CN102546509A - Carrier frequency offset estimation method based on chirp training sequence - Google Patents

Carrier frequency offset estimation method based on chirp training sequence Download PDF

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CN102546509A
CN102546509A CN2011104453774A CN201110445377A CN102546509A CN 102546509 A CN102546509 A CN 102546509A CN 2011104453774 A CN2011104453774 A CN 2011104453774A CN 201110445377 A CN201110445377 A CN 201110445377A CN 102546509 A CN102546509 A CN 102546509A
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frequency offset
signal
training sequence
peak value
correlation
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虞贵财
龙承志
向满天
罗建平
邹文生
余尧毅
周海
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Nanchang University
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Abstract

The invention provides a carrier frequency offset estimation and time synchronization algorithm based on chirp training sequence. A transmitted training sequence is divided into three parts with equal lengths, wherein the second part and the third part are the complex conjugates of the first part respectively; the received training sequence through a multi-path channel is subjected to autocorrelation and anti-autocorrelation respectively, wherein when the multi-path channel is adopted, the anti-autocorrelation operation can be not only used for frequency offset estimation, but also can be used for time synchronization, and a decimal time frequency offset can be estimated according to the position of related result peak value; signals of the decimal time frequency offset after being compensated are subjected to delay and complex conjugate, two parts of signals pass through the same filter, and cross-correlation operation is performed so as to estimate integral time frequency offset; the frequency offset is subjected deflection compensation; at last iteration operation is performed till the frequency offset is estimated correctly.

Description

Algorithm of Carrier Frequency Offset Estimation based on the chirp training sequence
Technical field
The present invention relates to the frequency offset estimating algorithm of wireless communication technology field, the frequency offset estimating algorithm at particularly a kind of TD-SCDMA terminal is equally applicable to the frequency offset estimating of ofdm communication system.
Background technology
TD-SCDMA technology as one of the world's three big standards; Successfully moved towards commercial in China; And the research of TD-SCDMA technology was never stopped; Especially frequency offset estimating in the communication process and correction is research focus and difficult point always, and a lot of experts and scholar always enjoy it for this reason.
The unsteadiness of crystal oscillator, Doppler effect, there are deviation in centre frequency and local crystal oscillator frequency that multipath transmission etc. all can cause communication system to receive signal, Here it is carrier wave frequency deviation.The frequency deviation of carrier wave can cause the raising that receives the error rate, and serious meeting causes the decoded in error of signal, therefore must estimate and proofread and correct.Common bearing calibration is to make the local crystal oscillator frequency of correcting circuit follow the tracks of the reception signal frequency exactly; This is a frequency deviation correcting method ground part; Frequency offset correction be can not guarantee to carry out exactly, especially when signal process multipath channel, research concrete frequency offset estimating algorithm and design accurate frequency offset estimating circuit needed; Make receiver to carry out frequency-tracking automatically, carry out frequency offset estimating and compensation.Equally, the terminal receiver of TD-SCDMA system also must be carried out automatic frequency tracking, and especially up frequency offset estimating is with synchronously.Because the base station receives the signal that sends from a plurality of portable terminals simultaneously, they have nothing in common with each other at frequency deviation separately, and therefore common correcting algorithm can't be estimated and proofread and correct, and the time that needs the individual subscriber signal of assurance to arrive the base station like this is identical with frequency.
Therefore needing a kind of simple effective method, solve the frequency deviation stationary problem in the TD-SCDMA system, is frequency offset estimating and correction and solve the synchronous key of frequency deviation, and this patent has proposed the frequency offset estimating algorithm at a kind of TD-SCDMA terminal to this respect.
Summary of the invention
The object of the present invention is to provide the frequency offset estimating and the time synchronized algorithm at a kind of TD-SCDMA terminal.
