CN1949754A - Method for estimating OFDM integer frequency shift based on virtual subcarrier and frequency domain differential sequence - Google Patents

Abstract

The invention relates to a method for estimating OFDM integral frequency offset based on virtual subcarrier and frequency domain differential sequence, belonging to communication technical field. And the invention only need one OFDM symbol as synchronous training symbol in each frame, having advantage of low training sequence data overhead and the peak mean power ratio of the symbol is very small; the invention comprises methods based on virtual subcarrier and frequency domain differential sequence, and according to maximum-likelihood criterion, estimates OFDM integral frequency offset and has better performance than those of the methods based on virtual subcarrier and frequency domain differential sequence; in addition, the invention selects proper frequency offset preselected value and can reduce searching range of frequency offset estimation, thus having lower calculating complexity.

Description

Method based on the estimating OFDM integer frequency deviation of virtual subnet carrier wave and frequency domain differential demodulation sequence

Technical field

The present invention relates to a kind of method of communication technical field, particularly a kind of method of the estimating OFDM integer frequency deviation based on virtual subnet carrier wave and frequency domain differential demodulation sequence.

Background technology

At present, the OFDM technology is applied at increasing wired, wireless communication field, and this has many advantages mainly due to the OFDM technology: effectively anti-multipath is disturbed and narrow band interference, and availability of frequency spectrum height, message transmission rate is high.Yet OFDM is for synchronism deviation, and is particularly very responsive to frequency departure.Frequency departure is divided into the decimal overtones band deviation of subcarrier spacing and the integer multiple frequency deviation of subcarrier spacing again, abbreviates decimal frequency bias and integer frequency bias hereinafter respectively as.Wherein, decimal frequency bias can cause and disturb (ICI) between subcarrier; Integer frequency bias can not cause ICI, but can cause the cyclic shift that receives data symbol, makes that the error probability of the information symbol after the demodulation is 50%.

The method of common estimating OFDM integer frequency deviation has three kinds:

(1) based on the virtual subnet carrier wave (virtual sub-carriers) of ofdm system, be that the synchronous training symbol of OFDM is on frequency domain, only use a part of subcarrier in the whole bandwidth (these subcarriers be called enable subcarrier (active sub-carriers)) frequency domain training sequence, remaining subcarrier zero setting, these subcarriers by zero setting are the virtual subnet carrier wave.In other words, the virtual subnet carrier wave is the subcarrier that is attached to synchronous training symbol on frequency domain.Owing to have orthogonality between the subcarrier of OFDM, so virtual sub-carrier space constitutes " zero subspace " of ofdm signal, utilizing inner product between the orthogonal sub-carriers is zero character, can extrapolate integer frequency bias.During specific implementation, can adopt energy measuring, estimate integer frequency bias by the energy-minimum that searching is enabled the energy maximum of subcarrier set or sought the virtual subnet carrier set.Referring to document: Huang D. etc., " Reduced complexity carrier frequency offset estimationfor OFDM systems ", IEEE Wireless Communications and NetworkingConference, Volume 3, Mar 2004, Page (s): 1411-1415 (" the OFDM frequency offset estimating method of low computation complexity " ieee communication and network field academic conference).Hereinafter, being called for short this method is method one.

(2) based on the frequency domain differential demodulation sequence, the method need be done fast Fourier transform (FFT) to the synchronous training symbol of OFDM, tries to achieve the frequency domain differential demodulation sequence then, and to make cyclic shift relevant with known difference sequence again, estimates integer frequency bias by seeking relevant peaks.Referring to document: Kim Y.H. etc., " An Efficient FrequencyOffset Estimator for Timing and Frequency Synchronization in OFDMSystems ", IEEE Pacific Rim Conference on Communications, Computers andSignal Processing, Aug 1999, Page (s): 580-583 (" a kind of time and frequency deviation method for synchronous that effectively is applied to ofdm system " IEEE Pacific rim about communicate by letter, the academic conference of computer and signal processing).Hereinafter, being called for short this method is method two.

(3) based on the synchronous training symbol structure of the OFDM of L five equilibrium, the method asks phase angle to estimate integer frequency bias by the auto-correlation of the specific delays of calculation training symbol again.Its estimation range becomes along with the increase of L greatly, but estimated accuracy variation thereupon, the also corresponding increase of computation complexity.Referring to document: Heiskala J. etc., " OFDMWireless LANs-A Theoretical and Practical Guide ", Indianapolis USA:Pearson Education Inc, 2002, Page (s): 70-73 (" guidance of OFDM WLAN (wireless local area network)---theory and practice " Pearson education publishing house).Hereinafter, being called for short this method is method three.

Method one and method two all need the synchronous training symbol of OFDM is done the FFT computing, belong to the frequency domain estimation technique.Compare, the performance of method two is better than method one, but needs bigger computing cost.Method three need not the synchronous training symbol of OFDM is made FFT, belongs to the time domain estimation technique, and itself and method one, method two do not have comparativity.As the time domain estimation technique, though the computation complexity of method three is lower, its estimated performance is difficult to satisfy the requirement of real system.

Summary of the invention

The objective of the invention is to shortcoming not good at the prior art estimated performance or that computation complexity is higher, a kind of method of estimating OFDM integer frequency deviation is provided, this method comprises based on the virtual subnet carrier wave with based on the method for frequency domain differential demodulation sequence, and according to ML (Maximum Likelihood, maximum likelihood) criterion, the OFDM integer frequency bias is made an estimate, its performance is better than the method based on the virtual subnet carrier wave, also be better than method based on the frequency domain differential demodulation sequence, simultaneously, this method is chosen suitable frequency deviation preset value, can dwindle the hunting zone of frequency offset estimating, has lower computation complexity.

The present invention is achieved through the following technical solutions, and specifically comprises the steps:

Step 1: transmitting terminal generates and to contain the virtual subnet carrier wave, and adjacent enable subcarrier on loaded the synchronous training symbol of OFDM of frequency domain differential demodulation sequence;

Step 2: receiving terminal obtains time synchronized and decimal Frequency Synchronization, and extracts the synchronous training symbol of OFDM according to utilizing prior art, removes Cyclic Prefix, through the decimal frequency bias compensation, remakes FFT, obtains the frequency domain sequence of the synchronous training symbol of OFDM;

Step 3: under assumed condition based on each integer frequency bias of virtual subnet carrier wave, obtain the synchronous training symbol of OFDM the energy of enabling the subcarrier set and, as possibility metric based on each integer frequency bias of virtual subnet carrier wave;

Step 4: under assumed condition, detect, obtain possibility metric based on each integer frequency bias of difference sequence by frequency domain differential demodulation demodulation and difference sequence based on each integer frequency bias of virtual subnet carrier wave;

Step 5: according to the ML criterion, merge based on the possibility metric of each integer frequency bias of virtual subnet carrier wave with based on the possibility metric of each integer frequency bias of difference sequence, the pairing frequency of the peak value of this metric is exactly the estimated value of integer frequency bias.

Described step 4 before frequency domain differential demodulation demodulation and difference sequence detection, is carried out preliminary election to described each integer frequency bias.

Described step 4 sorts the possibility metric of described each integer frequency bias based on the virtual subnet carrier wave from big to small, and λ the pairing integer frequency bias of possibility metric is as described preliminary election integer frequency bias before the order.

Described step 5, be specially: according to the ML criterion, real part addition with 1 times based on the possibility metric of each integer frequency bias of difference sequence based on the possibility metric of each integer frequency bias of virtual subnet carrier wave and 2 times, obtain possibility metric based on each integer frequency bias of ML criterion, seek its peak value, thereby integer frequency bias is made an estimate.

Below the invention will be further described:

(1) generate and to contain the virtual subnet carrier wave, and adjacent enable subcarrier on loaded the synchronous training symbol of OFDM of frequency domain differential demodulation sequence

OFDM is a kind of multicarrier modulation system, can carry qam symbol or PSK symbol on each subcarrier, and its modulation process can be represented with IDFT (discrete fourier inverse transformation) and DFT (discrete Fourier transform).If N represents the number of OFDM subcarrier, because the symmetry of IDFT and DFT, N represents that also the live part of OFDM symbol counts, and T represents the effective width of OFDM symbol, and subcarrier spacing is f _o=1/T.If the frequency domain data that a (k) expression transmitting terminal loads on k subcarrier of synchronous training symbol; In the synchronous training symbol of b (l) expression, the base band time domain data of l sampled point.A (k) is made b (l) some IDFT:

$b\left(l\right)=\frac{1}{N}\underset{k=-N_{u1}}{\overset{N_{u2}}{\mathrm{\&Sigma;}}}a\left(k\right)\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\frac{\mathrm{kl}}{N}\right)$ (l＝-N _g，...，0，1，...，N-1) (1)

In the formula, N _U1The number of the available subcarrier of the negative spectral regions of expression base band, N _U2The number of the available subcarrier of the positive spectral regions of expression base band, N _U1+ N _U2=N _uThe total number of expression available subcarrier, N _gBe counting of Cyclic Prefix.

