ∈ [1 ,+∞), the ratio thresholding β ∈ of idle sub-carrier power and system's gross power [0,1) and the Error Vector Magnitude thresholding ε ∈ of OFDM signal distortion [0 ,+∞);

(5), calculate peak-to-average ratio auxiliary variable G according to above-mentioned each initializaing variable and threshold value _i, idle sub-carrier power and the gross power ratio auxiliary variable G of system _Nl+1, B _Nl+1, peak value auxiliary variable B _i, signal distortion auxiliary variable P _GapWith idle sub-carrier auxiliary variable P _Free, wherein, i=1 ..., lN;

(6) according to system requirements, the relevant auxiliary variable of utilizing step (5) to be calculated calculates expectation symbol f ':

If the ratio of system requirements system peak-to-average ratio and idle sub-carrier power and system's gross power is satisfying under the prerequisite that limits thresholding, the signal distortion minimum is then utilized peak-to-average ratio auxiliary variable G _i, idle sub-carrier power and system's gross power ratio auxiliary variable G _Nl+1And signal distortion auxiliary variable P _Gap, obtain expecting symbol f ' by finding the solution the protruding Optimization Model of following positive semidefinite:

Target function:

Constraints: s.t.Tr (G _iF) 〉=0 i=1 ..., lN+1,1)

$\left[\begin{array}{cc}F& f^{\&prime;}\\ f^{\&prime;H}& 1\end{array}\right]\&GreaterEqual;0$

Tr () representing matrix trace function wherein;

If the ratio of system requirements idle sub-carrier power and system's gross power, and the Error Vector Magnitude of OFDM signal distortion satisfy to limit under the prerequisite of thresholding, the peak value minimum is then utilized the auxiliary variable B of idle sub-carrier power and system's gross power ratio _Nl+1, the OFDM signal distortion Error Vector Magnitude thresholding ε and peak value auxiliary variable B _i, obtain expecting symbol f ' by finding the solution the protruding Optimization Model of following positive semidefinite:

Target function:

Constraints: s.t.Tr (B _iF)≤p i=1 ..., lN

$\mathrm{Tr}\left(\mathrm{SF}\right)-2\mathrm{Re}\left(f_o^H{\mathrm{Sf}}^{\&prime;}\right)\&le;({\mathrm{\&epsiv;}}^2-1){\left|\right|{\mathrm{Sf}}_o\left|\right|}_2^2,---2)$

Tr(B _lN+1F)≤0

$\left[\begin{array}{cc}F& f^{\&prime;}\\ f^{\&prime;H}& 1\end{array}\right]\&GreaterEqual;0$

Wherein real is got in Re () expression;

If the Error Vector Magnitude of system requirements system peak-to-average ratio and OFDM signal distortion is satisfying under the prerequisite that limits thresholding, idle sub-carrier power minimum is then utilized peak-to-average ratio auxiliary variable G _i, the OFDM signal distortion Error Vector Magnitude thresholding ε and idle sub-carrier auxiliary variable P _Free, obtain expecting symbol f ' by finding the solution the protruding Optimization Model of following positive semidefinite:

Target function:

Constraints: s.t.Tr (G _iF) 〉=0 i=1 ..., lN

$\mathrm{Tr}\left(\mathrm{SF}\right)-2\mathrm{Re}\left(f_o^H{\mathrm{Sf}}^{\&prime;}\right)\&le;({\mathrm{\&epsiv;}}^2-1){\left|\right|{\mathrm{Sf}}_o\left|\right|}_2^2;---3)$

$\left[\begin{array}{cc}F& f^{\&prime;}\\ f^{\&prime;H}& 1\end{array}\right]\&GreaterEqual;0$

(7) f ' that step (6) is obtained successively through IFFT, and string change, add Cyclic Prefix, D A conversion and radio frequency amplify the back and launch by antenna.

2. optimization method as claimed in claim 1 is characterized in that the described peak-to-average ratio auxiliary variable of step (5) G _i, computing formula is:

$G_i=A^H(\frac{\mathrm{\&alpha;}}{\mathrm{lN}}\tilde{I}-T_i)A,i=1,\&CenterDot;\&CenterDot;\&CenterDot;,\mathrm{lN}.$

3. a kind of method as claimed in claim 1 is characterized in that described idle sub-carrier power of step (5) and the gross power ratio auxiliary variable G of system _Nl+1And B _Nl+1, computing formula is respectively:

G _lN+1＝(β+1)S-I，

B _Nl+1＝-G _Nl+1。

4. optimization method as claimed in claim 1 is characterized in that the described peak value auxiliary variable of step (5) B _i, computing formula is:

B _i＝A ^HT _iA，i＝1，…，lN。

5. optimization method as claimed in claim 1 is characterized in that the described signal distortion auxiliary variable of step (5) P _Gap, computing formula is:

$P_{\mathrm{gap}}=\mathrm{Tr}\left(\mathrm{SF}\right)-2\mathrm{Re}\left(f_o^H\mathrm{SF}\right).$

6. optimization method as claimed in claim 1 is characterized in that the described idle sub-carrier auxiliary variable of step (5) P _Free, computing formula is:

P _free＝Tr(I-S)F]。

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