CN111131116A - Frequency offset estimation method and system - Google Patents

Frequency offset estimation method and system Download PDF

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Publication number
CN111131116A
CN111131116A CN201911271796.3A CN201911271796A CN111131116A CN 111131116 A CN111131116 A CN 111131116A CN 201911271796 A CN201911271796 A CN 201911271796A CN 111131116 A CN111131116 A CN 111131116A
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matrix
frequency offset
offset estimation
estimation
received signal
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戴勇
李伟
李程
贾平
李沛
蒋春霞
赵金城
吴细老
柳旭
刘金锁
张立武
丁晨阳
张笑源
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Nari Information and Communication Technology Co
Information and Telecommunication Branch of State Grid Jiangsu Electric Power Co Ltd
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Nari Information and Communication Technology Co
Information and Telecommunication Branch of State Grid Jiangsu Electric Power Co Ltd
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
    • H04L27/2657—Carrier synchronisation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
    • H04L27/2668—Details of algorithms
    • H04L27/2681—Details of algorithms characterised by constraints
    • H04L27/2684—Complexity

Abstract

The invention discloses a frequency offset estimation method, which comprises the steps of constructing an orthogonal frequency division system mathematical model; solving a covariance matrix of a received signal based on an orthogonal frequency division system mathematical model; calculating a propagation operator estimated value based on the covariance matrix; and estimating the frequency offset of the orthogonal frequency division system by using the propagation operator estimation value to obtain a frequency offset estimation value. A corresponding system is also disclosed. The invention adopts the propagation operator to carry out frequency offset estimation, does not need to carry out characteristic decomposition on the signal covariance and reduces the complexity under the condition of ensuring the accuracy.

Description

Frequency offset estimation method and system
Technical Field
The invention relates to a frequency offset estimation method and a frequency offset estimation system, and belongs to the technical field of communication.
Background
A4G TD-LTE network is built in a 1.8GHz frequency band of the power wireless private network, and OFDM is one of key technologies. The Orthogonal Frequency Division Multiplexing (OFDM) technology started in the nineties and was developed from a multi-carrier modulation technology, which is characterized in that sub-carriers are Orthogonal to each other. Compared with other systems, the OFDM system has many advantages, such as higher spectrum utilization rate, good resistance to frequency selective fading, and the like.
However, the OFDM system is sensitive to the Frequency Offset (CFO) generated by the channel, and the Carrier Frequency Offset is caused by the Frequency Offset between the transmitter and the receiver, which may destroy the orthogonality between subcarriers, resulting in a serious degradation of the system performance. Therefore, there is a need for an accurate estimation of frequency offset in an OFDM system, which provides a basis for compensation to ensure the performance of the system. The currently known frequency offset estimation methods cannot reduce complexity while guaranteeing accuracy.
Disclosure of Invention
The invention provides a frequency offset estimation method and a frequency offset estimation system, which solve the problems disclosed in the background technology.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a method of frequency offset estimation, comprising,
constructing an orthogonal frequency division system mathematical model;
solving a covariance matrix of a received signal based on an orthogonal frequency division system mathematical model;
calculating a propagation operator estimated value based on the covariance matrix;
and estimating the frequency offset of the orthogonal frequency division system by using the propagation operator estimation value to obtain a frequency offset estimation value.
The mathematical model of the orthogonal frequency division system is that,
Figure BDA0002314405470000021
wherein the content of the first and second substances,
Figure BDA0002314405470000022
the received signal under the noise-containing condition, W is the noise in the receiving process, S is the matrix of all data blocks transmitted by P channels, and A is the direction matrix with van der Monte property.
The covariance matrix is formulated as,
Figure BDA0002314405470000023
wherein the content of the first and second substances,
Figure BDA0002314405470000024
a covariance matrix for the received signal, (-)HIs a conjugate transpose of the original image,
Figure BDA0002314405470000025
the received signal is the received signal in the case of noise.
The propagation operator estimated value is calculated by the formula,
Figure BDA0002314405470000026
wherein the content of the first and second substances,
Figure BDA0002314405470000027
for propagation of operator PcEstimate of (c) (. 1)H、(·)+Respectively, conjugate transpose and pseudo inverse, the data covariance matrix is partitioned into
Figure BDA0002314405470000028
Representing the front P columns and the back P columns of the covariance matrix, respectively.