Consider the design of virtual subnet carrier wave, according to the subcarrier loading data, the set of definition subcarrier sequence number is as follows:

Available subcarrier S generally determines by the related protocol standard is unique, contains (C (S)=N _u) individual element:

S＝{S(i)|1≤i≤C(S)，S(i)＜S(i+1)，-N _u1≤S(i)≤N _u2，S(i)≠0} (2)

Participate in generating the subcarrier S of virtual subnet carrier wave _Origin, it contains C (S _Origin) individual element:

S _origin＝{S _o(i)|1≤i≤C(S _origin)，S _o(i)＜S _o(i+1)，S _o(i)∈S} (3)

S _OriginWith the relation of S be: S _Origin S.

The design masterplate of virtual subnet carrier wave can (B be the length of d, and B=C (S with a binary sequence d={d (j) 1≤j≤B} _Origin)) expression, the S of 0 element institute correspondence position among the d _OriginSubcarrier be virtual subnet carrier wave, not loading data; The S of 1 element institute correspondence position _OriginSubcarrier for enabling subcarrier, loading data is shown S with the set form with above-mentioned two kinds of information slips _VirAnd S _Act:

S _VirAnd S _ActThe element number that contains respectively is C (S _Vir) and C (S _Act), promptly the number of 0 element and 1 element is respectively C (S among the d _Vir) and C (S _Act).Because S _VirUS _Act=S _Origin, and S _VirI S _ActSo= is C (S _Vir)+C (S _Act)=C (S _Origin)=B.

According to method one, choose d for having the autocorrelative pseudo random sequence of sharp-pointed peak value, such as the m sequence, the m sequence of brachymemma, the Gold sequence is (referring to document: Gold R., " Optimal binary sequences forspread spectrum multiplexing ", IEEE Transactions on Information Theory, 1967, Volume 13, NO.4, Page (s): 619-621 (" being applied to the multiplexing best binary sequence of spread spectrum " IEEE information theory periodical)), quadratic residue sequence is (referring to document: Klapper A. etc., " Cascaded GMW sequences ", IEEE Transactions on Information Theory, 1993, Volume 39, NO.1, Page (s): 177-183 (" cascade GMW sequence " IEEE information theory periodical)) or the like.In a word, can be as long as satisfy the binary sequence of anti-forge random property substantially as d.

It is pointed out that in real system the integer frequency bias scope generally has the upper limit, such as, be 2GHz with the carrier frequency, subcarrier spacing is 5KHz, the worst error of user side crystal oscillator is an example for the system of ± 10ppm, its maximum integer frequency bias be 2G * (± 10ppm)/5K=± 4.So the auto-correlation function of binary sequence d only needs to present sharp-pointed peak value in [4,4] and gets final product.Make the maximum integer frequency deviation of system be ± g _Max(g _MaxBe positive integer).

Therefore, the design process of d generally can be divided into for three steps: at first, determine the sequence classification (m sequence, the m sequence of brachymemma, Gold sequence, quadratic residue sequence or the like) of d; Then, at B=C (S _Origin) condition under, by all d of computer exhaustive search at maximum frequency deviation scope [g _Max, g _Max] interior auto-correlation function; At last, choose the design masterplate of the most sharp-pointed d of auto-correlation function form as the virtual subnet carrier wave.

Determined the design masterplate of virtual subnet carrier wave, determined S with regard to unique _VirAnd S _ActAt S _ActThe middle pairing adjacent sub-carrier of adjacent element is to last loading frequency domain differential demodulation sequence, and this process and method two is similar, but there is essential distinction in the two.The way of method two can equivalence be 1 binary sequence d for adopting an all elements, then adjacent sub-carrier on load the frequency domain differential demodulation sequence, therefore, the S in the method two _ActThe adjacent element strictness uniformly-spaced, and on frequency domain, evenly distribute.So in method two, adjacent sub-carrier does not need artificial design to being intrinsic.But S in the present invention, _ActBecause be subjected to the effect of d, it presents pseudo-random distribution on frequency domain, so its corresponding adjacent sub-carrier redefines and designs needs, and is as follows:

For S _Act, search for its adjacent sub-carrier to (S _A1(i), S _A2(i)), make all subcarriers to belonging to S set _Adj:

In the formula (6), α is the maximum definition distance of adjacent sub-carrier, usually, is subjected to approximately uniform channel effect in order to guarantee adjacent sub-carrier, generally gets α≤4, promptly when the distance between two subcarriers surpasses 4 subcarrier spacings, thinks that just the two is non-conterminous.S _AdjElement number be C (S _Adj), this is that this value is big more in order to the length of loading frequency domain differential demodulation sequence, the estimated performance of system is good more.Obviously, according to formula (6) to different S _ActSearch for, will obtain different S _Adj, when the design system parameter, need be to d and S _AdjTake all factors into consideration, should make the autocorrelation of d comparatively sharp-pointed, also will make C (S _Adj) bigger.

Usually, choose the more sharp-pointed permanent envelope sequence of autocorrelation (for example PN sequence) as being loaded into S _AdjOn frequency domain differential demodulation sequence p={p (i) | 1≤i≤C (S _Adj), so, the S of the synchronous training symbol of OFDM _ActOn date expression be:

In the formula (7), θ is a random phase arbitrarily, and the expression part is enabled the constraint that data on the subcarrier are not subjected to p, can be used to improve the PAPR (peak-to-average power ratio) of synchronous training symbol.

(2) time synchronized and decimal Frequency Synchronization

If r (m) expression receiving terminal is received the base band time domain data of m sampled point of the synchronous training symbol of OFDM, h (l) expression time-delay is l the pairing time domain channel response in sampling instant path; N (m) expression channel is to the time domain additive Gaussian noise of r (m); ψ is a first phase; f _ΔBe to the frequency deviation after the subcarrier spacing normalization, equal decimal frequency bias  and integer frequency bias g sum; ε is that then the expression formula of r (m) is to the time synchronized deviation after the sampled point interval normalization:

$r\left(m\right)=\exp (\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_{\mathrm{\&Delta;}}(m-\mathrm{\&epsiv;})/N+\mathrm{j\&psi;})\underset{l}{\mathrm{\&Sigma;}}b(m-\mathrm{\&epsiv;}-l)h\left(l\right)+n(m-\mathrm{\&epsiv;})...\left(8\right)$

At present, the time synchronized of OFDM and decimal Frequency Synchronization are comparatively mature technique.Such as, choose:

S _origin＝{S _o(i)1≤i≤C(S _origin)，S _o(i)＜S _o(i+1)，S _o(i)∈S，S _o(i)＝0(mod L)} (9)

Then S S _OriginSubcarrier on loading data not, just can generate the synchronous training symbol of OFDM of separation structures such as L, especially, when L=2, calculate the auto-correlation of the half symbols delay of synchronous training symbol on time domain, seek peak value and determine the time starting point, the phase angle of peaking estimates decimal frequency bias again.Referring to document: Keller T. etc., " Orthogonal Frequency Division Multiplex Synchroni-zation Techniques for Frequency-Selective Fading Channels ", IEEEJournal on Selected Areas in Communications, Volume.19, NO.6, June2001 Page (s): 999-1007.(the selected communication technical field periodical of " the OFDM simultaneous techniques under the frequency selective fading channels " IEEE)

Again such as, S S _OriginIn a part of subcarrier on load fixing frequency domain sequence, thereby generate fixing time domain sequences, this time domain sequences all is in advance known for transmitting terminal and receiving terminal, receiving terminal carries out continuous relevant search to the received signal with this time domain sequences, the relevant peaks position is exactly the original position of OFDM symbol, investigate the phase property of receiving sequence then, estimate decimal frequency bias.Referring to document: 3GPP, R1-060781, NTT DoCoMo, " Cell Search Time Performance ofThree-Step Cell Search Method ".(3GPP document, numbering: R1-060781, NTT DoCoMo company, " three step small region search methods are in the performance of the performance aspect search time ")

Suppose that time synchronized is estimated and the decimal frequency bias estimation is entirely true, then r (m) is carried out corresponding compensation, and after removing Cyclic Prefix:

$\stackrel{\&OverBar;}{r}\left(m\right)=\exp (\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;gm}/N+\mathrm{j\&psi;})\underset{l}{\mathrm{\&Sigma;}}b(m-l)h\left(l\right)+n\left(m\right)$ (m＝0，1，...，N-1) (10)

R (m) is made N point FFT, obtains the frequency domain sequence of synchronous training symbol:

$z\left(k\right)=\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{r}\left(m\right)\exp (-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;mk}/N)$ (-N _u1≤k≤N _u2) (11)

With formula (1) substitution formula (10), substitution formula again (11) obtains its equivalent frequency-domain expression and is:

z(k)＝a(k-g)H(k-g)exp(jψ)+n′(k-g)(-N _u1≤k≤N _u2) (12)

In the formula, H (k) is the frequency domain influence of multidiameter fading channel to k subcarrier, and n ' is the frequency domain additive noise of channel to k subcarrier (k).

