CN103607369A - LS algorithm-based sampling frequency shift and carrier residual frequency shift joint estimation method - Google Patents

Abstract

The invention discloses an LS algorithm-based sampling frequency shift and carrier residual frequency shift joint estimation method and belongs to the technical field of communication system signal processing. The LS algorithm-based sampling frequency shift and carrier residual frequency shift joint estimation method comprises the following steps that: the total quantity of phase rotation, caused by sampling frequency shift and carrier residual frequency shift, is calculated according to comb-type pilot frequency symbols of a transmitting end of an OFDM system, actual comb-type pilot frequency symbols of a corresponding receiving end of the OFDM system and a channel transmission function which is obtained through frequency domain channel estimation; modeling is performed for the total quantity of the phase rotation according to comb-type pilot frequency position numbers in the OFDM system; a coefficient matrix of corresponding dimensions is obtained based on the number of comb-type pilot frequencies; and finally, the joint estimation of the sampling frequency shift and the carrier residual frequency shift can be realized through using the least squares algorithm. The LS algorithm-based sampling frequency shift and carrier residual frequency shift joint estimation method of the invention can be applied to wireless communication scenes of indoor and outdoor walking as well as outdoor low/mediate-speed movement, and can reduce system pilot frequency cost, and at the same time, can track and compensate phase rotation real time caused by the sampling frequency shift and the carrier residual frequency shift.

Description

Sampling frequency deviation and carrier residual frequency deviation based on LS algorithm are combined estimation

Technical field

The invention belongs to communication system signal processing technology field, be specifically related to a kind of combined estimation method that is applicable to multi-carrier wireless communications system sampling frequency deviation and carrier residual frequency deviation.

Background technology

Multi-transceiver technology adopts a plurality of subcarrier parallel transmission data symbols, can effectively suppress the impact of multipath effect on systematic function.Particularly adopt OFDM (OFDM) mode, not only can improve by the orthogonality between subcarrier the spectrum efficiency of system, can also use fast Fourier transform (FFT) algorithm greatly to reduce system implementation complexity, so this technology obtain a wide range of applications in the standards such as the 4th third-generation mobile communication (4G) and WLAN (wireless local area network) IEEE802.11a/g/n.Yet when having excellent properties, OFDM technology also exists intrinsic problem, high peak-to-average ratio and frequency deviation are responsive.The non-integral multiple skew of carrier frequency is the orthogonality of destroying between subcarrier, thereby causes inter-carrier interference (ICI).Although carrier frequency synchronization algorithm can control to frequency deviation in certain scope, carrier residual frequency deviation can cause the phase rotating of data symbol, and this phase rotating is accumulated in time.When the data symbol number of system crystal oscillator precision not or in system wireless frame is larger, the serious phase rotating producing will make system work.Have the sampling frequency deviation that also has of same problem, this side-play amount also can cause the phase rotating of data symbol accumulation in time.Therefore, how effectively to solve carrier residual frequency deviation and sampling frequency deviation, this is the Tough questions that ofdm system faces.

By frequency domain, carry out channel estimating, in balanced wireless channel impact, can follow the tracks of compensation carrier residual frequency deviation and the caused phase rotating of sampling frequency deviation.But this will take a lot of system resource, bring a large amount of extra overheads.During especially in conjunction with multiple-input and multiple-output (MIMO) technology, MIMO-OFDM system need to provide for the channel estimating of each root antenna independently reference signal, and this can cause the remarkable decline of system spectral efficiency.For example, LTE-A standard (3GPP TS36.211v10.7.0 in 4G, Physical Channels and Modulation (Release10) .Feb., 2013),, in regular circulation prefix (CP) situation, 4 antennas are more than 14% running time-frequency resource by the system that takies, in unconventional CP situation, this expense will reach 17%, if further adopt 8 antennas, expense will be larger.In fact, the scene moving for indoor, outdoor walking and middle low speed, because Doppler frequency shift is less, will have longer coherence time so.When the frame length of system wireless frame is far smaller than this coherence time, only need to carry out at the frame head of each radio frames of system channel estimating just passable, to follow the tracks of compensation and adopt Comb Pilot, this will reduce the shared system resource of reference signal greatly.For example, WLAN standard IEEE802.11a/g, Comb Pilot expense only accounts for 7%, if many antennas adopt time division multiplexing, block pilot tone is carried out channel estimating, the increase of number of antennas is very little on the impact of overhead so.In this case, adopt which kind of method to carry out estimation compensation to carrier residual frequency deviation and sampling frequency deviation and will become particularly important.