The frequency offset estimation formula is as follows,
Figure BDA0002314405470000029
Figure BDA00023144054700000210
Figure BDA00023144054700000211
where Δ f is frequency offset, N is the number of subcarriers of the OFDM system, P is the number of channels used by the system, tr (-) is the trace of the matrix, and the matrix
Figure BDA0002314405470000031
diag (. circle.) denotes a diagonal matrix, A1Is a full rank matrix, representing the first P rows, P, of a directional matrix A with van der Mond propertiesaAnd PbRepresentation matrix
Figure BDA0002314405470000032
The first N-1 row and the last N-1 row,
Figure BDA0002314405470000033
for propagation of operator PcEstimation of (I)PIs a P-dimensional identity matrix.
A frequency offset estimation system, comprising,
a modeling module: constructing an orthogonal frequency division system mathematical model;
a covariance module: solving a covariance matrix of a received signal based on an orthogonal frequency division system mathematical model;
a propagation operator module: calculating a propagation operator estimated value based on the covariance matrix;
an estimation module: and estimating the frequency offset of the orthogonal frequency division system by using the propagation operator estimation value to obtain a frequency offset estimation value.
The modeling module constructs an orthogonal frequency division system mathematical model of,
Figure BDA0002314405470000034
wherein the content of the first and second substances,
Figure BDA0002314405470000035
the received signal under the noise-containing condition, W is the noise in the receiving process, S is the matrix of all data blocks transmitted by P channels, and A is the direction matrix with van der Monte property.
The covariance matrix formula used by the covariance module is,
Figure BDA0002314405470000036
wherein the content of the first and second substances,
Figure BDA0002314405470000037
a covariance matrix for the received signal, (-)HIs a conjugate transpose of the original image,
Figure BDA0002314405470000038
the received signal is the received signal in the case of noise.
The propagation operator estimated value calculation formula adopted by the propagation operator module is as follows,
Figure BDA0002314405470000039
wherein the content of the first and second substances,
Figure BDA00023144054700000310
for propagation of operator PcEstimate of (c) (. 1)H、(·)+Respectively, conjugate transpose and pseudo inverse, the data covariance matrix is partitioned into
Figure BDA0002314405470000041
Representing the front P columns and the back P columns of the covariance matrix, respectively.
The estimation module uses the frequency offset estimation formula as,
Figure BDA0002314405470000042
Figure BDA0002314405470000043
Figure BDA0002314405470000044
where Δ f is frequency offset, N is the number of subcarriers of the OFDM system, P is the number of channels used by the system, tr (-) is the trace of the matrix, and the matrix
Figure BDA0002314405470000045
diag (. circle.) denotes a diagonal matrix, A1Is a full rank matrix, representing the first P rows, P, of a directional matrix A with van der Mond propertiesaAnd PbRepresentation matrix
Figure BDA0002314405470000046
The first N-1 row and the last N-1 row,
Figure BDA0002314405470000047
for propagation of operator PcEstimation of (I)PIs a P-dimensional identity matrix. .
The invention achieves the following beneficial effects: the invention adopts the propagation operator to carry out frequency offset estimation, does not need to carry out characteristic decomposition on the signal covariance and reduces the complexity under the condition of ensuring the accuracy.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a diagram illustrating CFO estimation performance for a system at a frequency offset of 0.4;
FIG. 3 is a comparison graph of CFO estimation performance of the method of the present invention, the ESPRIT algorithm and the MUSIC algorithm;
FIG. 4 is a comparison graph of CFO estimation performance of the method of the present invention under different sub-carriers;
FIG. 5 is a comparison of CFO estimation performance of the method of the present invention at different snapshot counts;
FIG. 6 is a comparison of CFO estimation performance for different channel numbers according to the method of the present invention;
fig. 7 is a comparison graph of CFO estimation performance for different CFO cases.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
As shown in fig. 1, a method for estimating a frequency offset includes the following steps:
step 1, an Orthogonal Frequency Division (OFDM) system mathematical model is constructed.
An OFDM system is defined having N subcarriers, where P channels are used for data transmission and the remaining N-P channels are virtual carriers. And adding a cyclic prefix with the length of L to eliminate the inter-channel interference caused by the multipath effect, wherein L is larger than the maximum time delay of the signal.
