CN111464477A - Low-complexity carrier synchronization method in OFDM power wireless private network - Google Patents

Low-complexity carrier synchronization method in OFDM power wireless private network Download PDF

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CN111464477A
CN111464477A CN202010189901.5A CN202010189901A CN111464477A CN 111464477 A CN111464477 A CN 111464477A CN 202010189901 A CN202010189901 A CN 202010189901A CN 111464477 A CN111464477 A CN 111464477A
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matrix
cfo
ofdm
private network
antenna
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丁晨阳
胡阳
张笑源
蒯本链
蒋苏明
罗先南
张明
邵刚
吴文勤
殷磊
张曦
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State Grid Corp of China SGCC
Nari Information and Communication Technology Co
NangAn Power Supply Co of State Grid Chongqing Electric Power Co Ltd
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State Grid Corp of China SGCC
Nari Information and Communication Technology Co
NangAn Power Supply Co of State Grid Chongqing 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
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
    • 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
    • H04L27/2659—Coarse or integer frequency offset determination and synchronisation

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Abstract

The invention discloses a low-complexity carrier synchronization method in an OFDM electric wireless private network, which is characterized by comprising the following steps of: 1) arranging a multi-antenna OFDM system, and reconstructing a received signal of the OFDM system; 2) and obtaining the CFO of the OFDM system by using a multi-shift invariance PM algorithm. The present invention reconstructs the received signal, utilizing shift invariance to estimate the Carrier Frequency Offset (CFO). The method provided by the invention can well realize CFO estimation without knowing constant modulus and statistical characteristics, and has better CFO estimation performance compared with the traditional PM algorithm and ESPRIT algorithm. The method provided by the invention does not need to carry out eigenvalue decomposition on the cross-correlation matrix and also does not need to carry out singular value decomposition on the received data, so the algorithm complexity is lower.

