CN101022442A - Joint time synchronizing and frequency-offset estimating method in OFDM system - Google Patents

Abstract

A synchronization and frequency deviation estimating method of united time in OFDM system includes utilizing a receiving signal data in observing window and applying iteration formula derived out by the present invention to carry out adaptive weight value update, using updated weight value to calculate normalization output energy, comparing and judging said energy with threshold to estimate frequency deviation and to realize time synchronization.

Description

Associating time synchronized and frequency deviation estimating method in a kind of ofdm system

Technical field

The present invention relates to the frequency deviation estimating method of OFDM (OFDM) communication system, associating time synchronized and frequency deviation estimating method in particularly a kind of ofdm system.

Background technology

OFDM (OFDM) technology is a kind of high speed data transfer technology, it decomposes several low rate data streams with high-speed data-flow, each low rate data streams is parallel transmission on the subcarrier of several quadratures, use Cyclic Prefix (CP) simultaneously, thereby can effectively overcome the intersymbol interference (ISI) that brings by frequency selective fading, and has high spectrum efficiency.The OFDM technology is the core technology of the 4th third-generation mobile communication system, is adopted by a lot of industrial standards.

Time synchronized and Nonlinear Transformation in Frequency Offset Estimation are key factors that influences the ofdm system performance.Time synchronized is meant that receiver need determine the original position of each OFDM frame or symbolic blocks, so that go CP and inverse-Fourier transform (IFFT) operation.And, reduce the performance of system because the carrier wave frequency deviation that frequency difference caused of the crystal oscillator of transmitter and receiver with the orthogonality of destroying between the subcarrier, disturbs (ICI) thereby produce between serious subcarrier.Therefore, before the demodulation of OFDM symbol, must carry out the estimation and the compensation of sign synchronization and carrier wave frequency deviation.

J.van de Beek, M.Sandell, people such as and P.O.Borjesson are at IEEE Transactions onSignal Processing, vol.45, pp.1800-1805, " ML estimationof time and frequency offset in OFDM systems " (documents one) delivered on the July 1997 proposed a kind of associating time synchronized and frequency deviation estimating method (also can be described as maximum likelihood method) that utilizes Cyclic Prefix, this method need not be utilized training sequence, is a kind of blind associating estimation approach.Yet this method can only be used for the white Gaussian noise channel, and for the applied frequency selectivity multipath channel of ofdm system, this method effect is relatively poor.

Tureli U., Liu H, people such as Zoltowski M D. are at IEEE Trans.on Communication, 48 (9): 1459～1461,2000. on deliver " OFDM blind carrier offset estimation:ESPRIT " (documents two), a kind of new blind frequency-offset estimating method that utilizes the virtual subnet carrier wave has been proposed.This method is based on the method for subspace, can provide the enclosed analytic solutions of frequency deviation, and its estimated performance has the characteristic of super-resolution.But this method can only estimate frequency deviation and can not be used for time synchronized, and need carry out singular value decomposition to N dimension (N is an an OFDM symbol total number of sub-carriers) covariance matrix, and amount of calculation is big, and has uncertain problem under frequency-selective channel.

Application number is that 200410009868.4 Chinese invention patent (documents three) discloses associating time synchronized and frequency deviation estimating method and device in a kind of ofdm system, but this invention is based on training symbol, because the insertion of training symbol has reduced the spectrum efficiency of system.

Summary of the invention

The present invention is directed to the existing defective separately of combined estimation method of prior OFDM system, associating time synchronized and frequency deviation estimating method in a kind of ofdm system have been proposed, this method is a kind of based on adaptive blind combined estimation method, training sequence need not be utilized, only the Cyclic Prefix (CP) that is not polluted in the OFDM symbolic blocks need be utilized by channel.This method amount of calculation is little, and hardware is realized simple, not only can be applicable to the white Gaussian noise channel, and also can be applicable to the occasion of frequency selectivity multipath channel.

For reaching above purpose, the present invention takes following technical scheme to be achieved: associating time synchronized and frequency deviation estimating method in a kind of ofdm system comprise the steps:

Step 1: establish initial weight W (0)=1, determine step size mu (0～1), select smoothing factor M, it is an integer; Selecting convergence threshold α is 0.5～1;

Step 2: utilize received signal data y in the observation window _n=[y _n, y _N+N] ^T, superscript " T " representing matrix transposition wherein, adopt following iterative formula to carry out adaptive weight value updating:

$W(n+1)=W\left(n\right)-\mathrm{\μ}\frac{1}{{\left|\right|y_n\left|\right|}^2}(y_n^{*}+W{y}_{n+N}^{*})y_{n+N}$

$W(n+1)=\frac{W(n+1)}{\left|W(n+1)\right|}---\left(10\right)$

ω(n+1)＝[1，W(n+1)] ^T

‖ y wherein _n‖ ²For asking vectorial y _nTwo norms, conjugation is got in " * " expression;

Step 3: utilize the weights that upgrade to calculate normalization output energy J (n):

$J\left(n\right)=\frac{{\left|\mathrm{\ω}{\left(n\right)}^H{y}_n\right|}^2}{{\left|\right|y_n\left|\right|}^2}$

Step 4: energy and threshold alpha comparison are exported in normalization:

Step 4.1 is as J (n)＜α, during and J (n-1)＜α, thinks that current observation window is positioned at non-training section, and can not carry out frequency offset estimating this moment, carry out step 5 at this moment;

Step 4.2 during and J (n-1)＜α, can think that observation window has just entered converging portion when J (n)＞α, this moment, current weights can be used for estimating frequency deviation ${\widehat{\mathrm{\φ}}}_n=\frac{\∠W_n}{N};$

Step 4.3 is as J (n)＞α, during and J (n-1)＞α, can think when front window still at converging portion, current weights also can be used for estimating frequency deviation ${\widehat{\mathrm{\φ}}}_n=\frac{\∠W_n}{N};$

Step 4.4 is as J (n)＜α, and during J (n-1)＞α, the trailing edge that the output energy also promptly occurred, promptly go up a moment observation window still at converging portion, and entered non-training section this moment, because last sampled point of converging portion is exactly last sampled point of CP section and its corresponding data section, that is to say that the sampled point in the observation window this moment is exactly the initial sampled point of an OFDM symbolic blocks data segment, so just realized that symbol time is synchronous;

Step 5 makes n=n+1, gets back to step 2, carries out next iterative cycles.

In the such scheme, the selection of the convergence threshold α in the described step 1 is relevant with signal to noise ratio, when signal to noise ratio respectively at 5～9dB, 10～14dB and＞during 15dB, convergence threshold α gets 0.75,0.85,0.95 respectively.

The derivation of the iterative formula in the described step 2 is as follows:

At first ask the eigenvalue of maximum and the characteristic of correspondence vector of autocorrelation matrix, can be converted into Rayleigh (Rayleigh) the merchant problem of asking.Following formula is promptly arranged:

$\underset{\mathrm{\ω}}{\max }J\left(\mathrm{\ω}\right)=\underset{\mathrm{\ω}}{\max }\left(E\left\{\frac{{\left|{\mathrm{\ω}}^{H}y\right|}^2}{{\left|\right|y\left|\right|}^2}\right\}\right)=\underset{\mathrm{\ω}}{\max }\frac{{\mathrm{\ω}}^H\mathrm{R\ω}}{{\mathrm{\ω}}^H\mathrm{\ω}}={\mathrm{\λ}}_{\max }$ If R ω=λ _Maxω

Y=[y wherein _n, y _N+N] ^T, promptly be spaced apart the vector that two sampled points of N are formed, ω is weights, its have form [1, e ^{J  N}], make W=e ^{J  N}, then gradient is at random:

$\▿J\left(\mathrm{\ω}\right)=\frac{1}{{\left|\right|y\left|\right|}^2}\∂{\left|\left(1W^{*}\right)\left(\begin{array}{c}{y}_n\\ y_{n+N}\end{array}\right)\right|}^2/{\∂W}^{*}$

$=\frac{1}{{\left|\right|y\left|\right|}^2}(y_n^{*}+W{y}_{n+N}^{*})y_{n+N}$

Getting iterative formula is:

$W(n+1)=W\left(n\right)-\mathrm{\μ}\frac{1}{{\left|\right|y_n\left|\right|}^2}(y_n^{*}+W{y}_{n+N}^{*})y_{n+N}$

$W(n+1)=\frac{W(n+1)}{\left|W(n+1)\right|}$

ω(n+1)＝[1，W(n+1)] ^T

This step 2 can also be simultaneously or is arbitraryly taked following two kinds of y _nProcessing method:

A. to data in one group of observation window, adopt forward and reverse twice iteration, promptly use y successively to accelerate convergence rate _n=[y _n, y _N+N] ^TAnd y _n=[y _N+N, y _n] ^HCome refreshing weight, wherein conjugate transpose is got in superscript " H " expression;

B. above-mentioned adaptive process adopts to such an extent that be gradient at random, can adopt the gradient under certain statistical significance in the real system, promptly utilizes the training section that belongs to a plurality of different OFDM symbolic blocks to average, and when adopting M group data, promptly uses:

$y_n=\left[\begin{array}{cccc}{y}_n& y_{n+(N+G)}& ...& y_{n+(M-1)(N+G)}\\ y_{n+N}& y_{n+(N+G)+N}& ...& y_{n+(M-1)(N+G)+N}\end{array}\right]$

Refreshing weight.Wherein, M is " smoothing factor ".

In the described step 4.2,4.3,, can repeatedly estimate frequency deviation, ask average then when converging portion during greater than a sampling length.

Adopt resultant associating time synchronized of the inventive method and frequency offset estimating performance, no matter in the white Gaussian noise channel or the occasion of frequency selectivity multipath channel, performance than art methods is more superior, when even the relative circulating prefix-length of channel exponent number is very big, the estimated performance of the inventive method still obviously is better than maximum likelihood method.

Description of drawings

Fig. 1 for the present invention in ofdm system adaptive combined time synchronized and the flow chart of steps of frequency deviation estimating method.

The adaptive combined estimation output valve procedure chart of Fig. 2 for obtaining according to the embodiment of the invention 1.Wherein, Fig. 2 (1) is the value of the frequency offset estimating of adaptive process output; Fig. 2 (2) is the value of normalization output energy in the adaptive process.

