CN104917714B - The method for reducing extensive MIMO OFDM downlinks work(peak-to-average force ratio - Google Patents

The method for reducing extensive MIMO OFDM downlinks work(peak-to-average force ratio Download PDF

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CN104917714B
CN104917714B CN201510309345.XA CN201510309345A CN104917714B CN 104917714 B CN104917714 B CN 104917714B CN 201510309345 A CN201510309345 A CN 201510309345A CN 104917714 B CN104917714 B CN 104917714B
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mrow
msub
mover
msubsup
mfrac
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CN104917714A (en
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方俊
包恒耀
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University of Electronic Science and Technology of China
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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
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2614—Peak power aspects
    • H04L27/2615—Reduction thereof using coding

Abstract

The invention belongs to the field of signal processing of radio communication, more particularly in extensive MIMO-OFDM downlinks reduce signal work(peak-to-average force ratio (Peak-to-Average Power Ratio, PAPR) method.The present invention first constrains precoding, OFDM is modulated to combine and is expressed as an equation group for owing fixed, then a prior model that can promote low PAPR features is established, finally utilize greatest hope (Expectation Maximization, EM) and generalized approximate message transmission (Generalized Approximate Message Passing, GAMP) algorithm designs an algorithm that can ask for low PAPR solutions.The free degree that the present invention is provided using a large amount of antennas of base station end in extensive MIMO ofdm systems, reduce the PAPR of downlink transmitted signal.The energy of resulting transmission signal is concentrated very much, and in the case where transmission antenna is enough, signal tends to permanent envelope state so that radio circuit and linear power amplifier that need not be expensive, so can effectively reduce the construction cost of future base stations.

