CN104836652B - A kind of space-time block code MIMO ofdm system Time and Frequency Synchronization new methods under low signal-to-noise ratio - Google Patents
A kind of space-time block code MIMO ofdm system Time and Frequency Synchronization new methods under low signal-to-noise ratio Download PDFInfo
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- H04L5/00—Arrangements affording multiple use of the transmission path
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Abstract
The present invention is the STBC MIMO ofdm system Time and Frequency Synchronization new methods under a kind of low signal-to-noise ratio, it is characterised in that:It is difficult to obtain accurate Time and Frequency Synchronization problem for STBC MIMO ofdm systems, the present invention proposes the STBC MIMO ofdm system Time and Frequency Synchronization new methods under a kind of Low SNR under Low SNR.This method constructs a multiple orthogonal complement sequence first with one group of multiple complementary sequence set and orthogonal matrix, is converted by orthogonal matrix and extends the sequence, so as to obtain the multiple orthogonal complement sequence of appropriate length;To improve the autocorrelation of the sequence and cross correlation, training sequence is to negate characteristic construction by the conjugation of the sequence, and is superimposed on data-signal.Good synchronizing signal is obtained by the way that training sequence is related to data-signal in receiving terminal, and integer frequency bias estimation range can reach ε ∈ (N/4, N/4).Under Low SNR, synchronous method proposed by the present invention compared with the conventional method, more accurate time synchronized and larger frequency deviation region can be obtained in 15dB, and computation complexity is lower.
Description
Technical field
The present invention relates to MIMO-OFDM technical fields, the STBC MIMO-OFDM systems under particularly a kind of low signal-to-noise ratio
Time and Frequency Synchronization new method.
Background technology
With the fast development of wireless communication technology, people are to the transmission rate and stability of wireless communication technology and can
By property specifically higher and higher requirement.Existing OFDM (OFDM) technology is a kind of Multicarrier Transmission Technology, and it has
There is the features such as higher availability of frequency spectrum, anti-multipath fading.Multiple-input and multiple-output (MIMO) technology is then to make full use of space resources,
The function that multi-emitting receives more is realized, in the case where not increasing frequency spectrum resource and transmitting antenna power, improves the capacity of channel.
The MIMO systems combined with OFDM are had the characteristics that into stable signal transmission, availability of frequency spectrum height, high-speed transfer rate, can be fine
Ground meets the requirement of wireless-transmission network of future generation, and is also the inexorable trend of later stage wireless communication technology development.Its is main
The field of application includes:WLAN (WLAN), wireless broadband Internet access (Wimax), future generation mobile radio system
(B3G/4G) etc..
In order to improve the transmission rate of wireless communication technology and stability and reliability, the sky under Low SNR
In time block code (STBC) multi-I/O OFDM (MIMO-OFDM) system, MIMO-OFDM technologies have letter
The features such as number transmission is stable, the availability of frequency spectrum is high, high-speed transfer rate, and multiple antenna joint can be realized using STBC codings
Coding techniques, antenna diversity can resist the decline of channel, improve the reliability of wireless communication link;Increase is encoded by STBC to pass
Defeated space-time redundancy, improve the Stability and dependability of wireless communication transmissions.
Under Low SNR, existing MIMO-OFDM synchronized algorithms time-frequency synchronization performance is affected.Cause
This, under Low SNR, wants to obtain Time and Frequency Synchronization performance of good performance, the time-frequency synchronization is to be worth deeply grinding
Study carefully.Ali Rachini et al. propose STBC MIMO ofdm system Time synchronization algorithms, using the good CAZAC sequences of orthogonality
Row and Walsh-Hadamard sequences are used as training sequence, using the acquisition related to data-signal of local training sequence it is good when
Between net synchronization capability.Simulation result shows that under Low SNR time synchronized performance is more excellent.But offset estimation pair is not accounted for
The influence of systematic function.FAN Hui-li et al. propose MIMO-OFDM system time frequency synchronized algorithms, using conjugated structure
CAZAC sequences obtain synchronizing information as training sequence using receiving terminal data message auto-correlation.Simulation result shows this method
Time and Frequency Synchronization is preferable under Low SNR, but this method deficiency is that frequency offset estimation range is smaller.Documents:[1]
R.N.Ali,B.D.Ali,N.Fabienne and B.Bilal.Timing synchronization method for
MIMO-OFDM system using orthogonal preamble[C].19th International Conference
on Telecommunications(ICT 2012),2012:1-6.[2]H.L.Fan,J.F.Sun,P.Yang,D.S.Li.A
Robust Timing and Frequency Synchronization Algorithm for HF MIMO OFDM
Systems[C].IEEE Conference on Global Mobile Congress(GMC),2010:These synchronization sides of 1-4.