Fig. 3 for the time synchronized that obtains according to the embodiment of the invention 2 estimate the performance that under different smoothing factors, changes with signal to noise ratio and and the comparison diagram of prior art;

The performance that Fig. 4 changes with signal to noise ratio under different smoothing factors for the frequency offset estimating that obtains according to the embodiment of the invention 2 and and the comparison diagram of prior art;

Fig. 5 for the time synchronized that obtains according to the embodiment of the invention 3 estimate the performance that under different signal to noise ratios, changes with the channel exponent number and with the comparison diagram of prior art;

The performance that Fig. 6 changes with the channel exponent number under different signal to noise ratios for the frequency offset estimating that obtains according to the embodiment of the invention 3 and with the comparison diagram of prior art;

Frequency offset estimating performance under different signal to noise ratios and the comparison diagram of prior art of Fig. 7 for obtaining according to the embodiment of the invention 4.

Embodiment

Below the present invention is described in further detail.

In ofdm system, the principle of carrying out frequency offset estimating is as follows: consider that the data subcarrier number is the ofdm system of N, the length of supposing Cyclic Prefix (CP) is that (N＞G), the time-domain representation of k the OFDM symbol that receives at receiver end is G so

y _k＝EWHs _ke ^{j(k-1)φ(N+G)}+n _k (1)

Wherein E=diag (1, ^{Ej φ}... e ^{J (N-1) φ}), diag () is to be the diagonal matrix of diagonal element with (), φ=2 π Δ f/Nf ₀Be the normalization frequency deviation, Δ f is a carrier wave frequency deviation, f ₀Be subcarrier spacing.Matrix W is the inverse fourier transform matrix of N * N.The length of supposing multipath channel is L _c, be designated as h=[h ₁, h ₂... h _Lc].In order to guarantee thoroughly to eliminate ISI, G＞L is arranged _c, matrix H=diag (H0, H so ₁..., H _N-1), $H_i={\mathrm{\&Sigma;}}_{l=0}^{L_c-1}{h}_l\exp (-\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20071001724200181.png,A20071001724200191.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&pi;l}/N),$ i＝0，…N-1。s _k=[s _{K, 0}, s _{K, 1}..., s _{K, N-1}] ^TFrequency domain symbol for emission.n _kBe additive Gaussian noise.

The present invention can unite the time synchronized frequency offset estimating simultaneously, be based on the independent frequency deviation estimating method of following condition, suppose time synchronized finished and the situation of known channel length under, provide the method for a kind of frequency offset estimating of the present invention earlier, then on this basis, provide the estimation of uniting of time synchronized under the Unknown Channel length and frequency offset estimating again.

At first, do not consider Cyclic Prefix, at receiver end, the n point sampling y of k the OFDM symbolic blocks that receives _{K, n}Can be expressed as:

$y_{k,n}=e^{\mathrm{j\&phi;n}}\underset{q=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\tilde{s}}_{k,\mathrm{<figure-callout\; id="2"\; label="q\; e\; j"\; filenames="A20071001724200181.png,A20071001724200191.png"\; state="\{\{state\}\}">q</figure-callout>}}{e}^j{2\mathrm{\&pi;qn}/N}^{}$

$\stackrel{q=\mathrm{pL}+i}{=}{e}^{\mathrm{j\&phi;n}}\underset{i=0}{\overset{L-1}{\mathrm{\&Sigma;}}}\underset{p=0}{\overset{P-1}{\mathrm{\&Sigma;}}}{\tilde{s}}_{k,\mathrm{pL}+\mathrm{<figure-callout\; id="2"\; label="i\; e\; j"\; filenames="A20071001724200181.png,A20071001724200191.png"\; state="\{\{state\}\}">i</figure-callout>}}{e}^j{2\mathrm{\&pi;}(\mathrm{pL}+i)n/N}^{}$

$=\underset{i=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{e}^{\mathrm{jn}(\mathrm{\&phi;}+\frac{2\mathrm{\&pi;i}}{N})}\underset{p=0}{\overset{P-1}{\mathrm{\&Sigma;}}}{\tilde{s}}_{k,\mathrm{pL}+\mathrm{<figure-callout\; id="2"\; label="i\; e\; j"\; filenames="A20071001724200181.png,A20071001724200191.png"\; state="\{\{state\}\}">i</figure-callout>}}{e}^j{2\mathrm{\&pi;n}\frac{p}{P}}^{}---\left(2\right)$

$=\underset{i=0}{\overset{L-1}{\mathrm{\&Sigma;}}}\left[Z_{k,n}^i\right]$

Wherein ${\tilde{S}}_{k,q}=H_q{S}_{k,q}{e}^{j(k-1)\mathrm{\&phi;}(N+G)},$ $Z_{k,n}^i=e^{\mathrm{in}(\mathrm{\&phi;}+\frac{2\mathrm{\&pi;i}}{N})}\underset{p=0}{\overset{P-1}{\mathrm{\&Sigma;}}}{\tilde{s}}_{k,\mathrm{pL}+\mathrm{<figure-callout\; id="2"\; label="i\; e\; j"\; filenames="A20071001724200181.png,A20071001724200191.png"\; state="\{\{state\}\}">i</figure-callout>}}{e}^j{2\mathrm{\&pi;n}\frac{p}{P}}^{}.$ In like manner, can be somebody's turn to do

