CN106789786A - A kind of novel sampling frequency synchronization algorithm - Google Patents

Abstract

The invention discloses a novel sampling frequency synchronization algorithm, which relates to a communication algorithm. It uses an iterative method to quickly converge the estimation result to an accurate value, and can achieve high estimation accuracy with very few symbols; through theoretical derivation, the sampling frequency offset estimation formula of the traditional algorithm is corrected to obtain a more accurate capture value ; By proposing a tracking threshold suitable for practical engineering in the algorithm, and through the selection of the pilot position and the optimization of data processing, a compromise between precision and complexity is achieved, which is more suitable for practical engineering. The invention has the advantages of low complexity, high precision and fast estimation, and can be better applied to the actual NG-DSL system.

Description

A New Sampling Frequency Synchronization Algorithm

technical field

The invention relates to a communication algorithm, in particular to a novel sampling frequency synchronization algorithm.

Background technique

At present, there are not many studies on OFDM sampling deviation in the existing technology, mainly because the carrier number and modulation level of OFDM are not high in traditional applications, and the precision of clock crystal oscillator is relatively high, so the error effect caused by sampling frequency deviation Not obvious, little impact on the system. But for the NG-DSL system with high level modulation and high carrier number, the error generated by the crystal oscillator will have a certain impact on the system in one OFDM data frame, so it is necessary to compensate the output signal of the system in time .

In the traditional sampling frequency offset estimation algorithm, it is mainly divided into two types: data-assisted and non-data-assisted. The data-assisted algorithm mainly relies on adding pilot symbols to OFDM symbols. Correlation operations can estimate the sampling frequency deviation. The disadvantage of this estimation method is that it needs to occupy a certain carrier resource as a pilot; the method of non-data-assisted estimation of sampling deviation is mainly to estimate by extracting the information contained in the signal itself. The disadvantage of is more obvious, that is, the complexity of the algorithm will be higher, and the estimation accuracy is not as good as the data-assisted algorithm. Based on this, it is necessary to design a new sampling frequency synchronization algorithm.

Contents of the invention

Aiming at the deficiencies in the prior art, the purpose of the present invention is to provide a novel sampling frequency synchronization algorithm with high precision, low computational complexity and fast estimation speed, which can be better applied to the actual NG-DSL system.

In order to achieve the above object, the present invention is realized through the following technical solutions: a novel sampling frequency synchronization algorithm, the estimation process of which algorithm is:

Insert a pilot at the sender Demodulate the corresponding pilot symbols at the receiving end: Divide the pilot symbol at the receiving end by the original pilot symbol of the corresponding bit, namely:

Taking the angle from the result of formula (1), let:

When the number of subcarriers is large, the second term in formula (1) can be approximately considered to obey the Gaussian distribution, so it can be classified as additive noise together with channel noise, which will not affect the result and affect OFDM The main factor of the signal angle rotation is the first term of the formula (1), and the ICI interference term of the second term of the formula (1) just makes the demodulated frequency domain signal randomly diverge around the central standard signal. Therefore value of:

and for:

Through the above derivation, it can be found that formula (4) is problematic, and will have a certain impact on the estimated results (especially the estimated values of the first few symbols), and it needs to be corrected, because this will affect the estimated value of Δf Accuracy, analytically known The size of increases with the increase of the carrier number k, the number of symbols m and the normalized sampling frequency offset Δf. Next, the estimation method of Δf needs to be derived.

In the same OFDM symbol make:

can get:

In the above formula, A _m,k and For the observed value, it is necessary to estimate Δf, and the estimation of the sampling frequency offset is to use the least square method:

The least squares estimation method can be used to estimate Δf more accurately, but it needs to go through multiple multiplications, additions and divisions. This method can better weaken the influence of noise on each estimated value in a channel environment with a low signal-to-noise ratio. influences. However, since the input signal-to-noise ratio of the NG-DSL system will be relatively high, the above estimation process can be simplified to reduce the computational complexity. The least square estimation method is changed to the weighted average method with the pilot carrier number k as the weighting factor. which is:

Compared with formula (7), the computational complexity of formula (8) is much lower, and the simulation in the NG-DSL environment shows that the accuracy of formula (8) will not decrease, so the combination of computational complexity and precision In this algorithm, formula (8) will be used to process the observed values.

