CN103929394A - High-precision frequency offset estimation method based on iteration algorithm - Google Patents

Abstract

The invention discloses a high-precision frequency offset estimation method based on an iteration algorithm. The innovation point is that under the condition that a channel is low in signal-to-noise ratio, high-precision frequency offset estimation can be performed, and the method mainly includes the following steps that (1), two adjacent training sequences are extracted; (2), two training sequence blocks are used for correlation operation, so that an initial frequency offset estimation value is obtained; (3), the frequency offset estimation value obtained in the last step is used for performing phase compensation on the receipt sequences; (4), the training sequence blocks after phase compensation are summed up in a segmentation mode to obtain new sequences; (5), the new sequences are used for correlation operation, so that a residual frequency offset value is obtained, and the residual frequency offset value is updated; (6), whether segmentation length meets the requirement or not is judged, if yes, the step3 is repeated, and if not, iteration is finished. The two sequence blocks are effectively used for iteration operation, under the condition that pilot frequency cost is not increased, the high-precision frequency offset estimation value is obtained, and meanwhile due to the method, frequency offset estimation performance under the condition of the low signal-to-noise ratio can be effectively improved.

Description

High accuracy frequency deviation estimating method based on iterative algorithm

Technical field:

The invention belongs to wireless communication field, relate to a kind of carrier frequency bias estimation, particularly a kind of frequency deviation estimating method based on iterative algorithm.

Background technology:

In wireless communication system, there is certain deviation in local crystal oscillator and the carrier frequency clock of receiving terminal, and in mobile communication system, Doppler's existence also can be to frequency shift (FS).Only have to estimate accurately frequency shift (FS) as far as possible and could carry out to received signal phase compensation, accurately digital signal is carried out to demodulation.The performance that frequency deviation is estimated will directly affect data recovery performance, and especially at multicarrier modulation system (as 0FDM, MC-CDMA), residual frequency deviation is crossed senior general and made multiple signals lose orthogonality, phase mutual interference between multi-user.Therefore, can accurately and simply estimate frequency departure, and then compensate to received signal, be a key technology of the communications field.

Current, estimate it is mainly to ask for phase information and obtain frequency deviation estimated value based on training sequence for frequency deviation, more accurate for frequency deviation is estimated, can use two training sequences to do fixed length related operation, this algorithm estimated accuracy is high, but estimation range is little.After overdeviation is estimated, receiving terminal and transmitting terminal carrier wave basic synchronization.But traditional frequency deviation algorithm for estimating mostly has the threshold value of a signal to noise ratio, in practical application, be difficult to the signal to noise ratio that reaches higher, the application of these algorithms is restricted.

Classical frequency deviation algorithm for estimating is to sue for peace by a window function after utilizing a training sequence piece to carry out related calculation, but utilizes individualized training sequence blocks because symbol is shorter and interval is too little, to cause estimated accuracy not high.Meanwhile, utilize the relevant algorithm in adjacent training sequence piece front and back to do frequency deviation and carefully estimate, although estimated accuracy is high, estimation range is little, and estimated performance can also further improve under low signal-to-noise ratio.

Summary of the invention:

The object of the invention is to the deficiency for prior art, propose a kind of estimated accuracy high, the frequency offset estimation technique that signal-noise ratio threshold is low, has reduced the residual frequency deviation in carrier wave recovery process.

The technical solution used in the present invention is: utilize the fix related operation of length of two training sequence pieces, obtain a frequency deviation estimated value, utilize this value to carry out phase compensation to the signal receiving, again to the segmentation summation respectively of two sections of training sequences, obtain two new sequences, and use new sequence again to carry out related calculation, and obtain residual frequency deviation estimated value, carry out iteration with this.Its concrete performing step is as follows:

1) receiving terminal, according to the position of training sequence, extracts and receives burst x ₀(n) in, adjacent two training sequence pieces, are respectively T ₁and T ₂, training sequence block length is N, T ₁and T ₂be spaced apart L;

