CN103516659B - Method for estimating carrier frequency offset of OFDM system with time varying direct current offset - Google Patents
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Abstract
The invention provides a method for estimating carrier frequency offset of an OFDM system with time varying direct current offset, relates to the field of communications, and can accurately estimate the carrier frequency offset with a relatively small error. The method for estimating carrier frequency offset (CFO) of an orthogonal frequency division multiplexing (OFDM) system with the time varying direct current offset (TV-DCO) comprises the following steps: establishing a mathematical model for the OFDM system with the CFO and the TV-DCO; estimating the CFO through the methods of DCO compensation and power leakage minimization. The embodiment of the invention is mainly applied to the estimation process of the CFO.
Description
Technical field
The present invention relates to communication technical field, particularly relates to a kind of orthogonal frequency division multiplex system with time-varying direct current offset
Carrier frequency deviation estimating method.
Background technology
In wireless communications, OFDM (Orthogonal Frequency Division Multiplexing,
Abbreviation OFDM) technology is a kind of up-and-coming technology, with efficient spectrum utilization, has robust to the multipath fading of channel
Property, and fast fourier transform (FFT) and inverse FFT (IFFT) simple realization can be based on, therefore by emerging wireless
System is widely used, such as digital audio broadcasting (DAB), DVB (DVB), WLAN (WLAN), 3GPP
Long Term Evolution (LTE) etc..
But, OFDM is highly susceptible to the impact of various interference in actual applications.Carrier frequency shift (CFO) is people
One of OFDM interference the most familiar.It can produce inter-carrier interference (ICI), so as to reduce the performance of OFDM.It is negative in order to reduce
Face rings, and needs CFO is carried out estimating and corresponding compensation during the reception of OFDM.The ofdm system that prior art is provided
CFO estimate that this method is in additive white Gaussian noise (AWGN) channel typically using maximum likelihood (ML) estimation
The CFO of ofdm system estimates, and its performance will deteriorate in microcellular mobile radio channel.Further, prior art also teaches one
Plant blind CFO methods of estimation, it turned out that its properties equivalent blind CFO of maximum likelihood in fading channel estimates.
In addition to CFO, OFDM is likely to by affecting that other disturb, such as direct current offset (DCO).In recent years, in order to
Cost-effective and power consumption efficiency, mobile receiver framework develop to Direct Conversion from superhet.DCO is that Direct Conversion formula connects
A kind of modal interference of receipts machine (DCR).Its mixing certainly from local oscillator (LO) signal or radio frequency (RF) signal, by
The limited isolation between mixer input port, as shown in Fig. 1.In an ofdm system, DCO not only reduces demodulation performance,
And affect CFO to estimate.In ofdm system, the CFO of static state DCO estimates to have been obtained for solution well, can be by simulation
High pass filter (HPF) is filtered, or carries out data-aided compensation or blind compensation in numeric field.Except static DCO, DCR may be used also
To introduce time dependent DCO (TV-DCO).In an ofdm system, in order to cover the HDR of decline ofdm signal,
DCR is generally using the low-noise amplifier (LNA) of various gain modes.During gain mode switch-phases shown in fig. 2,
DCO level may be mutated, and the high fdrequency components being mutated can pass through the HPF after low-noise amplifier (LNA), straighten when which results in
The generation of stream skew (TV-DCO).Only a few studies are related to the CFO estimations of the ofdm system with TV-DCO.Prior art is carried
Go out the impact estimated to CFO with difference filter (DFE) suppression TV-DCO.In addition, it is also proposed that least-squares estimation (LSE) is calculated
Method, the performance of this algorithm are more preferable than DFE, but with higher amount of calculation.DFE and LSE algorithm can be extended respectively for solving
Certainly the CFO of TV-DCO and the unbalanced ofdm system of inphase/orthogonal (I/Q) estimates.Fig. 1 illustrates the generation of DCO in DCR.Fig. 2
Illustrate the generation in LNA gain mode switch steps TV-DCO.Having at present is carried out for the ofdm system with TV-DCO
The algorithm that CFO estimates, such as DFE and LSE are data aided algorithm.They depend on the training sequence of transmission, so as to reduce
Valid data transfer rates.
The content of the invention
The technical problem to be solved in the present invention is to provide a kind of carrier frequency of the ofdm system with time-varying direct current offset
Deviation estimating method, its method of estimation accuracy are high, and error is little.