The expression of symbolic blocks n+tP data sampling point constantly:

$y_{k,n+\mathrm{tP}}=\underset{i=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{e}^{\mathrm{jtP}(\frac{2\mathrm{\&pi;i}}{N}+\mathrm{\&phi;})}\left[e^{\mathrm{jn}(\mathrm{\&phi;}+\frac{2\mathrm{\&pi;i}}{N})}\underset{p=0}{\overset{P-1}{\mathrm{\&Sigma;}}}{\tilde{s}}_{k,\mathrm{pL}+i}{e}^{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20071001724200181.png,A20071001724200191.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\frac{p}{P}}\right]---\left(3\right)$

$=\underset{i=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{e}^{\mathrm{jtP}(\frac{2\mathrm{\&pi;i}}{N}+\mathrm{\&phi;})}\left[Z_{k,n}^i\right]$

According to (2) (3) two formulas, for the arbitrary integer P and the L that satisfy N=P * L, k OFDM symbolic blocks is spaced apart between two point samplings that P orders specific relation, and each OFDM symbolic blocks that will receive like this can be lined up following matrix form:

Wherein

$\mathrm{\&theta;}\left(i\right)=(\frac{2\mathrm{\&pi;i}}{L}+\mathrm{P\&phi;})---\left(5\right)$

As consider cyclic prefix CP, exactly the G point of current OFDM data block afterbody is copied to front end owing to add the CP operation, so the CP section still can be write as the form of following formula (2).Ofdm system must guarantee CP length greater than channel length, i.e. G＞L in order thoroughly to eliminate intersymbol interference _c, the OFDM symbolic blocks still has individual N by channel like this _c=G-L _c+ 1CP sampling point is not polluted by ISI.Consider not have contaminated CP sampling point, note [y _{K ,-Nc}..., y _{K ,-2}, y _{K ,-1}] be N _cThe individual CP sampled point that is not polluted by ISI when not considering noise, has:

${\stackrel{-}{y}}_k=e^{-\mathrm{j\&phi;N}}[y_{k,N-N_c},\&CenterDot;\&CenterDot;\&CenterDot;,y_{k,N-2},y_{k,N-1}]$

Convolution (4), (6) two formulas have:

$={\mathrm{AZ}}_k$

As seen, matrix A is the Fan Demeng battle array of (L+1) * L dimension, and available various subspace methods obtain θ (i), i=0, and 1 ..., the estimation of L-1, thus the estimation of frequency deviation obtained

What more than provide is accurately to have finished and frequency deviation estimating method during receiver known channel length in the hypothesis time synchronized.

Above-mentioned frequency deviation estimating method is compared with the blind frequency-offset estimating method in the documents two, and its advantage is:

1) need not to utilize the virtual subnet carrier wave, all subcarriers all can be used for the data transmission like this, have improved the availability of frequency spectrum.2) utilized and do not utilize used Cyclic Prefix, but the Cyclic Prefix (CP) that has utilized the intersymbol interference that do not caused by the selectivity channel to pollute makes that the performance of this method under selective channel is more sane than existing method.3) receiver end has been constructed new autocorrelation matrix, thereby has reduced the amount of calculation that its dimension reduces feature decomposition greatly, from original o (N ³) reduce to the o (L among the present invention ³), wherein L is the 1/P of N.4) do not deposit in the conventional method uncertain problem.

But in real system, the length of channel is accurately known than difficulty, and general time synchronized is not also finished.Therefore, the present invention looks for another way, and on above-mentioned frequency deviation estimating method basis, has proposed a kind of associating time synchronized and frequency deviation estimating method of practicality, and it specifically derives as follows:

By (2) (3) formula as can be known (7) formula integer P and the L that satisfies N=P * L arbitrarily all set up, consider L=1, the special circumstances of P=N, (7) formula can abbreviation be at this moment:

${\stackrel{-}{Y}}_k=\left[\begin{array}{cccc}{y}_{k,-1}& y_{k+1,-1}& \&CenterDot;\&CenterDot;\&CenterDot;& y_{k+M-1,-1}\\ y_{k,N-1}& y_{k+1,N-1}& \&CenterDot;\&CenterDot;\&CenterDot;& y_{k+M-1,N-1}\end{array}\right]---\left(8\right)$

Obtain being estimated as of its autocorrelation matrix $\stackrel{-}{R}=\frac{1}{M}{\stackrel{-}{Y}}_k{\stackrel{-}{Y_k}}^H,$ Wherein conjugate transpose is got in superscript " H " expression, and it is that a dimension is 2 * 2 matrix.This moment, its signal subspace and noise subspace all were one dimensions.Like this, at L=1 in particular cases, can carry out the synchronous and frequency offset estimating of symbol time simultaneously by adaptive method.