Description

The method for reducing extensive MIMO-OFDM downlinks work(peak-to-average force ratio
Technical field
The invention belongs to the field of signal processing of radio communication, more particularly in extensive MIMO-OFDM downlinks The method for reducing signal work(peak-to-average force ratio (Peak-to-Average Power Ratio, PAPR).
Background technology
Because extensive MIMO disclosure satisfy that growing traffic rate and capacity requirement, the Guang Faguan of industry is received Note.Because OFDM technology can be readily applied in mimo system, MIMO-OFDM has been defaulted as next generation wireless communication System is eated dishes without rice or wine scheme.OFDM modulation is a kind of technology different pieces of information being respectively mapped on mutually orthogonal subcarrier, can Effectively antagonize frequency selective fading and realize simply, be widely used in various communication systems, such as：LTE and WIFI.But It is that ofdm modulation signal is the linear superposition of multiple Independent Carrier Waves, generally there is very high PAPR so that the radio frequency of ofdm system Circuit needs the very high linear amplifier of a cost.
In traditional SISO-OFDM systems, existing many ripe reduction PAPR method, they are generally in transmitting terminal Original high PAPR Signal Compressions are launched into a low PAPR signal, while launches one to user and can correctly demodulate The additional information of this signal.But in multi-user MIMO system, the user of receiving terminal can not possibly cooperate the PAPR after demodulation compression Signal, therefore conventional method is difficult to be extended in multi-user MIMO system.
In extensive mimo system, the antenna number that usual base station possesses is far longer than serviced number of users, and this causes The multi-user pre-coding constraint and OFDM modulation of MIMO-OFDM systems, which can combine, establishes an equation group for owing fixed so that energy Glitch-free modulated signal has infinite between meeting user.Therefore, large-scale transmission antenna provides for extra discretion Find the ofdm modulation signal with low PAPR characteristics.At present, optimal solution typically is found using the scheme of convex optimization, but it is multiple Miscellaneous degree is high, and convergence rate is slow.
The content of the invention
In view of the shortcomings of the prior art, the present invention provides a kind of statistical property using low PAPR signals to reduce signal PAPR low complexity algorithm.
The present invention thinking be：Precoding is constrained first, OFDM modulation is combined and is expressed as one and owes fixed equation group, so A prior model that can promote low PAPR features is established afterwards, finally utilizes greatest hope (Expectation- Maximization, EM) and generalized approximate message transmission (Generalized Approximate Message Passing, GAMP) algorithm designs an algorithm that can ask for low PAPR solutions.
In order to easily describe present disclosure, the term used in the present invention is defined first.
Extensive MIMO-OFDM downlinks：As shown in figure 1, snThe qam signal sent respectively for N number of subcarrier, N=1 ..., N,Be ensure it is noiseless and carry out the vector after precoding between user,(m=1 ..., M it is) frequency-region signal sent on M base station transmission antennas,For the time domain letter sent on M base station transmission antennas Number, K be extensive MIMO in number of users, K ＜ ＜ M,Represent complex field.
Precoding：In MIMO-OFDM systems, in order to ensure the reception letter in same time and frequency zone resource between multiple users It is number noiseless, it is necessary to sending signal snCarry out precoding.Channel isVector after so encoding S should be metn=Hnwn.So, the signal that user receives just is free of the interference of other users.
Work(peak-to-average force ratio：The PAPR of m root transmission antennas is defined asSend The ratio between the peak value of signal and average energy, wherein,Parameter real part is represented,Parameter imaginary part is represented,For operator two Norm.
Normal distribution：Average is μ, variance σ2The probability density function of normal distribution (Gaussian Profile) be defined asThe cumulative distribution function of standardized normal distribution is defined as Φ (f), wherein, f represents independent variable.
Protect bandwidth：In order to protect used frequency band not disturbed by nearby frequency bands in OFDM modulation, generally will not Use the subcarrier positioned at frequency band both ends.Therefore, N number of subcarrier is divided into two set：WithFor subcarrierTransmission signal is qam signal,For subcarriersnNull vector is tieed up for M.
Greatest hope：A kind of iterative algorithm for asking for maximal possibility estimation.The lower bound of likelihood function is constantly established, and under Boundary optimizes, and then maximizes likelihood function.
Generalized approximate message transmission：A kind of algorithm for asking for variable approximation Posterior distrbutionp function.
Digamma functions：The derivative of Gamma function natural logrithms is defined as, i.e.,
The method for reducing extensive MIMO-OFDM downlinks work(peak-to-average force ratio, is comprised the following steps that：
S1, the signal model y=Ax for calculating joint precoding and OFDM modulation, it is specially：
S11, precoding constraint and extensive MIMO-OFDM downlinks by extensive MIMO-OFDM downlinks OFDM modulation, which is combined, is expressed as a system of linear equationsWherein, It is described for block diagonal matrixByIndividual channel matrix HnWithIndividual M dimensions unit matrix composition,T The signal after precoding to be assigned to the permutation matrix of each transmission antenna,It is described for block diagonal matrixBy M N-dimensional Inverse discrete fourier transform matrix forms,For unknown quantity, [*]TThe transposition of representing matrix, | * | represent of set interior element Number；
S12, by complex number equation group described in S11Transform to real number field：Y=Ax, the dimension for making x are I, y dimension For J, wherein,
S2, prior model is introduced, be specially：
S21, make each element of x described in S1 independent, the x is introduced and blocks gauss hybrid models prioriWherein, i-th yuan of i=1 ..., I, the x Plain xi∈ [- v, v], αi1And αi2It is Gauss against variance, κiFor the discrete variable that value is 0 and 1, v is the border of priori, is normalized The factorNormalization factor
S22, to linear equation described in S11It is zero to introduce an average, the Gaussian noise that inverse variance is β；
S3, iteration renewal, outputIt is specific as follows：
S31, initialization, to all j=1 ..., J：To all i=1 ..., I：αi1(0) =αi2(0)=1, κi(0)=1/2, v (0)=| | y | |∞/||A||∞,Make iterations t=1；
S32, with GAMP approximate Posterior distrbutionp is calculated, it is specific as follows：
