CN104601518B - Sampling frequency offset and carrier wave frequency deviation combined estimation method based on maximal possibility estimation - Google Patents
Sampling frequency offset and carrier wave frequency deviation combined estimation method based on maximal possibility estimation Download PDFInfo
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Abstract
The invention discloses a kind of sampling frequency offset based on maximal possibility estimation and carrier wave frequency deviation combined estimation method, purpose is that solve two-dimentional global search in existing SFO and CFO combined estimation methods to cause computation complexity high, the problem of error floor estimated accuracy can not continue convergence in high SNR be present.Technical scheme is first to determine SFO span and SFO span is transformed to variable t span, is approached using single order Legnedre polynomialObtained single order Legnedre polynomial is approached and by the approximant substitutionFormula, obtain t；By t conversions SFO final estimateAnd byObtain CFO estimateThe present invention need not carry out two-dimentional global search, greatly reduce computation complexity, while eliminate existing method of estimation and the problem of error floor be present in high SNR, improve estimated accuracy.
Description
Technical field
The invention mainly relates to the synchronous estimation field in wireless communication system base band signal process, it is desirable to provide Yi Zhongji
Calculate the sampling frequency offset (SFO) and carrier wave frequency deviation (CFO) combined estimation method that complexity is low, estimated accuracy is high.
Background technology
OFDM (OFDM) technology is widely used in modern wireless communication systems because of its high spectrum utilization
In, used by multiple communication protocols such as IEEE 802.11a, IEEE 802.16a, DVB-T and DRM.But OFDM skills
Art is quite sensitive to synchronous error, causes the performance of its receiver to significantly reduce.SFO and CFO be in ofdm system most based on
The synchronous error wanted.In order to improve the performance of receiver, it is necessary to estimate in receivers SFO and CFO value, and according to
Estimate compensates to reception signal.
SFO and CFO is as caused by the factors such as the sampling clock mismatch of transmitter and receiver and Doppler frequency shift.Pass
The synchronous estimation method of system is to be estimated SFO and CFO respectively, is then compensated.In recent years, combining for SFO and CFO is estimated
Meter method is proposed in succession.2004, M.M.Freda etc. was in " Joint channel estimation and
Synchronization for OFDM systems " (" joint channel estimation and synchronous method in ofdm system ")
In propose SFO the and CFO combined estimation methods of time domain earliest, but this method needs an extra inversefouriertransform portion
Part, add the complexity of receiver synchronization module；In order to reduce the complexity of system；2009, H.Nguyen-Le et al. existed
“RLS-based joint estimation and tracking of channel response,sampling,and
Carrier frequency offsets for OFDM " (" letters based on recurrence least square in ofdm system
Road, sampling frequency offset and carrier wave frequency deviation Combined estimator and tracking ") in propose and a kind of utilize two identical long instructions in frequency domain
Practice SFO the and CFO combined estimation methods that sequence carries out maximal possibility estimation, however, due to weight factor in this method
Influence is restricted its estimated accuracy；2011, Y.-H.Kim et al. was in " Joint maximum likelihood
Estimation of carrier and sampling frequency offsets for OFDM systems " (" are based on
The sampling frequency offset and carrier wave frequency deviation combined estimation method of maximal possibility estimation ") in by H.Nguyen-Le et al. Combined estimators
The cost function of method is improved so that estimated accuracy greatly improves.Above-mentioned various combined estimation methods are required to SFO
Two-dimentional global search is carried out with CFO cost function so that the calculating time greatly increases, particularly in high s/n ratio, due to
The limitation of step-size in search causes error floor be present to SFO and CFO Combined estimator, and estimated accuracy can not continue to restrain.Such as Fig. 1
Shown, Y.-H.Kim et al. is in " Joint maximum likelihood estimation of carrier and
Sampling frequency offsets for OFDM systems " (" sampling frequency offset and load based on maximal possibility estimation
Ripple diviation combined estimation method ") in propose SFO and CFO combined estimation methods be broadly divided into the following steps：
The first step：Two long training sequence R are obtained in the symbol flow data received from receiver0And R (k)1(k)；
Second step：CFO is divided into 100 parts in span [- 0.5,0.5] section, i.e., it is CFO step-size in search is true
It is set to 0.01, SFO is divided into 100 parts in span [- 0.0015,0.0015], i.e., is defined as SFO step-size in search
0.00003；
3rd step：Two-dimentional global search is performed in section of the cost function described in CFO and SFO according to (1) formula,
And the SFO values and CFO values for making cost function minimum are found out, as respective estimate；
Wherein, R0(k) it is the first frequency domain long training sequence received, R1(k) second frequency domain length instruction to receive
Practicing sequence, ε represents the possible values of CFO, and η represents the possible values of SFO,The final estimated results of CFO are represented,Represent SFO
Final estimated result,Represent to cause ε and η value conducts when cost function $ (ε, η) takes minimum value
CFO and SFO final estimate.