To solve above-mentioned technical problem, embodiments of the invention provide a kind of ofdm system with time-varying direct current offset
Carrier frequency deviation estimating method, including：
The mathematical model of the ofdm system with CFO and TV-DCO is set up, wherein, CFO represents carrier frequency shift, DCO
Direct current offset is represented, TV-DCO represents time dependent direct current offset, and the mathematical model is expressed as rN(m)=PN(ε)UNxK
(m)+INa(m)+cNb(m)+wN(m)；
The method minimized by DCO compensation and Power leakage estimates CFO.
In the mathematical model for setting up the ofdm system with CFO and TV-DCO：
The vector sample for receiving is：Wherein, m tables
Show m-th OFDM block；
Real subcarrier is：Its
In, S (k, m) is the modulated symbol of k-th subcarrier for being mapped to m-th OFDM block；H (k, m) is the sound of corresponding frequency domain channel
Should, φ (m) represents the phase offset of an accumulation；
Noise symbol is：Wherein, the transposition of T representing matrixs,
WithRespectively represent length for N complete 1 vector sum length for N linear vector, PN(ε) represent what ε caused
Incremental phase offset,ε represents the normalized CFO of subcarrier spacing.
Matrix U of the inverse discrete Fourier transform (IDFT) of real subcarrier with N × K rankNRepresent, wherein (n, l)
Input beul∈Cr
The method minimized by DCO compensation and Power leakage estimates that CFO includes：
DC-free O signal yNM () is obtained by way of weighted linear combination, i.e.,
Wherein,And weight vectorsMeet
b(m)go(0)+g0(2)=0 and a (m) go(0)+go(1)=0, wherein, a (m) and b (m) are represented m-th respectively
TV-DCO static and linear changing unit in OFDM blocks.
Obtaining DC-free O signal yNInclude after (m)：
Build cost function：, by rN(m), INAnd cNWith a weighting arrow
First linear combination of amount g compensates CFO with eigenvalue v, then allied signal is mapped on empty subcarrier suppressing DCO,
Wherein, wherein | |. | |2Represent 2- norms, VNIt is the matrix of a N × (N-K), H represents conjugate transpose, PN(- v) represents that-v draws
The incremental phase offset for rising ,-v represent the normalized CFO of subcarrier spacing.
Include after f (v, g) is obtained：
WhereinWherein,Represent table
Show the estimation to ε,Represent the estimation to g.
The above-mentioned technical proposal of the present invention has the beneficial effect that：
In such scheme, based on the linear approximation of TV-DCO, it is that CFO estimates to propose a kind of blind arithmetic, the method is common
Including 2 steps：1) founding mathematical models；2) method of estimation to CFO is proposed, is minimized by DCO compensation and Power leakage
Method estimate CFO, the method is named as LVD-EDE, that is, there is the EDE in linear change DCO, and the LVD-EDE methods have
Effect, and error is little, better than existing other methods.
Description of the drawings
Generation schematic diagrams of the Fig. 1 for DCO in DCR in prior art；
Fig. 2 is the generation schematic diagram of LNA gain modes conversion stage TV-DCO in prior art；
Fig. 3 is the carrier frequency deviation estimating method stream of the ofdm system with time-varying direct current offset in the embodiment of the present invention
Cheng Tu；
Fig. 4 is the carrier frequency deviation estimating method of the ofdm system with time-varying direct current offset in the embodiment of the present invention
Overall plan schematic diagram；
Fig. 5 estimates performance (ε=0.1) schematic diagram for the CFO in SNR range interested in the embodiment of the present invention；
Fig. 6 estimates performance (SNR=40dB) schematic diagram for the CFO in the range of CFO interested in the embodiment of the present invention；
Fig. 7 is the SER schematic diagrams after DCO in the embodiment of the present invention and CFO compensation.
Specific embodiment
To make the technical problem to be solved in the present invention, technical scheme and advantage clearer, below in conjunction with accompanying drawing and tool
Body embodiment is described in detail.
The present invention is low for existing carrier frequency deviation estimating method accuracy, a kind of big problem of error, there is provided band
Sometimes inversion of direct current offset quadrature divides the carrier frequency deviation estimating method of multiplex system.
As shown in Figure 3 and Figure 4, embodiments of the invention provide a kind of orthogonal point with time-varying direct current offset (TV-DCO)
Frequency is multiplexed carrier frequency shift (CFO) method of estimation of (OFDM) system, and the method includes：
Step 101, the mathematical model for setting up the ofdm system with CFO and TV-DCO；
Step 102, the method minimized by DCO compensation and Power leakage estimate CFO.
