CN110380996A - Frequency dependence IQ imbalance compensation method in SC-FDE system - Google Patents

Frequency dependence IQ imbalance compensation method in SC-FDE system Download PDF

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CN110380996A
CN110380996A CN201910628302.6A CN201910628302A CN110380996A CN 110380996 A CN110380996 A CN 110380996A CN 201910628302 A CN201910628302 A CN 201910628302A CN 110380996 A CN110380996 A CN 110380996A
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CN110380996B (en
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杨莹
成先涛
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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
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L25/03159—Arrangements for removing intersymbol interference operating in the frequency domain

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  • Digital Transmission Methods That Use Modulated Carrier Waves (AREA)

Abstract

The invention belongs to wireless communication technology field, a kind of be related in SD-FDE system frequency dependence IQ imbalance compensation method.Multipath channel and IQ imbalance parameter are respectively seen as stochastic variable and unknown deterministic parameter with being transformed into estimation problem in expectation maximization (EM) frame by the present invention, by maximizing objective function, the posterior probability and IQ imbalance parameter of multi-path coefficients are updated in an iterative manner.When iteration ends, the estimated value of IQ imbalance parameter can be obtained, and using the Posterior Mean of multi-path coefficients as channel estimation value.Beneficial effects of the present invention are that can carry out effective compensation to the signal interfered by IQ imbalance, significantly improve the performance of BER of system.