(3) calculating is based on the possibility metric of each integer frequency bias of virtual subnet carrier wave

Assumed condition g at each integer frequency bias ^%Down, { z (k) } carried out corresponding compensation, promptly cyclic shift gets { z (k+g ^%).Calculate k ∈ S _OriginThe energy sequence of corresponding subcarrier, obtain its energy of enabling the subcarrier set and, as possibility metric, as the formula (13) based on each integer frequency bias of virtual subnet carrier wave:

$R\left(g^{\%}\right)=\underset{k\&Element;S_{\mathrm{act}}}{\mathrm{\&Sigma;}}{\left|z(k+g^{\%})\right|}^2(g^{\%}\&Element;G_{\mathrm{assump}})...\left(13\right)$

In the formula, G _AssumpRepresent all possible g ^%Set, i.e. G _AssumpBe [g _Max, g _Max] interior all possible integer frequency bias value, and establish G _AssumpContain C _gIndividual element.

Method one is obtaining formula (13) afterwards, by seeking R (g ^%) peak value, promptly integer frequency bias is made an estimate.

The calculating of this step mainly concentrates on formula (13), calculates | z (k+g ^%) | ²Need C (S altogether _Origin) inferior complex multiplication.Also need C in addition _g* C (S _Act) inferior real number addition, equivalence is C _g* C (S _Act)/2 time complex addition.The present invention is basic identical in the computation complexity and the method one of this step.

(4) the integer frequency bias value that goes out based on the virtual subnet carrier estimation is carried out preliminary election, calculate again under the assumed condition of each integer frequency bias, based on the possibility metric of each integer frequency bias of difference sequence

To sort from big to small based on the possibility metric of each integer frequency bias of virtual subnet carrier wave, λ integer frequency bias is designated as and gathers G as preset value before the order _Assump ^λ:

(1≤λ≤C _g) (14)

In the formula, λ is big more, and performance of the present invention is good more, but computation complexity is high more.As λ=C _gThe time, formula (14) is equivalent to does not carry out any preliminary election to integer frequency bias, promptly integer frequency bias is carried out global search, and it is optimum that performance of the present invention reaches at this moment.A parameter when λ is system design, the decisions such as time, hardware resource of giving the Frequency Synchronization unit by system assignment.

For each $g^{\%}\&Element;G_{\mathrm{assump}}^{\mathrm{\&lambda;}},$ { z (k) } carried out corresponding compensation, and promptly cyclic shift gets { z (k+g ^%).When not considering noise, when only considering multidiameter fading channel, differential ference spiral S _A1(i)+g ^%And S _A2(i)+g ^%Data on the corresponding adjacent sub-carrier are got by formula (7) and formula (12):

$w^{g^{\%}}\left(i\right)=z{(S_{a1}\left(i\right)+g^{\%})}^{*}z(S_2\left(i\right)+g^{\%})$

$=\left[a(S_{a1}\left(i\right)+g^{\%}-g)H(S_{a1}\left(i\right)+g^{\%}-g){]}^{*}\right[a(S_{a2}\left(i\right)+g^{\%}-g)H(S_{a2}\left(i\right)+g^{\%}-g)]$

$(g^{\%}\&Element;G_{\mathrm{assump}}^{\mathrm{\&lambda;}},1\&le;i\&le;C\left(S_{\mathrm{adj}}\right))...\left(15\right)$

The condition of consideration formula (6), when α hour, can think H (S _A2(i)) ≈ H (S _A1(i)), so, have only the g of working as ^%During=g, formula (15) just can be reduced to:

$w^{g^{\%}}\left(i\right)\&ap;a{\left(S_1\left(i\right)\right)}^{*}a\left(S_2\left(i\right)\right){\left|H\left(S_1\left(i\right)\right)\right|}^2=p\left(i\right){\left|H\left(S_1\left(i\right)\right)\right|}^2...\left(16\right)$

Calculate each $g^{\%}\&Element;G_{\mathrm{assump}}^{\mathrm{\&lambda;}}$ The time sequence $w^{g^{\%}}=\left\{w^{g^{\%}}\left(i\right)\right\}$ With the correlation of p:

$T\left(g^{\%}\right)=\underset{i=1}{\overset{C\left(S_{\mathrm{adj}}\right)}{\mathrm{\&Sigma;}}}{\left(w^{g^{\%}}\left(i\right)\right)}^{*}p\left(i\right)(g^{\%}\&Element;G_{\mathrm{assump}}^{\mathrm{\&lambda;}})...\left(17\right)$

T (g ^%) be under the assumed condition of each integer frequency bias, detect by frequency domain differential demodulation demodulation and difference sequence, obtain possibility metric based on each integer frequency bias of difference sequence.

Method two is obtaining formula (17) afterwards, by seeking T (g ^%) peak value of squared absolute value, integer frequency bias is made an estimate.

The calculating of this step mainly concentrates on formula (15) and formula (17), needs 2 λ C (S _Adj) inferior complex multiplication and λ C (S _Adj) inferior complex addition, equivalence is λ C (S _Adj)/2 time complex addition.Method two is also wanted calculating formula (15) and formula (17), but it can't carry out preliminary election to integer frequency bias, so, need 2C altogether _g* C (S _Origin) inferior complex multiplication and C _g* C (S _Origin) inferior complex addition, equivalence is C _g* C (S _Origin)/2 time complex addition.Therefore, the present invention is significantly less than method two at the computation complexity of this step.

(5) according to the ML criterion, merge based on the possibility metric of each integer frequency bias of virtual subnet carrier wave with based on the possibility metric of each integer frequency bias of difference sequence, estimate integer frequency bias then

According to the ML criterion, integer frequency bias estimation metric is derived, at first the signal that receives is done hypothesis.By formula (12), to g, H and ψ are hypothesis g ^%, H ^%And ψ ^%If v ^%(m) be according to H ^%The time domain sequences of the synchronous training symbol that obtains:

$v^{\%}\left(m\right)=\frac{1}{N}\underset{k=-N_{u1}}{\overset{N_{u2}}{\mathrm{\&Sigma;}}}a\left(k\right)H^{\%}\left(k\right)\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\frac{\mathrm{km}}{N}\right)$ (m＝0，1，...，N-1) (18)

Know that by formula (10) r (m) is the time domain sequences of the synchronous training symbol that receives, so, about (g ^%, H ^%, ψ ^%) likelihood function (likelihood function) can be expressed as:

$\mathrm{\&Lambda;}(g^{\%},H^{\%},{\mathrm{\&psi;}}^{\%})=\frac{1}{{\left({\mathrm{\&pi;\&sigma;}}^2\right)}^N}\exp \{-\frac{1}{{\mathrm{\&sigma;}}^2}\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}|\stackrel{\&OverBar;}{r}\left(m\right)-\exp (\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{g}^{\%}/N+j{\mathrm{\&psi;}}^{\%})v^{\%}\left(m\right){|}^2\}$

$=\frac{\exp \{-\frac{1}{{\mathrm{\&sigma;}}^2}\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}[{\left|\stackrel{\&OverBar;}{r}\left(m\right)\right|}^2+{\left|v^{\%}\left(m\right)\right|}^2-2\mathrm{Re}\left[\stackrel{\&OverBar;}{r}\left(m\right)\exp (-j(2\mathrm{\&pi;}{g}^{\%}m/N+{\mathrm{\&psi;}}^{\%}))v^{\%*}\left(m\right)\right]\left]\right\}}{{\left({\mathrm{\&pi;\&sigma;}}^2\right)}^N}...\left(19\right)$