In embodiments of the present invention, the linear approximation based on TV-DCO, is that CFO estimates to propose a kind of blind arithmetic, should
Method includes 2 steps altogether：1) founding mathematical models；2) method of estimation to CFO is proposed, by DCO compensation and Power leakage
The method of minimum estimates CFO, and the method is named as LVD-EDE, that is, there is the EDE in linear change DCO, the LVD-EDE
Method is effective, and error is little, better than existing other methods.
Specifically, in a step 101, it is assumed that an ofdm system has N number of subcarrier, wherein shared by data transfer
K subcarrier is known as real subcarrier, and the N-K subcarrier that other are not occupied is referred to as empty subcarrier.AllowRepresent
The sampling interval in Digital Signal Processing (DSP) stage, wherein T are the cycles of the OFDM blocks of non-cycle prefix (CP).After CP is removed,
The reception sample for belonging to m-th OFDM block can be expressed as：
Wherein n=0 ..., N-1.Represent the indexed set of k real subcarrier.S (k, m) is to be mapped to
Modulated symbol H (k, m) of k-th subcarrier of m-th OFDM block is the response of corresponding frequency domain channel.Assume S (k, m) and H (k,
M) all it is zero-mean and separate.The phase offset of an accumulation is represented,
Wherein ε and NCPRefer to the length of CP in the normalized CFO of sub-carrier space and sample respectively.D (n, m) and w (n, m) are represented respectively
The TV-DCO of HPF and AWGN outputs.As the incoming level of HPF occurs suddenly the change that saltus step causes d (n, m), accurately say it is d
(n, m) is depending on HPF step responses.For single order HPF, its step response is represented by：
Wherein β and τ are positive real constants.τ is time constant, and it is inversely proportional to the cut-off frequency of HPF.In order to avoid symbol it
Between interference, the HPF with low cut-off frequency is usually used.Therefore, (2) can be approximated to be a linear model
According to (3) formula, we can set the TV-DCO in (1) formula two parameters a (m) and b (m), then
Wherein, a (m) and b (m) represent changing unit TV-DCO static and linear in m-th OFDM block respectively.(4) formula
In TV-DCO linear models be also widely adopted as HPF export one of TV-DCO it is effectively approximate.For expression is simplified, will
(4) formula is rewritten as matrix form：
rN(m)=PN(ε)UNxK(m)+INa(m)+cNb(m)+wN(m) (5)
The vector sample for wherein receiving, real subcarrier and noise symbol are used respectively
With
The transposition of label T representing matrixs therein,WithUnit vector and length are represented respectively
For the linear vector of N.Matrix U of the inverse discrete Fourier transform (IDFT) of real subcarrier with N × K rankKRepresent, wherein the
The input of (n, l) item isul∈Cr.This judgment matrixRepresent that CFO causes
Incremental phase offset.
In a step 102, CFO methods of estimation LVD-EDE
The basic thought of the LVD-EDE methods for being proposed comes from 2 points.First, a DC-free O signal yNM () can be simple
Ground is obtained by way of weighted linear combination (WLC)
WhereinAnd weight vectorsMeet
b(m)go(0)+g0(2)=0 (7)
With
a(m)go(0)+go(1)=0 (8)
Secondly, there will not be Power leakage etc. with the empty subcarrier for improving CFO compensation,
Wherein, | |. | |2Represent 2- norms, VNIt is the matrix of a N × (N-K), VN(n, l) individual element beIt is the index of N-K ranks void subcarrier.It should be noted that for the sake of clarity (9) later
Ignore influence of noise in formula, but effect of noise has been comprised in the emulation of LVD-EDE performance evaluations.In the base that the two are put
On plinth, we construct a cost function and are defined as：
By rN(m), INAnd cNThe first linear combination with a weight vectors g is compensated with eigenvalue v suppressing DCO
CFO, is then mapped to allied signal on empty subcarrier.If it is easily verified that ignoring influence of noise f (ε, g0)=0, this meaning
Taste (ε, g0) reach the minima of non-negative cost function.Based on this observation, we can consider to estimate by following research
CFO
Wherein,However, (ε, g0) it is not the unique solution of (11) formula by (5) formula generation
Enter YNM () and then substitution (10) formula are obtained
It is zero that pressure is made on the right of (12) formula, equivalent to
This equation has multiple solutions.Except the solution for intentionally getting, there are some to be not intended to the solution for obtaining.One of them is neat
Secondary solution, g are the null vectors of a 3*1.Another solution is WithIt is
Linear correlation.Some solutions for being not intended to obtain make us by (11) direct estimation carrier frequency shift but lucky
Can be to solve this problem by some way.By arranging a constraint to minimizingHomogeneous solution can be avoided.To the greatest extent
The solution for managing that linear dependence cannot be avoided, but the probability that it is present is less, because xkM () is achieved independently of TV-
DCO.Therefore its impact can be ignored in practice, not interfere with CFO estimations.Finally, in LVD-EDE, by (11)
Solution obtains CFO estimations, causes
Wherein, λmin{ z } and vmin{ z } represents minimal eigenvalue and its corresponding characteristic vector respectively.