2) utilize training sequence T ₁n symbol and T ₂n symbol conjugate multiplication, acquired results summation is added, and summed result is got to phase value, and divided by L, obtain frequency deviation initial estimate and set an initial count value k=1;

3) utilize frequency deviation estimated value obtained in the previous step, to sequence x ₀(n) carry out phase compensation, obtain new sequence x _k(n), training sequence piece T ₁and T ₂becoming accordingly training sequence piece is T ₁' and T ₂';

4) by training sequence piece T ₁' symbol segmentation summation, section length M=2 ^k, obtaining new sequence is v _1M(n), i.e. T ₁' the summation of front M symbol, result is v _1M(0), M+1 to the 2M symbol summation, result is v _1M(1), (N-M+1) to N symbol summed result be v _1M(N/2-1), to training sequence T ₂' do identical processing, obtain sequence v _2M(n);

5) by sequence v _1M(n) n symbol and sequence v _2M(n) n symbol conjugate multiplication, acquired results summation is added, summed result is got to phase information, and divided by L, obtains residual frequency deviation estimated value, frequency deviation estimated value be updated to previous step acquisition value and this estimation residual frequency deviation and value;

6) use T ₁length N divided by 2 ^k, whether court verdict meets is greater than 4, if result is greater than 4, k adds 1, and enters step 3), if result is less than or equal to 4, the result that previous step is tried to achieve is the estimated value of frequency deviation.

Further, the method for extracting training sequence in described step 1) is: after frame timing, according to the position of the training sequence setting in advance, by the receiving symbol location training sequence of correspondence position.

Further, in described step 1), train the selection rule of length to be: two sections of training sequence total length 2N and whole sequence length ratio 2N/ (L+2N) are not less than total length 10%, be not more than 30%, this is while being less than 10% due to training sequence accounting, training sequence is too short, estimated performance is not good, and while being greater than 30%, the performance boost that the expense increase of training sequence brings is very little.

Further, the value of the N described in described step 1) is chosen as follows: the integral number power that N is 2.

Further, described step 2) computation rule of described frequency deviation initial estimation scope is: the phase deviation that the frequency deviation between two sections of training sequences causes is no more than π, and frequency deviation region is

Further, described step 2) in the computation rule of conjugate multiplication be: by T ₁first symbol get conjugation again with T ₂first symbol multiply each other, T ₁second symbol get conjugation again with T ₂second symbol multiply each other, until T ₁n symbol get conjugation again with T ₂n symbol multiply each other, by the summation of all multiplied result.

Further, in wherein said step 3), to the method for phase compensation be: to the original series x receiving ₀(n) carry out phase compensation, the frequency deviation estimated value that the frequency deviation value of compensation is previous step.

Further, in described step 4), after each iteration, training sequence length computation rule is: iteration section length is 2 for the first time, and formation sequence length is N/2, and iteration section length is 4 for the second time, formation sequence length is N/4, and the section length of the k time iteration is 2 ^k, formation sequence length is N/2 ^k.

Further, the principle that described step 5) frequency deviation estimated value is upgraded is: the frequency deviation estimated value that the last time obtains is the estimated value of the training sequence that the frequency deviation estimated value that this iteration draws is this generation with and, be:

${\hat{w}}_k={\hat{w}}_{k-1}+\frac{1}{L}\×\arg \left(\underset{n=0}{\overset{N/2-1}{\mathrm{\Σ}}}{v}_{1M}^{*}\left(n\right)v_{2M}\left(n\right)\right)$

Further, while entering step 3) in described step 6), step 6) is as the previous step of step 3), and the phase compensation in step 3) utilizes the value estimating in step 6); In described step 6), judgement can be according to the following rules: if N/2 ^k>4, enters step 3), utilizes the frequency deviation estimated value of this iteration to original series phase compensation, if N/2 ^k≤ 4, the frequency deviation estimated value of this iteration is final frequency deviation estimated value, and iteration finishes.