Description

Frequency dependence IQ imbalance compensation method in SC-FDE system
Technical field
The invention belongs to wireless communication technology field, a kind of be related in SC-FDE system frequency dependence IQ imbalance compensation Method.
Background technique
In order to meet growing high data rate transfer demand, orthogonal frequency division multiplexing (OFDM) and single-carrier frequency-domain are equal Weighing apparatus (SC-FDE) is widely used.Compared with OFDM, SC-FDE has much lower modulated signal peak-to-average power ratio (PAPR).This Mean for SC-FDE, the requirement to power amplifier linearity can be mitigated, this simplifies transmitter designs.Another party Face, since PAPR is low, SC-FDE has robustness to amplifier nonlinearity, therefore can more effectively utilize the output of amplifier Power.Based on above-mentioned advantage, SC-FDE is used by many wireless communication standards, such as IEEE 802.15.3c and IEEE 802.11ad。
Meanwhile the transceiver in order to realize low cost, small size and high effect, it is necessary to solve in transceiver by analog device Imperfection caused by rf injury problem, one of this rf injury is exactly the width between I the and Q branch in AFE(analog front end) It is IQ uneven that degree, phase and frequency response, which mismatch,.In order to describe IQ imbalance, it is generally divided into following two model: frequency Independence and frequency dependence.Frequency independence IQ imbalance is as caused by non-ideal mixer.For ideal frequency mixer, IQ divides Prevaricate amplitude having the same and accurate 90 degree of phase shifts.However, there are some defects in actual frequency mixer, so as to cause Frequency independence IQ is uneven.In contrast, frequency dependent model not only considers that frequency independence IQ is uneven, it is also contemplated that frequency dependence IQ is uneven.Frequency dependence IQ imbalance is the uneven frequency caused by being mismatched as filter, and corresponding to IQ branch It responds and changes with system bandwidth.Obviously, frequency dependent model when characterizing IQ imbalance more comprehensively than frequency independent model. IQ imbalance destroys the orthogonality between I branch and Q branch signal, and the significant reduction system performance of meeting, it is therefore necessary to IQ imbalance is compensated.For the frequency dependent model in SD-FDE system, common document compensation scheme, which has, only to be considered Transmitting terminal or receiving end IQ are uneven, or estimate channel and IQ imbalance parameter simultaneously to compensate sending and receiving end IQ imbalance but have There is higher computation complexity, in order to further decrease algorithm complexity, it is necessary to propose that a kind of new sending and receiving end IQ is uneven Hybrid compensation scheme.
Summary of the invention
In the presence of having IQ imbalance it is an object of the invention to transmitting terminal and receiving end, one kind is provided and is directed to The method that frequency dependence IQ imbalance in SD-FDE system compensates, lifting system performance.
Multipath channel and IQ imbalance parameter are respectively seen as stochastic variable and unknown deterministic parameter to incite somebody to action by the present invention Estimation problem is transformed into expectation maximization (EM) frame, by maximizing objective function, updates multipath in an iterative manner The posterior probability and IQ imbalance parameter of coefficient.When iteration ends, the estimated value of IQ imbalance parameter can be obtained, and will be more The Posterior Mean of diameter coefficient is as channel estimation value.
Understanding for the ease of those skilled in that art to technical solution of the present invention, the system that the present invention is used first Model is illustrated.
Consider sending and receiving end frequency dependence IQ imbalance model, parameter εT、ΔφTIt is illustrated respectively in the amplitude of transmitting terminal introducing The introducing of uneven and unbalance in phase, frequency dependence passes through equivalent low-pass filter hIT(t)、hQT(t) Lai Shixian.Similarly ε is used respectively in receiving endR、ΔφR、hIR(t)、hQR(t) drawing for amplitude imbalance, unbalance in phase and frequency dependence is indicated Enter.Assuming that the ideal complex baseband signal of transmitting terminal transmission is x (t)=xI(t)+jxQ(t), due to the unbalanced shadow of transmitting terminal IQ It rings, the radio frequency in real system sends signal are as follows:
Wherein, tBB(t)=tI(t)+jtQIt (t) is tRF(t) equivalent complex baseband signal.It is available from (1):
Wherein αT=cos Δ φT+jεTsinΔφT, βT=εTcosΔφT+jsinΔφT。
Radio frequency sends signal and passes through channel hRF(t) it propagates and by white Gaussian noise wRF(t) it after Additive effect, is sent into The bandpass signal of receiving end are as follows:
Enable h (t), w (t) respectively and hRF(t)、wRF(t) corresponding equivalent complex base band shock response, equivalent complex base band are high This white noise, then with rRF(t) corresponding equivalent complex baseband signal r (t) may be expressed as:
rRF(t) it is multiplied first with the local carrier interfered by IQ imbalance and passes through low-pass filter and downconvert to base band, The complex baseband signal interfered at this time by receiving end IQ imbalance is denoted as y (t)=yI(t)+jyQ(t), wherein the road I and the road Q are distinguished Are as follows:
yI(t)=LPF { 2 (1+ εR)cos(2πfct+ΔφR)rRF(t)}
=(1+ εR)cos(ΔφR)rI(t)+(1+εR)sin(ΔφR)rQ(t) (5)
yQ(t)=LPF { -2 (1- εR)sin(2πfct-ΔφR)rRF(t)}
=(1- εR)sin(ΔφR)rI(t)+(1-εR)cos(ΔφR)rQ(t) (6)
Remember r (t)=rI(t)+jrQ(t) and y (t)=y is brought intoI(t)+jyQ(t), it is obtained by a series of operations:
Y (t)=αRr(t)+βRr*(t) (7)
Wherein, αR=cos Δ φR-jεRsinΔφR, βR=εRcosΔφR+jsinΔφR。
The introducing of receiving end IQ imbalance frequency dependence passes through yI(t)、yQ(t) respectively with equivalent low-pass filter hIR (t)、hQR(t) convolution realizes, therefore, final received equivalent complex baseband signal are as follows:
Wherein,
Enabling x [n] is the training sequence that known length is N, x [n] and its conjugated signal x*The N of [n]SPoint FFT is respectively Xk WithSimilarly, channel h [n] and its conjugation h*[n] passes through NSThe frequency domain response that point FFT is obtained is respectively HkWithEquivalent low-pass FIR filter for introducing IQ two-way frequency response difference is respectively hIT=[hIT1,hIT2,...,hITL']、 hQT=[hQT1,hQT2,...,hQTL']、hIR=[hIR1,hIR2,...,hIRL']、hQR=[hQR1,hQR2,...,hQRL'], wherein subscript I, Q respectively indicates the road I and the road Q signal, and subscript T, R respectively indicates transmitting terminal and receiving end, they contain L' tap.Cause This, in transmitting terminal IQ imbalance situation related to receiving end while pull-in frequency, the final frequency-domain expression for receiving signal are as follows:
Wherein, It makes an uproar for frequency domain Sound vector, HIT,k、HQT,k、HIR,k、HQR,kIt is h respectivelyIT、hQT、hIR、hQRNSPoint FFT, can by the definition of discrete Fourier transform :
Coefficient A in frequency-domain expressionk、Bk、With transmitting terminal IQ imbalance parameter alphaT、βT、hIT、hQTIt is related Connection, Ck、DkWith receiving end IQ imbalance parameter alphaR、βR、hIR、hQRIt is associated, it is contemplated that it is mutually indepedent between each parameter, meanwhile, In most of actual conditions, there is α to transmitting terminal and receiving end frequency dependence IQ imbalance parameterT≈ 1, βT≈ 0, αR≈ 1, βR≈ 0, hIT≈ei, hQT≈ej, hIR≈ei, hQR≈ej, e thereinmThe vector that (m=i, j) expression length is L', its m-th yuan Element is 1, remaining element is 0.In consideration of it, being joined based on the algorithm of EM to sending and receiving end frequency dependence IQ imbalance set forth herein a kind of It is several to carry out Combined estimator compensation with channel.Due to αT、βTAnd αR、βRBetween there is conversion relation:WhereinTable respectively Show and real and imaginary parts are taken to element.Therefore when carrying out parameter Estimation, without individually to αTAnd αREstimated, it only need to be by βTWith βREstimated value substitute into above formula α can be obtainedTAnd αREstimated value.
The present invention is achieved by the steps of:
S1, parameter initialization: the initialization including IQ imbalance parameter Yu variance item
By the amplitude imbalance ε of transmitting terminalTWith unbalance in phase Δ φTThe transmitting terminal IQ imbalance parameter alpha of co-determinationT、 βTIt is initialized as 1 and 0 respectively, by the amplitude imbalance ε of receiving endRWith unbalance in phase Δ φRThe receiving end IQ of co-determination is not Balance parameters αR、βRIt is initialized as 1 and 0 respectively, the equivalent low-pass FIR filter on the road transmitting terminal I and the road Q is initialized as h respectivelyIT =eiAnd hQT=ej, the equivalent low-pass FIR filter on the receiving end road I and the road Q initializes h respectivelyIR=eiAnd hQR=ej, therein em(m=i, j) indicates that length is the vector of L', its m-th of element is 1, remaining element is 0.ChannelPrior varianceIt is initialized asWherein L indicates the effective length of channel time domain impulse response h, and l indicates channelUnder Mark, with season noise variance β-1=Pn(PnIndicate the noise power variance obtained by signal-to-noise ratio).
S2, the iteration that EM algorithm is realized by following step:
S21, the Posterior Mean for updating channel h:
For the ease of utilizing the sparse characteristic of channel, according toAndHkWithTable respectively Show channel h and h*NSPoint FFT, andIndicate that k-th of subcarrier is corresponding FFT column vector, wherein N indicates the length of training sequence.Therefore frequency-domain received signal is separately denoted as WhereinConsider NSHeight carries Wave then has:
Indicate that above formula is denoted as with matrix form: S=Mh+Nh*+ W, then switching to real number field can obtain:
Wherein,WhereinIt respectively indicates and real and imaginary parts is taken to element.To due to channel h be it is sparse,It is also sparse, and AndWithShare identical sparsity.It is assumed thatIn each element to obey mean value be 0, variance isIt is identical Gaussian Profile, and α=[α1,α2,...,α2L] indicateThe set of all elements variance；In each element obey mean value and be 0, variance β-1Identical Gaussian Profile.SoPrior probability can be denoted as:
Conditional probabilityAre as follows:
It is based onChannel can be obtained using formula (12), (13)Posterior probability
Wherein,T=(β ΦHΦ+D)-1, and D=diag (α1,α2,…αL,α1,α2,…αL).Therefore plural number The posterior probability mean value of channel h is μ1=μ (1:L, 1)+i μ (L+1:2L, 1), i indicate the imaginary part of plural number.Posterior Mean at this time The as estimated value of channel h.The estimation of h Posterior Mean needs while estimating hyper parameter α, β, utilizes sparse Bayesian (SBL) standard Then, consider the complete likelihood function about α, β:
By maximizing complete likelihood function relative to parameter alpha, β and respectively to parameter alphal, β ask single order to lead juxtaposition 0, obtain Parameter alphal, β more new formula are as follows:
S22, IQ imbalance parameter is updatedEstimated value
Consider objective function Q (θ) and retain only item related with θ:
Due in a practical situation, tr (ΦHΦ t) value be much smaller thanTherefore only consider here The wherein mark of tr () representing matrix.By channel h and HkPosterior Mean be denoted as υ and Vk, formula (18) may be expressed as:
Minimize q (θ) by maximizing objective function Q (θ) come undated parameter θ.DefinitionWherein t=[βT,βR]TAnd estimated using Newton method every in parameter θ A subset θi:
θi=θi m-H-1(θi)δ(θi) (20)
Wherein, different parameters θiCorresponding Hessian matrix H and gradient δ are respectively as follows:
Above-mentioned an,k(n=1,2,3,4,5), b1,k, c1,k, d1,k, e1,kIt is intended merely to facilitate Hessian matrix H and gradient δ Expression and the intermediate variable that introduces, without physical meaning.
S23, circulation step S21, S22, until reaching maximum outer iteration times Nt, and by Posterior Mean μ at this time1Make For the estimated value of channel h.
S3, frequency dependence IQ imbalance compensation and channel effect remove:
The reception signal of formula (9) is separately denoted as matrix form:
Based on MMSE criterion, the initial transmission signal that recovers are as follows:
Wherein, η indicates that signal-to-noise ratio, I are unit matrix.
Beneficial effects of the present invention are, can carry out effective compensation to the signal interfered by IQ imbalance, significantly improve and are The performance of BER of system.
Detailed description of the invention
Fig. 1 is the sending and receiving end frequency dependence IQ imbalance model figure that the present invention uses；
Fig. 2 is the BER performance chart of the inventive algorithm under LOS channel conditions 1；
Fig. 3 is the BER performance curve curve graph of the inventive algorithm under NLOS channel conditions 1；
Fig. 4 is the BER performance chart of the inventive algorithm under LOS channel conditions 2；
Fig. 5 is the BER performance curve curve graph of the inventive algorithm under NLOS channel conditions 2.
Specific embodiment
Illustrate effectiveness of the invention with simulated example with reference to the accompanying drawing:
Emulation is based on SC-FDE system, using the modulation system of QPSK, symbol rate 1.76GHz, raised cosine roll off filtering Up-sampling multiple be 8, roll-off factor 0.25, lead code and channel use 802.11.ad standard, and amplitude imbalance is set as εT =εR=1dB, unbalance in phase are set as Δ φT=Δ φR=5 ° (in a true system, the unbalanced situation of IQ is usual Than emulation setting than get well).For frequency dependence, the case where considering two kinds of three taps:
Situation 1:hI=[1.02,0.04, -0.03]T, hQ=[1.03, -0.02,0.012]T
Situation 2:hI=[0.01,1,0.01]T, hQ=[0.01,1,0.2]T
Wherein the introduced frequency dependence of situation 1 is smaller, similar with the frequency independence unbalanced situation of IQ, 2 institute of situation The frequency dependence of introducing is larger.
Fig. 2 and Fig. 3 is the BER Simulation curve graph of the lower LOS and NLOS channel of situation 1, can from this two width figure Out, the estimation unbalanced for sending and receiving end IQ of proposed Iterative Method is excellent with compensation performance, and sufficiently connects It is bordering on the performance curve of ideal communication channel MMSE compensation, illustrates that proposed algorithm sufficiently connects the estimation of channel state information It is bordering on imperfect channel state information.Meanwhile the error performance after iteration single compensation very close to no IQI the case where , therefore need to carry out an iteration i.e. can reach the excellent impact of performance only to reduce the unbalanced adverse effect of IQ.
Fig. 4 and Fig. 5 is the BER Simulation curve graph of the lower LOS and NLOS channel of situation 2, can from this two width figure Out, in the case where frequency dependence is more serious, the iterative algorithm of this paper is to the unbalanced estimation of sending and receiving end IQ and compensation performance It is still better.