Method is all the synchronous method being inserted into training sequence on OFDM data symbol, the availability of frequency spectrum for place is reduction system that its is insufficient
With the transmission power for reducing emitter.
Therefore, insufficient existing for existing MIMO-OFDM system synchronization methods in order to overcome, the present invention proposes a kind of low noise
STBC MIMO-OFDM system time frequency synchronization new algorithms than under, the training sequence of the synchronous method are the OFDM data symbols that is added to
On number, it can effectively improve the transmission power of band efficiency and emitter.
The content of the invention
The purpose of the present invention is to be to propose the STBC MIMO-OFDM system time frequency synchronization new methods under a kind of low noise,
So as to overcome the shortcomings of existing MIMO-OFDM system synchronization methods.The present invention proposes synchronous new method, is that design is a kind of first
The good multiple orthogonal complement sequence of orthogonality, secondly negating characteristic using the conjugation of the sequence constructs new training sequence, should
Training sequence has good autocorrelation and weaker cross correlation, and has excellent orthogonality.Training sequence is superimposed
Turn into transmission signal on to a complete OFDM data symbol, in receiving terminal, utilize receiving terminal data-signal and local training
Sequence correlation can obtain accurate synchronizing information, and phase is sought using receiving terminal data-signal and local training sequence related operation
To obtain integer frequency bias estimate.Accurate time synchronized and Frequency Synchronization can ensure that the data message of transmission correctly demodulates.
To achieve these goals, the STBC MIMO-OFDM system time frequencies under a kind of low signal-to-noise ratio proposed by the present invention are same
Walk the innovative point of new method:
(1) present invention designs a kind of training sequence based on multiple orthogonal complement sequence, and the training sequence is negated using conjugation
Characteristic improves the autocorrelation of training sequence.
(2) new time-frequency synchronization proposed by the present invention, Time synchronization algorithm are to use receiving terminal data message and local
Training sequence obtains synchronizing information, and accurate timing synchronization position is determined with maximum, on timing synchronous foundation is realized,
Frequency Synchronization is carried out, and larger frequency deviation region can be estimated in time domain, so as to ensure the correct demodulation of the data message of transmission.
The present invention proposes the STBC MIMO-OFDM system time frequency synchronization new methods under a kind of low signal-to-noise ratio, the day of the system
Line sets NTIndividual transmitting antenna and NRIndividual reception antenna, it is comprised the following steps that:
Step 1:Multiple orthogonal complement sequences Design:
(1) a multiple complementary sequence set { A is designed1,B1,C1,D1, wherein A1=[1,1, j ,-j], B1=[1,1 ,-j, j],WithC2=B1,D2=-A1, whereinIt is A1Conjugation negate computing ,-A1Represent A1's
Negative value, j represent imaginary symbols, j2=-1;
(2) it is 4 using above-mentioned multiple complementary sequence set construction row vector, column vector is 8 matrix E4×8, whereinIn formula ()TRepresenting matrix transposition;
(3) orthogonal matrix is utilizedIt is 16 to reconfigure row vector, and column vector is 16 new matrixes
E16×16, its matrixIn formula ()TRepresenting matrix transposition;
(4) orthogonal matrix is utilizedIt is 32 to reconfigure row vector, and column vector is 32 new matrix E32×32, obtain
Matrix
(5) above-mentioned (4) step is repeated, can be with extended matrix so as to obtaining longer orthogonal sequence;
Step 2:Using above-mentioned multiple orthogonal complement sequences Design step, then orthogonal matrix can be obtained
Pass through matrixConstruct one group of sequence ai(n), wherein n span n ∈ [0, N/4-1], i span i ∈ [1, N/
4], N represents sub-carrier number;
Step 3:As i=1, the sequence a that length is N/4 is constructed1(n), by sequence a1(n) conjugation is taken to negate computing acquisition
New sequence b1(n), have:
In formula:Represent sequence a1() sequence takes conjugate operation;
By sequence a1And b (n)1(n) the sequence t that length is N/2 is formed1(n), have:
Step 4:By sequence t1(n) it is repeated once the sequence c that construction length is N1(n), have:
Step 5:The training sequence signal in a complete OFDM symbol that is added to is expressed as:
In formula:P represents the general power of emitter, and β is power allocation factor, its span 0<β<1, it is defined asWhereinxi(n) it is the i-th frame transmission signal, x (n) is represented