To achieve these goals, provided by the invention based on Nonlinear Transformation in Frequency Offset Estimation and time synchronized algorithm in the TD-SCDMA system of chirp training sequence, the training sequence of transmission is divided into three isometric parts; If the training sequence that sends is the chirp signal; In order to tell the peak value of channel impulse response; Here
Figure 2011104453774100002DEST_PATH_IMAGE001
;
Figure 279816DEST_PATH_IMAGE002
is the disperse factor (time-bandwidth product) of chirp signal, and training sequence can be expressed as like this
(1)
Therefore the training sequence that sends does
Figure 306285DEST_PATH_IMAGE004
(2)
Suppose channel impulse for
Figure 2011104453774100002DEST_PATH_IMAGE005
, the signal that receives of receiving terminal does so
(3)
Wherein
Figure 2011104453774100002DEST_PATH_IMAGE007
(normalization of
Figure 70289DEST_PATH_IMAGE008
) is total frequency deviation;
Figure 2011104453774100002DEST_PATH_IMAGE009
is fractional part of frequency offset;
Figure 869618DEST_PATH_IMAGE010
is the integer frequency offset of
Figure 2011104453774100002DEST_PATH_IMAGE011
;
Figure 517637DEST_PATH_IMAGE012
(normalization of
Figure 2011104453774100002DEST_PATH_IMAGE013
) is corresponding time delay directly; and
Figure 609014DEST_PATH_IMAGE016
arranged so; is the multipath tap number,
Figure 212033DEST_PATH_IMAGE018
be multiple AWGN signal.
If do the relevant of different delay with local chirp sequence with the receiving sequence that contains the chirp sign indicating number that receives; So because the good correlation properties of chirp sign indicating number; Can make each correlation of acquisition receive single footpath channel and carrier wave frequency deviation with the time caused partially phase place rotate these three influences of taking advantage of sex factor; Therefore to each correlation carry out channel estimating based on known array can obtain comprising this directly respond and the carrier phase rotation and the time inclined to one side comprehensive response; But can't to channel impulse response and the time partially and carrier wave frequency deviation separate lotus root; Especially the time partially with the lotus root problem of separating of frequency deviation, and on different impulses, send upwards with chirp signal downwards can be well to the time inclined to one side and frequency deviation separate lotus root.This paper adopts earlier and receives the signal autocorrelation method and anti-correlation method is estimated carrier wave frequency deviation and the time is carried out synchronously; Then frequency deviation is proofreaied and correct; Next the signal after compensating fractional part of frequency offset postpones respectively and complex conjugate, and two parts of signals through identical filter, is carried out computing cross-correlation respectively then, estimates integer frequency offset; Then to the carrier integer frequency multiplication partially and the time estimate partially; Obtain total frequency offset estimating value at last and carry out compensate of frequency deviation simultaneously.
1. fractional part of frequency offset
Figure 419286DEST_PATH_IMAGE009
is estimated
Carry out earlier the auto-correlation function computing to received signal
(4)
The received signal
Figure 879086DEST_PATH_IMAGE020
into
Figure 2011104453774100002DEST_PATH_IMAGE021
and simplifying too
Figure 670325DEST_PATH_IMAGE022
(5)
Wherein
Figure 2011104453774100002DEST_PATH_IMAGE023
is trigonometric equation.
Therefore
Figure 372308DEST_PATH_IMAGE024
(6)
Signal after proofreading and correct through
Figure 2011104453774100002DEST_PATH_IMAGE025
like this does
Figure 932602DEST_PATH_IMAGE026
(7)
But, when channel impulse response postpones to expand to a plurality of sample value, the peak of trigonometric equation be not special obviously, in order well to distinguish peak value, we have introduced anti-auto-correlation algorithm.
At first define anti-auto-correlation function: this algorithm needs two sequences; Second sequence is the complex conjugate that first sequence is overturn on time-domain; With the chirp signal is example; Suppose that first sequence (goes up the chirp signal) for
Figure 2011104453774100002DEST_PATH_IMAGE027
; So second sequence is
Figure 64769DEST_PATH_IMAGE028
(the following chirp signal that a time delay is arranged), the anti-auto-correlation function that therefore receives signal
Figure 280986DEST_PATH_IMAGE020
can be expressed as
Figure 2011104453774100002DEST_PATH_IMAGE029
(8)
Thereby anti-auto-correlation function has provided the variable of an impulse type, finds the position of impulse response, obtains phase place when being used for time synchronized, can obtain frequency deviation more accurately like this.