In the formula, σ ²Be the power of additive white Gaussian noise.The influence of some constants in the removal formula (19), and consideration formula (11) and formula (18) through abbreviation, are rewritten as formula (19):

$\mathrm{\&Lambda;}(g^{\%},H^{\%},{\mathrm{\&psi;}}^{\%})=\exp \left\{\frac{1}{{\mathrm{\&sigma;}}^2}\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\mathrm{Re}\right[\stackrel{\&OverBar;}{r}\left(m\right)\exp (-j(2\mathrm{\&pi;}{g}^{\%}m/N+{\mathrm{\&psi;}}^{\%}))v^{\%*}\left(m\right)\left]\right\}$

$=\exp \left\{\frac{1}{{\mathrm{\&sigma;}}^2}\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\mathrm{Re}\right[\stackrel{\&OverBar;}{r}\left(m\right)\exp (-j(2\mathrm{\&pi;}{g}^{\%}m/N+{\mathrm{\&psi;}}^{\%})){\left(\frac{1}{N}\underset{k=-N_{u2}}{\overset{N_{u1}}{\mathrm{\&Sigma;}}}a\left(k\right)H^{\%}\left(k\right)\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;mk}}{N}\right)\right)}^{*}\left]\right\}$

$=\exp \left\{\frac{1}{N{\mathrm{\&sigma;}}^2}\underset{k=-N_{u2}}{\overset{{\mathrm{<figure-callout\; id="1"\; label="N\; u"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">N</figure-callout>}}_u}{\mathrm{\&Sigma;}}}\mathrm{Re}\right[a^{*}\left(k\right)H^{\%}\left(k\right)\exp (-j{\mathrm{\&psi;}}^{\%})\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{r}\left(m\right)\exp (-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;m}\left(k+g^{\%}\right)}{N})\left]\right\}$

$=\exp \left\{\frac{1}{{\mathrm{N\&sigma;}}^2}\underset{k=-N_{u2}}{\overset{{\mathrm{<figure-callout\; id="1"\; label="N\; u"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">N</figure-callout>}}_u}{\mathrm{\&Sigma;}}}\mathrm{Re}\right[a^{*}\left(k\right)H^{\%}\left(k\right)\exp (-j{\mathrm{\&psi;}}^{\%})z(k+g^{\%})\left]\right\}...\left(20\right)$

In the formula, Re[g] the expression computing of getting real part.When noise is big, to formula (20) as multinomial approach (according to Taylor series expansion, when x hour, exp (x) ≈ 1+x+x is arranged ²/ 2):

$\mathrm{\&Lambda;}(g^{\%},H^{\%},{\mathrm{\&psi;}}^{\%})\&ap;1+\frac{1}{N{\mathrm{\&sigma;}}^2}\underset{k=-N_{u1}}{\overset{{\mathrm{<figure-callout\; id="2"\; label="N\; u"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">N</figure-callout>}}_u}{\mathrm{\&Sigma;}}}\mathrm{Re}\left[a^{*}\left(k\right)H^{\%}\left(k\right)\exp (-j{\mathrm{\&psi;}}^{\%})z(k+g^{\%})\right]$

$+\frac{2}{2{\left(N{\mathrm{\&sigma;}}^2\right)}^2}{\left(\underset{k=-N_{u1}}{\overset{{\mathrm{<figure-callout\; id="2"\; label="N\; u"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">N</figure-callout>}}_u}{\mathrm{\&Sigma;}}}\mathrm{Re}\right[a^{*}\left(k\right)H^{\%}\left(k\right)\exp (-j{\mathrm{\&psi;}}^{\%})z(k+g^{\%})\left]\right)}^2...\left(21\right)$

To the H in the formula (21) ^%And ψ ^%Do on average, these two variablees of cancellation, thus obtain about g ^%Likelihood function:

$\mathrm{\&Lambda;}\left(g^{\%}\right)\&ap;\underset{H^{\%},{\mathrm{\&psi;}}^{\%}}{\mathrm{AVE}}\left\{{\left[\underset{k=-N_{u2}}{\overset{N_{u1}}{\mathrm{\&Sigma;}}}\right[a^{*}\left(k\right)H^{\%}\left(k\right)\exp (-j{\mathrm{\&psi;}}^{\%})z(k+g^{\%})+a\left(k\right)H^{\%}\left(k\right)\exp \left({\mathrm{j\&psi;}}^{\%}\right)z^{*}(k+g^{\%})\left]\right]}^2\right\}$

$=\underset{H^{\%},{\mathrm{\&psi;}}^{\%}}{\mathrm{AVE}}\{2\underset{k=-N_{u2}}{\overset{{\mathrm{<figure-callout\; id="1"\; label="N\; u"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">N</figure-callout>}}_u}{\mathrm{\&Sigma;}}}{\left|a\left(k\right)\right|}^2{\left|H^{\%}\left(k\right)\right|}^2{\left|z(k+g^{\%})\right|}^2$

$+4\mathrm{Re}\left[\underset{({\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">k</figure-callout>}}_1,k_2)\&Element;S_{\mathrm{adj}}}{\mathrm{\&Sigma;}}a\left(k_1{H}^{\%}\right)\left(k_1\right)\exp (-j{\mathrm{\&psi;}}^{\%})z^{*}({\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">k</figure-callout>}}_1+g^{\%})a^{*}\left(k_2\right)H^{\%}\left(k_2\right)\exp \left(j{\mathrm{\&psi;}}^{\%}\right)z({\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">k</figure-callout>}}_2+g^{\%})\right]\}...\left(22\right)$

In the formula,

Expression is to H ^%And ψ ^%Do average.Think H ^%To not gain and the decline of synchronous training symbol, then $\underset{H^{\%},{\mathrm{\&psi;}}^{\%}}{\mathrm{AVE}}\left\{{\left|H^{\%}\left(k\right)\right|}^2\right\}=1.$ In addition, consideration formula (15) and formula (17), and ignore some constants once more, abbreviation formula (22):

$\mathrm{\&Lambda;}\left(g^{\%}\right)=\underset{H^{\%},{\mathrm{\&psi;}}^{\%}}{\mathrm{AVE}}\{\underset{k=-N_{u2}}{\overset{{\mathrm{<figure-callout\; id="1"\; label="N\; u"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">N</figure-callout>}}_u}{\mathrm{\&Sigma;}}}{\left|z(k+g^{\%})\right|}^2+2\mathrm{Re}[\underset{({\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">k</figure-callout>}}_1,k_2)\&Element;S_{\mathrm{adj}}}{\mathrm{\&Sigma;}}{z}^{*}({\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">k</figure-callout>}}_1+g^{\%})z({\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">k</figure-callout>}}_2+g^{\%})a\left(k_1\right)a^{\%*}\left(k_2\right){\left|H^{\%}\left(k_1\right)\right|}^2\left]\right\}$

$=\underset{k=-N_{u2}}{\overset{{\mathrm{<figure-callout\; id="1"\; label="N\; u"\; filenames="A20061011811000281.png,A20061011811000282.png"\; state="\{\{state\}\}">N</figure-callout>}}_u}{\mathrm{\&Sigma;}}}{\left|z(k+g^{\%})\right|}^2+2\mathrm{Re}\left[\underset{i=1}{\overset{C\left(S_{\mathrm{adj}}\right)}{\mathrm{\&Sigma;}}}{\left(w^{g^{\%}}\left(i\right)\right)}^{*}p\left(i\right)\right]$

$=R\left(g^{\%}\right)+2\mathrm{Re}\left[T\left(g^{\%}\right)\right],(g^{\%}\&Element;G_{\mathrm{assump}}^{\mathrm{\&lambda;}})...\left(23\right)$

So, seek A (g ^%) peak value, g makes an estimate to integer frequency bias:

$\hat{g}=\arg \underset{g^{\%}}{\max }\left\{\mathrm{\&Lambda;}\left(g^{\%}\right)|g^{\%}\&Element;G_{\mathrm{assump}}\right\}...\left(24\right)$

The calculating of this step mainly concentrates on formula (23), only needs 1 real multiplications and 1 real number addition, can ignore.