The computing capability of LVD-EDE depends primarily on Ω3The Eigenvalues Decomposition of (v), because it can be held in each step
OK, other computing Exactly-onces.With regard to Eigenvalues Decomposition, because Ω3V () is a little conjugate matrices, size is 3*
3. there is effective method to calculate the corresponding characteristic vector of its minimal eigenvalue.
Below by way of the simulation results show method of the present invention.
In this section, the performance of LVD-EDE is compared with four benchmark algorithms by emulation and is shown.MUE,
NBE, CP-DFE and CP-LSE.MUE and NBE are ML CFO methods of estimation, respectively using DC-free O and static state DCO.CP-DFE with
CP-LSE is the blind version of DFE and LSE respectively.DFE and LSE are the only known algorithms of CFO estimations in TV-DCO.As data
Aided algorithm, they depend on transmission identical training sequence, this prevent we from directly with blind LVD-EDE methods and they
Relatively.In order to carry out the comparison of justice, two blind versions, CP-DFE and CP-LSE are we have developed.The two blind version difference
From the basic thought of DFE and LSE, the training sequence for being relied on originally is removed, be Cyclic Prefix using OFDM tail portions
CP is replacing.
Table 1
The condition of emulation is summarized in shown in table 1., similar to wlan system, when receiving beginning, TV-DCO is than letter for ofdm system
It is number high 10 decibels, and the cut-off frequency according to HPF of decaying.Estimate that performance has normalization mean square deviation (NMSE) to be defined asWherein E {. } represents desired computing.For the change of estimation CFO as fast as possible, only one of which OFDM block by with
In estimation.Except emulation, Cram é r-Rao lower bound (CRLB) of CFO estimations is reference is also made to.It is consistent with emulation,
CRLB is derived in the case where CFO estimates only to obtain from an OFDM block.First, defined parameters vector is used to estimateWith average observation vector
Here subscript R and I represents real and imaginary part respectively.Because the w in (5)NIt is assumed awgn channel, wherein F squares
The calculating of battle array can be reduced to
Wherein,
0NRepresent N*1 complete zero to
Amount.The CRLB of CFO estimates can be from F-1Last element on diagonal is obtained.
CFO of the distinct methods in SNR range is illustrated in Fig. 5 and estimates performance.In medium high s/n ratio region, except
Beyond LVD-EDE, wanted method all has not eliminable error.For MUE and NBE, this is due to lacking TV-DCO letters
Caused by number model.For CP-DFE and CP-LSE, this is because the intersymbol interference (ISI) caused by multipath channel
Cause, ISI causes the ending of CP OFDM symbols associated there inconsistent.Due to the linear model using TV-DCO
Remove to avoid ISI, LVD-EDE from not showing Error floor with CP, and its performance with the rising of signal to noise ratio it is asymptotic
Be close to CRLB.In low signal-to-noise ratio region, LVD-EDE reduces its performance due to the threshold effect of Eigenvalues Decomposition.This is
One of major defect of LVD-EDE.
Fig. 6 shows that LVD-EDE is effective in whole CFO during | ε | ＜ 0.5, better than additive method.
CFO in Fig. 5 in the range of SNR gain estimates performance (ε=0.1).
In Fig. 6, the CFO in CFO gain rangings estimates performance (SNR=40dB).The purpose that CFO estimates in ofdm system
It is according to the demodulation performance compensation CFO for receiving.Fig. 7 has shown according to the demodulation performance after symbol error rate compensation CFO and TV-DCO.
Wherein attenuation channel is considered as to be understood by receptor completely.CFO is compensated according to estimated value, and TV-DCO is according to its actual value
Compensated.According to the estimation performance of CFO, the lasting symbol error rate that only LVD-EDE is received is obtained with the increase of signal to noise ratio
To improvement.In low signal-to-noise ratio region, NBE, CP-DFE and CP-LSE receptivity is better than LVD-EDE, but their error in label
Rate is unacceptablely high.Fig. 7 is the SER performances after DCO and CFO compensation.