To all j=1 ..., J,
Wherein, subscript *pPlay differentiation,The function related to x described in S12 is represented, AjiThe column element of jth row i-th of matrix A described in S12 is represented,Square of the column element of jth row i-th of matrix A described in S12 is represented,
Wherein,For intermediate parameters,
Wherein, subscript *zPlay differentiation,
Wherein,For intermediate parameters,
Wherein,For intermediate parameters,
Wherein, subscript *sPlay differentiation,
To all i=1 ..., I,
Wherein, subscript *rPlay differentiation,
Wherein,For intermediate parameters；
S33, more new signal xiAnd parameter alphai1, αi2And κi： κi(t+1)=q (κi=1),
Wherein,
To κiPosterior probability q (κi) have
Inverse variance β described in S34, renewal S22：
Border v described in S35, renewal S21：V (t+1)=v (t)+Δ v, wherein,
S36, judged, if t=T, jump out iteration and exportIf t ＜ T, t=t+1 is made to turn Enter S31, wherein, T is maximum iteration, and the T is empirical value.
The beneficial effects of the invention are as follows：
The free degree that the present invention is provided using a large amount of antennas of base station end in extensive MIMO-OFDM systems, reduce descending Link sends the PAPR of signal.The energy of resulting transmission signal is concentrated very much, is believed in the case where transmission antenna is enough Number tend to permanent envelope state so that the linear power amplifier that radio circuit simultaneously need not be expensive, so can effectively reduce not Carry out the construction cost of base station.
Brief description of the drawings
Fig. 1 is MIMO-OFDM system down link block diagrams.
Time-domain signals and corresponding frequency-region signal of the Fig. 2 for transmission, (a) time-domain signal, (b) frequency-region signal, wherein, EM- TGM-GAMP represents the method just invented, and ZF is the traditional method for precoding for not carrying out PAPR processing.
Fig. 3 is PAPR benefit cumulative distribution figure.
Embodiment
With reference to embodiment and accompanying drawing, technical scheme is described in detail.
Base station end has M=100 root transmission antennas；Service user number is K=10；OFDM subcarriers number is N=128, its In effectively sub-carrier number be
Assuming that channel perfection is, it is known that from 16QAM modulating modes.
The A and y in signal model are calculated according to channel matrix and user data first；Then initialization algorithm parameter：αi1(0)=αi2(0)=1, κi(0)=1/2, v (0)=| | y | |∞/||A||∞、According to GAMP and EM algorithm iterations more new signal and model parameter, jump out and export when reaching maximum iteration Solved.
S1, the signal model y=Ax for calculating joint precoding and OFDM modulation, it is specially：
S11, precoding constraint and extensive MIMO-OFDM downlinks by extensive MIMO-OFDM downlinks OFDM modulation, which is combined, is expressed as a system of linear equationsWherein, It is described for block diagonal matrixByIndividual channel matrix HnWithIndividual M dimensions unit matrix composition,T is precoding Signal afterwards is assigned to the permutation matrix of each transmission antenna,It is described for block diagonal matrixBy M N-dimensional discrete fourier Reverse transform matrix forms,For unknown quantity, [*]TThe transposition of representing matrix, | * | represent the number of set interior element；
S12, by complex number equation group described in S11Transform to real number field：Y=Ax, the dimension for making x are I, y dimension For J, wherein,Due to K ＜ ＜ M, A is deficient fixed , the equation has infinite solution, using below the step of ask for the minimum solutions of wherein PAPR；
S2, prior model is introduced, be specially：
S21, the low PAPR characteristics for rent solution, make each element of x described in S1 independent, the x is introduced and blocks height This mixed model prioriWherein, i=1 ..., I, I-th of element x of the xi∈ [- v, v], αi1And αi2It is Gauss against variance, κiFor the discrete variable that value is 0 and 1, v is first The border tested, normalization factorNormalization factor
S22, to linear equation described in S11It is zero to introduce an average, the Gaussian noise that inverse variance is β, so Can utilizes following iterative algorithm Combined estimator x, α1、α2, κ, v, β, so as to obtain low PAPR signals；
S3, iteration renewal, outputIt is specific as follows：
S31, initialization, to all j=1 ..., J：To all i=1 ..., I：αi1(0) =αi2(0)=1, κi(0)=1/2, v (0)=| | y | |∞/||A||∞,Make iterations t=1；
S32, with GAMP approximate Posterior distrbutionp is calculated, it is specific as follows：
To all j=1 ..., J,
Wherein, subscript *pPlay differentiation,The function related to x described in S12 is represented, AjiThe column element of jth row i-th of matrix A described in S12 is represented,Square of the column element of jth row i-th of matrix A described in S12 is represented,
Wherein,For intermediate parameters,
Wherein, subscript *zPlay differentiation,
Wherein,For intermediate parameters,
Wherein,For intermediate parameters,
Wherein, subscript *sPlay differentiation,
To all i=1 ..., I,
Wherein, subscript *rPlay differentiation,
Wherein,For intermediate parameters；
S33, more new signal xiAnd parameter alphai1, αi2And κi： κi(t+1)=q (κi=1),
Wherein,
To κiPosterior probability q (κi) have
Inverse variance β described in S34, renewal S22：
Border v described in S35, renewal S21：V (t+1)=v (t)+Δ v, wherein,
S36, judged, if t=T, jump out iteration and exportIf t ＜ T, t=t+1 is made to turn Enter S31, wherein, T is maximum iteration, and the T is empirical value.
The transmission signal with low PAPR is can be obtained by after interative computation above, and this signal can ensure to use There is no signal energy substantially in noiseless and protection bandwidth between family.
As shown in Fig. 2 time-domain signal and its frequency spectrum on the 1st transmission antenna.Wherein, curve shown in EM-TGM-GAMP For the signal obtained using the inventive method, ZF is to be calculated without the common ZF (ZeroForcing, ZF) for carrying out PAPR processing Method.From Fig. 2 (a) it can be seen that the most energy of sample of signal obtained using the present invention all concentrates on a peak value, and remain Remaining sample energy is less than this peak value, therefore the PAPR very littles of signal, only 0.6dB, and does not carry out the signal of PAPR processing PAPR is up to 11.9dB.Fig. 2 (b) is the frequency spectrum of signal, it can be seen that is used as at some on the subcarrier of protection bandwidth, EM- TGM-GAMP is the same with ZF and energy is not present.
Fig. 3 show two schemes signal PAPR benefit cumulative distribution contrast, it can be seen that the modulation letter that the present invention obtains Number PAPR be always less than 1dB substantially, it is and better more than 10dB than ZF.Therefore, can effectively be reduced not using the solution of the present invention Carry out the construction cost of antenna for base station radio frequency.