Description

Low-complexity carrier synchronization method in OFDM power wireless private network
Technical Field
The invention relates to a low-complexity carrier synchronization method in an OFDM electric power wireless private network system, belonging to the blind CFO estimation problem in the OFDM electric power wireless private network.
Background
The power wireless private network builds a 4G TD-L TE network in a 1.8GHz Frequency band, Orthogonal Frequency Division Multiplexing (OFDM) is one of the key technologies, an OFDM system is sensitive to Carrier Frequency Offset (CFO) generated by a channel, and the CFO causes serious reduction of system performance.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the blind CFO estimation problem in the OFDM power wireless private network is solved, and the estimation performance is improved.
In order to solve the problems proposed above, the present invention adopts the following scheme:
a low-complexity carrier synchronization method in an OFDM power wireless private network is characterized by comprising the following steps:
1) arranging a multi-antenna OFDM system, and reconstructing a received signal of the OFDM system;
2) and obtaining the CFO of the OFDM system by using a multi-shift invariance PM algorithm.
The invention achieves the following beneficial effects:
the invention provides a Multi-shift invariance propagation operator method (MI-PM) aiming at the problem of Carrier Frequency Offset (CFO) estimation of an OFDM power wireless private network system. The method provided by the invention can well realize CFO estimation without knowing constant modulus and statistical characteristics, and has better CFO estimation performance compared with the traditional PM algorithm and ESPRIT algorithm. The method provided by the invention does not need to carry out eigenvalue decomposition on the cross-correlation matrix and also does not need to carry out singular value decomposition on the received data, so the algorithm complexity is lower.
Drawings
FIG. 1 is a plot of CFO estimation performance versus conventional PM and ESPRIT algorithms for different signal-to-noise ratios;
FIG. 2 is a comparison graph of CFO estimation performance under different signal block numbers according to the method of the present invention under different SNR conditions;
FIG. 3 is a comparison graph of CFO estimation performance under different antenna numbers according to the method of the present invention under different SNR conditions;
FIG. 4 is a comparison graph of CFO estimation performance under different channel numbers according to the method of the present invention under different SNR conditions;
fig. 5 is a comparison graph of CFO estimation performance under different numbers of subcarriers by the method of the present invention under different snr conditions.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
The symbols represent: used in the invention (·)TRepresentation matrix transposition, (.)HRepresenting the conjugate transpose of the matrix (.)*Representation matrix conjugation, (.)+Representing Mole-Penrose inverse (pseudo-inverse), | · |. Y phosphorFDenotes the norm, diag (v) denotes the diagonal matrix made up of the elements in v.
The invention discloses a low-complexity carrier synchronization method in an OFDM power wireless private network, which comprises the following steps:
1) the method for reconstructing the OFDM system comprises the following steps of arranging a multi-antenna OFDM system and reconstructing a received signal of the OFDM system:
11) the OFDM uplink system comprises a receiver, wherein the receiver is provided with 1 transmitting antenna and I receiving antennas, the number of subcarriers is N, and the cyclic prefix uses L sampling intervals, so that the number of samples of each OFDM system is N + L which is larger than the maximum propagation delay;
12) the transmission array defining the kth block is s (k) ═ s1(k),s2(k),K,sP(k)]TWherein s isp(k) For the kth data block transmitted on the P subcarrier, P parallel data are modulated on P subcarriers, that is, the number of channels of the system is P, P is less than N, the remaining N-P subcarriers are virtual carriers, and the multicarrier modulation signal is filled by a Cyclic Prefix (CP) before being transmitted into a multipath fading channel;
removing the cyclic prefix CP, the output signal of the k block of the ith antenna is
xi(k)＝EFPdiag(hi)s(k)ej2πΔf(k-1)(N+L)(1)
Wherein j represents an imaginary number symbol,
Figure RE-GDA0002521888440000031
represents a set of complex numbers, Δ f is CFO; e is a natural index;
intermediate variables