Tool of the present invention has the following advantages:

1) the present invention utilizes two training symbol pieces of receiving terminal, because data break is large, thereby can reach very high estimated accuracy; Owing to not needing associating estimation, therefore its computation complexity is much smaller than the amount of calculation of combining estimation;

2) the present invention is through interative computation several times, and compared with traditional front and back training sequence related operation, frequency deviation estimated performance is significantly improved under low signal-to-noise ratio, and signal-noise ratio threshold is low;

3) the present invention can flexible configuration, goes for the frame that comprises individualized training piece and multiple training pieces.

Brief description of the drawings:

Fig. 1 is training sequence figure of the present invention;

Fig. 2 is flow chart of the present invention;

Fig. 3 is the concrete block diagram of the present invention;

Fig. 4 is simulation performance of the present invention.

Embodiment:

For making the object, technical solutions and advantages of the present invention clearer, below by by reference to the accompanying drawings and specific embodiment, technical method of the present invention is further described.

See figures.1.and.2, specific implementation step of the present invention comprises:

Step 1: after frame synchronization, according to the position of the training sequence inserting, extract and receive two training sequence pieces in signal, be respectively T ₁and T ₂, training sequence length is N, T ₁and T ₂be spaced apart L, as shown in Figure 1.The value of N and L is according to the following rules:

1a) two sections of training sequence total length 2N and whole sequence length ratio 2N/ (L+2N) are not less than total length 10%, be not more than 30%, this is while being less than 10% due to training sequence accounting, training sequence is too short, estimated performance is not good, and while being greater than 30%, the performance boost that the expense increase of training sequence brings is very little;

1b) value of N is chosen as follows: the integral number power that N is 2;

The phase deviation that 1c) frequency deviation between two sections of training sequences causes can not exceed π, and frequency deviation region is exceed this scope estimation range inaccurate.

Step 2: utilize T ₁conjugation and the T of n symbol ₂n symbol multiply each other, acquired results summation is added, and summed result is got to phase value, and divided by L, obtain frequency deviation initial estimate and set an initial count value k=1.When frequency deviation value is e ^jwntime, the estimated value that obtains normalization frequency deviation is:

$\begin{array}{c}{\hat{w}}_0=\frac{1}{L}\×\arg \left[\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}{x}_0^{*}\left(n\right)x_0(n+L)\right]\\ =w+e_0\end{array}$

Wherein, arg () is for getting phase bit arithmetic, x ₀(n) initiation sequence for receiving, for initial normalization frequency deviation estimated value, w is frequency deviation exact value, e ₀for initial estimation error;

Step 3: utilize initial frequency deviation estimated value obtained in the previous step, the signal receiving is carried out to phase compensation, obtain new sequence x _k(n), training sequence piece T ₁and T ₂becoming accordingly training sequence piece is T ₁' and T ₂'; The method of compensation is herein: taking first training sequence as initiating terminal, first symbol is multiplied by 1, the second symbol and is multiplied by n symbol is multiplied by

$\begin{array}{c}{x}_k\left(n\right)=e^{-j{\hat{w}}_{k-1}n}{x}_0\left(n\right)\\ =e^{j(w-{\hat{w}}_{k-1})n}{x}_0\left(n\right)+z\left(n\right)e^{-j{\hat{w}}_{k-1}n}\\ =e^{\mathrm{j\Δ}{w}_{k-1}n}{x}_0\left(n\right)+z\left(n\right)e^{-j{\hat{w}}_{k-1}n}\end{array}$

Wherein, Z (n) is white Gaussian noise, x _k(n) be the sequence through overdeviation compensation after the k time iteration.