After inserting the cyclic prefix, the signal is transmitted through a multi-channel fading channel,
Figure BDA0002314405470000051
which is the frequency response of the different channel, after removing the cyclic prefix, the received signal can be represented as,
x(k)＝EFPdiag(h)s(k)ej2πΔf(k-1)(N+L)
wherein, E ═ diag (1, E)j2πΔf/N,...,ej2πΔf(N-1)/N)∈CN×NIs the frequency offset matrix in the system, C is the complex set, Δ F is the frequency offset (CFO), FP∈CN×PIs the first P column of the inverse discrete fourier transform matrix, H ═ H (1), H (2),.., H (P)]TFor the frequency vector matrix of the receiving antenna, s (k) ═ s1(k),s2(k),...,sP(k)]TThe kth data block transmitted for the P lanes.
The acceptance signal formula may be changed to,
X＝Adiag(h)BT
wherein, B ═ diag (1, e)j2πΔf(N+L),...,ej2πΔf(K-1)(N+L))S∈CK×PC is a complex set, S ═ S (1), S (2),. S (k)]T∈CK×PA matrix of all data blocks (i.e., K data blocks) transmitted for P channels; the matrix a has a van der mond character,
Figure BDA0002314405470000061
the received signal in the noisy case may be expressed as,
Figure BDA0002314405470000062
where W is the noise in the reception process, S ═ diag (h) BTAnd diag (·) denotes a diagonal matrix (·)TIs transposed.
And 2, solving the covariance matrix of the received signal based on the orthogonal frequency division system mathematical model.
According to
Figure BDA0002314405470000063
The covariance matrix of the received signal can be calculated as
Figure BDA0002314405470000064
Wherein the content of the first and second substances,
Figure BDA0002314405470000065
a covariance matrix for the received signal, (-)HIs transposed for conjugation。
And 3, calculating a propagation operator estimated value based on the covariance matrix.
By X ═ Adiag (h) BTThe direction matrix a is known as a van der mond matrix, and a propagation operator algorithm based on rotation invariance can be used for CFO estimation.
The direction matrix a may be partitioned into,
Figure BDA0002314405470000066
wherein A is1∈CP×PFor a full rank matrix, the first P rows of matrix A are represented, A2∈C(N-P)×PIs the last N-P rows of the matrix A; there is a linear factor between the two matrices, expressed as,
A2＝PcA1
wherein, PcIs a propagation operator;
partitioning the covariance matrix into blocks
Figure BDA0002314405470000071
Wherein
Figure BDA0002314405470000072
Respectively representing the front P column and the back P column of the covariance matrix; wherein, CN×P、CN×(N-P)Respectively representing a complex matrix of N P and N (N-P).
P can be obtained by the following formulacIs estimated as (a) being,
Figure BDA0002314405470000073
wherein the content of the first and second substances,
Figure BDA0002314405470000074
for propagation of operator PcEstimate of (c) (. 1)H、(·)+Respectively, conjugate transpose and pseudo inverse.
And 4, estimating the frequency offset of the orthogonal frequency division system by using the propagation operator estimation value to obtain a frequency offset estimation value.
Definition matrix P' is belonged to CN×PIn order to realize the purpose,
Figure BDA0002314405470000075
wherein, IP∈CP×PIs a P-dimensional identity matrix, PcIs a propagation operator;
from the propagation operator estimated value obtained, an estimated value of the matrix P' can be obtained
Figure BDA0002314405470000076
The expression is as follows,
Figure BDA0002314405470000077
A1∈CP×Pfor a full rank matrix, the first P rows of matrix A are represented, A2∈C(N-P)×PFor the last N-P rows of matrix A, according to the direction matrix A and the matrix
Figure BDA0002314405470000078
The expression of (a) is that,
Figure BDA0002314405470000079
respectively with Pa∈C(N-1)×PAnd Pb∈C(N-1)×PRepresentation matrix
Figure BDA00023144054700000710
The first N-1 line and the last N-1 line, N is the number of the sub-carriers of the orthogonal frequency division system, and A is useda∈C(N-1)×PAnd Ab∈C(N-1)×PThe first N-1 line and the last N-1 line of A, then according to the above formula,
Figure BDA0002314405470000081
wherein the content of the first and second substances,
Figure BDA0002314405470000082
then the following relationship exists for the purpose of,
Figure BDA0002314405470000083
wherein, (.)+、(·)-1Are pseudo-inversion and inversion, respectively
Definition of
Figure BDA0002314405470000084
Due to ΨrAnd phirBy using the same eigenvalues, by pair ΨrThe characteristic decomposition can obtain phirAnd then, it is possible to obtain,
Figure BDA0002314405470000085
where Δ f is the frequency offset, tr (-) is the trace of the matrix, and P is the number of channels used by the system.