Transmission signal, ci(n) training sequence being superimposed for the training sequence of the i-th frame transmission signal superposition, c (n) for transmission signal, E
(●) represents to do mean value computation to sequence in bracket;
Step 6:The local training sequence sum received using receiving terminal obtains time synchronized, timing degree it is believed that manner of breathing closes
Flow function expression formula is:
Wherein:
In formula:Nt is the number of transmitting antenna, and Nr is the number of reception antenna, and Ng is the length of cyclic prefix,Represent
Receiving terminal data message takes conjugate operation, and n is the number of sampled point, ci(n) training sequence on transmitting antenna is represented, d is whole
Numerical value, it represents the relative sliding position of local training sequence and receiving terminal data message, and m represents cycle-index;
In order to facilitate mathematical analysis, it is assumed that the general power P of emitter is 1, and training sequence is made an uproar with data message and channel
Sound is unrelated.
(8) formula is brought into (5) formula to obtain:
In formula:Represent the transmission power of training sequence.When the overlying training sequence of receiving terminal data-signal is instructed with local
When practicing data block sequence alignment, B { P (d) } reaches maximum.Because timing metric function R (d) is that normalizing is turned into formula (5)
With when then M (d) reaches maximum, you can judge that d this moment is OFDM symbol starting position, synchronized algorithm is expressed as:
In formula:Represent Timing Synchronization estimate;
Step 6:It can be seen that synchronous exact position is relevant with training sequence power allocation factor by (9) formula, when power point
Bigger with the factor, timing net synchronization capability is better;
Step 7:Using receiving terminal data message autocorrelation, decimal frequency bias estimation is obtained, its mathematical formulae is expressed as:
In formula:Real () is representedReal part computing is taken, imag () is representedTake imaginary-part operation,Represent decimal
Offset estimation value, its estimation range:
Step 8:It is the integer frequency bias estimation for the laggard line frequency of fractional frequency migration that will be estimated, passes through local instruction
Practice sequence and seek phase with receiving terminal data-signal related operation to obtain integer frequency bias estimate, expression formula:
In formula:Integer frequency bias estimation is represented, its estimation range is:
Brief description of the drawings
For the STBC MIMO-OFDM system time frequency synchronization new methods under a kind of low signal-to-noise ratio detailed further, for
The chart that the present invention relates to is described in detail.
Fig. 1 is STBC MIMO-OFDM system block diagrams of the present invention.In figure, STBC MIMO-OFDM system block diagrams are mainly by two
Part forms, and mainly has in transmitting terminal:The data message of input is by MPSK modulation 102, Space Time Coding 103, IFFT modulation 104
Etc. module;Mainly have in receiving terminal:Synchronous and channel estimation 112, FFT demodulation 116, space-time decoding 117, MPSK demodulation 118 etc.
Module.
Fig. 2 is the structured flowchart that training sequence of the present invention is added in OFDM symbol.In figure, training sequence is to be added to respectively
On transmission antenna OFDM data symbol.
Fig. 3 is the organigram of the multiple orthogonal complement sequence of the present invention.In figure, multiple orthogonal complement sequence is to utilize multiple complementation
Sequence sets structural matrix, and pass through orthogonal matrix and the orthogonal sequence of matrixing extension appropriate length.
Fig. 4 is the training sequence structure schematic diagram of the invention based on multiple orthogonal complement sequence.In figure, using appropriate length
Multiple orthogonal complement sequence, and negated by conjugation and reconfigure the training sequence based on multiple orthogonal complement sequence with repeat property.
Fig. 5 is STBC MIMO-OFDM system time frequencies synchronized algorithm flow chart of the present invention.In figure, the local of receiving terminal is utilized
Training sequence sum obtains timing synchronisation information it is believed that manner of breathing closes, and judges timing synchronization position with maximum, then carries out decimal
Offset estimation and compensation, finally phase is asked to obtain integer frequency bias using local training sequence and receiving terminal data-signal related operation
Estimate.