Figure RE-GDA0002521888440000032
Is a CFO matrix, an intermediate variable
Figure RE-GDA0002521888440000033
Figure RE-GDA0002521888440000034
Representing the first P columns of the inverse Fourier transform, the frequency domain channel vector for the ith receive antenna is hi＝[Hi(1),Hi(2),K,Hi(P)]T(ii) a The frequency response defined as the nth subcarrier is Hi(n) corresponding to the ith antenna, the multi-antenna frequency domain channel matrix H is:
Figure RE-GDA0002521888440000035
13) assuming that K block channel parameters are constants, defining a source matrix
Figure RE-GDA0002521888440000036
Figure RE-GDA0002521888440000037
Xi＝[xi(1)xi(2)Lxi(K)]Is defined as
Xi＝Adiag(hi)BT＝ADi(H)BT,i＝1,2,...,I (3)
Where the matrix B ═ diag {1, e ═ dj2πΔf(N+L),K,ej2πΔf(K-1)(N+L)}，Di() Represents the ith row of the extraction matrixConstructing a diagonal matrix; a ═ EFP∈CN×PIs a Vandermonde matrix, a data model of the received signal taking into account the presence of noise
Figure RE-GDA0002521888440000038
Is written as
Figure RE-GDA0002521888440000041
Wherein WiIs the noise received by the ith array element;
the signal in equation (3) can also be expressed as a trilinear model
Figure RE-GDA0002521888440000042
Wherein xn,k,iRepresenting X in the matrix equation (3)iThe (n, k) th element of (a)n,pRepresents the (n, p) th element of the matrix A, bk,pRepresents the (k, p) th element, h, of the matrix Bi,pRepresents the (i, p) th element of the frequency domain channel matrix H, and the rest is the same; n, K, I are the number of subcarriers, the number of blocks of the source and the number of antennas, respectively;
output signal X of ith antennai＝ADi(H)BTI may be regarded as a slice of the trilinear model along the antenna direction, and a reconstructed matrix Y is obtained by matrix reconstruction according to the symmetry of the trilinear modeln：
Yn＝HDn(A)BT,n＝1,2,...,N (6)
Wherein Y isnN1, 2.., N, which may be considered as the reconstruction of equation (3);
14) receiving a signal
Figure RE-GDA0002521888440000043
Has a covariance matrix of
Figure RE-GDA0002521888440000044
Wherein L is the number of fast beats.
2) And obtaining the CFO of the OFDM system by using a multi-shift invariance PM algorithm.
The multi-shift invariance PM algorithm provided by the invention is a popularization of the PM algorithm, is used for DOA estimation, and utilizes the MI-PM algorithm to estimate CFO.
From equation (6), the following matrix is constructed
Figure RE-GDA0002521888440000045
Wherein
Figure RE-GDA0002521888440000046
Is a rotation matrix; using the MI-PM algorithm to estimate CFO, Y can be expressed as
Y＝AEBT(9)
Wherein
Figure RE-GDA0002521888440000051
Matrix array
Figure RE-GDA0002521888440000052
Wherein, I, N and P are the number of antennas, the number of subcarriers and the number of channels used by the system respectively, and the matrix AEThe block-shaped materials are divided into blocks,
Figure RE-GDA0002521888440000053
represents a complex set of a plurality of
Figure RE-GDA0002521888440000054
Wherein the matrix one
Figure RE-GDA0002521888440000055
Is a full rank matrix, matrix two
Figure RE-GDA0002521888440000056
Thus in matrix one A1And the matrix two A2There is one linear transformation operator to satisfy
A2＝PcA1(12)
Order to
Figure RE-GDA0002521888440000057
Wherein P iscIs a matrix of propagation operators, IPIs an identity matrix of P × P, and the propagation operator P is obtained by minimizing the cost function in the presence of noisecIs estimated value of
Figure RE-GDA0002521888440000058
Figure RE-GDA0002521888440000059
Wherein Jcsm() To relate to
Figure RE-GDA00025218884400000510
Of a convex function of the second order, matrix
Figure RE-GDA00025218884400000511
Is a received signal
Figure RE-GDA00025218884400000512
First P columns of, matrix
Figure RE-GDA00025218884400000513
Is a received signal
Figure RE-GDA00025218884400000514
The remaining columns;
by the formula (14), the value is estimated
Figure RE-GDA00025218884400000515
Is estimated as
Figure RE-GDA00025218884400000516
From the equations (12) and (13), the following relational expression is obtained
Figure RE-GDA00025218884400000517
Thus, it is possible to provide
Figure RE-GDA0002521888440000061
According to equation (16), a relationship matrix P is defined1And relation matrix bip2Is composed of
Figure RE-GDA0002521888440000062
Thus, the relationship matrix P1And relation matrix bip2There exists the following relation
Figure RE-GDA0002521888440000063
Defining the matrix Ψ:
Figure RE-GDA0002521888440000064
so equation (19) is expressed as
P2＝P1Ψ(21)
Then
Figure RE-GDA0002521888440000065