According to the fourth step, a CFO estimation value can be obtained, in order to judge the performance of the estimation method, the performance of the method is analyzed from two aspects, firstly, noise error analysis is carried out, and from the theoretical angle, the performance of the method is judged by utilizing a strict mathematical derivation process; and then, simulating to visually judge the performance of the method. The error analysis mathematical derivation process is as follows:
under the influence of noise, the signal covariance matrix is estimated as,
Figure BDA0002314405470000086
wherein R is a true value;
Figure BDA0002314405470000087
is an error matrix.
Then is provided with
Figure BDA0002314405470000088
In the formula (I), the compound is shown in the specification,
Figure BDA0002314405470000089
and
Figure BDA00023144054700000810
errors corresponding to G and H, respectively.
By
Figure BDA0002314405470000091
Evaluating an estimate of a propagation operator
Figure BDA0002314405470000092
Is composed of
Figure BDA0002314405470000093
First order expansion
Figure BDA0002314405470000094
In the formula (I), the compound is shown in the specification,
Figure BDA0002314405470000095
the data covariance matrix is partitioned into
Figure BDA0002314405470000096
Wherein
Figure BDA0002314405470000097
Representing the first P columns and the last N-P columns of the covariance matrix, respectively.
The error of matrix P' is then
Figure BDA0002314405470000098
In the formula (DEG)HRepresenting the conjugate transpose of the matrix.
According to the expression of the direction matrix A
Figure BDA0002314405470000099
Wherein P1 and PNRespectively the first and last row of the matrix P',
Figure BDA00023144054700000910
and
Figure BDA00023144054700000911
are respectively as
Figure BDA00023144054700000912
First and last row of (A), PaAnd PbThe first N-1 row and the last N-1 row of the matrix P' are represented, the same way
Figure BDA00023144054700000913
And
Figure BDA00023144054700000914
respectively represent
Figure BDA00023144054700000915
The first N-1 line and the last N-1 line. According to
Figure BDA00023144054700000916
To a first order approximation of
Figure BDA00023144054700000917
In the formula (I), the compound is shown in the specification,
Figure BDA00023144054700000918
has the m-th characteristic value of
Figure BDA00023144054700000919
Wherein
Figure BDA00023144054700000920
emIs a unit vector, the mth element is 1, and the rest are 0. The mean square error of the CFO estimate based on a first order Taylor series expansion is
Figure BDA00023144054700000921
Comparing the method with the existing methods, the method comprises the following specific steps:
the complexity of each algorithm is shown in table 1, where N, P is the number of subcarriers and the number of channels used by the system, K1 represents the number of fast beats, ngRepresenting the search times of the MUSIC algorithm;
TABLE 1 Algorithm complexity calculation
Algorithm Complexity of
PM Algorithm (i.e. the invention) O(K1N2+PN(P+N)+3P2(P-1)+P3)
ESPRIT algorithm O(K1N2+N3+3P2(N-1)+P3)
MUSIC algorithm [5 ]] O(K1N2+ng(N3+3N2(N-P)+N(N-P)2))
The PM algorithm does not need to carry out characteristic decomposition on the signal covariance matrix, so the complexity is lower than that of the ESPRIT algorithm, while the MUSIC algorithm needs to carry out spectral peak search ngThe secondary event has higher computational complexity. In thatUnder the parameters of the simulation, the PM algorithm has the lowest computational complexity.
Fig. 2 shows the CFO estimation case when the frequency offset Δ f is 0.4, the number of subcarriers is 32, the number of channels used for transmission is 20, the number of cyclic prefixes L is 8, the number of snapshots K1 is 200, and the SNR is 30dB, and it can be seen that the algorithm herein can accurately estimate the CFO in the OFDM system.
Fig. 3 shows a comparison of the performance of the PM, ESPRIT and MUSIC algorithms herein, where N is 32, P is 20, L is 8, and K1 is 100, with 500 simulations. It can be seen that the MUSIC algorithm performs poorly at low signal-to-noise ratios, while the PM algorithm and the ESPRIT algorithm perform better at low signal-to-noise ratios. The performance of the PM algorithm approaches the ESPRIT algorithm under high signal-to-noise ratio conditions. Of the three algorithms, the complexity of the PM algorithm is the lowest.