Step 4: the sequence blocks T obtaining after compensate of frequency deviation ₁' and T ₂' segmentation summation, section length is M=2 ^k, obtain the sequence v of equal length _1Mand v _2M.Be T ₁' front M symbol directly sue for peace, result is v _1M(0), M+1 to the 2M symbol summation, result is v _1M(1), (N-M+1) to N symbol summed result be v _1M(N/2-1), second training sequence piece done to identical processing:

$v_{1M}\left(n\right)=\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}{x}_k(\mathrm{nM}+m),n=\mathrm{0,1},...,K-1$

$v_{2M}\left(n\right)=\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}{x}_k(\mathrm{nM}+m+L),n=\mathrm{0,1},...,K-1$

Wherein, K=N/M is integer, is section length, x ₀(n) be initiation sequence, v _m(n) be the sequence after segmentation summation, v _m(n) can merge into:

v _1M(n)＝C _M(w)e ^jwMn+n _v(n)

v _2M(n)＝e ^jwLC _M(w)e ^jwMn+n _v(n)

Wherein, $C_M\left(w\right)={\mathrm{MAe}}^{\mathrm{jMw}/2}\sin c_M\left(\frac{w}{2}\right),$ ${\sin c}_M\left(x\right)\stackrel{\mathrm{\Δ}}{=}\frac{\sin \left(\mathrm{Mx}\right)}{M\sin \left(x\right)}$ N _vfor zero-mean white Gaussian noise.

Step 5: utilize sequence v _1Mconjugation and the v of n symbol _2Mn symbol multiply each other, acquired results summation is added, summed result is got to phase information, and divided by L, obtains residual frequency deviation estimated value, frequency deviation estimated value be updated to previous step acquired results and this estimation residual frequency deviation and value:

${\hat{w}}_k={\hat{w}}_{k-1}+\frac{1}{L}\×\arg \left(\underset{n=1}{\overset{K}{\mathrm{\Σ}}}{v}_{1M}^{*}\left(n\right)v_{2M}\left(n\right)\right)$

Step 6: to T ₁length N divided by 2 ^k, whether court verdict meets is greater than 4, if result is greater than 4, k adds 1, and enters step 3), if result is less than or equal to 4, the result that previous step is tried to achieve is the estimated value of frequency deviation.It is as follows that court verdict and 4 does the proof contrasting: first estimate after compensation to received signal, and be x by the sequence definition of compensate of frequency deviation for the first time ₁(n):

$x_1\left(n\right)=e^{-j{\hat{w}}_{0}n}{x}_0\left(n\right)=e^{\mathrm{j\Δ}{w}_{1}n}{x}_0\left(n\right)+z\left(n\right)e^{-j{\hat{w}}_{0}n}$

Wherein:

$\mathrm{\Δ}{w}_1\stackrel{\mathrm{\Δ}}{=}\mathrm{mod}({-e}_0,2\mathrm{\π})$

Can be used as sequence x ₁(n) frequency deviation, to x ₁(n) sample, obtain new sequence as follows:

$v_M\left(n\right)=\underset{m=0}{\overset{M_1-1}{\mathrm{\Σ}}}{x}_1(M_{1}n+m)$

N/M ₁for integer, use the sequence of newly obtaining to carry out iterative estimate for the first time:

$\begin{array}{c}\mathrm{\Δ}{\hat{w}}_1=\frac{1}{L}\×\arg \left[\underset{n=1}{\overset{N/M_1-1}{\mathrm{\Σ}}}{v}_{1M}^{*}\left(n\right)v_{2M}\left(n\right)\right]\\ ={\mathrm{\Δw}}_1+e_1\end{array}$

Wherein, for residual frequency deviation estimated value, Δ w ₁for actual residual frequency deviation, the frequency deviation that the frequency deviation that again obtains of definition is each iteration and:

$\begin{array}{c}{\hat{w}}_1=\mathrm{mod}({\hat{w}}_0+\mathrm{\Δ}{\hat{w}}_1,2\mathrm{\π})\\ =\mathrm{mod}({\hat{w}}_0+\mathrm{\Δ}{w}_1+e_1,2\mathrm{\π})\\ =\mathrm{mod}(w+e_1+2m_0\mathrm{\π},2\mathrm{\π})\end{array}$

After an iteration, evaluated error e ₁for residual frequency deviation, after single compensation, be worth littlely, can effectively suppress phase hit.E so ₁mean square error be less than e ₀.Iterations increases, and frequency deviation estimated value is upgraded once:

${\hat{w}}_k=\mathrm{mod}(w+e_k,2\mathrm{\π})$

And x _kand v _kalso upgrade simultaneously.

