CN110798416A - CFO estimation algorithm based on local search Capon in OFDM system - Google Patents

CFO estimation algorithm based on local search Capon in OFDM system Download PDF

Info

Publication number
CN110798416A
CN110798416A CN201911027685.8A CN201911027685A CN110798416A CN 110798416 A CN110798416 A CN 110798416A CN 201911027685 A CN201911027685 A CN 201911027685A CN 110798416 A CN110798416 A CN 110798416A
Authority
CN
China
Prior art keywords
capon
search
algorithm
local
local search
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN201911027685.8A
Other languages
Chinese (zh)
Inventor
陈曦
叶长波
张小飞
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Nanjing University of Aeronautics and Astronautics
Original Assignee
Nanjing University of Aeronautics and Astronautics
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Nanjing University of Aeronautics and Astronautics filed Critical Nanjing University of Aeronautics and Astronautics
Priority to CN201911027685.8A priority Critical patent/CN110798416A/en
Publication of CN110798416A publication Critical patent/CN110798416A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/024—Channel estimation channel estimation algorithms
    • H04L25/0242—Channel estimation channel estimation algorithms using matrix methods
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/391—Modelling the propagation channel
    • 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

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Mathematical Physics (AREA)
  • Power Engineering (AREA)
  • Mobile Radio Communication Systems (AREA)

Abstract

The invention discloses a CFO estimation algorithm based on local search Capon in an OFDM system, which is improved on the basis of a global search Capon algorithm. The local search greatly reduces the calculation complexity, and the algorithm solves the problem that the estimation performance is seriously reduced due to unobvious spectral peaks or spectral peak loss of the traditional Capon algorithm under the condition of low signal-to-noise ratio. The simulation demonstrates the effectiveness of the method.