FIGS. 4-6 show the performance of the PM algorithm under different parameters. Fig. 4 and 5 show the estimation performance of the PM algorithm under different subcarrier numbers N and different fast beat numbers K1, respectively, and the estimation performance of the CFO improves as K1 and N increase; fig. 6 shows the estimated performance of the algorithm at different channel numbers P, and it can be seen that the performance of the CFO algorithm decreases as P increases. Because as the number of channels increases, the interference between the channels increases, resulting in a deterioration of the CFO estimation performance.
Fig. 7 shows CFO estimation performance for different CFO cases. The simulation parameters are N32, P20, K1 200 and the CFO range is [ - ω, ω ], where ω 2 pi/N is the normalized subcarrier space, it can be seen that the PM algorithm has very close CFO estimation performance for different CFOs.
The propagation operator is adopted for frequency offset estimation, the signal covariance is not required to be subjected to characteristic decomposition, the complexity is effectively reduced, and meanwhile, the method has estimation performance, namely accuracy, similar to an ESPRIT algorithm and an MUSIC algorithm under the condition of ensuring lower complexity.
A frequency offset estimation system, comprising:
a modeling module: and constructing an orthogonal frequency division system mathematical model.
The modeling module constructs an orthogonal frequency division system mathematical model of,
Figure BDA0002314405470000111
wherein the content of the first and second substances,
Figure BDA0002314405470000112
the received signal under the noise-containing condition, W is the noise in the receiving process, S is the matrix of all data blocks transmitted by P channels, and A is the direction matrix with van der Monte property.
A covariance module: and solving the covariance matrix of the received signal based on the orthogonal frequency division system mathematical model.
The covariance matrix formula used by the covariance module is,
Figure BDA0002314405470000113
wherein the content of the first and second substances,
Figure BDA0002314405470000114
a covariance matrix for the received signal, (-)HIs a conjugate transpose of the original image,
Figure BDA0002314405470000115
the received signal is the received signal in the case of noise.
A propagation operator module: based on the covariance matrix, a propagation operator estimated value is calculated.
The propagation operator estimated value calculation formula adopted by the propagation operator module is as follows,
Figure BDA0002314405470000116
wherein the content of the first and second substances,
Figure BDA0002314405470000117
for propagation of operator PcEstimate of (c) (. 1)H、(·)+Respectively, conjugate transpose and pseudo inverse, the data covariance matrix is partitioned into
Figure BDA0002314405470000121
Representing the front P columns and the back P columns of the covariance matrix, respectively.
An estimation module: and estimating the frequency offset of the orthogonal frequency division system by using the propagation operator estimation value to obtain a frequency offset estimation value.
The estimation module uses the frequency offset estimation formula as,
Figure BDA0002314405470000122
Figure BDA0002314405470000123
Figure BDA0002314405470000124
where Δ f is frequency offset, N is the number of subcarriers of the OFDM system, P is the number of channels used by the system, tr (-) is the trace of the matrix, and the matrix
Figure BDA0002314405470000125
diag (. circle.) denotes a diagonal matrix, A1Is a full rank matrix, representing the first P rows, P, of a directional matrix A with van der Mond propertiesaAnd PbRepresentation matrix
Figure BDA0002314405470000126
The first N-1 row and the last N-1 row,
Figure BDA0002314405470000127
for propagation of operator PcEstimation of (I)PIs a P-dimensional identity matrix.
A computer readable storage medium storing one or more programs, the one or more programs comprising instructions, which when executed by a computing device, cause the computing device to perform a method of frequency offset estimation.
A computing device comprising one or more processors, memory, and one or more programs stored in the memory and configured to be executed by the one or more processors, the one or more programs including instructions for performing a frequency offset estimation method.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The present invention is not limited to the above embodiments, and any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention are included in the scope of the claims of the present invention which are filed as the application.

Claims (10)

1. A method of frequency offset estimation, characterized by: comprises the steps of (a) preparing a mixture of a plurality of raw materials,
constructing an orthogonal frequency division system mathematical model;
solving a covariance matrix of a received signal based on an orthogonal frequency division system mathematical model;
calculating a propagation operator estimated value based on the covariance matrix;
and estimating the frequency offset of the orthogonal frequency division system by using the propagation operator estimation value to obtain a frequency offset estimation value.
2. A method of frequency offset estimation as claimed in claim 1, characterized by: the mathematical model of the orthogonal frequency division system is that,
Figure FDA0002314405460000011
wherein the content of the first and second substances,
Figure FDA0002314405460000012
the received signal under the noise-containing condition, W is the noise in the receiving process, S is the matrix of all data blocks transmitted by P channels, and A is the direction matrix with van der Monte property.