In order to further reduce the computational complexity, the location selection of the pilot is optimized. When the pilot location meets certain conditions, the computational complexity of the algorithm can be reduced. The algorithm is simulated in the NG-DSL system simulation environment, and the algorithm only needs 8 A more precise sampling frequency synchronization can be accomplished with just one pilot symbol. According to formula (8), it is necessary to divide the observed value by the sum of the pilot serial numbers, so by selecting the appropriate pilot position, the division can be changed into a displacement operation to reduce the computational complexity. For example, the positions of 8 selected pilots are: {505507509511513515517519}, and the result of adding the subcarrier numbers of these pilots is 4096. In the computer, the calculation amount of displacement operation is much smaller than that of division operation. If the divisor is the power of 2, the division operation can become a displacement operation. For example, if the divisor is 2, the dividend will be shifted to the left by 1 bit; Shift 2 bits to the left; and so on, the divisor at this time is 4096, and the dividend only needs to be shifted 12 bits to the left without relatively complex division operations. At this time, the division operation only needs to be changed into a displacement operation in the computer, which reduces the reaction time of the computer. The pilot position can also be selected according to the result of channel estimation feedback, and the carrier with better channel response is selected as the pilot carrier. Only the pilot position meets the above requirements to reduce the computational complexity.

After the above steps, the sampling frequency synchronization using the first symbol as a sample is completed. Starting from the second symbol, the pilot symbols at the receiving end are pre-corrected using the estimated value of the previous symbol. The purpose of this is to suppress the angle rotation caused by the sampling frequency deviation and cause a large error with the increase in the number of symbols. The angle deviation affects the new result estimation; and then the pre-corrected pilot symbol is estimated by sampling frequency offset, and a new estimated value can be obtained, and the two results are added and fed back as the third OFDM pilot symbol The pre-correction value of , and then repeat the operation for the second symbol. The estimated value obtained by this iterative method will converge quickly and will be very close to the real value.

Through the above analysis, the algorithm can be divided into two processes: deviation capture and tracking. The capture process generally does not exceed 3 symbols (the number of captured symbols may be increased in the case of high noise). After several symbol iterations, the algorithm can estimate a more accurate frequency offset. The tracking process essentially uses new estimates to fine-tune previous estimated biases.

Beneficial effects of the present invention: Compared with other algorithms, the algorithm is more accurate and estimates faster, and has the advantages of low complexity, high precision and fast estimation, so that the algorithm can be better used in the actual NG-DSL system.

Description of drawings

The present invention is described in detail below in conjunction with accompanying drawing and specific embodiment;

Fig. 1 is a frequency offset estimation curve diagram of the present invention;

Fig. 2 is the frequency offset estimation graph of the tracking phase of the present invention;

Fig. 3 is the frequency offset estimation curve diagram under different tracking threshold coefficients of the present invention;

Fig. 4 is a working flow diagram of the present invention.

detailed description

In order to make the technical means, creative features, goals and effects achieved by the present invention easy to understand, the present invention will be further described below in conjunction with specific embodiments.

With reference to Fig. 1-4, present embodiment adopts following technical scheme: a kind of novel sampling frequency synchronization algorithm, the estimation process of its algorithm is:

Insert a pilot at the sender Demodulate the corresponding pilot symbols at the receiving end: Divide the pilot symbol at the receiving end by the original pilot symbol of the corresponding bit, namely:

Taking the angle from the result of formula (1), let:

When the number of subcarriers is large, the second term in formula (1) can be approximately considered to obey the Gaussian distribution, so it can be classified as additive noise together with channel noise, which will not affect the result and affect OFDM The main factor of the signal angle rotation is the first term of the formula (1), and the ICI interference term of the second term of the formula (1) just makes the demodulated frequency domain signal randomly diverge around the central standard signal. Therefore value of:

and for:

Through the above derivation, it can be found that formula (4) is problematic, and will have a certain impact on the estimated results (especially the estimated values of the first few symbols), and it needs to be corrected, because this will affect the estimated value of Δf Accuracy, analytically known The size of increases with the increase of the carrier number k, the number of symbols m and the normalized sampling frequency offset Δf. Next, the estimation method of Δf needs to be derived.

In the same OFDM symbol make:

can get:

In the above formula, A _m,k and For the observed value, it is necessary to estimate Δf, and the estimation of the sampling frequency offset is to use the least square method:

The least squares estimation method can be used to estimate Δf more accurately, but it needs to go through multiple multiplications, additions and divisions. This method can better weaken the influence of noise on each estimated value in a channel environment with a low signal-to-noise ratio. influences. However, since the input signal-to-noise ratio of the NG-DSL system will be relatively high, the above estimation process can be simplified to reduce the computational complexity. The least square estimation method is changed to the weighted average method with the pilot carrier number k as the weighting factor. which is:

Compared with formula (7), the computational complexity of formula (8) is much lower, and the simulation in the NG-DSL environment shows that the accuracy of formula (8) will not decrease, so the combination of computational complexity and precision In this algorithm, formula (8) will be used to process the observed values.