2. integer frequency offset is estimated
The estimation of integer frequency offset, be equivalent to obtain earlier integral multiple the time inclined to one side, confirm integer frequency offset through peak, confirm integer frequency offset through peak value here.
In (8), obtain
Figure 640609DEST_PATH_IMAGE030
(9)
The peak value that formula (9) obtains has surpassed the number of channel impulse response; In order to obtain integer frequency offset; We can set two other variable
Figure 2011104453774100002DEST_PATH_IMAGE031
and
Figure 206327DEST_PATH_IMAGE032
equally; In this patent supposition they corresponding respectively be training sequence first and relevant (being equivalent to pass through filtering to
Figure 189512DEST_PATH_IMAGE033
and
Figure 724399DEST_PATH_IMAGE034
) of and
Figure 706578DEST_PATH_IMAGE034
, as
Figure 2011104453774100002DEST_PATH_IMAGE035
(10)
The peak of formula (10) with the time partially relevant with multidiameter; The amplitude square of
Figure 136051DEST_PATH_IMAGE031
and
Figure 123598DEST_PATH_IMAGE032
is approximately the form of
Figure 410223DEST_PATH_IMAGE036
, and peak value satisfies following positions
(11)
Can estimate integer frequency offset through the distance of calculating between
Figure 799616DEST_PATH_IMAGE031
and
Figure 644819DEST_PATH_IMAGE032
peak value; But it is under the multipath situation, relatively more difficult.In order better to get the peak value of
Figure 119663DEST_PATH_IMAGE031
and ; Set two thresholding factors
Figure 125982DEST_PATH_IMAGE038
and
Figure 2011104453774100002DEST_PATH_IMAGE039
; Get two peak value threshold
Figure 207332DEST_PATH_IMAGE040
and
Figure 2011104453774100002DEST_PATH_IMAGE041
; And during as
Figure 169472DEST_PATH_IMAGE042
, make
Figure 2011104453774100002DEST_PATH_IMAGE043
; During as
Figure 797900DEST_PATH_IMAGE044
; Make
Figure 2011104453774100002DEST_PATH_IMAGE045
; The purpose of doing like this is to reduce small leak to estimation effect, the noise reduction process that is equivalent to use in the channel estimation method.Then take after peak after treatment
Figure 480595DEST_PATH_IMAGE031
and
Figure 169066DEST_PATH_IMAGE032
correlation
(12)
So
Figure 2011104453774100002DEST_PATH_IMAGE047
get to the cross-correlation peak position
Figure 785041DEST_PATH_IMAGE048
met
Figure 2011104453774100002DEST_PATH_IMAGE049
(13)
Association type (6), the estimated value that obtains integer frequency offset
Figure 504997DEST_PATH_IMAGE010
does
Figure 364369DEST_PATH_IMAGE050
(14)
Therefore total frequency deviation satisfies
Figure 2011104453774100002DEST_PATH_IMAGE051
(15)
3. through the signal behind total frequency offset correction do
Figure 35522DEST_PATH_IMAGE052
(16)
Description of drawings
Fig. 1 is the theory diagram of training sequence
Fig. 2 is that the closure of frequency offset estimating realizes theory diagram
Fig. 3 is that fractional part of frequency offset is estimated and the compensation principle block diagram
Fig. 4 is integer frequency offset estimation and compensation and frequency offset correction block diagram
Embodiment
Below in conjunction with accompanying drawing frequency offset estimating provided by the invention and correcting algorithm are done corresponding the description.
  
As shown in Figure 1; The training sequence that sends is divided into three parts that length is L; Be respectively
Figure 2011104453774100002DEST_PATH_IMAGE053
,
Figure 832183DEST_PATH_IMAGE054
and
Figure 2011104453774100002DEST_PATH_IMAGE055
; And corresponding X is last chirp signal to suppose
Figure 905181DEST_PATH_IMAGE053
; The X* that
Figure 935454DEST_PATH_IMAGE054
and
Figure 93903DEST_PATH_IMAGE055
is corresponding is following chirp signal, satisfies like this
Figure 103709DEST_PATH_IMAGE056
(1)
Therefore the training sequence that sends does
Figure 234477DEST_PATH_IMAGE004
(2)
Wherein
Figure 435651DEST_PATH_IMAGE002
is the disperse factor (time-bandwidth product) of chirp signal; In order to tell the peak value of channel impulse response,
Figure 81396DEST_PATH_IMAGE017
is length and
Figure 393428DEST_PATH_IMAGE001
of channel impulse response window here.