The invention has the advantages that: only need 1 OFDM symbol as synchronous training symbol, has the low advantage of training sequence data expense, and the peak-to-average power ratio of this symbol is very low, in addition, the present invention comprises based on the virtual subnet carrier wave with based on the method for frequency domain differential demodulation sequence, and according to the ML criterion, above-mentioned two kinds of frequency deviation estimating methods of being derived by the different technologies condition is combined, the OFDM integer frequency bias is made an estimate, thereby obtain estimated gain than independent method.Therefore, performance of the present invention both had been better than the method based on the virtual subnet carrier wave, also was better than the method based on the frequency domain differential demodulation sequence.Simultaneously, the present invention chooses suitable frequency deviation preset value, can dwindle the hunting zone of frequency offset estimating, makes the present invention have lower computation complexity.

Description of drawings

Fig. 1 is the circulation auto-correlation function of d in [4,4]

Fig. 2 is an OFDM baseband modulation and demodulation block diagram

Fig. 3 is an enforcement block diagram of the present invention

Fig. 4 is the auto-correlation function of frequency domain differential demodulation sequence p

Fig. 5 is when integer frequency bias is 2, R (g ^%) typical case figure

Fig. 6 is when integer frequency bias is 2, Re[T (g ^%)] typical case figure

Fig. 7 is when integer frequency bias is 2, Λ (g ^%) typical case figure

Fig. 8 is that not carry out preliminary election (be λ=C in the present invention _g=5) and when carrying out preliminary election (λ=3, λ=2), with method one and method two in the performance aspect the integer frequency bias estimated error rate relatively

Fig. 9 is that not carry out preliminary election (be λ=C in the present invention _g=5) and when carrying out preliminary election (λ=3, λ=2), with method one and method two in the performance aspect the frequency offset estimating mean square error relatively

Embodiment

Provide a concrete OFDM parameter configuration below, set forth performing step of the present invention.Need to prove that the parameter in the following example does not influence generality of the present invention.

The document of 3GPP tissue: TR 25.892 V6.0.0, " Feasibility Study for OrthogonalFrequency Division Multiplexing (OFDM) for UTRAN enhancement (Release6) " (OFDM technology feasibility study in improved universal mobile telecommunications system and continental rise radio access network), the one group of OFDM parameter that provides is as follows:

Carrier frequency 2GHz

System bandwidth 6.528MHz

Sub-carrier number N 1024

Effective sub-carrier number N _u704 (N _U1=N _U2=352)

Effective bandwidth 4.495MHz

Subcarrier spacing f _o6.375kHz

Cyclic Prefix N _g64 points (9.803us)

Symbol period T 156.85+9.81=166.66us

Because carrier frequency is 2GHz, suppose that the worst error of user side crystal oscillator is ± 10ppm, the maximum frequency deviation error is ± 20KHz so, and subcarrier spacing is 6.375KHz, therefore, the maximum frequency deviation error is ± 3.14.So, get g _Max=4 can covering system the maximum frequency deviation scope.

Performing step of the present invention is as follows:

(1) generate and to contain the virtual subnet carrier wave, and adjacent enable subcarrier on loaded the synchronous training symbol of OFDM of frequency domain differential demodulation sequence

By N _N1=N _N2=352, obtain S={-352 ,-351 ... ,-1,1 ..., 351,352}, C (S)=704.Make S _Origin={ S _o(i) 1≤i≤C (S _Origin), S _o(i)＜S _o(i+1), S _o(i) ∈ S, S _o(i)=0 (mod 2) }, that is:

S _origin＝{-352，-350，...，-2，2，...，350，352} (25)

C (S then _Origin)=352.S S _OriginSubcarrier on loading data not, thereby generate the synchronous training symbol of 2 five equilibriums.

Choosing d is the m sequence of brachymemma, because B=C (S _Origin)=352, and the length of m sequence is 2 ^t-1 (t is a positive integer) is 2 so generate length ⁹The m sequence M of-1=511 ₅₁₁For brachymemma.Selecting its primitive polynomial is 1+x ³+ x ⁴+ x ⁶+ x ⁹, then, by computer search M ₅₁₁511 cyclic shift samples, and each cyclic shift sample is truncated to length is 352, investigates it at maximum frequency deviation scope [g _Max, g _Max]=[-4,4] interior auto-correlation function.At last, choose the design masterplate of the most sharp-pointed d of auto-correlation function form as the virtual subnet carrier wave.It is as follows that d is expressed as binary sequence:

d
	1001001011110011111101111010101010000111110110100110111110000001 1110010110001101100110100100100110101101000100011110110000000110 1010011101010001110010100010101001010011001100000101011011000100 1010111111101011100100001001000100111000111011001001111000010100 1000000001001100010110011110100011000011001110011101110111111001 10110111100011001010101100101110

It is pointed out that the m sequence of choosing brachymemma in this example as d, does not influence versatility of the present invention.In real system, can choose other sequences as d.The circulation auto-correlation function of d in [4,4] as shown in Figure 1, its auto-correlation peak value is 352, other correlations are 170, difference is 182.This difference is M ₅₁₁All 511 cyclic shift samples in maximum, at this moment, d has the most sharp-pointed auto-correlation function form.

In addition, in Fig. 1, the transverse axis unit gap of the circulation auto-correlation function of d is 2, and this is that promptly 1 unit of d cyclic shift is equivalent to 2 subcarriers of frequency domain superior displacement because d dual numbers subcarrier of formula (25) decision is effective.

According to d, and formula (4) and formula (5), can unique definite S _VirAnd S _ActWith S _ActBe listed as follows:

S act

-352 -346 -340 -336 -334 -332 -330 -324 -322 -320 -318 -316 -314 -310 -308 -306 -304 -300 -296 -292 -288 -278 -276 -274 -272 -270 -266 -264 -260 -254 -252 -248 -246 -244 -242 -240 -226 -224 -222 -220 -214 -210 -208 -200 -198 -194 -192 -186 -184 -180 -174 -168 -162 -160 -156 -152 -150 -146 -138 -130 -128 -126 -124 -120 -118 -102 -100 -96 -92 -86 -84 -82 -78 -74 -66 -64 -62 -56 -52 -44 -40 -36 -30 -26 -20 -18 -12 -10 48 12 14 18 20 28 34 38 42 44 46 48 50 52 54 58 62 64 66 72 82 88 96 102 104 106 114 116 118 122 124 130 136 138 140 142 152 156 162 180 186 188 196 200 202 208 210 212 214 218 226 228 238 240 246 248 250 256 258 260 264 266 268 272 274 276 278 280 282 288 290 294 296 300 302 304 306 314 316 322 326 330 334 336 342 346 348 350

Through counting, C (S _Act)=177.For above-mentioned S _Act, under the condition of α=4, obtain S by formula (6) search _Adj, through counting, C (S _Adj)=129.With S _AdjIn S _A1(i) and S _A2(i) it is as follows to make form:

S a1(i)1≤i≤129

-340 -336 -334 -332 -324 -322 -320 -318 -316 -314 -310 -308 -306 -304 -300 -296 -292 -278 -276 -274 -272 -270 -266 -264 -254 -252 -248 -246 -244 -242 -226 -224 -222 -214 -210 -200 -198 -194 -186 -184 -162 -160 -156 -152 -150 -130 -128 -126 -124 -120 -102 -100 -96 -86 -84 -82 -78 -66 -64 -56 -44 -40 -30 -20 -12 4 8 12 14 18 34 38 42 44 46 48 50 52 54 58 62 64 102 104 114 116 118 122 136 138 140 152 186 196 200 208 210 212 214 226 238 246 248 256 258 260 264 266 268 272 274 276 278 280 288 290 294 296 300 302 304 314 322 326 330 334 342 346 348

S a2(i)1≤i≤129

-336 -334 -332 -330 -322 -320 -318 -316 -314 -310 -308 -306 -304 -300 -296 -292 -288 -276 -274 -272 -270 -266 -264 -260 -252 -248 -246 -244 -242 -240 -224 -222 -220 -210 -208 -198 -194 -192 -184 -180 -160 -156 -152 -150 -146 -128 -126 -124 -120 -118 -100 -96 -92 -84 -82 -78 -74 -64 -62 -52 -40 -36 -26 -18 -10 8 12 14 18 20 38 42 44 46 48 50 52 54 58 62 64 66 104 106 116 118 122 124 138 140 142 156 188 200 202 210 212 214 218 228 240 248 250 258 260 264 266 268 272 274 276 278 280 282 290 294 296 300 302 304 306 316 326 330 334 336 346 348 350