The core of this method is to perform two-dimentional global search to cost function $ (ε, η) in SFO and CFO spans,
Find and cause cost function to take the estimate of η and ε during minimum value as SFO and CFO.The combined estimation method has following two
Individual shortcoming.
1. the global search of two dimension causes amount of calculation to be significantly increased, computation complexity is added so that complete Combined estimator
Need the longer calculating time；
2. the precision of the combined estimation method depends on the step-size in search of two-dimensional search, although reducing step-size in search contributes to
Estimated accuracy is improved, but computation complexity is consequently increased.So step-size in search can only be in estimated accuracy and computation complexity
Between seek to compromise, which results at high s/n ratio (SNR), there is error floor in the combined estimation method, estimated accuracy without
Method continues to restrain.
The content of the invention
The technical problem to be solved in the present invention is：For two-dimentional global search in existing SFO and CFO combined estimation methods
The computation complexity brought is high, and the problem of error floor estimated accuracy can not continue convergence in high SNR be present, proposes a kind of
SFO and CFO combined estimation methods based on maximal possibility estimation.Carried combined estimation method need not carry out the two-dimentional overall situation and search
Rope, therefore computation complexity is greatly reduced, while eliminate existing method of estimation and asking for error floor in high SNR be present
Topic, improves estimated accuracy.
The feature of the present invention comprises the following steps：
The first step：Determine the span of SFO in real system；
It is [- 20 × 10 by the SFO tolerance limits of IEEE 802.11a agreement defineds-6,+20×10-6], i.e., it is it is required that logical
The SFO of letter system falls [- 20 × 10-6,+20×10-6] in the range of, in the combined estimation method proposed, in order that obtaining institute
There are SFO values to fall within the span of estimation, set SFO tolerance limit as β times of IEEE 802.11a agreement tolerance limits, even if
The variable η for obtaining SFO falls in [- 2 β × 10-5,2β×10-5] in the range of, β is positive integer, general to recommend to be more than 3.
Second step：SFO span is transformed to t span so that t ∈ [- 1,1]；
Require that the variable of approximated function belongs to section [- 1,1] when being approached due to Legnedre polynomial, therefore by SFO change
Amount η is multiplied by 105/ 2 β transform to variable t, this variations per hour t ∈ [- 1,1], meet the condition that Legnedre polynomial is approached.
3rd step：Approached using single order Legnedre polynomial
Wherein, N is the sum (in IEEE 802.11a agreements be 64) of communication system sub-carriers, NmFor in communication system
Total number of sub-carriers adds the length (being 80 in IEEE 802.11a agreements) of cyclic prefix, and p and q are less than N natural number.
4th step：WillSingle order Legnedre polynomial approach substitution (2) formula, solve on t once
Function, obtain t value；
Wherein, Im (x) represents plural x imaginary part, R (q)*Represent the conjugation of plural R (q).
5th step：SFO estimate is obtained by t
Understand that t is the final estimates of SFO by second step105/ 2 β times, therefore the t values divided by 10 that the 4th step is obtained5/2β
As finally estimate obtained SFO estimate
6th step：The estimate for the SFO that 5th step is obtained(3) formula of substitution, obtains CFO estimate
Wherein, θ is (4) formulaPhase,In parameter K represent the sub-carrier number that uses in communication system
(being 52 in IEEE 802.11a agreements), k is the positive integer for being less than K/2-1 more than or equal to-K/2,
Compared with prior art, advantages of the present invention is that：
1. the global search that the present invention need not be two-dimentional, the two long training sequence R received by receiver0And R (k)1
(k) can solves SFO estimateWith CFO estimateSignificantly reduce computation complexity；2. due to the present invention
The global search of two dimension need not be carried out, therefore in high SNR, the present invention carries combined estimation method and error floor, phase is not present
Need the combined estimation method of two-dimensional search that there is higher precision than tradition.
Brief description of the drawings
Fig. 1 is SFO the and CFO combined estimation method flow charts that Y.-H.Kim et al. is proposed；
Fig. 2 is SFO the and CFO combined estimation method flow charts of the present invention；
Fig. 3 represents SFO the and CFO combined estimation methods and Y.-H.Kim that the present invention and H.Nguyen-Le et al. are proposed
Et al. propose SFO and CFO combined estimation methods estimation sampling frequency offset mean square error comparison diagram；
Fig. 4 represents SFO the and CFO combined estimation methods and Y.-H.Kim that the present invention and H.Nguyen-Le et al. are proposed
Et al. propose SFO and CFO combined estimation methods estimation carrier wave frequency deviation mean square error comparison diagram.