    
Fig. 2 is that frequency offset estimating realizes general frame figure, and the first step is estimated fractional part of frequency offset; Second step was carried out the fractional part of frequency offset compensation to the signal that receives; The 3rd step was estimated integer frequency offset; The 4th step integer frequency offset is to received signal estimated; The 5th step carried out iteration to frequency deviation and estimates; Above several steps constituted closed frequency offset estimating and compensation flow process, through after the iteration repeatedly, estimate comparatively accurately frequency deviation and proofread and correct.
    
Fig. 3 is the algorithm for estimating flow chart of fractional part of frequency offset estimator; At first with the training sequence process multipath channel of sending; Suppose channel impulse for
Figure 378702DEST_PATH_IMAGE005
, the signal that receives of receiving terminal does so
Figure 249313DEST_PATH_IMAGE006
(3)
Wherein
Figure 382354DEST_PATH_IMAGE007
(normalization of
Figure 498077DEST_PATH_IMAGE008
) is total frequency deviation;
Figure 400174DEST_PATH_IMAGE009
is fractional part of frequency offset;
Figure 880834DEST_PATH_IMAGE010
is the integer frequency offset of
Figure 737057DEST_PATH_IMAGE011
;
Figure 656471DEST_PATH_IMAGE012
(normalization of
Figure 413075DEST_PATH_IMAGE013
) is corresponding
Figure 64636DEST_PATH_IMAGE014
time delay directly;
Figure 2011104453774100002DEST_PATH_IMAGE057
and arranged so;
Figure 190647DEST_PATH_IMAGE017
is the multipath tap number,
Figure 739440DEST_PATH_IMAGE018
be multiple AWGN signal.
The signal that receiving terminal is received is through autocorrelator and anti-autocorrelator, and the auto-correlation function that obtains receiving signal does
Figure 889799DEST_PATH_IMAGE019
(4)
The received signal into
Figure 152470DEST_PATH_IMAGE021
and simplifying too
Figure 385131DEST_PATH_IMAGE022
(5)
Wherein is trigonometric equation.
And the anti-auto-correlation function that receives signal does
Figure 257458DEST_PATH_IMAGE029
(6)
Here need define anti-auto-correlation function: this algorithm needs two sequences; Second sequence is the complex conjugate that first sequence is overturn on time-domain; With the chirp signal is example; Suppose that first sequence (goes up the chirp signal) for
Figure 260049DEST_PATH_IMAGE027
; So second sequence is (the following chirp signal that a time delay is arranged), the anti-auto-correlation function that therefore receives signal
Figure 570868DEST_PATH_IMAGE020
can be expressed as formula (6).
In the formula (5); When channel impulse response postpones to expand to a plurality of sample value, the peak of trigonometric equation be not special obviously, in order well to distinguish peak value; Formula (6) has provided the variable of an impulse type; Find the position of impulse response, obtain phase place when being used for time synchronized, can obtain frequency deviation more accurately like this.The fractional part of frequency offset estimated value of estimating through the fractional part of frequency offset estimator like this does
Figure 812493DEST_PATH_IMAGE024
(7)
The fractional part of frequency offset estimated value is used for the fractional part of frequency offset compensator, thereby the signal after the correction does through
Figure 415513DEST_PATH_IMAGE025
Figure 855722DEST_PATH_IMAGE026
(8)
Fig. 4 is the system flow block diagram of integer frequency offset estimation and frequency offset correction; The signal through after the fractional part of frequency offset correction that at first formula (8) is obtained postpones and complex conjugate operation, obtains
Figure 2011104453774100002DEST_PATH_IMAGE059
and
Figure 518784DEST_PATH_IMAGE060
; To through delay and complex conjugate operation after signal pass through filter process respectively; The filtering signal here is taken as
Figure 545908DEST_PATH_IMAGE027