Choose p={p (i) } be loaded into S for the more sharp-pointed permanent envelope PN sequence of autocorrelation _AdjOn, because C (S _Adj)=129, so, 1≤i≤129.P such as following table that certain once generates at random:

i	p(i)	i	p(i)	i	p(i)
						1	0.9866+0.1242j	44	-0.9852-0.1349j	87	0.9463+0.3052j
2	0.6074-0.7873j	45	-0.9621+0.2512j	88	0.9751+0.1946j
						3	-0.9872+0.1186j	46	0.2840-0.9529j	89	0.9938+0.0318j
4	0.4729+0.8747j	47	0.0844+0.9907j	90	-0.5973+0.7949j
						5	-0.3393-0.9347j	48	-0.7075+0.6986j	91	0.9938-0.0339j
6	-0.5123+0.8522j	49	0.9607+0.2565j	92	0.4921-0.8640j
						7	0.9811+0.1618j	50	0.8686-0.4841j	93	-0.9355-0.3368j
8	-0.3429+0.9334j	51	-0.3907-0.9144j	94	0.9802-0.1672j
						9	-0.2278+0.9679j	52	0.9942-0.0157j	95	0.6297-0.7696j
10	0.9145+0.3905j	53	-0.5565-0.8240j	96	0.5123-0.8522j
						11	0.7226+0.6831j	54	-0.9299+0.3523j	97	-0.8329-0.5432j
12	-0.9031+0.4161j	55	0.9944-0.0047j	98	-0.3129-0.9438j
						13	-0.8874-0.4485j	56	0.7021+0.7041j	99	-0.8079+0.5797j
14	-0.4961-0.8617j	57	0.9814+0.1602j	100	-0.1765+0.9785j
						15	0.4280+0.8975j	58	-0.2443+0.9639j	101	0.0966-0.9896j
16	-0.5814+0.8067j	59	0.5009-0.8590j	102	-0.9647+0.2410j
						17	0.8707-0.4802j	60	0.3780+0.9198j	103	0.8756+0.4711j
18	0.9655-0.2380j	61	0.8373+0.5364j	104	0.4983+0.8605j
						19	0.6804+0.7252j	62	0.4792+0.8713j	105	0.0330+0.9938j
20	-0.8765+0.4696j	63	-0.9326-0.3449j	106	0.9670-0.2318j
						21	-0.9807+0.1642j	64	0.2282-0.9678j	107	-0.1699+0.9797j
22	0.7511-0.6516j	65	-0.9819-0.1565j	108	0.6507+0.7519j
						23	-0.9815+0.1594j	66	0.9786+0.1763j	109	0.8988+0.4255j
24	0.1610-0.9812j	67	-0.7163+0.6897j	110	0.8908-0.4418j
						25	0.4086+0.9065j	68	-0.9228+0.3703j	111	-0.7956-0.5965j

26	-0.5174+0.8492j	69	0.9704+0.2167j	112	0.9094-0.4023j
						27	-0.3516+0.9301j	70	0.9493-0.2958j	113	-0.9922-0.0658j
28	-0.0497+0.9931j	71	0.2029+0.9734j	114	-0.8727+0.4765j
						29	0.7500-0.6529j	72	-0.9115+0.3973j	115	0.8022+0.5876j
30	0.8476-0.5200j	73	-0.9620-0.2517j	116	0.8115+0.5746j
						31	0.6819-0.7237j	74	-0.9928+0.0541j	117	-0.8872+0.4489j
32	0.5519-0.8271j	75	0.9314-0.3480j	118	-0.6758+0.7294j
						33	-0.7455+0.6580j	76	-0.5794+0.8081j	119	-0.4128+0.9046j
34	0.6396-0.7613j	77	0.0969+0.9896j	120	0.8042+0.5848j
						35	0.1544+0.9823j	78	-0.5870+0.8026j	121	-0.8808+0.4614j
36	0.9447-0.3103j	79	0.7846-0.6109j	122	0.9224+0.3714j
						37	-0.9602+0.2585j	80	-0.8481-0.5191j	123	-0.9625+0.2499j
38	0.5753-0.8110j	81	0.3286-0.9385j	124	0.4703+0.8761j
						39	0.1608+0.9813j	82	0.9741+0.1993j	125	0.8589-0.5011j
40	-0.6636-0.7405j	83	-0.6719-0.7330j	126	-0.5526-0.8266j
						41	0.0943+0.9899j	84	0.2454-0.9636j	127	-0.5762+0.8104j
42	-0.6868+0.7190j	85	-0.7397+0.6644j	128	-0.6737+0.7314j
						43	-0.9203+0.3765j	86	-0.9814+0.1597j	129	0.9936+0.0381j

In the table, j represents imaginary unit.

The auto-correlation function of frequency domain differential demodulation sequence p as shown in Figure 4.So, according to formula (7), at the S of the synchronous training symbol of OFDM _ActOn loaded data as shown in the table:

k	A (k) and k=S a(i) 1≤i≤C(S act)	k	A (k) and k=S a(i) 1≤i≤C(S act)	k	A (k) and k=S a(i) 1≤i≤C(S act)
						-352	-0.9042+0.4272j	-130	0.6056+0.7958j	122	0.9557-0.2944j
-346	0.9488+0.3160j	-128	0.9356-0.3531j	124	0.9948-0.1017j
						-340	-0.6791-0.7340j	-126	0.4312+0.9023j	130	-0.9737-0.2279j
-336	-0.5822-0.8131j	-124	-0.9408-0.3391j	136	-0.2342+0.9722j
						-334	-0.9994-0.0358j	-120	-0.8215-0.5703j	138	-0.2652+0.9642j

-332	0.9965-0.0837j	-118	-0.9952-0.0982j	140	-0.6115-0.7913j
						-330	0.5476+0.8368j	-102	-0.5356-0.8445j	142	-0.6382-0.7699j
-324	-0.9994-0.0346j	-100	-0.5661+0.8243j	152	-0.9472+0.3205j
						-322	0.3084+0.9513j	-96	-0.5530+0.8332j	156	-0.1903+0.9817j
-320	-0.9742-0.2258j	-92	1.0000-0.0080j	162	0.7453-0.6668j
						-318	-0.9245-0.3813j	-86	0.6080+0.7939j	180	-0.9995+0.0322j
-316	0.6767-0.7363j	-84	-0.8499-0.5270j	186	0.8771-0.4802j
						-314	0.5617+0.8274j	-82	-0.8524-0.5229j	188	-0.9880+0.1547j
-310	0.1916+0.9815j	-78	-0.2316-0.9728j	196	-0.1275-0.9919j
						-308	-0.5350+0.8449j	-74	-0.0718-0.9974j	200	-0.2925-0.9563j
-306	0.1324-0.9912j	-66	0.4359+0.9000j	202	-0.9253-0.3792j
						-304	-0.5653+0.8249j	-64	-0.9795+0.2014j	208	-0.9867+0.1629j
-300	0.9969+0.0783j	-62	-0.3194+0.9477j	210	-0.3687+0.9295j
						-296	0.3585+0.9336j	-56	-0.4581-0.8889j	212	0.8166-0.5772j
-292	-0.9670-0.2551j	-52	0.6481-0.7616j	214	-0.8048-0.5935j
						-288	-0.9699+0.2436j	-44	-0.5776-0.8164j	218	0.9999+0.0130j
-278	0.3551-0.9349j	-40	-0.0460-0.9989j	226	-0.0026-1.0000j
						-276	0.1210-0.9927j	-36	0.8531-0.5217j	228	0.9846+0.1749j
-274	0.8067-0.5909j	-30	-0.9677-0.2521j	238	0.3397+0.9405j
						-272	-0.4321+0.9019j	-26	0.8201+0.5722j	240	0.9691-0.2467j
-270	0.2772-0.9608j	-20	-0.4439-0.8961j	246	0.7419+0.6705j
						-266	-0.4203-0.9074j	-18	-0.9740+0.2264j	248	-0.8823-0.4707j
-264	0.5603+0.8283j	-12	-0.9055-0.4244j	250	-0.5540-0.8325j
						-260	0.9081-0.4188j	-10	0.8274+0.5617j	256	0.9999+0.0124j
-254	-0.9860-0.1672j	4	0.8896+0.4568j	258	0.4904+0.8715j
						-252	-0.2527-0.9676j	8	0.7946+0.6072j	260	-0.8548+0.5190j
-248	0.9578+0.2876j	12	-0.9935+0.1137j	264	-0.7103+0.7040j
						-246	-0.6077+0.7942j	14	0.8797-0.4755j	266	-0.5723-0.8201j
-244	-0.7628-0.6467j	18	0.9622-0.2724j	268	0.2456-0.9694j