In order to further reduce the computational complexity, the location selection of the pilot is optimized. When the pilot location meets certain conditions, the computational complexity of the algorithm can be reduced. The algorithm is simulated in the NG-DSL system simulation environment, and the algorithm only needs 8 A more precise sampling frequency synchronization can be accomplished with just one pilot symbol. According to formula (8), it is necessary to divide the observed value by the sum of the pilot serial numbers, so by selecting the appropriate pilot position, the division can be changed into a displacement operation to reduce the computational complexity. For example, the positions of 8 selected pilots are: {505507509511513515517519}, and the result of adding the subcarrier numbers of these pilots is 4096. In the computer, the calculation amount of displacement operation is much smaller than that of division operation. If the divisor is the power of 2, the division operation can become a displacement operation. For example, if the divisor is 2, the dividend will be shifted to the left by 1 bit; Shift 2 bits to the left; and so on, the divisor at this time is 4096, and the dividend only needs to be shifted 12 bits to the left without relatively complex division operations. At this time, the division operation only needs to be changed into a displacement operation in the computer, which reduces the reaction time of the computer. The pilot position can also be selected according to the result of channel estimation feedback, and the carrier with better channel response is selected as the pilot carrier. Only the pilot position meets the above requirements to reduce the computational complexity.

After the above steps, the sampling frequency synchronization using the first symbol as a sample is completed. Starting from the second symbol, the pilot symbols at the receiving end are pre-corrected using the estimated value of the previous symbol. The purpose of this is to suppress the angle rotation caused by the sampling frequency deviation and cause a large error with the increase in the number of symbols. The angle deviation affects the new result estimation; and then the pre-corrected pilot symbol is estimated by sampling frequency offset, and a new estimated value can be obtained, and the two results are added and fed back as the third OFDM pilot symbol The pre-correction value of , and then repeat the operation for the second symbol. The estimated value obtained by this iterative method will converge quickly and will be very close to the real value.

Through the above analysis, the algorithm can be divided into two processes: deviation capture and tracking. The capture process generally does not exceed 3 symbols (the number of captured symbols may be increased in the case of high noise). After several symbol iterations, the algorithm can estimate a more accurate frequency offset. The tracking process essentially uses new estimates to fine-tune previous estimated biases.

Figure 1 is the frequency offset estimation curve of the NG-DSL system with the normalized sampling frequency offset of 0.3ppm (3e-7) by this algorithm. It can be seen that the first capture value (2.75e-7) is higher than the standard value (3e-7) -7) is small, immediately after the second capture value (0.26e-7) begins to correct the previous value. After the capture process of the first two symbols, the amplitudes of the following tracking values are all very small (below the order of magnitude of 1e-9). Figure 2 is the estimation curve of the algorithm tracking process in the above simulation environment. It can be found that the final estimation results are very small in both variance and mean, showing relatively accurate estimation performance. The above simulation shows that the algorithm can quickly converge to the exact value, and the estimated value is very close to the exact value, which can meet the accuracy and complexity requirements of the NG-DSL system for the synchronization algorithm.

In actual engineering, when the accuracy meets certain requirements, the algorithm can be improved, and a tracking threshold will be set in the tracking phase, that is, when the tracking value exceeds this threshold, the algorithm uses a new estimate for the frequency domain symbols of the system When the tracking value is lower than this threshold, the frequency domain signal of the current symbol does not need to be corrected with a new estimated value, only the result of the pre-correction stage is used. According to the analysis of the synchronization parameters of the NG-DSL system, the tracking threshold can be approximately set as follows:

where Δ is the revision value for tracking, m is the number of symbols, and ρ is the tracking threshold coefficient.

The tracking threshold coefficient in formula (9) is very important. This parameter is determined by both precision and complexity. That is, when ρ takes a larger value, the estimation accuracy and complexity of the algorithm are higher; when ρ takes a smaller value, The estimation accuracy and complexity of the algorithm are low, so it is necessary to make a compromise between the estimation accuracy and complexity according to the actual situation.