Wherein the matrix Ψ and the rotation matrix Φ have the same Eigenvalue, and the matrix Ψ is subjected to Eigenvalue Decomposition (EVD) to obtain the Eigenvalue Decomposition
Figure RE-GDA0002521888440000066
Where tr (.) is defined as the sum of the main diagonal elements of the matrix,
Figure RE-GDA0002521888440000067
an estimate of the rotation matrix Φ, an estimate of the CFO
Figure RE-GDA0002521888440000068
Estimated by equation (23).
The carrier synchronization method of the invention is analyzed and simulated, and the analysis process comprises the following steps:
(1) and (3) complexity analysis: the multi-shift invariance algorithm (MI-PM algorithm) does not need to carry out characteristic decomposition on the cross-correlation matrix and singular value decomposition on the received data, so the complexity is low, and the main calculation complexity of the MI-PM algorithm is O (KI)2N2+P3) Where O (-) represents the computational complexity.
(2) And (3) error analysis: i.e. the estimation error is analyzed. Suppose that
Figure RE-GDA0002521888440000069
Wherein
Figure RE-GDA00025218884400000610
Is an error estimation matrix, then
Figure RE-GDA0002521888440000071
By pairs
Figure RE-GDA0002521888440000072
To obtain an estimate of the matrix Ψ
Figure RE-GDA0002521888440000073
Figure RE-GDA0002521888440000074
Figure RE-GDA0002521888440000075
Has a k-th characteristic value of
Figure RE-GDA0002521888440000076
β thereinpThe eigenvalues of the matrix Ψ are represented,
Figure RE-GDA0002521888440000077
epis a unit vector whose p-th element is 1 and the remaining elements are 0. Using a first order approximation, the variance of the CFO estimation error is
Figure RE-GDA0002521888440000078
Wherein, E2]E { } denotes the desired value, φ p2 pi Δ f, Re { } denotes the real part of the complex number.
The method reconstructs the received signal and utilizes the multiple shift invariance to estimate the CFO, so that the method has higher CFO estimation performance than the traditional PM algorithm and ESPRIT algorithm.
And (3) simulation results:
the CFO estimation performance is evaluated by 1000 Monte Carlo simulations, and a noisy signal model is expressed as
Figure RE-GDA0002521888440000079
Wherein WnTo receive noise, the Signal-to-noise ratio (SNR) can be defined as
Figure RE-GDA00025218884400000710
In all simulations, let us say that the OFDM system in the simulation has N-32 subcarriers, P-20, and the sampling interval of CP is 8, and the channel model is Lm＝4(Lm< L), where Δ ω ═ 2 π Δ f is taken to be 0.4 ω, where ω ═ 2 π/N is the subcarrier spacing, dB represents one unit of the magnitude of the signal-to-noise ratio.
The performance of the CFO estimate was quantitatively evaluated using Mean Square Error (MSE), defined as follows
Figure RE-GDA00025218884400000711
Wherein
Figure RE-GDA00025218884400000712
Is the CFO estimate for the mth Monte Carlo simulation, M is the Monte Carlo simulation times, Δ f is the exact value of CFO.
Fig. 1 is a comparison graph of CFO estimation performance of the method of the present invention and the conventional PM algorithm and ESPRIT algorithm under different snr conditions, where the simulation parameters are total carrier number N of 32, antenna number I of 4, signal block number K of 100 and channel number P of 20 for transmitting data.
It is apparent from fig. 1 that the CFO estimation performance of the MI-PM algorithm is superior to the conventional PM algorithm and the ESPRIT algorithm.
Fig. 2 is a comparison graph of CFO estimation performance under different signal-to-noise ratios, where N is 36, P is 20, and I is 7.
It can be seen from fig. 2 that the CFO estimation performance of the MI-PM algorithm is significantly improved as the number of signal blocks K increases.
Fig. 3 is a comparison graph of CFO estimation performance under different antenna numbers and under different snr conditions, where N is 36, P is 20, and K is 100.
As is apparent from FIG. 3, the CFO estimation performance of the MI-PM algorithm improves significantly as I increases.
Fig. 4 is a comparison graph of CFO estimation performance under different channel numbers under different snr conditions, where N is 32, I is 4, and K is 100.
As is apparent from fig. 4, the CFO estimation performance of the MI-PM algorithm significantly degrades as P increases.
Fig. 5 is a comparison graph of CFO estimation performance under different carrier numbers under different snr conditions, where the parameter is set to K-100, I-4, and P-5N/8.
It is apparent from fig. 5 that the CFO estimation performance of the MI-PM algorithm significantly degrades as N increases.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.