-242	-0.9999+0.0131j	20	0.8376-0.5463j	272	0.6368-0.7711j
						-240	-0.8455+0.5341j	28	-0.7249+0.6889j	274	0.2278-0.9737j
-226	0.2059+0.9786j	34	1.0000+0.0043j	276	-0.7664+0.6424j
						-224	0.8534+0.5212j	38	0.1998+0.9798j	278	-0.4410+0.8975j
-222	0.9073-0.4206j	42	-0.5747-0.8184j	280	0.4995-0.8664j
						-220	-0.4019+0.9157j	44	0.3489+0.9372j	282	-0.0232+0.9997j
-214	-0.9662-0.2578j	46	-0.3993-0.9168j	288	-0.4708-0.8823j
						-210	-0.8189+0.5739j	48	-0.6950-0.7190j	290	0.1416-0.9900j
-208	-0.6941-0.7200j	50	0.9893-0.1458j	294	0.6876-0.7261j
						-200	0.4224-0.9064j	52	0.2415+0.9704j	296	-0.2857+0.9583j
-198	0.1184-0.9930j	54	-0.9259-0.3779j	300	-0.5088-0.8609j
						-194	0.1438+0.9896j	58	-0.9627+0.2706j	302	0.9944-0.1055j
-192	0.8904+0.4553j	62	0.9624+0.2717j	304	0.8663+0.4995j
						-186	-0.9312+0.3647j	64	0.5745-0.8185j	306	-0.9992-0.0405j
-184	-0.5105-0.8599j	66	0.7269-0.6868j	314	-0.0079+1.0000j
						-180	-0.2997+0.9541j	72	-0.8510-0.5252j	316	-0.3808+0.9247j
-174	0.9861-0.1664j	82	0.5979-0.8016j	322	0.6451-0.7642j
						-168	0.9194+0.3934j	88	-0.9191-0.3942j	326	-0.4323+0.9018j
-162	0.6042-0.7969j	96	0.7698+0.6383j	330	-0.9990+0.0456j
						-160	0.8506+0.5258j	102	-0.8154+0.5789j	334	-0.8398+0.5428j
-156	-0.9678+0.2519j	104	0.9777+0.2099j	336	0.9181+0.3965j
						-152	0.8003-0.5996j	106	0.4447-0.8957j	342	0.9707-0.2402j
-150	-0.8743+0.4854j	114	0.9604+0.2786j	346	-0.3668+0.9304j
						-146	0.7233-0.6906j	116	-0.9007+0.4345j	348	-0.4358-0.9001j
-138	-0.8823+0.4707j	118	0.8192-0.5735j	350	-0.4010-0.9161j

For the transmitting power that guarantees signal keeps constant, on a (k), will multiply by compensating factor $\sqrt{N_u/C\left(S_{\mathrm{act}}\right)}=\sqrt{704/177}$ With string and the modular converter 1, IDFT module 2, parallel serial conversion module 3 of such a (k) by Fig. 2, just can generate and contain the virtual subnet carrier wave, and adjacent enable subcarrier on loaded synchronous training symbols of branch OFDM such as 2 of frequency domain differential demodulation sequence, this synchronous training symbol inserts cyclic prefix module 4, the synchronous training symbol module 5 of insertion, D/A modular converter 6, sends Filtering Processing module 7 through the module of Fig. 2 then, arrives receiving terminal.

(2) time synchronized and decimal Frequency Synchronization

At first, receiving terminal carries out time synchronized and decimal Frequency Synchronization according to Fig. 3.The data that receive are through the processing module 8 that accepts filter of Fig. 2, A/D modular converter 9, lock unit module 15.

Because the synchronous training symbol that generates has the characteristic of 2 five equilibriums, so calculating the half symbols of synchronous training symbol on time domain, receiving terminal postpones auto-correlation, seek the original position that peak value is determined frame, the phase angle of peaking estimates the decimal frequency departure again.Result according to time synchronized and decimal Frequency Synchronization carries out corresponding compensation to synchronous training symbol.

Training symbol obtains as the formula (12) { z (k) } through the synchronous training symbol module 10 of extraction, removal cyclic prefix module 11, string and modular converter 12, DFT and frequency domain equalization module 13, the parallel serial conversion module 14 of Fig. 2 synchronously.Then, receiving terminal begins to carry out the integer frequency bias estimation according to Fig. 3.

(3) calculating is based on the possibility metric of each integer frequency bias of virtual subnet carrier wave

Receiving terminal calculates the possibility metric based on each integer frequency bias of virtual subnet carrier wave according to Fig. 3.

Assumed condition g at each integer frequency bias ^%Down, { z (k) } carried out corresponding compensation, promptly cyclic shift gets { z (k+g ^%).According to formula (13), obtain R (g ^%) (g ^%∈ [4,4]). $R\left(g^{\%}\right)(g^{\%}\&Element;[-\mathrm{4,4}\left]\right).$ Because d dual numbers subcarrier of formula (25) decision is effective, so, the probable value set G of integer frequency bias _Assump={ 4 ,-2,0,2, so 4} is C _g=5.

With R (2) is example, is got by formula (13):

$R\left(2\right)=\underset{k\&Element;S_{\mathrm{act}}}{\mathrm{\&Sigma;}}{\left|z(k+2)\right|}^2...\left(26\right)$

Because S _ActKnown, can be with k+2 (k ∈ S _Act) be listed as follows:

k+2(k∈S act)
	-350 -344 -338 -334 -332 -330 -328 -322 -320 -318 -316 -314 -312 -308 -306 -304 -302 -298 -294 -290 -286 -276 -274 -272 -270 -268 -264 -262 -258 -252 -250 -246 -244 -242 -240 -238 -224 -222 -220 -218

-212 -208 -206 -198 -196 -192 -190 -184 -182 -178 -172 -166 -160 -158 -154 -150 -148 -144 -136 -128 -126 -124 -122 -118 -116 -100 -98 -94 -90 -84 -82 -80 -76 -72 -64 -62 -60 -54 -50 -42 -38 -34 -28 -24 -18 -16 -10 -8 6 10 14 16 20 22 30 36 40 44 46 48 50 52 54 56 60 64 66 68 74 84 90 98 104 106 108 116 118 120 124 126 132 138 140 142 144 154 158 164 182 188 190 198 202 204 210 212 214 216 220 228 230 240 242 248 250 252 258 260 262 266 268 270 274 276 278 280 282 284 290 292 296 298 302 304 306 308 316 318 324 328 332 336 338 344 348 350 352

Under multipath channel condition and 0dB white Gaussian noise situation, when integer frequency bias is 2, R (g ^%) typical case as shown in Figure 5.As seen, R (g ^%) peak value has appearred at the g%=2 place.

The calculating of this step mainly concentrates on formula (13), calculates | z (k+g ^%) | ²Need C (S altogether _Origin)=352 time complex multiplication.Also need C in addition _g* C (S _Act)=885 time real number addition, equivalence are 442 complex addition.The computation complexity of this step of the present invention is identical with method one.

(4) the integer frequency bias value is carried out preliminary election, calculate again under the assumed condition of each integer frequency bias, based on the possibility metric of each integer frequency bias of difference sequence

Receiving terminal calculates the possibility metric based on each integer frequency bias of difference sequence according to Fig. 3.

To sort from big to small based on the possibility metric of each integer frequency bias of virtual subnet carrier wave, λ integer frequency bias obtains gathering G as preset value before the order _Assump ^λFor each $g^{\%}\&Element;G_{\mathrm{assump}}^{\mathrm{\&lambda;}},$ To { z (k) } do be shifted { z (k+g ^%).Then, according to formula (15) differential ference spiral S _A1(i)+g ^%And S _A2(i)+g ^%Data on the corresponding adjacent sub-carrier obtain sequence $w^{g^{\%}}=\left\{w^{g^{\%}}\left(i\right)\right\}.$ Again by the possibility metric T (g of formula (17) calculating based on each integer frequency bias of difference sequence ^%).Under multipath channel condition and 0dB white Gaussian noise situation, when integer frequency bias is 2, Re[T (g ^%)] typical case as shown in Figure 6.As seen, Re[T (g ^%)] at g ^%Peak value has appearred in=2 places.