3. A method of frequency offset estimation as claimed in claim 1, characterized by: the covariance matrix is formulated as,
Figure FDA0002314405460000013
wherein the content of the first and second substances,
Figure FDA0002314405460000014
a covariance matrix for the received signal, (-)HIs a conjugate transpose of the original image,
Figure FDA0002314405460000015
the received signal is the received signal in the case of noise.
4. A method of frequency offset estimation as claimed in claim 1, characterized by: the propagation operator estimated value is calculated by the formula,
Figure FDA0002314405460000016
wherein the content of the first and second substances,
Figure FDA0002314405460000017
for propagation of operator PcEstimate of (c) (. 1)H、(·)+Respectively, conjugate transpose and pseudo inverse, the data covariance matrix is partitioned into
Figure FDA0002314405460000018
Representing the front P columns and the back P columns of the covariance matrix, respectively.
5. A method of frequency offset estimation as claimed in claim 1, characterized by: the frequency offset estimation formula is as follows,
Figure FDA0002314405460000021
Figure FDA0002314405460000022
Figure FDA0002314405460000023
where Δ f is frequency offset, N is the number of subcarriers of the OFDM system, P is the number of channels used by the system, tr (-) is the trace of the matrix, and the matrix
Figure FDA0002314405460000024
diag (. circle.) denotes a diagonal matrix, A1Is a full rank matrix, representing the first P rows, P, of a directional matrix A with van der Mond propertiesaAnd PbRepresentation matrix
Figure FDA0002314405460000025
The first N-1 row and the last N-1 row,
Figure FDA0002314405460000026
for propagation of operator PcEstimation of (I)PIs a P-dimensional identity matrix.
6. A frequency offset estimation system, characterized by: comprises the steps of (a) preparing a mixture of a plurality of raw materials,
a modeling module: constructing an orthogonal frequency division system mathematical model;
a covariance module: solving a covariance matrix of a received signal based on an orthogonal frequency division system mathematical model;
a propagation operator module: calculating a propagation operator estimated value based on the covariance matrix;
an estimation module: and estimating the frequency offset of the orthogonal frequency division system by using the propagation operator estimation value to obtain a frequency offset estimation value.
7. A frequency offset estimation system according to claim 6, characterized in that: the modeling module constructs an orthogonal frequency division system mathematical model of,
Figure FDA0002314405460000031
wherein the content of the first and second substances,
Figure FDA0002314405460000032
the received signal under the noise-containing condition, W is the noise in the receiving process, S is the matrix of all data blocks transmitted by P channels, and A is the direction matrix with van der Monte property.
8. A frequency offset estimation system according to claim 6, characterized in that: the covariance matrix formula used by the covariance module is,
Figure FDA0002314405460000033
wherein the content of the first and second substances,
Figure FDA0002314405460000034
a covariance matrix for the received signal, (-)HIs a conjugate transpose of the original image,
Figure FDA0002314405460000035
the received signal is the received signal in the case of noise.
9. A frequency offset estimation system according to claim 6, characterized in that: the propagation operator estimated value calculation formula adopted by the propagation operator module is as follows,
Figure FDA0002314405460000036
wherein the content of the first and second substances,
Figure FDA0002314405460000037
for propagation of operator PcEstimate of (c) (. 1)H、(·)+Respectively, conjugate transpose and pseudo inverse, the data covariance matrix is partitioned into
Figure FDA0002314405460000038
Are respectively provided withRepresenting the front P columns and the back P columns of the covariance matrix.
10. A frequency offset estimation system according to claim 6, characterized in that: the estimation module uses the frequency offset estimation formula as,
Figure FDA0002314405460000039
Figure FDA00023144054600000310
Figure FDA0002314405460000041
where Δ f is frequency offset, N is the number of subcarriers of the OFDM system, P is the number of channels used by the system, tr (-) is the trace of the matrix, and the matrix
Figure FDA0002314405460000042
diag (. circle.) denotes a diagonal matrix, A1Is a full rank matrix, representing the first P rows, P, of a directional matrix A with van der Mond propertiesaAnd PbRepresentation matrix
Figure FDA0002314405460000043
The first N-1 row and the last N-1 row,
Figure FDA0002314405460000044
for propagation of operator PcEstimation of (I)PIs a P-dimensional identity matrix.
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