Fig. 6 is the BER Simulation figure of different capacity distribution factor of the present invention.In figure, abscissa represents signal to noise ratio (SNR),
Ordinate represents bit error rate performance (BER), and β represents power allocation factor, by finding out in figure, with power allocation factor β increasing
Greatly, error rate of system performance reduces.
Fig. 7 is the synchronous correct probability figure of different capacity distribution factor of the present invention.In figure, abscissa represents signal to noise ratio
(SNR), ordinate represent time synchronized correct probability, β represent power allocation factor, by finding out in figure, with power distribution because
Sub- β increase, system time synchronization correct probability performance improve.
Fig. 8 is time synchronized correct probability performance comparision figure of the present invention.In figure, abscissa represents signal to noise ratio (SNR), indulges and sits
Mark represents time synchronized correct probability, is that Ali Rachini et al. use the good Walsh- of orthogonality in document [1]
Hadamard sequences and CAZAC sequences are Fan in document [2] respectively as two kinds of Time synchronization algorithms of training sequence
Hui-li et al. is found out, the time synchronized of innovatory algorithm is just using the CAZAC sequence time synchronized algorithms of shift-orthogonal by figure
The performance of true probability is substantially better than document [1] and [2].Documents:[1]R.N.Ali,B.D.Ali,N.Fabienne and
B.Bilal.Timing synchronization method for MIMO-OFDM system using orthogonal
preamble[C].19th International Conference on Telecommunications(ICT 2012),
2012:1-6.[2]H.L.Fan,J.F.Sun,P.Yang,D.S.Li.A Robust Timing and Frequency
Synchronization Algorithm for HF MIMO OFDM Systems[C].IEEE Conference on
Global Mobile Congress(GMC),2010:1-4.
Fig. 9 is offset estimation mean square error performance comparision figure of the present invention.In figure, abscissa represents signal to noise ratio (SNR), indulges and sits
Mark represents offset estimation mean square error (MSE), is that Fan Hui-li et al. propose to use reception signal auto-correlation in document [2]
Decimal frequency bias algorithm for estimating is obtained, is found out by figure, the offset estimation mean square error performance of innovatory algorithm is better than document [2].It is right
Compare document:[2]H.L.Fan,J.F.Sun,P.Yang,D.S.Li.A Robust Timing and Frequency
Synchronization Algorithm for HF MIMO OFDM Systems[C].IEEE Conference on
Global Mobile Congress(GMC),2010:1-4.
Embodiment
Patent of the present invention is described in further details below in conjunction with the accompanying drawings.
Fig. 1 is that the present invention has NTRoot transmitting antenna and NRThe STBC MIMO-OFDM system fundamental block diagrams of root reception antenna.
The system block diagram is mainly made up of transmitter and receiver, and in transmitter terminal, the module mainly included has data bit flow mould
Block 101, modulation module (MPSK) 102, Space Time Coding module 103, inverse Fourier transform (IFFT) module 104, parallel serial conversion mould
Block 105, parallel training block 106, power distribution module 107, laminating module 108, the sum of insertion protection interval module 109
Mould changes (D/A) module.In receiver end, the module mainly included has analog-to-digital conversion (A/D) module 111, synchronization and channel to estimate
Count module 112, training sequence and data separating module 113, deprotection interval module 114, serial to parallel conversion module 115, Fourier
(FFT) module 116 is converted, space-time decoding module 117, demodulates (MPSK) module 118, data bit flow module 119.The present invention is main
Parallel training block 106 is added on OFDM data symbol if being used in transmitter terminal, can so improve system
The availability of frequency spectrum and efficiency of transmission, save bandwidth resources.Space Time Coding module 103 is used to realize multiple antenna before
Coding techniques, antenna diversity are also act against the decline of channel, so as to improve the reliability of communication link, in addition, also increase passes
Defeated space-time redundancy, improve the Stability and dependability of wireless communication transmissions.In receiver end, synchronous and channel estimation mould
Block is mainly to determine the original position of FFT window and ensures the orthogonality of each subcarrier, then carries out space-time decoding module 117
The correct demodulation to OFDM data module is realized with demodulation (MPSK) module 118.