Summary of the invention

The object of the invention is the application scenarios moving for indoor, outdoor walking and outdoor middle low speed, based on LS algorithm, sampling frequency deviation and carrier residual frequency deviation are combined to estimation, utilize the block pilot tone of the every frame frame head of ofdm system to complete channel estimating, then use a small amount of Comb Pilot to realize associating estimation, thereby when reducing system pilot expense, follow the tracks of in real time compensating sampling frequency shift (FS) and the caused phase rotating of carrier residual frequency deviation.

For realizing the technical scheme that the object of the invention adopts, be such, sampling frequency deviation and carrier residual frequency deviation based on LS algorithm are combined estimation, comprise the following steps:

1) according to ofdm system transmitting terminal Comb Pilot symbol the actual Comb Pilot symbol of corresponding receiving terminal

the channel transfer functions obtaining with channel estimation in frequency domain

calculate the caused phase rotating total amount of sampling frequency deviation and carrier residual frequency deviation

2) according to the Comb Pilot Position Number in ofdm system, described phase rotating total amount is carried out to modeling,

wherein, k _irepresent Comb Pilot Position Number,

represent the caused phase rotating of sampling frequency deviation, represent the caused phase rotating of carrier residual frequency deviation, n _irepresent that i the white noise on Comb Pilot subcarrier disturbs;

3) based on Comb Pilot number, obtain the coefficient matrix K of corresponding dimension;

4) utilize LS algorithm to realize the estimation of combining of sampling frequency deviation and carrier residual frequency deviation, $\widehat{\mathrm{\φ}}={\left[\begin{array}{cc}{\widehat{\mathrm{\φ}}}_l^{\left(1\right)}& {\widehat{\mathrm{\φ}}}_l^{\left(2\right)}\end{array}\right]}^T.$

According to above-mentioned generation step, the sampling frequency deviation obtaining and carrier residual frequency deviation cause estimates to have following technique effect combining of phase rotating:

1) can complete the estimation of combining of sampling frequency deviation and phase rotating that carrier residual frequency deviation causes, interference and impact each other while avoiding both to estimate separately simultaneously;

2) for the situation of coherence time much larger than the ofdm system radio frames duration, only need a small amount of Comb Pilot just can complete the estimation of combining of phase rotating, greatly reduce the expense of system;

3) adopt LS algorithm, without any need for priori, reduced to estimate the implementation complexity of operation.

Above-mentioned steps 1 of the present invention)-4) what propose has an above-mentioned effect 1)-3) sampling frequency deviation and phase rotating that carrier residual frequency deviation causes combine estimation, be applicable to the slower wireless communication system of translational speed, such as WLAN standard IEEE802.11a/g/n etc., can effectively solve in low-cost ofdm system due to crystal oscillator precision not and the caused frequency shift (FS) of factor such as Doppler frequency shift affect.

Accompanying drawing explanation

Fig. 1 is the block diagram of position in the ofdm system receiver of sampling frequency deviation and carrier residual frequency deviation associating estimation module place in the present invention, wherein combines estimation module and is gone out by dotted line collimation mark.System completes the thick synchronous of Symbol Timing and carrier frequency in the Time and Frequency Synchronization module of front end, after FFT conversion, generates frequency domain data symbol, and the impact of fading channel is directly carried out equilibrium by channel estimating at frequency domain.Comb Pilot symbol on the Comb Pilot subcarrier that utilization is extracted, and in conjunction with channel estimation results, sampling frequency deviation and phase rotating that carrier residual frequency deviation causes are combined to estimation, then according to estimated result, carry out corresponding phase compensation;