Figure 3 verifies the above analysis of the tracking threshold coefficient; the estimated curve when ρ is 4 in the figure shows that there are many flat estimated values at this time, indicating that in the case of this threshold coefficient value, the algorithm does not need to carry out too much The correction of the estimated value only needs to estimate and correct the frequency domain signal when several estimated values have large deviations, but it can also be found that the deviation of the estimated value in this case is the largest, which is equivalent to The algorithm uses the loss of precision in exchange for the reduction of complexity; the estimated curve when ρ is 8 in the figure, it can be found that the curve at this time is not as flat as the estimated curve when ρ is 4, but the accuracy is higher, which is a compromise ; The estimated curve when ρ is 20 in the figure, this curve basically needs to be re-estimated and corrected for each symbol, which is approximately consistent with the situation without adding a threshold. It can be seen that the estimation accuracy is the highest in this case, but it is complicated is also the highest. Therefore, through the above analysis, the tracking threshold coefficient value can be set to 8, which can achieve a compromise between accuracy and complexity. Through the above analysis, the workflow of the algorithm is represented by a flow chart, as shown in Figure 4.

This specific implementation mode adopts the method of frequency domain correction to correct the received signal, and observe the output signal-to-noise ratio of the system after the estimated value obtained by the algorithm corrects the biased system. It can be found through simulation that the uncorrected In this case, the output signal-to-noise ratio of the system is very low, and there are a lot of bit errors, which cannot meet the transmission requirements of NG-DSL; while the corrected system output signal-to-noise ratio has been significantly improved, and it is close to the input signal in the low frequency band. The noise ratio will be about 2.5dB lower than the input signal-to-noise ratio after high-frequency correction. This is because the frequency domain correction algorithm is difficult to completely eliminate ICI. The NG-DSL system will reduce the QAM modulation level of the sub-carriers in the high frequency band, and the requirements for the signal-to-noise ratio are not as strict as those in the low frequency band and can be correctly demodulated. Through the above analysis, it can be known that the correction result of this algorithm meets the output signal-to-noise ratio requirement of NG-DSL.

This specific embodiment is an iteration-based fast convergence sampling frequency synchronization algorithm, which has the advantages of high precision, low complexity and fast estimation speed, and can better meet the needs of NG-DSL systems. Its innovative advantages lie in: (1) through The iterative method enables the estimation results to quickly converge to an accurate value, and can achieve high estimation accuracy with very few symbols; (2) Through theoretical derivation, the sampling frequency offset estimation formula of the traditional algorithm is corrected to obtain a more accurate capture value, which is conducive to the fast and accurate estimation of the algorithm; (3) by proposing a tracking threshold suitable for practical engineering in the algorithm, and through the selection of the pilot position and the optimization of data processing, the trade-off between accuracy and complexity is achieved. , which is more suitable for practical engineering.

The basic principles and main features of the present invention and the advantages of the present invention have been shown and described above. Those skilled in the industry should understand that the present invention is not limited by the above-mentioned embodiments. What are described in the above-mentioned embodiments and the description only illustrate the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will also have Variations and improvements all fall within the scope of the claimed invention. The protection scope of the present invention is defined by the appended claims and their equivalents.

Claims (1)

1. a kind of novel sampling frequency synchronization algorithm, it is characterised in that the estimation procedure of its algorithm is：

One section of pilot tone is inserted in transmitting terminalCorresponding frequency pilot sign is demodulated in receiving terminal Come：By receiving terminal frequency pilot sign divided by correspondence position raw pilot symbols, i.e.,：

$\begin{array}{c}\frac{R_{m,k}}{P_{m,k}}=\frac{1}{N}\frac{\sin \left(\mathrm{\π}k\mathrm{\Δ}f\right)}{\sin (\mathrm{\π}k\mathrm{\Δ}f/N)}\exp \left(j\mathrm{\π}k\mathrm{\Δ}f\frac{N-1}{N}\right)\exp \left(j\mathrm{\π}k\mathrm{\Δ}f\frac{(m-1)(N+L)+L}{N}\right)\\ +\underset{s\≠k}{\overset{N-1}{\underset{s=0,}{\Σ}}}\frac{X_{m,s}}{P_{m,k}}\frac{\sin \[\mathrm{\π}(s-k+s\mathrm{\Δ}f)\]}{\sin \[\mathrm{\π}(s-k+s\mathrm{\Δ}f)/N\]}\exp \[j\mathrm{\π}\left(\frac{N-1}{N}\right)(s-k+s\mathrm{\Δ}f)\]\\ \exp \[j2\mathrm{\π}(s-k+s\mathrm{\Δ}f)\frac{(m-1)(N+L)+L}{N}\]+{\mathrm{\η}}^{\′}\end{array}---\left(1\right)$