Claims (6)

1. A low-complexity carrier synchronization method in an OFDM power wireless private network is characterized by comprising the following steps:
1) arranging a multi-antenna OFDM system, and reconstructing a received signal of the OFDM system;
2) and obtaining the CFO of the OFDM system by using a multi-shift invariance PM algorithm.
2. The low complexity carrier synchronization method in the OFDM power wireless private network according to claim 1, wherein: in step 1), the method comprises the following steps:
11) the OFDM uplink system comprises a receiver, wherein the receiver is provided with 1 transmitting antenna and I receiving antennas, the number of subcarriers is N, and the cyclic prefix uses L sampling intervals, so that the number of samples of each OFDM system is N + L which is larger than the maximum propagation delay;
12) the transmission array defining the kth block is s (k) ═ s1(k),s2(k),K,sP(k)]TWherein s isp(k) For the kth data block transmitted on the P subcarrier, P parallel data are modulated on P subcarriers, namely the number of channels of the system is P, P is less than N, the remaining N-P subcarriers are virtual carriers, and the multicarrier modulation signal is filled by a cyclic prefix before being transmitted into a multipath fading channel;
removing the cyclic prefix CP, the output signal of the k block of the ith antenna is
xi(k)＝EFPdiag(hi)s(k)ej2πΔf(k-1)(N+L)(1)
Wherein j represents an imaginary number symbol,
Figure RE-FDA0002521888430000011
represents a set of complex numbers, Δ f is CFO; e is a natural index;
intermediate variables
Figure RE-FDA0002521888430000012
Is a CFO matrix, an intermediate variable
Figure RE-FDA0002521888430000013
Figure RE-FDA0002521888430000014
Representing the first P columns of the inverse Fourier transform, the frequency domain channel vector for the ith receive antenna is hi＝[Hi(1),Hi(2),K,Hi(P)]T(ii) a The frequency response defined as the nth subcarrier is Hi(n) corresponding to the ith antenna, the multi-antenna frequency domain channel matrix H is:
Figure RE-FDA0002521888430000015
13) assuming that K block channel parameters are constants, defining a source matrix
Figure RE-FDA0002521888430000016
Figure RE-FDA0002521888430000017
Xi＝[xi(1) xi(2)…xi(K)]Is defined as
Xi＝Adiag(hi)BT＝ADi(H)BT,i＝1,2,...,I (3)
Where the matrix B ═ diag {1, e ═ dj2πΔf(N+L),K,ej2πΔf(K-1)(N+L)}，Di() Representing the ith row of the extraction matrix and constructing a diagonal matrix by using the ith row; a ═ EFP∈CN×PIs a Vandermonde matrix, a data model of the received signal taking into account the presence of noise
Figure RE-FDA0002521888430000021
Is written as
Figure RE-FDA0002521888430000022
Wherein WiIs the noise received by the ith array element;
output signal X of ith antennai＝ADi(H)BTI is regarded as a slice of the trilinear model along the antenna direction, and a reconstructed matrix Y is obtained after matrix reconstruction according to the symmetry of the trilinear modeln：
Yn＝HDn(A)BT,n＝1,2,...,N (6)
Wherein Y isnN1, 2, as a reconstruction of equation (3);
14) receiving a signal
Figure RE-FDA0002521888430000023
Has a covariance matrix of
Figure RE-FDA0002521888430000024
Wherein L is the number of fast beats.
3. The low complexity carrier synchronization method in the OFDM power wireless private network according to claim 1, wherein: the signal in equation (3) is either expressed as a trilinear model
Figure RE-FDA0002521888430000025
Wherein xn,k,iRepresenting X in the matrix equation (3)iThe (n, k) th element of (a)n,pRepresents the (n, p) th element of the matrix A, bk,pRepresents the (k, p) th element, h, of the matrix Bi,pRepresents the (i, p) th element of the frequency domain channel matrix H,the rest is the same; n, K, I are the number of subcarriers, the number of blocks of the source and the number of antennas, respectively.
4. The method for synchronizing low complexity carriers in an OFDM power wireless private network according to claim 3, wherein the number of subcarriers N is 32, the number of antennas I is 4, the number of signal blocks K is 100, and the number of system channels P for transmitting data P is 20.