Claims (1)

1. reduce the method for extensive MIMO-OFDM downlinks work(peak-to-average force ratio, it is characterised in that comprise the following steps：
S1, the signal model y=Ax for calculating joint precoding and OFDM modulation, it is specially：
S11, by the precodings of extensive MIMO-OFDM downlinks constraint and the OFDM of extensive MIMO-OFDM downlinks Modulation, which is combined, is expressed as a system of linear equationsWherein, It is described for block diagonal matrixByIndividual channel matrix HnWithIndividual M dimensions unit matrix composition,T is precoding Signal afterwards is assigned to the permutation matrix of each transmission antenna,It is described for block diagonal matrixIt is anti-by M N-dimensional discrete fourier Transformation matrix forms,For unknown quantity, [*]TThe transposition of representing matrix, | * | represent the number of set interior element；
S12, by system of linear equations described in S11Transform to real number field：Y=Ax, the dimension for making x are I, and y dimension is J, Wherein,
S2, prior model is introduced, be specially：
S21, make each element of x described in S1 independent, the x is introduced and blocks gauss hybrid models prioriWherein, i=1 ..., I, the x i-th of element xi∈ [- v, v], αi1And αi2It is Gauss against variance, κiFor the discrete variable that value is 0 and 1, v is the border of priori, normalization because SonNormalization factor
S22, to linear equation described in S11It is zero to introduce an average, the Gaussian noise that inverse variance is β；
S3, iteration renewal, outputIt is specific as follows：
S31, initialization, to all j=1 ..., J：To all i=1 ..., I：αi1(0)=αi2 (0)=1, κi(0)=1/2, v (0)=| | y | |∞/|||A||∞,Make iterations t=1；
S32, with GAMP approximate Posterior distrbutionp is calculated, it is specific as follows：
To all j=1 ..., J,
Wherein, subscript *pPlay differentiation,Represent the function related to x described in S12, AjiRepresent The column element of jth row i-th of matrix A described in S12,Square of the column element of jth row i-th of matrix A described in S12 is represented,
Wherein,For intermediate parameters,
Wherein, subscript *zPlay differentiation,
Wherein,For intermediate parameters,
Wherein,For intermediate parameters,
Wherein, subscript *sPlay differentiation,
To all i=1 ..., I,
Wherein, subscript *rPlay differentiation,
Wherein,For intermediate parameters；
S33, more new signal xiAnd parameter alphai1, αi2And κi： κi(t+1)=q (κi=1),
Wherein,
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To κiPosterior probability q (κi) have
<mrow> <mi>ln</mi> <mi> </mi> <mi>q</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;kappa;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mo>&lt;</mo> <msub> <mi>ln&amp;alpha;</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>&gt;</mo> <mo>-</mo> <mo>&lt;</mo> <msub> <mi>ln&amp;alpha;</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> </msub> <mo>&gt;</mo> <mo>+</mo> <mn>4</mn> <mi>v</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>ln&amp;eta;</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>ln&amp;eta;</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;kappa;</mi> <mi>i</mi> </msub> <mo>+</mo> <mi>c</mi> <mi>o</mi> <mi>n</mi> <mi>s</mi> <mi>tan</mi> <mi>t</mi> <mo>,</mo> </mrow>
<mrow> <mo>&lt;</mo> <msub> <mi>ln&amp;alpha;</mi> <mrow> <mi>i</mi> <mi>l</mi> </mrow> </msub> <mo>&gt;</mo> <mo>=</mo> <mi>&amp;psi;</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>a</mi> <mo>~</mo> </mover> <mrow> <mi>i</mi> <mi>l</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>b</mi> <mo>~</mo> </mover> <mrow> <mi>i</mi> <mi>l</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>l</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>;</mo> </mrow>
Inverse variance β described in S34, renewal S22：
Border v described in S35, renewal S21：V (t+1)=v (t)+Δ v, wherein,
S36, judged, if t=T, jump out iteration and exportIf t ＜ T, make t=t+1 be transferred to S31, Wherein, T is maximum iteration, and the T is empirical value.
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