The present invention is based on adaptive combined estimation method, in maximum Rayleigh merchant, can obtain following formula according to the problem equivalent of the eigenvalue of maximum of yoke Er Mite matrix R and its characteristic of correspondence vector:

$\underset{\mathrm{\&omega;}}{\max }J\left(\mathrm{\&omega;}\right)=\underset{\mathrm{\&omega;}}{\max }\left(E\left\{\frac{{\left|{\mathrm{\&omega;}}^{H}y\right|}^2}{{\left|\right|y\left|\right|}^2}\right\}\right)=\underset{\mathrm{\&omega;}}{\max }\frac{{\mathrm{\&omega;}}^H\mathrm{R\&omega;}}{{\mathrm{\&omega;}}^H\mathrm{\&omega;}}={\mathrm{\&lambda;}}_{\max }$ If R ω=λ _Maxω

Y=[y wherein _n, y _N+N] ^T, superscript " T " representing matrix transposition wherein is the vector that two sampled points being spaced apart N are formed, ω is weights, its have form [1, e ^{J  N}].Like this, ask the eigenvalue of maximum of autocorrelation matrix and the problem of characteristic of correspondence vector just to change into the normalization output energy problem that maximizes filter.Provide maximization Rayleigh merchant below $\underset{\mathrm{\&omega;}}{\max }\frac{{\mathrm{\&omega;}}^H\mathrm{R\&omega;}}{{\mathrm{\&omega;}}^H\mathrm{\&omega;}}$ Adaptive approach.

Make W=e ^{J  N}, then gradient is at random:

$\&dtri;J\left(\mathrm{\&omega;}\right)=\frac{1}{{\left|\right|y\left|\right|}^2}\&PartialD;{\left|\left(1W^{*}\right)\left(\begin{array}{c}{y}_n\\ y_{n+N}\end{array}\right)\right|}^2/\&PartialD;W^{*}---\left(9\right)$

$=\frac{1}{{\left|\right|y\left|\right|}^2}(y_n^{*}+W{y}_{n+N}^{*})y_{n+N}$

Conjugation is got in " * " expression in the formula.Getting iterative formula is:

$W(n+1)=W\left(n\right)-\mathrm{\&mu;}\frac{1}{{\left|\right|y_n\left|\right|}^2}(y_n^{*}+W{y}_{n+N}^{*})y_{n+N}$

$W(n+1)\frac{W(n+1)}{\left|W(n+1)\right|}---\left(10\right)$

ω(n+1)＝[1，W(n+1)] ^T

Second formula in the formula (10) is in order to guarantee $\left|W\left(n\right)\right|=\left|e^{j\widehat{\mathrm{\&phi;}}N}\right|=1,$ μ is an adaptive step.Because normalization frequency deviation φ ∈ [π, π], the initial value of weights is taken as W (0)=1.

Should be pointed out that because also not carry out symbol time this moment synchronous, so receiver utilizes following formula to handle the data that all receive.As sampled point y _nBeing positioned at untainted CP is y _n∈ { y _{K ,-Nc}..., y _{K ,-2}, y _{K ,-1}The time, adaptive process will make weights W (n) → e ^{J φ N}Do not having under the situation of noise, after the process convergence, the normalization output energy of filter must arranged $J\left(n\right)=\frac{{\left|\mathrm{\&omega;}{\left(n\right)}^H{y}_n\right|}^2}{{\left|\right|y_n\left|\right|}^2}=1;$ And under the situation of making an uproar, think during J (n)＞α to reach convergence that α is a preset threshold.Frequency offset estimating is arranged this moment $\widehat{\mathrm{\&phi;}}=\&angle;\hat{W}/N,$

For restraining later weights.And work as y _nWhen not being certain CP that is not polluted by channel sampling, right value update can not make its convergence, filter normalization output this moment energy J (n)＜＜α, to export the trailing edge of energy be exactly the initial sampled point of OFDM symbolic blocks data segment to filter like this.As seen, above-mentioned processing procedure can be finished symbol time and frequency offset estimating simultaneously.Said process also can be regarded two length as, and to be 1 observation window slide receiving on the sample sequence, and utilize the sampled data in the window to carry out right value update.For brevity, CP and corresponding data segment that the present invention will not polluted by ISI are called " training section ", when observation window slides in the training section, adaptive process will make weights restrain gradually, the data segment of J (the n)＞α that can make in " training section " is called " converging portion ", and the weights in the converging portion can be used for estimating frequency deviation.Data segment except that the training section all is called " non-training section ".

In the adaptive updates process, can adopt following two measures to improve performance:

A. to data in one group of observation window, adopt forward and reverse twice iteration can accelerate convergence rate.As using y successively _n=[y _n, y _N+N] ^TAnd y _n=[y _N+N, y _n] ^HCome the self adaptation refreshing weight.

B. the observation window length of above-mentioned adaptive process is 1, just uses gradient at random.In order to accelerate convergence rate, and suppress noise, can adopt the gradient under certain statistical significance, promptly utilize the training section that belongs to a plurality of different OFDM symbolic blocks to average.If adopt M group data, have:

$y_n=\left[\begin{array}{cccc}{y}_n& y_{n+(N+G)}& \&CenterDot;\&CenterDot;\&CenterDot;& y_{n+(M-1)(N+G)}\\ y_{n+N}& y_{n+(N+G)+N}& \&CenterDot;\&CenterDot;\&CenterDot;& y_{n+(M-1)(N+G)+N}\end{array}\right]$

Wherein, M is " smoothing factor ".