In the time that signal to noise ratio is enough large, the frequency deviation after iteration is enough little, has:

$\sin c_M^2\left(\frac{{\mathrm{\Δw}}_k}{2}\right)\≈1$

Use above formula approximate formula, can obtain the computing formula of CramerRao circle:

$\mathrm{var}\left(e_k\right)=\frac{1}{M_k\left(\frac{A^2}{{\mathrm{\σ}}^2}\right){(N-M_k)}^2}\×[1+\frac{N-M_k}{2M_k^2\left(\frac{A^2}{{\mathrm{\σ}}^2}\right)}]$

In the time that signal to noise ratio enough meets following condition greatly:

$\frac{A^2}{{\mathrm{\σ}}^2}>>\frac{N-M_k}{{2M}_k^2}$

:

$\mathrm{var}\left(\hat{w}\right)\≈\frac{1}{M_k(A^2/{\mathrm{\σ}}^2){(N-M_k)}^2}=\frac{{(N/M_k)}^3}{N^3(A^2/{\mathrm{\σ}}^2){(N/M_k-1)}^2}$

For M ₁=2, M ₂=4 ..., M _k=N/4, can be equivalent to following formula:

$\frac{A^2}{{\mathrm{\σ}}^2}>>\frac{6}{N}$

CramerRao circle ratio with respect to traditional algorithm is:

$\frac{\mathrm{var}\left(\hat{w}\right)}{{\mathrm{\σ}}_{\mathrm{CR}}^2}=\frac{{(N/M_k)}^3(N^2-1)N}{6{(N/M_k-1)}^2{N}^3}$

Can find out at N/M _kcan make value minimum at=3 o'clock, iteration block diagram is as Fig. 3.Therefore, training sequence is longer, and exponent number that can iteration is larger.Under optimum iterated conditional, the frequency deviation estimated performance that the method for use iteration is obtained is a little less than CramerRao circle.

Effect of the present invention can further illustrate by following emulation:

1. simulated conditions

Adopt QPSK modulate as analogue system, the frequency deviation of interpolation can not exceed estimation range, and channel is Gaussian white noise channel, and channel coefficients obedience average is zero, the multiple Gaussian Profile that variance is 1.The number of times of emulation is 10 ⁵inferior.

2. emulation content and result

The algorithm that the present invention is directly related with front and back contrasts, and using CramerRao circle as with reference to dotted line, simulation result as shown in Figure 4.As shown in Figure 4, signal to noise ratio is below 10dB time, and frequency deviation estimated performance of the present invention is significantly improved.

Claims (10)

1. the high accuracy frequency deviation estimating method based on iterative algorithm, is characterized in that: comprise the following steps:

1) receiving terminal, according to the position of training sequence, extracts and receives burst x ₀(n) in, adjacent two training sequence pieces, are respectively T ₁and T ₂, training sequence block length is N, T ₁and T ₂be spaced apart L;

2) utilize training sequence T ₁n symbol and T ₂n symbol conjugate multiplication, acquired results summation is added, and summed result is got to phase value, and divided by L, obtain frequency deviation initial estimate and set an initial count value k=1;

3) utilize frequency deviation estimated value obtained in the previous step, to sequence x ₀(n) carry out phase compensation, obtain new sequence x _k(n), training sequence piece T ₁and T ₂becoming accordingly training sequence piece is T ₁' and T ₂';

4) by training sequence piece T ₁' symbol segmentation summation, section length M=2 ^k, obtaining new sequence is v _1M(n), i.e. T ₁' the summation of front M symbol, result is v _1M(0), M+1 to the 2M symbol summation, result is v _1M(1), (N-M+1) to N symbol summed result be v _1M(N/2-1), to training sequence T ₂' do identical processing, obtain sequence v _2M(n);