Fig. 2 is the computing schematic diagram that in the present invention, sampling frequency deviation and carrier residual frequency deviation are combined estimation.Calculate respectively ofdm system transmitting terminal Comb Pilot symbol

the actual Comb Pilot symbol of corresponding receiving terminal

and the channel transfer functions that obtains of channel estimation in frequency domain

phase place, thereby obtain sampling frequency deviation and the caused phase rotating total amount of carrier residual frequency deviation θ.Utilize the Position Number of Comb Pilot symbol to produce coefficient matrix K, by computings such as matrix transpose and matrix inversions, in conjunction with the phase rotating total amount θ having calculated, according to LS algorithm, obtain phase rotating estimated vector $\widehat{\mathrm{\φ}}={\left[\begin{array}{cc}{\widehat{\mathrm{\φ}}}_l^{\left(1\right)}& {\widehat{\mathrm{\φ}}}_l^{\left(2\right)}\end{array}\right]}^T;$

To be the system of the present invention in embodiment 2 do not adopting the planisphere of combining the data symbol receiving while estimating to Fig. 3.Wherein, signal to noise ratio is 10dB, and sampling frequency deviation is 1% of subcarrier spacing Δ F, and carrier residual frequency deviation is 5% of subcarrier spacing Δ F;

To be the system of the present invention in embodiment 2 combine the planisphere of the data symbol receiving after estimating in employing to Fig. 4.Wherein, signal to noise ratio is 10dB, and sampling frequency deviation is 1% of subcarrier spacing Δ F, and carrier residual frequency deviation is 5% of subcarrier spacing Δ F.

Embodiment

Below in conjunction with drawings and Examples, the invention will be further described, but should not be construed the above-mentioned subject area of the present invention, only limits to following embodiment.Without departing from the idea case in the present invention described above, according to ordinary skill knowledge and customary means, make various replacements and change, all should be included in protection scope of the present invention.

Embodiment 1:

Open sampling frequency deviation and the carrier residual frequency deviation based on least-squares algorithm of the present embodiment combined estimation, comprises the following steps:

1) channel transfer functions obtaining according to ofdm system transmitting terminal Comb Pilot symbol, the corresponding actual Comb Pilot symbol of receiving terminal and channel estimation in frequency domain, calculates the caused phase rotating total amount of sampling frequency deviation and carrier residual frequency deviation.In the present embodiment, can utilize Comb Pilot in ofdm system to set up phase rotating model

wherein,

represent the actual reception Comb Pilot symbol on i Comb Pilot subcarrier in l OFDM symbol of receiving terminal, i Comb Pilot subcarrier correspondence k in ofdm system _iindividual subcarrier,

represent the channel transfer functions obtaining by channel estimation in frequency domain on i Comb Pilot subcarrier,

represent the Comb Pilot symbol on i Comb Pilot subcarrier in l OFDM symbol of transmitting terminal,

represent in l OFDM symbol on i Comb Pilot subcarrier due to sampling frequency deviation and the caused phase rotating total amount of carrier residual frequency deviation.According to known

with

obtain

here ∠ () represents to calculate phase operation.

2) according to the Comb Pilot Position Number in ofdm system, described phase rotating total amount is carried out to modeling, ${\mathrm{\θ}}_{l,k_i}=k_i\·{\mathrm{\φ}}_l^{\left(1\right)}+{\mathrm{\φ}}_l^{\left(2\right)}+n_i,i=\mathrm{1,2},\·\·\·,M,$ Here M represents the sum of Comb Pilot in each OFDM symbol, wherein, and k _irepresent Comb Pilot Position Number,

represent the caused phase rotating of sampling frequency deviation, represent the caused phase rotating of carrier residual frequency deviation, n _irepresent that i the white noise on Comb Pilot subcarrier disturbs; What deserves to be explained is, two class phase rotatings are all the functions of the numbering l of OFDM symbol, so phase rotating is all along with accumulated time, and for sampling frequency deviation, phase rotating or subcarrier number k _ifunction, different to the caused phase rotating of different subcarriers, suppose that channel estimating carried out corresponding compensation to the impact of multipath herein, therefore only consider the impact of white noise;