Fig. 2 is the structured flowchart that training sequence of the present invention is added in OFDM symbol, by the training based on multiple orthogonal complement
For its superimposition on one on each transmitting antenna complete OFDM data symbol, 201 be training sequence c1(n), 202 be training sequence
Arrange c2(n)。
Fig. 3 is the organigram of the multiple orthogonal complement sequence of the present invention, designs multiple orthogonal complement sequence step:301 first
It is the multiple complementary sequence set of design one, 302 utilize above-mentioned multiple complementary sequence set structural matrix E4×8, 303 utilize orthogonal matrix H2×4
Structural matrix E16×16, 304 utilize orthogonal matrix F2×2Reconfigure matrix E32×32, 305 the 4th steps that repeat the above steps can obtain
Obtain longer orthogonal sequence.
Fig. 4 is the training sequence structure schematic diagram of the invention based on multiple orthogonal complement sequence, again the instruction of orthogonal complement sequence
Practice the building method of sequence:401 obtain orthogonal matrix using the design procedure of multiple orthogonal complement sequenceAnd utilize the matrix
Construct one group of sequence ai(n), i=0 ..., N/4,402 illustrate as i=1, by the sequence a that length is N/41(n) negated as conjugation
Computing obtains new sequence b1(n), 403 by sequence a1And b (n)1(n) sequence t of the composite construction into length for N/21(n), 404
By sequence t1(n) it is repeated once the training sequence c that construction length is N1(n)。
Fig. 5 is STBC MIMO-OFDM system time frequencies synchronized algorithm flow chart of the present invention, and 501 be reception signal, and 502 utilize
The local training sequence sum of receiving terminal obtains Timing Synchronization it is believed that manner of breathing closes, and 503 judge timing synchronization position with maximum,
504 decimal frequency bias estimate that the compensation of 505 frequency deviations, 506 seek phase using local training sequence and receiving terminal data-signal related operation
To obtain integer frequency bias estimate.
Fig. 6 is the BER Simulation figure of different capacity distribution factor of the present invention, and Fig. 7 is the synchronization of different capacity distribution factor
Correct probability analogous diagram, main simulation parameter of the invention are set:Transmitting antenna number NT=2, reception antenna number NR=2, cover
Caro simulation times are 10000 times, and modulation system uses MPSK, and sub-carrier number N=1024, the length of cyclic prefix is Ng=
128, it is multidiameter fading channel to choose channel circumstance, and frequency deviation is arranged to ε=10.35.By error rate of system performance and synchronization just
The true probability performance tradeoff overlying training sequence power allocation factor β optimal power allocation factor.When smaller and same in the bit error rate
When step correct probability is higher, it is determined that power allocation factor now is optimal value.In identical noise it can be seen from Fig. 6 and Fig. 7
Than under, as power allocation factor increases β, bit error rate performance reduces, but time synchronized correct probability strengthens.For algorithm
It can compromise, choosing power allocation factor herein will be basic herein as follow-up simulation analysis with value β=0.3 similar in theoretical value
Upper progress.
Fig. 8 is time synchronized correct probability performance simulation figure of the present invention, and main simulation parameter of the invention is set:Launch day
Line number NT=2, reception antenna number NR=2, it is 10000 times to cover Caro simulation times, and modulation system uses MPSK, subcarrier
Number N=1024, the length of cyclic prefix be Ng=128, and selection channel circumstance is multidiameter fading channel, frequency deviation be arranged to ε=
10.35, power allocation factor is arranged to β=0.3.As seen from the figure, in SNR=-19dB, this paper correct probabilities can reach
More than 90%.Compared with documents [1] and [2], set forth herein method for synchronizing time better performances.
Fig. 9 is offset estimation mean square error performance simulation figure of the present invention, and main simulation parameter of the invention is set:Launch day
Line number NT=2, reception antenna number NR=2, it is 10000 times to cover Caro simulation times, and modulation system uses MPSK, subcarrier
Number N=1024, the length of cyclic prefix be Ng=128, and selection channel circumstance is multidiameter fading channel, frequency deviation be arranged to ε=
10.35, power allocation factor is arranged to β=0.3.As can be seen from Figure, the frequency deviation region of this paper decimal frequency bias algorithm for estimating is | εf
|≤1 has relatively low mean square error, and overcoming conventional algorithm frequency deviation region is | εf| the defects of≤0.5.In identical signal to noise ratio bar
Under part, set forth herein frequency excursion algorithm compared with the algorithm performance of documents [2].With relatively low mean square error.