Embodiment
Fig. 2 is the flow chart of the present invention, and the present invention comprises the following steps：
The first step：In IEEE 802.11a agreements, the typical error tolerances of SFO are [- 20 × 10-6,+20×10-6],
Therefore when progress single order Legnedre polynomial is approached, the span for setting SFO is η ∈ [- 2 β × 10-5,2β×10-5] be enough
Meet the scope of η values in real system；
Second step：Make t=(105/ 2 β) η, then t ∈ [- 1,1], therefore understand：
Because when the 3rd step, which carries out Legnedre polynomial, approaches, the independent variable of approximated function needs to be located at section [- 1,1]
It is interior, therefore need to be multiplied by 10 to η5/ 2 β are transformed to t, and the function progress Legnedre polynomial to the t containing variable is approached.
3rd step：It is rightSingle order Legnedre polynomial is carried out in t ∈ [- 1,1] section to approach；
3.1 set p0(t)=1, p1(t)=t；
Wherein, p0And p (t)1(t) it is respectively constant term and first order that single order Legnedre polynomial is approached, it is rightAsk single order Legnedre polynomial to approach, next will obtain the coefficient of constant term and first order respectively；
3.2 calculate (p0,p0)、(p1,p1)、(y,p0)、(y,p1)；
Wherein, (x, y) represents x and y inner product；
Wherein
3.3 obtain the coefficient a of single order Legnedre polynomial constant term and first order0, a1；
3.4 obtainSingle order Legnedre polynomial approach；
4th step：(5) formula is substituted into linear function of (2) formula solution on t, you can obtain working as receiver receives two
Individual long training sequence is R0And R (k)1(k) t values when, shown in t expression such as formula (6)；
5th step：According to the relation of SFO estimate η and t in second step, it is known that SFO final estimateCan be by t tables
It is shown as following formula；
6th step：By SFO estimateSubstitution formula (3) can obtain the estimate for obtaining CFO
Wherein,I.e. θ isPhase
Base band signal process link is established based on IEEE 802.11a wireless communication protocols in matlab, uses this hair
Bright carried combined estimation method and traditional combined estimation method are respectively to the sampling frequency offset SFO and carrier wave frequency deviation in the link
CFO carries out Combined estimator.When sampling frequency offset η being arranged to 0.000112, and carrier wave frequency deviation ε is arranged to 0.212, exist in SNR
The result of various combined estimation methods is as shown in Figure 3 and Figure 4 in the range of [0dB, 50dB].SFO and CFO, which combines, in Fig. 3 and Fig. 4 estimates
During meter emulation, CFO is arranged to 0.212, SFO and is arranged to 0.000112, each simulation parameter with reference to IEEE 802.11a standards,
OFDM total number of sub-carriers is 64, and the OFDM subcarriers number used is 52, circulating prefix-length 16.Circle in Fig. 3 and Fig. 4
The curve of mark be article " RLS-based joint estimation and tracking of channel response,
Sampling, and carrier frequency offsets for OFDM " (" are based on recurrence in ofdm system
Channel, sampling frequency offset and the carrier wave frequency deviation Combined estimator of least square and tracking ") in carry combined estimation method result song
Line, the curve of target cross is article " Joint maximum likelihood estimation of carrier and
Sampling frequency offsets for OFDM systems " (" sampling frequency offset and load based on maximal possibility estimation
Ripple diviation combined estimation method ") in put forward the result curve of combined estimation method, the curve of five-pointed star mark is carried to be of the invention
Result curve obtained by combined estimation method.
Fig. 3 and Fig. 4 abscissa is SNR, and unit dB, ordinate is mean square error, then observes Fig. 3 and Fig. 4 and understand：
In the case of identical SNR, the present invention puies forward combined estimation method result curve and is located under classical joint method of estimation curve
Side, i.e., under identical state of signal-to-noise, institute's extracting method of the present invention has smaller mean square error, so the present invention is with higher
Estimated accuracy.Particularly in high s/n ratio, this advantage will become apparent from.
Compared to traditional combined estimation method, SFO the and CFO combined estimation methods that the present invention is carried need not carry out two
The global search of dimension, so the present invention also has the advantages of computation complexity is low.
Claims (5)
1. a kind of sampling frequency offset and carrier wave frequency deviation combined estimation method based on maximal possibility estimation, it is characterised in that including following
Step：
The first step：The span of SFO in real system is determined, method is：SFO tolerance limit is set as IEEE 802.11a agreements
β times of tolerance limit, β are positive integer, that is, cause SFO variable η to be more than marginal range as defined in agreement, then η ∈ [- 2 β × 10-5,2β
×10-5]；
Second step：SFO span is transformed to variable t span so that t ∈ [- 1,1], meet that Legendre is multinomial
The condition that formula is approached, method are：
Make t=(105/ 2 β) η, then t ∈ [- 1,1],
Wherein, N be communication system sub-carriers sum, NmThe length of cyclic prefix is added for communication system sub-carriers sum,
P and q is less than N natural number；
3rd step：Approached using single order Legnedre polynomialObtainSingle order Legendre
Approximation by polynomi-als is as shown in (5) formula：
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2. a kind of sampling frequency offset and carrier wave frequency deviation combined estimation method based on maximal possibility estimation as claimed in claim 1,
It is characterized in that the total N of communication system sub-carriers is 64, communication system sub-carriers sum adds the length of cyclic prefix
NmFor 80.