3) based on Comb Pilot number, obtain the coefficient matrix K of corresponding dimension; What deserves to be explained is, vector form represents that phase rotating aggregative model is θ=K φ+N, wherein, $\mathrm{\&theta;}={\left[\begin{array}{cccc}{\mathrm{\&theta;}}_{l,{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000397707130000031.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}& {\mathrm{\&theta;}}_{l,{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000397707130000031.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&theta;}}_{l,k_M}\end{array}\right]}^T,$ $K={\left[\begin{array}{cccc}{k}_1& {\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000397707130000031.png"\; state="\{\{state\}\}">k</figure-callout>}}_2& \&CenterDot;\&CenterDot;\&CenterDot;& k_{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="HDA0000397707130000031.png"\; state="\{\{state\}\}">M</figure-callout>}}\\ 1& 1& \&CenterDot;\&CenterDot;\&CenterDot;& 1\end{array}\right]}^T,$ $\mathrm{\&phi;}={\left[\begin{array}{cc}{\mathrm{\&phi;}}_l^{\left(1\right)}& {\mathrm{\&phi;}}_l^{\left(2\right)}\end{array}\right]}^T,$ N=[n ₁n ₂n _m] ^t, [] here ^trepresent matrix transpose operation;

4) utilize LS algorithm to realize the estimation of combining of sampling frequency deviation and carrier residual frequency deviation, $\widehat{\mathrm{\&phi;}}={\left[\begin{array}{cc}{\widehat{\mathrm{\&phi;}}}_l^{\left(1\right)}& {\widehat{\mathrm{\&phi;}}}_l^{\left(2\right)}\end{array}\right]}^T.$ In embodiment, estimator should make ${(\mathrm{\&theta;}-K\&CenterDot;\widehat{\mathrm{\&phi;}})}^T\&CenterDot;(\mathrm{\&theta;}-K\&CenterDot;\widehat{\mathrm{\&phi;}})$ There is minimum, thereby obtain the estimation of combining of sampling frequency deviation and phase rotating that carrier residual frequency deviation causes here () ^-1expression is to matrix inversion operation.

Embodiment 2:

The present embodiment adopts single antenna ofdm system, and system parameters is as follows:

System bandwidth is 2MHz; Rf frequency is 339MHz; Digital intermediate frequency is 12.8MHz; Subcarrier spacing Δ F is 31.25kHz; It is 128 that IFFT/FFT counts; Data subcarrier number is 48; Comb Pilot number of sub carrier wave is 4, and Position Number is (7,21,107,121); 4 Comb Pilot symbol values are [1 ,-1,1,1], and its symbol polarity is g (x)=x according to generator polynomial ⁷+ x ⁴the m sequence variation of+1 127 length; Cyclic Prefix (CP) length is 8 μ s; Cyclic suffix length is 1.25 μ s; Raised cosine window rolloff-factor is 0.03125; Modulation system is QPSK; The radio frames duration is 10ms; In each radio frames, frame head length is 10 OFDM symbols, and data are 240 OFDM symbols.

The crystal oscillator precision of system transmitting-receiving two-end is made as 5ppm, considers that the frequency difference of transmitting-receiving two-end in the poorest situation will reach 3.39kHz.Moving velocity of terminal be made as 60 kilometers/time, maximum doppler frequency is approximately 18.8Hz, is approximately 53ms coherence time, much larger than the duration of system wireless frame, thereby can only in the block pilot tone of frame head utilization, complete the channel estimating of each radio frames.

In system, setting carrier residual frequency deviation is 5% of subcarrier spacing Δ F, i.e. 1.5625kHz.Sampling frequency deviation is set as 1% of subcarrier spacing Δ F, first at receiving terminal FFT place, carries out over-sampling, and then sampled point side-play amount is set, then carries out the sampling of owing of same multiple, thereby realizes sampling frequency deviation.