Result to formula (1) takes its angle, order：

When number of sub carrier wave is larger, the Section 2 in formula (1) can be approximately considered Gaussian distributed, it is possible to by its with Interchannel noise is classified as additive noise together, and do so will not produce influence to result, and influence what ofdm signal angle rotated Principal element is formula (1) Section 1, the ICI distracters of formula (1) Section 2 be allow demodulation frequency-region signal around central standard The random diverging of signal, it can thus be concluded thatValue：

AndFor：

It can be found that formula (4) is problematic by above-mentioned derivation, and certain influence can be produced (particularly to estimated result The estimate of preceding several symbols), it need to be modified, because this will have influence on the accuracy of Δ f estimates, analysis understandsSize increase with the increase of carrier wave sequence number k, symbol numbers m and normalization sampling frequency offset Δ f, next, need it is right The method of estimation of Δ f is derived；

Make in the same ofdm symbol：

$A_m=\mathrm{\π}\frac{N-1}{N}+2\mathrm{\π}\frac{(m-1)(N+L)+L}{N}---\left(5\right)$

Can obtain：

In above formula, A_m,kWithIt is to utilize least square method for the estimation of sampling frequency offset for observation, it is necessary to estimate Δ f：

Δ f can be more accurately estimated with least squares estimate, but to experience multiple multiplication, addition and division, this Kind of method can preferably weaken influence of the noise for each estimate in the relatively low channel circumstance of signal to noise ratio, but due to The input signal-to-noise ratio of NG-DSL systems can be higher, it is possible to is simplified above-mentioned estimation procedure, reduces computation complexity, Least squares estimate is changed to the weighted mean method with pilot frequency carrier wave sequence number k as weighted factor, i.e.,：

Formula (8) reduces many compared to formula (7) on computation complexity, and discovery is emulated under NG-DSL environment according to formula (8) way can't decline in precision, so with reference to the consideration of computation complexity and precision, will in the algorithm utilize formula (8) observation is processed；

In order to further reduce computation complexity, the position selection to pilot tone is optimized, when pilot frequency locations meet certain condition When can reduce the computation complexity of algorithm, the algorithm is emulated under NG-DSL system emulation environment, algorithm only needs to 8 Frequency pilot sign can just complete more accurate sampling frequency synchronization；According to formula (8) need by observation divided by pilot tone sequence number it With, therefore division can be become into shift operation by choosing suitable pilot frequency locations, reduce computation complexity；For example choose 8 The position of individual pilot tone is followed successively by：{ 505 507 509 511 513 515 517 519 }, the subcarrier sequence number of these pilot tones is added Result be 4096, in a computer the operand of shift operation will be much smaller than division arithmetic, if divisor be 2 power when Wait, division arithmetic can just become shift operation, such as divisor is 2, dividend is to moving to left 1；Divisor is 4, and dividend is to the left Move 2；The rest may be inferred, and now divisor is 4096, and dividend need to only be transported to moving to left 12 without carrying out relative complex division Calculate, division arithmetic at this time only needs to become shift operation in computer, reduces the reaction time of computer, pilot bit The selection put is chosen also dependent on the result of channel estimation feedback, chooses the preferable carrier wave of channel response and is carried as pilot tone Ripple, it is only necessary to which pilot frequency locations reduce computational complexity by meeting above-mentioned requirements；

By above-mentioned steps, it is the sampling frequency synchronization of sample to complete with first symbol；From second sign-on, first Receiving terminal frequency pilot sign is carried out into precorrection using the estimate of previous symbol, the purpose for the arrangement is that in order to suppress sampling frequency The angle rotation that rate deviation is caused causes larger angular deviation with the increase of symbolic number so as to influence new result to estimate； The estimation of sampling frequency offset is carried out to the frequency pilot sign for carrying out precorrection again, new estimate can be just obtained, by two times result phase Plus feedback, as the 3rd precorrection value of OFDM frequency pilot signs, then repeatedly second operation of symbol, using this iteration The estimate that obtains of method will soon restrain, and actual value can be in close proximity to；

By above-mentioned analysis, this algorithm can be divided into two processes：The capture of deviation and tracking, acquisition procedure is general among these No more than 3 symbols (capture symbolic number may be increased in the case where noise is larger), transported by the iteration of several symbols Calculate, the algorithm is just estimated that accurate frequency deviation size, and tracking process is mainly with new estimate come to previous institute The deviation of estimation is finely adjusted.