In order to describe validity of the present invention and superiority in detail, below in conjunction with accompanying drawing and under four kinds of different conditions, provide four embodiment respectively and further described.In four embodiment, following parameter is four total: the total number of sub-carriers of the ofdm system that uses is N=64, and cyclic prefix CP length is G=16, and the true value of frequency deviation is $\mathrm{\&phi;}=\frac{2\mathrm{\&pi;}}{N}\&times;(-0.2),$ The symbol that sends on the data subcarrier in each OFDM symbolic blocks is independent identically distributed QPSK (the strong control of four a phase places) symbol.Signal to noise ratio is defined as $\mathrm{SNR}={10\log }_{10}({\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A20071001724200181.png,A20071001724200191.png"\; state="\{\{state\}\}">c</figure-callout>}}^2/{\mathrm{\&sigma;}}_n^2),$ σ wherein _c ²Be received signal power, σ _n ²Be the white Gaussian noise variance.

Embodiment 1

Under white Gaussian noise (AWGN) channel, suppose SNR=15dB.

The first step, algorithm begins, and selects step size mu=0.05, and initial value W (0)=1 selects smoothing factor M=10, convergence threshold α=0.85.

In second step,, write the reception data in the observation window as matrix form at moment n:

$y_n=\left[\begin{array}{cccc}{y}_n& y_{n+80}& \&CenterDot;\&CenterDot;\&CenterDot;& y_{n+9\&times;80}\\ y_{n+64}& y_{n+144}& \&CenterDot;\&CenterDot;\&CenterDot;& y_{n+9\&times;80+64}\end{array}\right].$ Utilize y _nRefreshing weight, because the smoothing factor that adopts is M=10, so adopt the following formula refreshing weight:

$W(n+1)=W\left(n\right)-0.05\&times;\frac{1}{{\left|\right|y_n\left|\right|}^2}{({\mathrm{<figure-callout\; id="1"\; label="y\; n"\; filenames="A20071001724200181.png,A20071001724200191.png"\; state="\{\{state\}\}">y</figure-callout>}}_n^{}+W\left(n\right)y_n^2)\left(y_n^2\right)}^H$

$W(n+1)=\frac{W(n+1)}{\left|W(n+1)\right|}$

ω(n+1)＝[1，W(n+1)] ^T

Y wherein _n ¹Be y _nThe first row vector, y _n ²Be y _nThe second row vector.‖ y _n‖ ²For asking matrix y _nTwo norms.

In the 3rd step,, calculate normalization output energy by the new ω (n) that obtains $J\left(n\right)=\frac{{\left|\mathrm{\&omega;}{\left(n\right)}^H{y}_n\right|}^2}{{\left|\right|y_n\left|\right|}^2}.$

The 4th step, the J (n-1) that obtains constantly according to this J that obtains (n) and n-1 and the comparison of threshold alpha=0.85, and judgement current state, whether can carry out frequency offset estimating and symbol time synchronous.

The 5th step made n=n+1, got back to for second step.

Owing to adopt smoothing factor M=10 in the present embodiment, so the forward reception data that are used for refreshing weight constantly at n are:

$y_n=\left[\begin{array}{cccc}{y}_n& y_{n+80}& \&CenterDot;\&CenterDot;\&CenterDot;& y_{n+9\&times;80}\\ y_{n+64}& y_{n+80+64}& \&CenterDot;\&CenterDot;\&CenterDot;& y_{n+9\&times;80+64}\end{array}\right]$

Oppositely receiving data is:

$y_n=\left[\begin{array}{cccc}{y}_{n+64}^{*}& y_{n+80+64}^{*}& \&CenterDot;\&CenterDot;\&CenterDot;& y_{n+9\&times;80+64}^{*}\\ y_n^{*}& y_{n+80}^{*}& \&CenterDot;\&CenterDot;\&CenterDot;& y_{n+9\&times;80}^{*}\end{array}\right]$

Whole process iteration is successively carried out, and when Fig. 2 showed subsequent iteration through 10 OFDM symbolic blocks, second step of each iteration and the output valve in the 3rd step were seen Fig. 2, and Fig. 2 (1) is the value of the frequency offset estimating of adaptive process output; Fig. 2 (2) is the value of normalization output energy in the adaptive process.Can see, export the fluctuation that is not stopping when normalized energy, when its greater than threshold alpha=0.85, the estimation of frequency deviation approaches true value-0.2, when normalized energy output less than threshold alpha=0.85, the estimation of frequency deviation is invalid, and when normalized energy output from greater than threshold value to there is a very steep trailing edge less than threshold value, represent the end of the Cyclic Prefix of an OFDM symbolic blocks, the just estimated position of time synchronized this moment.