In embodiments of the present invention, the linear approximation based on TV-DCO, is that CFO estimates to propose a kind of blind arithmetic, should
Method includes 2 steps altogether：1) founding mathematical models；2) method of estimation to CFO is proposed, by DCO compensation and Power leakage
The method of minimum estimates CFO, and the method is named as LVD-EDE, that is, there is the EDE in linear change DCO, the LVD-EDE
Method is effective, and error is little, better than existing other methods.
The above is the preferred embodiment of the present invention, it is noted that for those skilled in the art
For, on the premise of without departing from principle of the present invention, some improvements and modifications can also be made, these improvements and modifications
Should be regarded as protection scope of the present invention.
Claims (3)
1. a kind of carrier frequency deviation estimating method of the ofdm system with time-varying direct current offset, it is characterised in that include：
The mathematical model of the ofdm system with CFO and TV-DCO is set up, wherein, CFO represents carrier frequency shift, and DCO is represented
Direct current offset, TV-DCO represent time dependent direct current offset, and the mathematical model is expressed as rN(m)=PN(ε)UNxK(m)+
INa(m)+cNb(m)+wN(m)；
The method minimized by DCO compensation and Power leakage estimates CFO；
Wherein, in the mathematical model for setting up the ofdm system with CFO and TV-DCO：The vector sample for receiving is：Wherein, m represents m-th OFDM block；
Real subcarrier is：Wherein,
S (k, m) is the modulated symbol of k-th subcarrier for being mapped to m-th OFDM block；H (k, m) is the response of corresponding frequency domain channel,
φ (m) represents the phase offset of an accumulation；
Noise symbol is：Wherein, the transposition of T representing matrixs,WithRespectively represent length for N complete 1 vector sum length for N linear vector, PN(ε) represent the increasing that ε causes
Amount phase offset,ε represents the normalized CFO of subcarrier spacing；
Matrix U of the inverse discrete Fourier transform (IDFT) of real subcarrier with N × K rankNRepresent, wherein (n, l) item is defeated
Entering isul∈Cr；
The method minimized by DCO compensation and Power leakage estimates that CFO includes：
DC-free O signal yNM () is obtained by way of weighted linear combination, i.e.,
Wherein,And weight vectorsMeet
b(m)go(0)+g0(2)=0 and a (m) go(0)+go(1)=0, wherein, a (m) and b (m) are represented in m-th OFDM block respectively
TV-DCO static and linear changing unit.
2. method according to claim 1, it is characterised in that obtaining DC-free O signal yNInclude after (m)：
Build cost function：By rN(m), INAnd cNWith a weight vectors g's
First linear combination compensates CFO with eigenvalue v, then allied signal is mapped on empty subcarrier suppressing DCO, wherein, its
In | | | |2Represent 2- norms, VNIt is the matrix of a N × (N-K), H represents conjugate transpose, PN(- v) represents the increasing that-v causes
Amount phase offset ,-v represent the normalized CFO of subcarrier spacing.
3. method according to claim 2, it is characterised in that include after f (v, g) is obtained：
WhereinWherein,Represent to ε
Estimation,Represent the estimation to g.
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| JP2008135888A (en) * | 2006-11-27 | 2008-06-12 | Osaka Prefecture Univ | Ofdm receiver with compensating function for cfo and dco |
| CN103152308A (en) * | 2013-03-04 | 2013-06-12 | 北京科技大学 | Joint estimation method of frequency offset, DC (Direct Current) and imbalance of orthogonal frequency division multiplexing system |
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| JP2008135888A (en) * | 2006-11-27 | 2008-06-12 | Osaka Prefecture Univ | Ofdm receiver with compensating function for cfo and dco |
| CN103152308A (en) * | 2013-03-04 | 2013-06-12 | 北京科技大学 | Joint estimation method of frequency offset, DC (Direct Current) and imbalance of orthogonal frequency division multiplexing system |
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| Title |
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| Pilot-based Frequency Offset Estimation in the Presence of Time-Varying DC Offset;Umut Yunus等;《2009 IEEE 20TH International Symposium on Personal, Indoor and Mobile Radio Communications》;20090916;第1567页右栏第3段、第1568页左栏第1段至第1569页左栏第6行 * |
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