The calculating of this step mainly concentrates on formula (15) and formula (17), needs 2 λ C (S _Adjλ complex multiplication in)=258 and λ C (S _Adjλ the complex addition in)=129, equivalence is λ C (S _Adjλ complex addition of)/2=64 is as λ=C _g=5 o'clock, it is maximum that the computation complexity of this step reaches, and needs 1290 complex multiplications and 320 complex addition.

Count the rapid computation complexity of previous step, then the complex multiplication that needs altogether of the present invention is 258 λ+352 time, and complex addition is 64 λ+442 time.

Method two is also wanted calculating formula (15) and formula (17), but it can't carry out preliminary election to integer frequency bias, so, need 2C altogether _g* C (S _Origin)=3520 time complex multiplication and C _g* C (S _Origin) inferior complex addition, equivalence is C _g* C (S _Origin)/2=880 time complex addition.

Method one, method two and computation complexity of the present invention are listed in the table below:

	The complex multiplication number of times	Percentage with respect to method two	The complex addition number of times	Percentage with respect to method two
					Method one	352	10％	442	50％
Method two	3520	100％	880	100％
					The present invention (λ=C g＝5)	1642	47％	762	87％
The present invention (λ=4)	1384	39％	698	79％
					The present invention (λ=3)	1126	32％	634	72％
The present invention (λ=2)	868	25％	570	65％

Therefore,, have remarkable advantages, and along with reducing of λ, the advantage of the present invention aspect computation complexity is more outstanding for method two though computation complexity of the present invention is higher than method one.

(5) according to the ML criterion, merge based on the possibility metric of each integer frequency bias of virtual subnet carrier wave with based on the possibility metric of each integer frequency bias of difference sequence, estimate integer frequency bias then

According to formula (23), merge based on the possibility metric of each integer frequency bias of virtual subnet carrier wave with based on the possibility metric Λ (g of each integer frequency bias of difference sequence ^%).Under multipath channel condition and 0dB white Gaussian noise situation, when integer frequency bias is 2, Λ (g ^%) typical case as shown in Figure 7.As seen, Λ (g ^%) at g ^%=2 places have occurred than Fig. 5 and the more obvious peak value of Fig. 6.

By formula (24) integer frequency bias is made an estimate at last.

Simulated channel is 6-ray GSM Typical Urban Channel (global mobile communication typical urban zone 6 footpath channels is called for short 6-ray TU), and its parameter is as follows:

	Postpone (us)	Relative power (dB)
			Path 1	0	-3
Path 2	0.2	0
			Path 3	0.5	-2
Path 4	1.6	-6
			Path 5	2.3	-8
Path 6	5.0	-10

Suppose that frequency deviation is 2.3.Think during emulation and obtained right-on time synchronized.

In emulation, the performance of having investigated the present invention and method one and method two compares.

Fig. 8 is that not carry out preliminary election (be λ=C in the present invention _g=5) and when carrying out preliminary election (λ=3, λ=2), with method one and method two in the performance aspect the integer frequency bias estimated error rate relatively.This figure shows that the performance of method two slightly is better than method one, but in general, the performance of method one and method two is identical.

Among Fig. 8, (be λ=C when the present invention does not carry out preliminary election _g=5) time, the present invention has the advantage of 1.3dB than above-mentioned two methods.Therefore, estimated performance ratio method one of the present invention and method two improve a lot.Especially, compare method two, the present invention has bigger improvement again aspect computation complexity.According to aforementioned analysis, the complex multiplication number of times that the present invention needs at this moment only is 47% of method two, and the complex addition number of times is 87% of a method two.

Among Fig. 8, when the present invention carried out preliminary election (λ=3), the performance curve that its performance curve and the present invention do not carry out preliminary election much at one.Therefore, its ratio method one and method two have the advantage of 1.3dB.In addition, compare method two, the present invention carries out preliminary election (λ=3) bigger improvement again aspect computation complexity.According to aforementioned analysis, the complex multiplication number of times that the present invention needs at this moment only is 32% of method two, and the complex addition number of times is 72% of a method two.

Among Fig. 8, when the present invention carried out preliminary election (λ=2), its performance ratio method one and method two had the advantage of 1dB.In addition, compare method two, the present invention carries out preliminary election (λ=2) bigger improvement again aspect computation complexity.According to aforementioned analysis, the complex multiplication number of times that the present invention needs at this moment only is 25% of method two, and the complex addition number of times is 65% of a method two.

Fig. 9 is that not carry out preliminary election (be λ=C in the present invention _g=5) and when carrying out preliminary election (λ=3, λ=2), with method one and method two in the performance aspect the frequency offset estimating mean square error relatively.This figure shows, (is λ=C when the present invention does not carry out preliminary election _g=5) and when carrying out preliminary election (λ=3), ratio method one of the present invention and method two have the advantage of 1.7dB and 1.6dB respectively.When the present invention carried out preliminary election (λ=2), ratio method one of the present invention and method two had the advantage of 1.2dB and 1.1dB respectively.

Simulation result shows, it is lower that the present invention has an integer frequency bias estimated error rate, and the lower advantage of computation complexity, has very high using value in ofdm system.

Above-mentioned embodiment of the present invention just is used to set forth the example of technology contents of the present invention.The present invention is not limited to above-mentioned embodiment, should not carry out the explanation of narrow sense to it.In the scope of spirit of the present invention and claim, can carry out various changes and implement it.

Claims (5)

1, a kind of method of the estimating OFDM integer frequency deviation based on virtual subnet carrier wave and frequency domain differential demodulation sequence is characterized in that, comprises the steps:

Step 1: transmitting terminal generates and to contain the virtual subnet carrier wave, and adjacent enable subcarrier on loaded the synchronous training symbol of OFDM of frequency domain differential demodulation sequence;

Step 2: receiving terminal obtains time synchronized and decimal Frequency Synchronization, and extracts synchronous training symbol, removes Cyclic Prefix, through the decimal frequency bias compensation, remakes FFT, obtains the frequency domain sequence of synchronous training symbol;

Step 3: under assumed condition based on each integer frequency bias of virtual subnet carrier wave, obtain the synchronous training symbol of OFDM the energy of enabling the subcarrier set and, as possibility metric based on each integer frequency bias of virtual subnet carrier wave;

Step 4: under assumed condition, detect, obtain possibility metric based on each integer frequency bias of difference sequence by frequency domain differential demodulation demodulation and difference sequence based on each integer frequency bias of virtual subnet carrier wave;

Step 5: according to maximum-likelihood criterion, merge, seek peak value, integer frequency bias is made an estimate based on the possibility metric of each integer frequency bias of virtual subnet carrier wave with based on the possibility metric of each integer frequency bias of difference sequence.

2, the method of the estimating OFDM integer frequency deviation based on virtual subnet carrier wave and frequency domain differential demodulation sequence according to claim 1, it is characterized in that, described step 4, be specially: enumerate described each integer frequency bias as condition, the frequency domain sequence of synchronous training symbol is done the cyclic shift compensation, again by the sequence number set of enabling adjacent sub-carrier in the subcarrier, this sequence number of differential ference spiral is gathered the frequency domain sequence of pairing synchronous training symbol, acquisition is used to estimate the frequency domain differential demodulation sequence of integer frequency bias, itself and in advance known frequency domain differential demodulation sequence are carried out correlation operation, obtain possibility metric based on described each integer frequency bias of difference sequence.

3, the method for the estimating OFDM integer frequency deviation based on virtual subnet carrier wave and frequency domain differential demodulation sequence according to claim 1, it is characterized in that, described step 4, synchronous training symbol and frequency domain sequence are being carried out described each integer frequency bias is carried out preliminary election before differential ference spiral and frequency domain sequence detect.

4. the method for the estimating OFDM integer frequency deviation based on virtual subnet carrier wave and frequency domain differential demodulation sequence according to claim 3, it is characterized in that, described step 4, the possibility metric based on each integer frequency bias of virtual subnet carrier wave that described step 3 is obtained sorts from big to small, and λ the pairing integer frequency bias of result is as the integer frequency bias preset value before the order.

5, the method for the estimating OFDM integer frequency deviation based on virtual subnet carrier wave and frequency domain differential demodulation sequence according to claim 1, it is characterized in that, described step 5, be specially: according to the ML criterion, real part addition with 1 times based on the possibility metric of each integer frequency bias of difference sequence based on the possibility metric of each integer frequency bias of virtual subnet carrier wave and 2 times, obtain possibility metric based on each integer frequency bias of ML criterion, seek its peak value, thereby integer frequency bias is made an estimate.

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