3. a kind of sampling frequency offset and carrier wave frequency deviation combined estimation method based on maximal possibility estimation as claimed in claim 1,
It is characterized in that approached using single order Legnedre polynomialMethod be：
3.1 set p0(t)=1, p1(t)=t；
Wherein, p0And p (t)1(t) it is respectively constant term and first order that single order Legnedre polynomial is approached；
3.2 calculate (p0,p0)、(p1,p1)、(y,p0)、(y,p1)；
Wherein, (x, y) represents x and y inner product；
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<mo>-</mo>
<mn>2</mn>
<mi>j</mi>
<mfrac>
<mrow>
<mi>a</mi>
<mi> </mi>
<mi>cos</mi>
<mi> </mi>
<mi>a</mi>
<mo>-</mo>
<mi>sin</mi>
<mi> </mi>
<mi>a</mi>
</mrow>
<msup>
<mi>a</mi>
<mn>2</mn>
</msup>
</mfrac>
</mrow>
Wherein
<mrow>
<mi>a</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<msub>
<mi>&pi;N</mi>
<mi>m</mi>
</msub>
</mrow>
<mi>N</mi>
</mfrac>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>-</mo>
<mi>q</mi>
<mo>)</mo>
</mrow>
<mo>&times;</mo>
<mn>2</mn>
<mi>&beta;</mi>
<mo>&times;</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>-</mo>
<mn>5</mn>
</mrow>
</msup>
<mo>;</mo>
</mrow>
3.3 obtain single order Legendre polynomials number a0, a1；
<mrow>
<msub>
<mi>a</mi>
<mn>0</mn>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>p</mi>
<mn>0</mn>
</msub>
<mo>,</mo>
<msub>
<mi>p</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>,</mo>
<msub>
<mi>p</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>sin</mi>
<mi> </mi>
<mi>a</mi>
</mrow>
<mi>a</mi>
</mfrac>
</mrow>
<mrow>
<msub>
<mi>a</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>p</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<msub>
<mi>p</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>,</mo>
<msub>
<mi>p</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>3</mn>
<mi>j</mi>
<mfrac>
<mrow>
<mi>sin</mi>
<mi> </mi>
<mi>a</mi>
<mo>-</mo>
<mi>a</mi>
<mi> </mi>
<mi>cos</mi>
<mi> </mi>
<mi>a</mi>
</mrow>
<msup>
<mi>a</mi>
<mn>2</mn>
</msup>
</mfrac>
</mrow>
3.4 obtainSingle order Legnedre polynomial approach as shown in (5) formula.
4. a kind of sampling frequency offset and carrier wave frequency deviation combined estimation method based on maximal possibility estimation as claimed in claim 1,
It is characterized in thatIn parameter K be 52.
5. a kind of sampling frequency offset and carrier wave frequency deviation combined estimation method based on maximal possibility estimation as claimed in claim 1,
It is characterized in that β is more than 3.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN101102299A (en) * | 2007-08-09 | 2008-01-09 | 复旦大学 | A carrier frequency deviation rough synchronization method based on D varying technology |
| CN101184078A (en) * | 2007-12-24 | 2008-05-21 | 清华大学 | Method for filling protection spacing in orthogonal frequency division multiplexing modulation system and communication system thereof |
| CN101499991A (en) * | 2009-03-17 | 2009-08-05 | 广东工业大学 | MIMO-OFDM system carrier frequency bias and sampling offset combined estimation method under IQ unbalance |
| US7999623B2 (en) * | 2005-12-05 | 2011-08-16 | Realtek Semiconductor Corp. | Digital fractional-N phase lock loop and method thereof |
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| US7999623B2 (en) * | 2005-12-05 | 2011-08-16 | Realtek Semiconductor Corp. | Digital fractional-N phase lock loop and method thereof |
| CN101102299A (en) * | 2007-08-09 | 2008-01-09 | 复旦大学 | A carrier frequency deviation rough synchronization method based on D varying technology |
| CN101184078A (en) * | 2007-12-24 | 2008-05-21 | 清华大学 | Method for filling protection spacing in orthogonal frequency division multiplexing modulation system and communication system thereof |
| CN101499991A (en) * | 2009-03-17 | 2009-08-05 | 广东工业大学 | MIMO-OFDM system carrier frequency bias and sampling offset combined estimation method under IQ unbalance |
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