5) by sequence v _1M(n) n symbol and sequence v _2M(n) n symbol conjugate multiplication, acquired results summation is added, summed result is got to phase information, and divided by L, obtains residual frequency deviation estimated value, frequency deviation estimated value be updated to previous step acquisition value and this estimation residual frequency deviation and value;

6) use T ₁length N divided by 2 ^k, whether court verdict meets is greater than 4, if result is greater than 4, k adds 1, and enters step 3), if result is less than or equal to 4, the result that previous step is tried to achieve is the estimated value of frequency deviation.

2. a kind of high accuracy frequency deviation estimating method based on iterative algorithm according to claim 1, it is characterized in that: the method for extracting training sequence in described step 1) is: after frame timing, according to the position of the training sequence setting in advance, by the receiving symbol location training sequence of correspondence position.

3. a kind of high accuracy frequency deviation estimating method based on iterative algorithm according to claim 1, it is characterized in that: in described step 1), train the selection rule of length to be: two sections of training sequence total length 2N and whole sequence length ratio 2N/ (L+2N) are not less than total length 10%, are not more than 30%.

4. a kind of high accuracy frequency deviation estimating method based on iterative algorithm according to claim 1, is characterized in that: the value of the N described in described step 1) is chosen as follows: the integral number power that N is 2.

5. a kind of high accuracy frequency deviation estimating method based on iterative algorithm according to claim 1, it is characterized in that: described step 2) computation rule of described frequency deviation initial estimation scope is: the phase deviation that the frequency deviation between two sections of training sequences causes is no more than π, and frequency deviation region is

6. a kind of high accuracy frequency deviation estimating method based on iterative algorithm according to claim 1, is characterized in that: described step 2) in the computation rule of conjugate multiplication be: by T ₁first symbol get conjugation again with T ₂first symbol multiply each other, T ₁second symbol get conjugation again with T ₂second symbol multiply each other, until T ₁n symbol get conjugation again with T ₂n symbol multiply each other, by the summation of all multiplied result.

7. a kind of high accuracy frequency deviation estimating method based on iterative algorithm according to claim 1, is characterized in that: the method to phase compensation in wherein said step 3) is: to the original series x receiving ₀(n) carry out phase compensation, the frequency deviation estimated value that the frequency deviation value of compensation is previous step.

8. a kind of high accuracy frequency deviation estimating method based on iterative algorithm according to claim 1, it is characterized in that: in described step 4), after each iteration, training sequence length computation rule is: iteration section length is 2 for the first time, formation sequence length is N/2, iteration section length is 4 for the second time, formation sequence length is N/4, and the section length of the k time iteration is 2 ^k, formation sequence length is N/2 ^k.

9. a kind of high accuracy frequency deviation estimating method based on iterative algorithm according to claim 1, is characterized in that: the principle that described step 5) frequency deviation estimated value is upgraded is: the frequency deviation estimated value that the last time obtains is the estimated value of the training sequence that the frequency deviation estimated value that this iteration draws is this generation with and, be:

${\hat{w}}_k={\hat{w}}_{k-1}+\frac{1}{L}\×\arg \left(\underset{n=0}{\overset{N/2-1}{\mathrm{\Σ}}}{v}_{1M}^{*}\left(n\right)v_{2M}\left(n\right)\right)$

10. a kind of high accuracy frequency deviation estimating method based on iterative algorithm according to claim 1, it is characterized in that: while entering step 3) in described step 6), step 6) is as the previous step of step 3), and the phase compensation in step 3) utilizes the value estimating in step 6); In step 6), decision rule is: if N/2 ^k>4, enters step 3), utilizes the frequency deviation estimated value of this iteration to original series phase compensation, if N/2 ^k≤ 4, the frequency deviation estimated value of this iteration is final frequency deviation estimated value, and iteration finishes.