Embodiment 2

This example is (AWGN) under the white Gaussian noise channel, utilizes Monte Carlo emulation mode, the simulation curve that the estimated performance that provides the present invention program changes with signal to noise ratio (SNR), and with background technology in the maximum likelihood method mentioned compare.Same step size mu=0.05 of selecting in this example, initial value W (0)=1 is 5～9dB in signal to noise ratio, 10～14dB and＞during 15dB, convergence threshold gets 0.75,0.85,0.95 respectively, other step is with embodiment 1.Emulation adopts 10000 Monte Carlo to realize, adopts and estimates that mean square error as performance index, is defined as $\mathrm{MSE}=\frac{N^2}{Q}\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\left(\frac{{\widehat{\mathrm{\&phi;}}}_q-\mathrm{\&phi;}}{2\mathrm{\&pi;}}\right)}^2,$ Q=10000 wherein.Fig. 3 is the time synchronized estimation performance of embodiment 2, and Fig. 4 is the performance of its frequency offset estimating.No matter as seen estimated performance when Fig. 3 and Fig. 4 have also provided simultaneously and adopted different smoothing factor M be that time synchronized is estimated or to frequency offset estimating, increased M and can improve estimation performance.And adopt resultant associating time synchronized of the inventive method and frequency offset estimating performance to be better than maximum likelihood method greatly.

Embodiment 3

This example is selected step size mu=0.05, initial value W (0)=1 under the frequency selectivity multipath channel, smoothing factor is taken as M=10, selecting signal to noise ratio is SNR=10dB and SNR=20dB, and corresponding convergence threshold is made as α=0.85 and α=0.9 respectively, and other step is with embodiment 1.Utilize Monte Carlo emulation mode, provide the simulation curve of the estimated performance of present embodiment, and compare with maximum likelihood method with the variation of channel exponent number.It is L that channel model adopts exponent number _cThe FIR filter, each channel parameter is independent Rayleigh fading, and the gross energy normalization of channel.Same emulation adopts 10000 Monte Carlo to realize, adopts and estimates that mean square error as performance index, is defined as $\mathrm{MSE}=\frac{N^2}{Q}\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\left(\frac{{\widehat{\mathrm{\&phi;}}}_q-\mathrm{\&phi;}}{2\mathrm{\&pi;}}\right)}^2,$ Q=10000 wherein.Fig. 5 is this routine time synchronized estimation performance, and Fig. 6 is the performance of its frequency offset estimating.No matter be that time synchronized is estimated or frequency offset estimating as seen from the figure, under the frequency selectivity multipath channel, the inventive method is more sane than the performance of prior art maximum likelihood method, even when the relative circulating prefix-length of channel exponent number was very big, the estimated performance of the inventive method was better than maximum likelihood method greatly.

Embodiment 4

This example is given in receiver known channel channel length, and under the time synchronized situation about having finished, and estimates the curve that the performance of frequency deviation changes with signal to noise ratio among the present invention separately, and is compared with the prior art document two relatively.The length of supposing the receiver known channel is L _c=14, adopt parameter L=4, hypothesis virtual subnet carrier number is 16 in the prior art.Both all adopt M=200 OFDM symbol to estimate.Emulation adopts 10000 Monte Carlo to realize, adopts and estimates that mean square error as performance index, is defined as $\mathrm{MSE}=\frac{N^2}{Q}\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\left(\frac{{\widehat{\mathrm{\&phi;}}}_{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="A20071001724200181.png,A20071001724200191.png"\; state="\{\{state\}\}">q</figure-callout>}}}{2\mathrm{\&pi;}}\right)}^2,$ Q=10000 wherein.

(7) formula of utilization, the OFDM symbol that k receives is constantly lined up down column matrix:

${\stackrel{-}{Y}}_k=\left[\begin{array}{cc}{y}_{k,-2}& y_{k,-1}\\ y_{k,14}& y_{k,15}\\ y_{k,30}& y_{k,31}\\ y_{k,46}& y_{k,47}\\ y_{k,62}& y_{k,63}\end{array}\right]$

Adopt M=200 continuous OFDM symbol, line up down column matrix:

$Y_k=\left[{\stackrel{-}{Y}}_k{\stackrel{-}{Y}}_{k+1}{\&CenterDot;\&CenterDot;\&CenterDot;\stackrel{-}{Y}}_{k+199}\right]$

Ask the autocorrelation matrix of this matrix, $R=\frac{1}{200}{Y}_k{Y}_k^H.$ This autocorrelation matrix is rotated constant technology (ESPRIT) method, can obtains frequency offset estimating.

Fig. 7 provided utilize above-mentioned steps estimate the frequency offset estimating performance that obtains with the variation of signal to noise ratio and with the comparison of prior art (documents two).

Claims (5)

1. unite time synchronized and frequency deviation estimating method in an ofdm system, it is characterized in that, comprise the steps:

Step 1: establish initial weight W (0)=1, determine that step size mu is 0～1, select smoothing factor M, it is an integer; Selecting convergence threshold α is 0.5～1;

Step 2: utilize received signal data y in the observation window _n=[y _n, y _N+N] ^T, wherein superscript " ^T" the representing matrix transposition, adopt following iterative formula to carry out adaptive weight W (n) and upgrade:

$W(n+1)=W\left(n\right)-\mathrm{\&mu;}\frac{1}{{\left|\right|y_n\left|\right|}^2}(y_n^{*}+W{y}_{n+N}^{*})y_{n+N}$

$W(n+1)=\frac{W(n+1)}{\left|W(n+1)\right|}$

ω(n+1)＝[1，W(n+1)] ^T

‖ y wherein _n‖ ²For asking vectorial y _nTwo norms, conjugation is got in " * " expression;