Sampling frequency deviation and carrier residual frequency deviation based on LS algorithm are combined estimation, comprise the following steps:

1) according to ofdm system transmitting terminal Comb Pilot symbol

the actual Comb Pilot symbol of corresponding receiving terminal

the channel transfer functions obtaining with channel estimation in frequency domain

calculate the caused phase rotating total amount of sampling frequency deviation and carrier residual frequency deviation

first calculate in each OFDM symbol in 4 Comb Pilot

with

the phase place of these three amounts, will

with

phase place be added, and by this phase place sum with

phase place subtract each other, thereby obtain the phase rotating vector that 4 Comb Pilot form $\mathrm{\&theta;}={\left[\begin{array}{cccc}{\mathrm{\&theta;}}_{{l,\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000397707130000031.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}& {\mathrm{\&theta;}}_{{l,\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000397707130000031.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}& {\mathrm{\&theta;}}_{{l,k}_3}& {\mathrm{\&theta;}}_{{l,k}_4}\end{array}\right]}^T.$ Wherein, k ₁, k ₂, k ₃and k ₄equal respectively 7,21,107 and 121.

2) according to the Comb Pilot Position Number in ofdm system, described phase rotating total amount is carried out to modeling, ${\mathrm{\&theta;}}_{l,k_i}=k_i\&CenterDot;{\mathrm{\&phi;}}_l^{\left(1\right)}+{\mathrm{\&phi;}}_l^{\left(2\right)}+n_i,i=\mathrm{1,2,3,4}.$ Wherein, k _irepresent Comb Pilot Position Number,

represent the caused phase rotating of sampling frequency deviation,

represent the caused phase rotating of carrier residual frequency deviation, n _irepresent that i the white noise on Comb Pilot subcarrier disturbs;

3) based on Comb Pilot number, obtain the coefficient matrix K of corresponding dimension; What deserves to be explained is, vector form represents that phase rotating aggregative model is θ=K φ+N, wherein, $\mathrm{\&theta;}={\left[\begin{array}{cccc}{\mathrm{\&theta;}}_{l,{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000397707130000031.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}& {\mathrm{\&theta;}}_{l,{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000397707130000031.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&theta;}}_{l,k_M}\end{array}\right]}^T,$ $K={\left[\begin{array}{cccc}{k}_1& {\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000397707130000031.png"\; state="\{\{state\}\}">k</figure-callout>}}_2& \&CenterDot;\&CenterDot;\&CenterDot;& k_{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="HDA0000397707130000031.png"\; state="\{\{state\}\}">M</figure-callout>}}\\ 1& 1& \&CenterDot;\&CenterDot;\&CenterDot;& 1\end{array}\right]}^T,$ $\mathrm{\&phi;}={\left[\begin{array}{cc}{\mathrm{\&phi;}}_l^{\left(1\right)}& {\mathrm{\&phi;}}_l^{\left(2\right)}\end{array}\right]}^T,$ N=[n ₁n ₂n _m] ^t, [] here ^trepresent matrix transpose operation; In embodiment, according to the Position Number of 4 Comb Pilot, generate coefficient matrix $K={\left[\begin{array}{cccc}7& 21& 107& 121\\ 1& 1& 1& 1\end{array}\right]}^T,$

4) utilize LS algorithm to realize the estimation of combining of sampling frequency deviation and carrier residual frequency deviation, $\widehat{\mathrm{\&phi;}}={\left[\begin{array}{cc}{\widehat{\mathrm{\&phi;}}}_l^{\left(1\right)}& {\widehat{\mathrm{\&phi;}}}_l^{\left(2\right)}\end{array}\right]}^T.$ What deserves to be explained is, estimator should make ${(\mathrm{\&theta;}-K\&CenterDot;\widehat{\mathrm{\&phi;}})}^T\&CenterDot;(\mathrm{\&theta;}-K\&CenterDot;\widehat{\mathrm{\&phi;}})$ There is minimum, thereby obtain the estimation of combining of sampling frequency deviation and phase rotating that carrier residual frequency deviation causes