Claims (1)

  1. Frequency dependence IQ imbalance compensation method in 1.SD-FDE system, which comprises the following steps:
    S1, parameter initialization: by the amplitude imbalance ε of transmitting terminalTWith unbalance in phase Δ φTThe transmitting terminal IQ of co-determination is not Balance parameters αT、βTIt is initialized as 1 and 0 respectively, by the amplitude imbalance ε of receiving endRWith unbalance in phase Δ φRIt codetermines Receiving end IQ imbalance parameter alphaR、βRIt is initialized as 1 and 0, the equivalent low-pass FIR filter point on the road transmitting terminal I and the road Q respectively H is not initialized as itIT=eiAnd hQT=ej, the equivalent low-pass FIR filter on the receiving end road I and the road Q initializes h respectivelyIR=eiWith hQR=ej, e thereinm(m=i, j) indicates that length is the vector of L', its m-th of element is 1, remaining element is 0；ChannelPrior varianceIt is initialized as1≤l≤2L, wherein L indicates the effective length of channel time domain impulse response h, l table Show channelSubscript, with season noise variance β-1=Pn, PnIndicate the noise power variance obtained by signal-to-noise ratio；
    S2, the iteration that EM algorithm is realized by following step:
    S21, the Posterior Mean for updating channel h:
    For the ease of utilizing the sparse characteristic of channel, according toAndHkWithIt respectively indicates Channel h and h*NSPoint FFT, and FkIndicate the corresponding FFT column vector of k-th of subcarrier, NSFor subcarrier number, wherein N is indicated Frequency-domain received signal is separately denoted as by the length of training sequenceWherein
    For noise vector, HIT,k、HQT,k、HIR,k、HQR,kIt is h respectivelyIT、hQT、hIR、hQRNSPoint FFT, XkFor known length For the N of the training sequence x [n] of NSPoint FFT,For the conjugated signal x of x [n]*The N of [n]SPoint FFT,1≤k≤NS；
    Then have:
    Indicate that above formula is denoted as with matrix form: S=Mh+Nh*+ W, then switching to real number field can obtain:
    Wherein,WhereinRespectively indicate and real and imaginary parts taken to element, because channel h be it is sparse, thereforeIt is also sparse, and WithIdentical sparsity is shared, is enabledIn each element to obey mean value be 0, variance isIdentical Gaussian Profile；In each element obey mean value be 0, variance β-1Identical Gaussian Profile；Prior probability are as follows:
    Conditional probabilityAre as follows:
    It is based onChannel can be obtained using formula (12), (13)Posterior probability
    Wherein,T=(β ΦHΦ+D)-1, and D=diag (α1,α2,…αL,α1,α2,…αL), therefore complex channel The posterior probability mean value of h is μ1=μ (1:L, 1)+i μ (L+1:2L, 1), i indicate that the imaginary part of plural number, Posterior Mean at this time are The estimated value of channel h；The estimation of h Posterior Mean needs while estimating hyper parameter α, β, using sparse Bayesian criterion SBL, considers Complete likelihood function about α, β:
    By maximizing complete likelihood function relative to parameter alpha, β and respectively to parameter alphal, β ask single order to lead juxtaposition 0, obtain parameter αl, β more new formula are as follows:
    S22, IQ imbalance parameter is updatedEstimated value
    Objective function Q (θ) retains only item related with θ:
    Due in a practical situation, tr (ΦHΦ t) value be much smaller thanThe mark of tr () representing matrix, therefore only examine ConsiderBy channel h and HkPosterior Mean be denoted as υ and Vk, formula (18) expression are as follows:
    Minimize q (θ) by maximizing objective function Q (θ) come undated parameter θ；DefinitionWherein t=[βT,βR]TAnd estimated using Newton method every in parameter θ A subset θi:
    θi=θi m-H-1(θi)δ(θi) (20)
    Wherein, different parameters θiCorresponding Hessian matrix and gradient are respectively as follows:
    Above-mentioned an,k(n=1,2,3,4,5), b1,k, c1,k, d1,k, e1,kIt is intended merely to facilitate the table of Hessian matrix H and gradient δ The intermediate variable for showing and introducing does not have actual physics meaning；
    S23, circulation step S21, S22, until reaching maximum outer iteration times Nt, and by Posterior Mean μ at this time1As letter The estimated value of road h.
    S3, frequency dependence IQ imbalance compensation and channel effect remove:
    The reception signal of formula (9) is separately denoted as matrix form:
    Based on MMSE criterion, the initial transmission signal that recovers are as follows:
    Wherein, η indicates that signal-to-noise ratio, I are unit matrix.
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CN111917672A (en) * 2020-07-18 2020-11-10 青岛鼎信通讯股份有限公司 IQ (in-phase/quadrature) estimation and calibration method for carrier wireless dual-mode communication
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