Step 3: utilize the weights that upgrade to calculate normalization output energy J (n):

$J\left(n\right)=\frac{{\left|\mathrm{\&omega;}{\left(n\right)}^H{y}_n\right|}^2}{{\left|\right|y_n\left|\right|}^2}$

Step 4: energy is exported in normalization and threshold alpha compares:

Step 4.1 is as J (n)＜α, during and J (n-1)＜α, thinks that current observation window is positioned at non-training section, and can not carry out frequency offset estimating this moment, arrives step 5;

Step 4.2 during and J (n-1)＜α, thinks that then observation window has just entered converging portion when J (n)＞α, this moment, current weights were used for estimating frequency deviation ${\widehat{\mathrm{\&phi;}}}_n=\frac{\&angle;W_n}{N};$

Step 4.3 is as J (n)＞α, during and J (n-1)＞α, then thinks observation window still at converging portion, and current weights also are used for estimating frequency deviation ${\widehat{\mathrm{\&phi;}}}_n=\frac{\&angle;W_n}{N};$

Step 4.4 is as J (n)＜α, during and J (n-1)＞α, can realize that symbol time is synchronous;

Step 5 makes n=n+1, gets back to step 2, carries out next iterative cycles.

2. associating time synchronized and frequency deviation estimating method in the ofdm system according to claim 1, it is characterized in that, the selection of convergence threshold α in the described step 1 is relevant with signal to noise ratio, when signal to noise ratio respectively at 5～9dB, 10～14dB and＞during 15dB, convergence threshold α gets 0.75 respectively, 0.85,0.95.

3. associating time synchronized and frequency deviation estimating method in the ofdm system according to claim 1 is characterized in that the derivation of the iterative formula in the described step 2 is as follows:

At first ask the eigenvalue of maximum and the characteristic of correspondence vector of autocorrelation matrix, be translated into the problem of asking Rayleigh merchant, following formula is promptly arranged:

$\underset{\mathrm{\&omega;}}{\max }J\left(\mathrm{\&omega;}\right)=\underset{\mathrm{\&omega;}}{\max }\left(E\right\{\frac{{\left|{\mathrm{\&omega;}}^{H}y\right|}^2}{{\left|\right|y\left|\right|}^2}\left\}\right)=\underset{\mathrm{\&omega;}}{\max }\frac{{\mathrm{\&omega;}}^H\mathrm{R\&omega;}}{{\mathrm{\&omega;}}^H\mathrm{\&omega;}}={\mathrm{\&lambda;}}_{\max }$ If R ω=λ _Maxω

Y=[y wherein _n, y _N+N] ^T, promptly be spaced apart the vector that two sampled points of N are formed, ω is weights, its have form [1, e ^{J  N}], make W=e ^{J  N}, then gradient is at random:

$\&dtri;J\left(\mathrm{\&omega;}\right)=\frac{1}{{\left|\right|y\left|\right|}^2}\&PartialD;{\left|\left(\begin{array}{cc}1& W^{*}\end{array}\right)\left(\begin{array}{c}{y}_n\\ y_{n+N}\end{array}\right)\right|}^2/\&PartialD;W^{*}$

$=\frac{1}{{\left|\right|y\left|\right|}^2}(y_n^{*}+W{y}_{n+N}^{*})y_{n+N}$

Promptly obtain iterative formula:

$W(n+1)=W\left(n\right)-\mathrm{\&mu;}\frac{1}{{\left|\right|y_n\left|\right|}^2}(y_n^{*}+W{y}_{n+N}^{*})y_{n+N}$

$W(n+1)=\frac{W(n+1)}{\left|W(n+1)\right|}.$

ω(n+1)＝[1，W(n+1)] ^T

4. associating time synchronized and frequency deviation estimating method is characterized in that in the ofdm system according to claim 1, and described step 2 is in the adaptive updates process, simultaneously or arbitraryly take following two kinds of y _nProcessing method:

A. to data in one group of observation window, adopt forward and reverse twice iteration, promptly use y successively to accelerate convergence rate _n=[y _n, y _N+N] ^TAnd y _n=[y _N+N, y _n] ^HCome refreshing weight, wherein conjugate transpose is got in superscript " H " expression;

B. above-mentioned adaptive process adopts is gradient at random, can adopt the gradient under certain statistical significance in the real system, promptly utilizes the training section that belongs to a plurality of different OFDM symbolic blocks to average, and when adopting M group data, promptly uses:

$y_n=\left[\begin{array}{cccc}{y}_n& y_{n+(N+G)}& \&CenterDot;\&CenterDot;\&CenterDot;& y_{n+(M-1)(N+G)}\\ y_{n+N}& y_{n+(N+G)+N}& \&CenterDot;\&CenterDot;\&CenterDot;& y_{n+(M-1)(N+G)+N}\end{array}\right]$

Refreshing weight, wherein, M is " smoothing factor ".

5. associating time synchronized and frequency deviation estimating method is characterized in that in the ofdm system according to claim 1, in the described step 4.2,4.3, when converging portion during greater than a sampling length, can repeatedly estimate frequency deviation, asks average then.

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