5. The low complexity carrier synchronization method in the OFDM power wireless private network according to claim 1, wherein: in the step 2), the method specifically comprises the following steps:
from equation (6), the matrix Y is constructed
Figure RE-FDA0002521888430000031
Wherein
Figure RE-FDA0002521888430000032
Is a rotation matrix; the CFO is estimated using the MI-PM algorithm according to the multiple shift invariant property of equation (8), and the matrix Y is expressed as
Y＝AEBT(9)
Wherein
Figure RE-FDA0002521888430000033
Matrix array
Figure RE-FDA0002521888430000034
Wherein, I, N and P are the number of antennas, the number of subcarriers and the number of channels used by the system respectively, and the matrix AEThe block-shaped materials are divided into blocks,
Figure RE-FDA0002521888430000035
represents a complex set of a plurality of
Figure RE-FDA0002521888430000036
Wherein the matrix one
Figure RE-FDA0002521888430000037
Is a full rank matrix, matrix two
Figure RE-FDA0002521888430000038
Thus in matrix one A1And the matrix two A2There is one linear transformation operator to satisfy
A2＝PcA1(12)
Order to
Figure RE-FDA0002521888430000039
Wherein P iscIs a matrix of propagation operators, IPIs an identity matrix of P × P, and the propagation operator P is obtained by minimizing the cost function in the presence of noisecIs estimated value of
Figure RE-FDA00025218884300000310
Figure RE-FDA00025218884300000311
Wherein Jcsm() To relate to
Figure RE-FDA00025218884300000312
Of a convex function of the second order, matrix
Figure RE-FDA00025218884300000313
Is a received signal
Figure RE-FDA00025218884300000314
First P columns of, matrix
Figure RE-FDA00025218884300000315
Is a received signal
Figure RE-FDA00025218884300000316
The remaining columns;
by the formula (14), the value is estimated
Figure RE-FDA00025218884300000317
Is estimated as
Figure RE-FDA00025218884300000318
From the equations (12) and (13), the following relational expression is obtained
Figure RE-FDA0002521888430000041
Thus, it is possible to provide
Figure RE-FDA0002521888430000042
According to equation (16), a relationship matrix P is defined1And relation matrix bip2Is composed of
Figure RE-FDA0002521888430000043
Thus, the relationship matrix P1And relation matrix bip2There exists the following relation
Figure RE-FDA0002521888430000044
Defining the matrix Ψ:
Figure RE-FDA0002521888430000045
so equation (19) is expressed as
P2＝P1Ψ (21)
Then
Ψ＝P1 +P2(22)
Wherein the matrix Ψ and the rotation matrix Φ have the same eigenvalue, and the matrix Ψ is subjected to eigenvalue decomposition to obtain
Figure RE-FDA0002521888430000046
Where tr (.) is defined as the sum of the main diagonal elements of the matrix,
Figure RE-FDA0002521888430000047
an estimate of the rotation matrix Φ, an estimate of the CFO
Figure RE-FDA0002521888430000048
Estimated by equation (23).
6. The low complexity carrier synchronization method in the OFDM power wireless private network according to claim 1, wherein: the performance of the CFO estimation is quantitatively evaluated using the mean square error MSE, defined as follows:
Figure RE-FDA0002521888430000051
wherein
Figure RE-FDA0002521888430000052
Is the CFO estimate for the mth Monte Carlo simulation, M is the Monte Carlo simulation times, Δ f is the exact value of CFO.
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Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110798416A (en) * 2019-10-28 2020-02-14 南京航空航天大学 CFO estimation algorithm based on local search Capon in OFDM system

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110798416A (en) * 2019-10-28 2020-02-14 南京航空航天大学 CFO estimation algorithm based on local search Capon in OFDM system

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* Cited by examiner, † Cited by third party
Title
YANG LI;YANG HU;BAO FENG;TAO MA: "Multiple Invariance PM-based Blind Carrier Frequency Offset Estimation for Multiple Antennas OFDM Electrical Special Network", 《2018 IEEE 3RD INTERNATIONAL CONFERENCE ON CLOUD COMPUTING AND INTERNET OF THINGS (CCIOT)》 *

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