Claims (1)
- A kind of 1. space-time block code MIMO-OFDM system time frequency synchronization new methods under low signal-to-noise ratio, it is characterised in that:Step 1:Multiple orthogonal complement sequences Design:(1) a multiple complementary sequence set { A is designed1,B1,C1,D1, wherein A1=[1,1, j ,-j], B1=[1,1 ,-j, j],WithC2=B1,D2=-A1, whereinIt is A1Conjugation negate computing ,-A1Represent A1's Negative value, j represent imaginary symbols, j2=-1;(2) it is 4 using above-mentioned multiple complementary sequence set construction row vector, column vector is 8 matrix E4×8, whereinIn formula ()TRepresenting matrix transposition;(3) orthogonal matrix is utilizedIt is 16 to reconfigure row vector, and column vector is 16 new matrix E16×16, Its matrix(4) orthogonal matrix is utilizedIt is 32 to reconfigure row vector, and column vector is 32 new matrix E32×32, obtain matrix(5) above-mentioned (4) one step process is repeated, changes row vector size, longer orthogonal sequence can be obtained;Step 2:Using above-mentioned multiple orthogonal complement sequences Design step, then orthogonal matrix can be obtained Pass through matrixConstruct one group of sequence ai(n), wherein n span n ∈ [0, N/4-1], i span i ∈ [1, N/ 4], N represents sub-carrier number;Step 3:As i=1, the sequence a that length is N/4 is constructed1(n), by sequence a1(n) take conjugation to negate computing to obtain newly Sequence b1(n), have:<mrow> <msub> <mi>b</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <msubsup> <mi>a</mi> <mn>1</mn> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>n</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>0</mn> <mo>,</mo> <mi>N</mi> <mo>/</mo> <mn>4</mn> <mo>-</mo> <mn>1</mn> <mo>&rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>In formula:Represent sequence a1() sequence takes conjugate operation;By sequence a1And b (n)1(n) the sequence t that length is N/2 is formed1(n), have:<mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>n</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>0</mn> <mo>,</mo> <mi>N</mi> <mo>/</mo> <mn>4</mn> <mo>-</mo> <mn>1</mn> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>b</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>n</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mi>N</mi> <mo>/</mo> <mn>4</mn> <mo>,</mo> <mi>N</mi> <mo>/</mo> <mn>2</mn> <mo>-</mo> <mn>1</mn> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>Step 4:By sequence t1(n) it is repeated once the sequence c that construction length is N1(n), have:<mrow> <msub> <mi>c</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>n</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>0</mn> <mo>,</mo> <mi>N</mi> <mo>/</mo> <mn>2</mn> <mo>-</mo> <mn>1</mn> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mi>N</mi> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>n</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mi>N</mi> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>Step 5:The training sequence signal in a complete OFDM symbol that is added to is expressed as:<mrow> <msub> <mi>r</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <mi>P</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </msqrt> <msub> <mi>x</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msqrt> <mrow> <mi>P</mi> <mi>&beta;</mi> </mrow> </msqrt> <msub> <mi>c</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mi>N</mi> <mo>+</mo> <mi>N</mi> <mi>g</mi> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>In formula:P represents the general power of emitter, and β is power allocation factor, its span 0<β<1, it is defined asWhereinxi(n) it is the i-th frame transmission signal, x (n) is represented Transmission signal, ci(n) training sequence being superimposed for the training sequence of the i-th frame transmission signal superposition, c (n) for transmission signal, E (●) represents to do mean value computation to sequence in bracket;Step 6:The local training sequence sum received using receiving terminal obtains time synchronized, timing metric letter it is believed that manner of breathing closes Counting expression formula is:<mrow> <mi>M</mi> <mrow> <mo>(</mo> <mi>d</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mi>P</mi> <mrow> <mo>(</mo> <mi>d</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> <mrow> <mo>|</mo> <mi>R</mi> <mrow> <mo>(</mo> <mi>d</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>Wherein:<mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>d</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>T</mi> </msub> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>R</mi> </msub> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mn>1</mn> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>4</mn> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>&lsqb;</mo> <msubsup> <mi>r</mi> <mi>j</mi> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>d</mi> <mo>+</mo> <mfrac> <mi>N</mi> <mn>4</mn> </mfrac> <mo>+</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mi>m</mi> <mo>+</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mi>c</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mfrac> <mi>N</mi> <mn>4</mn> </mfrac> <mo>+</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mi>m</mi> <mo>+</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>r</mi> <mi>j</mi> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>d</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mi>c</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>m</mi> <mo>+</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow><mrow> <mi>R</mi> <mrow> <mo>(</mo> <mi>d</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>T</mi> </msub> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>R</mi> </msub> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>2</mn> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>|</mo> <msub> <mi>r</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>d</mi> <mo>+</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>In formula:NTFor the number of transmitting antenna, NRFor the number of reception antenna, Ng is the length of cyclic prefix,Represent to receive End data information rj() takes conjugate operation, and n is the number of sampled point, ci(n) training sequence on transmitting antenna is represented, d is whole Numerical value, it represents the relative sliding position of local training sequence and receiving terminal data message, and m represents cycle-index;Step 6:Because timing metric function R (d) is normalization effect in formula (5), then when M (d) reaches maximum, you can sentence Disconnected d this moment is OFDM symbol starting position, and synchronized algorithm is expressed as:<mrow> <mover> <mi>&tau;</mi> <mo>^</mo> </mover> <mo>=</mo> <munder> <mi>argmax</mi> <mi>d</mi> </munder> <mo>{</mo> <mo>|</mo> <mi>M</mi> <mrow> <mo>(</mo> <mi>d</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>In formula:Represent Timing Synchronization estimate;Step 7:Using receiving terminal data message autocorrelation, decimal frequency bias estimation is obtained, its mathematical formulae is expressed as:<mrow> <mi>F</mi> <mrow> <mo>(</mo> <mover> <mi>&tau;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>T</mi> </msub> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>R</mi> </msub> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>2</mn> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msubsup> <mi>r</mi> <mi>j</mi> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mover> <mi>&tau;</mi> <mo>^</mo> </mover> <mo>+</mo> <mi>n</mi> <mo>+</mo> <mi>N</mi> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <msub> <mi>r</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow><mrow> <msub> <mover> <mi>&epsiv;</mi> <mo>^</mo> </mover> <mi>f</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&pi;</mi> </mrow> </mfrac> <mi>a</mi> <mi>n</mi> <mi>g</mi> <mi>l</mi> <mi>e</mi> <mo>{</mo> <mfrac> <mrow> <mi>r</mi> <mi>e</mi> <mi>a</mi> <mi>l</mi> <mo>&lsqb;</mo> <mi>F</mi> <mrow> <mo>(</mo> <mover> <mi>&tau;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> <mrow> <mi>i</mi> <mi>m</mi> <mi>a</mi> <mi>g</mi> <mo>&lsqb;</mo> <mi>F</mi> <mrow> <mo>(</mo> <mover> <mi>&tau;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> </mfrac> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>In formula:Real () is representedReal part computing is taken, imag () is representedTake imaginary-part operation,Represent that decimal frequency bias is estimated Evaluation, its estimation range:Step 8:The integer frequency bias of the laggard line frequency of fractional frequency migration estimated is estimated, passes through local training sequence Phase is sought with receiving terminal data-signal related operation to obtain integer frequency bias estimate, expression formula:<mrow> <msub> <mover> <mi>&epsiv;</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mi>N</mi> <mrow> <mn>4</mn> <mi>&pi;</mi> </mrow> </mfrac> <mi>a</mi> <mi>n</mi> <mi>g</mi> <mi>l</mi> <mi>e</mi> <mo>&lsqb;</mo> <mi>Q</mi> <msub> <mrow> <mo>(</mo> <mi>d</mi> <mo>)</mo> </mrow> <mrow> <mi>d</mi> <mo>=</mo> <mover> <mi>&tau;</mi> <mo>^</mo> </mover> </mrow> </msub> <mo>&rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow><mrow> <mi>Q</mi> <mrow> <mo>(</mo> <mi>d</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>T</mi> </msub> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>R</mi> </msub> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mn>1</mn> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>2</mn> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msubsup> <mi>r</mi> <mi>j</mi> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>d</mi> <mo>+</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mi>m</mi> <mo>+</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mi>m</mi> <mo>+</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>r</mi> <mi>j</mi> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>d</mi> <mo>+</mo> <mi>n</mi> <mo>+</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mi>m</mi> <mo>+</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mi>m</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>In formula:Integer frequency bias estimation is represented, its estimation range is:
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