; Be the first of training sequence, the signal behind wave filter satisfies
Figure 2011104453774100002DEST_PATH_IMAGE061
(9)
The peak of formula (9) with the time partially relevant with multidiameter; And the amplitude square of
Figure 14936DEST_PATH_IMAGE031
and is approximately the form of
Figure 81298DEST_PATH_IMAGE036
, and peak value satisfies formula (10) position relation so
Figure 858368DEST_PATH_IMAGE037
(10)
Here can estimate integer frequency offset through the distance of calculating between
Figure 740873DEST_PATH_IMAGE031
and
Figure 155674DEST_PATH_IMAGE032
peak value; But it is under the multipath situation, relatively more difficult.In order better to get the peak value of
Figure 894960DEST_PATH_IMAGE031
and , this patent is taked the output signal is handled.Set two thresholding factors and
Figure 852179DEST_PATH_IMAGE039
; Get two peak value threshold and
Figure 15493DEST_PATH_IMAGE041
; During as
Figure 239801DEST_PATH_IMAGE042
, make
Figure 629194DEST_PATH_IMAGE043
; During as
Figure 474397DEST_PATH_IMAGE044
; Make
Figure 711661DEST_PATH_IMAGE031
and cross-correlation after the peak value of learning from else's experience is then handled
Figure 473129DEST_PATH_IMAGE046
(11)
Output result to cross-correlator carries out the peak value detection, gets the position
Figure 502844DEST_PATH_IMAGE048
of cross-correlation peak value like this as and satisfies
Figure 601250DEST_PATH_IMAGE049
(12)
Association type (7); Through the integer frequency offset estimator, the estimated value that obtains integer frequency offset
Figure 289721DEST_PATH_IMAGE010
does
Figure 411260DEST_PATH_IMAGE050
(13)
Therefore total frequency offset estimating value satisfies
Figure 843379DEST_PATH_IMAGE051
(14)
Signal after proofreading and correct through the frequency offset correction device at last does
Figure 560406DEST_PATH_IMAGE052
(15)

Claims (10)

1. Algorithm of Carrier Frequency Offset Estimation based on the chirp training sequence, the training sequence of transmission is divided into three isometric parts; The training sequence that passes through after the multipath channel that receives is carried out auto-correlation and anti-auto-correlation respectively, and the position according to the correlated results peak value estimates fractional part of frequency offset; Signal after compensating fractional part of frequency offset postpones respectively and complex conjugate, and two parts of signals through identical filter, estimates integer frequency offset respectively; Frequency deviation is compensated correction; Last interative computation estimates frequency deviation up to accurately.
2. frequency offset estimating algorithm according to claim 1; The training sequence that wherein sends satisfies shown in Figure 1; If the training sequence that sends is the chirp signal; And the signal length that satisfies every part is L; In order to tell the peak value of channel impulse response; Here
Figure 431167DEST_PATH_IMAGE002
; is the disperse factor of chirp signal, and the training sequence that obtains like this does
(1)
Therefore the training sequence that sends does
(2)。
3. frequency offset estimating algorithm according to claim 1; Suppose channel impulse for
Figure 394871DEST_PATH_IMAGE010
, the reception signal of signal after through channel does so
Figure 172334DEST_PATH_IMAGE012
(3)
Wherein
Figure 839944DEST_PATH_IMAGE014
(normalization of
Figure 335648DEST_PATH_IMAGE016
) is total frequency deviation;
Figure 927166DEST_PATH_IMAGE018
is fractional part of frequency offset;
Figure 575447DEST_PATH_IMAGE020
is the integer frequency offset of
Figure 164692DEST_PATH_IMAGE022
;
Figure 131379DEST_PATH_IMAGE024
(normalization of
Figure 464272DEST_PATH_IMAGE026
) is corresponding
Figure 278644DEST_PATH_IMAGE028
time delay directly;
Figure 786592DEST_PATH_IMAGE030
and
Figure 178259DEST_PATH_IMAGE032
arranged so;
Figure 314843DEST_PATH_IMAGE034
is the multipath tap number,
Figure 672137DEST_PATH_IMAGE036
be multiple AWGN signal.