here [] ^-1expression is to matrix inversion operation.In the present embodiment, K is carried out to the square formation that multiplies each other and produce 2 * 2 with K after transposition $\left[\begin{array}{cc}26580& 256\\ 256& 4\end{array}\right].$ Then this square formation is tried to achieve to inverse matrix $\left[\begin{array}{cc}0.00098& -0.006\\ -0.006& 0.65\end{array}\right],$ The transposition of inverse matrix and K is multiplied each other, finally again by result of product $\left[\begin{array}{cccc}0.00086& 0.01458& 0.09886& 0.1125\\ 0.6108& 0.524& 0.008& -0.076\end{array}\right]$ Multiply each other with phase rotating vector theta, thereby obtain phase rotating estimated vector $\widehat{\mathrm{\&phi;}}={\left[\begin{array}{cc}{\widehat{\mathrm{\&phi;}}}_l^{\left(1\right)}& {\widehat{\mathrm{\&phi;}}}_l^{\left(2\right)}\end{array}\right]}^T.$

The maximum operand of the combined estimation method that the present embodiment proposes is matrix inversion and matrix multiple.The operation of inverting is the square formation for 2 * 2, and the exponent number of square formation is low, and wherein the data on a diagonal are identical, therefore inverts relatively simple.The operand of matrix multiple depends primarily on the number of Comb Pilot in each OFDM symbol, when this number hour, operand is very little.If only select a Comb Pilot, because the data of coefficient matrix the second row are fixed as 1, therefore K in fact ^tk only need multiplication (square) computing, inverse matrix and K ^tneed twice multiplying, result of product and θ also need twice multiplying.

Fig. 3 and Fig. 4 have provided respectively analogue system in the present embodiment and have combined while estimating and the planisphere of the reception data symbol after estimating is combined in employing not adopting.In this emulation, choose front 10 data symbols in a radio frames, altogether comprised 10 * 48=480 QPSK modulation constellation points.As can be seen from Figure 3, due to the impact of the sampling frequency deviation of 1% Δ F and the carrier residual frequency deviation of 5% Δ F, there is serious phase rotating in the constellation point of data symbol.When not having multipath to disturb and during white noise, phase rotating is by the circle that one of generation be take centered by initial point, radius is 1 in theory, and due to the impact of white noise under 10dB signal to noise ratio, planisphere is dispersed and formed an annulus herein.So, serious phase rotating has caused this ofdm system cisco unity malfunction.Utilize the sampling frequency deviation of this patent proposition and the combined estimation method of carrier residual frequency deviation, the phase rotating that two quefrencys skews are produced is followed the tracks of compensation, thereby can suppress preferably planisphere blooming.As can be seen from Figure 4, each constellation point of dispersing has converged near standard QPSK constellation point.Although because the impact of white noise still exists Divergent Phenomenon to a certain degree, the system that now can guarantee is normally worked.

Claims (1)

1. the sampling frequency deviation based on LS algorithm and carrier residual frequency deviation are combined estimation, it is characterized in that, comprise the following steps:

1) according to ofdm system transmitting terminal Comb Pilot symbol

the actual Comb Pilot symbol of corresponding receiving terminal

the channel transfer functions obtaining with channel estimation in frequency domain calculate the caused phase rotating total amount of sampling frequency deviation and carrier residual frequency deviation

2) according to the Comb Pilot Position Number in ofdm system, described phase rotating total amount is carried out to modeling,

wherein, k _irepresent Comb Pilot Position Number,

represent the caused phase rotating of sampling frequency deviation,

represent the caused phase rotating of carrier residual frequency deviation, n _irepresent that i the white noise on Comb Pilot subcarrier disturbs;

3) based on Comb Pilot number, obtain the coefficient matrix K of corresponding dimension;

4) utilize LS algorithm to realize the estimation of combining of sampling frequency deviation and carrier residual frequency deviation, $\widehat{\mathrm{\&phi;}}={\left[\begin{array}{cc}{\widehat{\mathrm{\&phi;}}}_l^{\left(1\right)}& {\widehat{\mathrm{\&phi;}}}_l^{\left(2\right)}\end{array}\right]}^T.$

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