4. frequency offset estimating algorithm according to claim 1, the auto-correlation function that receives signal does
Figure 665501DEST_PATH_IMAGE038
(4)
Wherein
Figure 357513DEST_PATH_IMAGE040
is trigonometric equation; When channel impulse response postpones to expand to a plurality of sample value; The peak of trigonometric equation be not special obviously; In order well to distinguish peak value, we have introduced anti-auto-correlation algorithm
(5)
Anti-auto-correlation function has provided the variable of an impulse type, finds the position of impulse response, obtains phase place when being used for time synchronized, can obtain frequency deviation more accurately like this.
5. estimate fractional part of frequency offset according to claim 4
Figure 8123DEST_PATH_IMAGE044
(6)。
6. according to the anti-auto-correlation of claim 4 definition: this algorithm needs two sequences; Second sequence is the complex conjugate that first sequence is overturn on time-domain; With the chirp signal is example; Suppose that first sequence (goes up the chirp signal) for
Figure 881312DEST_PATH_IMAGE046
; So second sequence is
Figure 122937DEST_PATH_IMAGE048
(the following chirp signal that a time delay is arranged), the upset auto-correlation function that therefore receives signal can be expressed as formula (5).
7. frequency offset estimating algorithm according to claim 1 compensates fractional part of frequency offset
Figure 166166DEST_PATH_IMAGE052
(7)。
8. frequency offset estimating algorithm according to claim 1 is estimated integer frequency offset, (7) is further simplified obtaining
Figure 704594DEST_PATH_IMAGE054
(8)
The peak value that formula (8) obtains has surpassed the number of channel impulse response.
9. frequency offset estimating algorithm according to claim 1; Signal after compensating fractional part of frequency offset postpones respectively and complex conjugate; Two parts of signals is respectively through identical filter (the filter here is the first of training sequence); Estimate integer frequency offset; We can set two other variable
Figure 856352DEST_PATH_IMAGE056
and
Figure 200746DEST_PATH_IMAGE058
equally; They are corresponding respectively is training sequence first and relevant (be equivalent to handle
Figure 217746DEST_PATH_IMAGE060
and
Figure 785738DEST_PATH_IMAGE062
and pass through filtering) of
Figure 370827DEST_PATH_IMAGE060
and
Figure 329425DEST_PATH_IMAGE062
, as
Figure 138221DEST_PATH_IMAGE064
(9)
The peak of formula (9) with the time partially relevant with path delay; The amplitude square of
Figure 205403DEST_PATH_IMAGE056
and
Figure 643338DEST_PATH_IMAGE058
is approximately the form of
Figure 267217DEST_PATH_IMAGE066
, and peak value satisfies following positions
(10)
Here can estimate integer frequency offset through the distance of calculating between
Figure 213756DEST_PATH_IMAGE056
and
Figure 325937DEST_PATH_IMAGE058
peak value; But under the multipath situation; Relatively more difficult; In order better to get the peak value of
Figure 487928DEST_PATH_IMAGE056
and
Figure 815005DEST_PATH_IMAGE058
; Set two thresholding factors
Figure 519262DEST_PATH_IMAGE070
and
Figure 869472DEST_PATH_IMAGE072
; Get peak value threshold
Figure 84421DEST_PATH_IMAGE074
and
Figure 203687DEST_PATH_IMAGE076
; During as
Figure 658939DEST_PATH_IMAGE078
, make
Figure 981598DEST_PATH_IMAGE080
; During as ; Make
Figure 974011DEST_PATH_IMAGE084
cross-correlation of getting
Figure 537848DEST_PATH_IMAGE056
and
Figure 344873DEST_PATH_IMAGE058
then
Figure 714675DEST_PATH_IMAGE086
(11)
So that when
Figure 808533DEST_PATH_IMAGE088
get to the cross-correlation peak position meet
Figure 339057DEST_PATH_IMAGE092
(12)
Therefore the estimated value of frequency deviation does
Figure 935386DEST_PATH_IMAGE094
(13)。
10. frequency offset estimating algorithm according to claim 1 is proofreaied and correct frequency deviation
Figure 946067DEST_PATH_IMAGE096
(14)
Frequency offset estimating algorithm according to claim 1 carries out iteration and estimates, estimates frequency deviation up to accurately.
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Application publication date: 20120704