Description

CFO estimation algorithm based on local search Capon in OFDM system
Technical Field
The invention relates to a CFO (Carrier Frequency offset) estimation algorithm based on local search Capon in an OFDM (orthogonal Frequency Division multiplexing) system, belonging to the technical field of wireless communication.
Background
OFDM, an orthogonal frequency division multiplexing technology, started in the nineties, and is characterized by taking full advantage of the orthogonality of subcarriers for multicarrier modulation. Currently, the OFDM system has been widely used in the fields of high definition television signal transmission, digital video transmission, wireless local area network, etc., and is applied to wireless wide area networks and fourth generation cellular communication networks. 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 orthogonality of the OFDM system to the self-check of each subcarrier is very strict, and any Carrier Frequency Offset (CFO) affects the orthogonality between subcarriers. Therefore, accurate estimation and compensation of CFO in an OFDM system is required to ensure the performance of the system. CFO estimation methods currently fall into two categories: non-blind CFO estimation and blind CFO estimation. Non-blind CFO estimation methods include pilot frequency-based and cyclic prefix-based methods; the blind CFO estimation adopts the traditional spectrum estimation method, such as a MUSIC algorithm, an ESPRIT algorithm based on rotation-invariant signal parameter estimation, a CFO estimation algorithm based on kurtosis and the like. Compared with a non-blind CFO estimation method, the blind CFO estimation method has higher frequency band utilization rate, and certain algorithms have higher CFO estimation performance.
Compared with a non-blind estimation method, the global search Capon algorithm has better estimation performance, but the algorithm needs to search all subcarriers, so that the calculation complexity is higher. The local Capon algorithm provided by the invention is improved on the basis of global search, and only one subcarrier is searched, so that the calculation complexity is lower. According to simulation results, when the signal-to-noise ratio is high, the local Capon algorithm has CFO estimation performance close to that of a global search Capon algorithm on the basis of lower complexity. The problem that the CFO estimation performance of the global search Capon algorithm is poor when the signal to noise ratio is low is greatly improved.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a CFO estimation algorithm based on local search Capon, and the method is improved on the basis of a global search Capon algorithm, so that the high complexity caused by the step of searching all P subcarriers by global search is reduced. Meanwhile, the algorithm of the invention adopts local search, so that the CFO estimation performance is approximately the same as that of the global search Capon algorithm when the signal-to-noise ratio is high. The CFO estimation performance is better than the global search Capon algorithm at low signal-to-noise ratio.
The invention adopts the following technical scheme for solving the problems:
a CFO estimation algorithm based on local search Capon in an OFDM system is basically characterized in that a mathematical model of a received signal is established, a covariance matrix of the received signal is calculated through the mathematical model of the received signal, and CFO estimation is obtained through local search.
Compared with the prior art, the invention adopting the technical scheme has the following beneficial effects:
① the algorithm of the invention adopts local spectral peak search, the search range is one subcarrier, while the traditional Capon algorithm adopts global search, the search range is all P subcarriers, the search range is large, and the calculation amount is large;
② the algorithm inherits the higher estimation performance of the traditional Capon algorithm and is better than the ESPRIT algorithm;
③ the algorithm superposes P spectral peaks during local search, which can effectively overcome the problem that the estimation performance is seriously reduced due to the unobvious spectral peaks or the missing spectral peaks in the low signal-to-noise ratio condition of the traditional Capon algorithm;
④ the method of the present invention can effectively perform CFO estimation in OFDM system.
Drawings
FIG. 1 is a flow chart of the algorithm of the present invention;
FIG. 2 is a graph of frequency offset estimation corresponding to the global search Capon algorithm when SNR is 0 dB;
FIG. 3 is a graph of frequency offset estimation corresponding to the global search Capon algorithm when SNR is 20 dB;
FIG. 4 is a graph of frequency offset estimation corresponding to the local search Capon algorithm when SNR is 0 dB;
FIG. 5 is a graph of frequency offset estimation corresponding to the local search Capon algorithm when SNR is 20 dB;
FIG. 6 is a comparison graph of CFO estimation performance for different algorithms;
FIG. 7 is a comparison graph of CFO estimation performance when N takes different values;
FIG. 8 is a comparison graph of CFO estimation performance when K takes different values;
FIG. 9 is a comparison graph of CFO estimation performance when P takes different values;
fig. 10 is a CFO estimation performance diagram for different CFO cases.
Detailed Description
The technical scheme of the invention is further described in detail by combining the drawings and the specific embodiments:
the symbols represent: in the invention, (.)T，(·)HAnd (·)-1Denoted as transpose, conjugate transpose and inversion, respectively. Capital X represents a matrix, lowercase X (-) represents a vector, E [ ·]Indicating that it is desired. Re (. cndot.) represents the real part. diag (v) denotes the diagonal element as a diagonal matrix of vector v.
The parameters involved in the method of the invention are as follows: consider an uplink OFDM system. The system has N subcarriers, where P channels are used for data transmission and the remaining N-P channels are virtual carriers. And a cyclic prefix with the length L is used for eliminating the inter-channel interference caused by the multipath effect, wherein L is larger than the maximum time delay of the signal. Firstly, obtaining an expression of a received signal according to a mathematical model of the received signal, then calculating a signal covariance matrix estimation value, and finally obtaining CFO estimation through local spectral peak search. In this example, a CFO estimation algorithm based on local search Capon in the OFDM system is specifically implemented as follows:
step 1: establishing a mathematical model of a received signal
After inserting the cyclic prefix, the signal is transmitted through the multi-channel fading channel, and after removing the cyclic prefix, the received signal can be expressed as
x(k)＝EFPdiag(h)s(k)ej2πΔf(k-1)(N+L)(1)
Wherein E ═ diag (1, E)j2πΔf/N,...,ej2πΔf(N-1)/N) Is a frequency offset matrix in the system; Δ f is a preset initial frequency offset; fPThe first P columns of the inverse discrete Fourier transform matrix; h ═ H (1), H (2),.., H (p)]T，
Figure BDA0002249159840000031
For frequency correspondence of different channels, s (k) ═ s1(k),s2(k),...,sP(k)]TAnd transmitting the kth data block for the P data transmission channels. From the formula (1)
X＝Adiag(h)BT(2)
Wherein B ═ diag (1, e)j2πΔf(N+L),...,ej2πΔf(K-1)(N+L))S；S＝[s(1),s(2),...s(K)]TAll K data blocks transmitted for the P channels; the matrix A has van der Mond properties
Figure BDA0002249159840000032
In the noisy case, the received signal may be represented as
Figure BDA0002249159840000033
Wherein W is noise during reception; s ═ diag (h) BT。
Step 2: calculating an estimate of a signal covariance matrix
Figure BDA0002249159840000034
The basic algorithm of the method is a global search Capon algorithm, which comprises the following steps:
the Capon algorithm is also called Minimum Variance Method (MVM), and the optimization problem solved by the Capon algorithm can be expressed as:
with the constraint of
Figure BDA0002249159840000036
Wherein P (ω) ωHE[XXH]ω＝ωHR omega is the power of the output signal, X represents a noise-free received signal matrix, and R represents a covariance matrix R-XX constructed from the noise-free received signalsH/K。
Capon's algorithm attempts to minimize the power of noise and interference contributions in the non-signal direction, while the power is constant in the signal direction. The optimal weighting vector can be solved by Lagrange multiplier method, and the result is
Figure BDA0002249159840000037
In the formula (I), the compound is shown in the specification,
Figure BDA0002249159840000038
is a received signal covariance matrix. For the data model represented by equation (3), the data covariance matrix can be estimated from equation (4). Substituting the formula (5) into the constraint condition to obtain the spatial spectrum of the Capon algorithm, wherein the CFO estimated value can be obtained by searching the spectrum peak of the spectrum function
Figure BDA0002249159840000041
In the formula (I), the compound is shown in the specification,
Figure BDA0002249159840000042
whereinRepresenting an angle search range, and performing global spectral peak search on the spectral function, wherein the search range is [0,2 pi P/N]P spectral peaks can be obtained, corresponding frequency shifts are respectively
Figure BDA0002249159840000044
Figure BDA0002249159840000045
As shown in fig. 3. Where Δ f represents a preset initial frequency offset.
The estimated value of the real frequency offset can be calculated and obtained according to the frequency offset values corresponding to the P spectral peaks
Figure BDA0002249159840000046
In the formula (I), the compound is shown in the specification,
Figure BDA0002249159840000047
and searching the angle value corresponding to the ith spectrum peak for the global condition. F represents global search trueThe real frequency deviation estimation value has the spectrum peak search range of [0,2 pi P/N]。
As can be seen from fig. 3, in the case of high signal-to-noise ratio, P distinct spectral peaks can be obtained, and then the frequency offset estimation value can be obtained according to equation (7). However, in the case of low signal-to-noise ratio, due to the interference of noise, the spectral peak is not obvious, and even the spectral peak is missing, as shown in fig. 2. Thus, the frequency offset estimation value obtained according to equation (7) has a large deviation from the actual frequency offset value. In addition, because a spectrum function needs to be searched globally, the traditional Capon algorithm has a large amount of operation and is not beneficial to being applied to actual CFO estimation.
And step 3: CFO estimation through local spectral peak search
In order to solve the problems of the conventional global search Capon algorithm, an improved local search method can be adopted to perform CFO estimation. It can be seen that the local search for P spectral peaks has the following relationship
Figure BDA0002249159840000048
Therefore, like equation (6), we can construct the following spectral function to obtain CFO estimation by local search
Figure BDA0002249159840000049
In the formula (I), the compound is shown in the specification,
Figure BDA00022491598400000410
the estimated value of the real frequency offset can be calculated and obtained according to the frequency offset values corresponding to the P spectral peaks
Figure BDA00022491598400000411
In the formula (I), the compound is shown in the specification,and searching the angle corresponding to the ith spectrum peak for the local part. FLS-CaponRepresenting the local search of the real frequency deviation estimated value, the search range is [0,2 pi/N]。
As can be seen from the equations (8) and (9), the search range of the local search Capon algorithm is greatly reduced, so the computation amount is reduced. In addition, because the spectral function of the algorithm is formed by overlapping P spectral peaks, even if individual spectral peaks are not obvious or spectral peaks are missing, the true frequency offset in the obtained spectral function still corresponds to a unique spectral peak under the condition of low signal to noise ratio.
The algorithm computational complexity analysis of the invention is shown in table 1:
table 1 is a comparison table of complexity calculation of each algorithm, wherein N, P is the number of subcarriers and the number of channels used by the system, K is the number of fast beats, n isgRepresenting the number of searches of the MUSIC algorithm or Capon global search, nlRepresenting the number of searches of the local search Capon algorithm. The traditional Capon algorithm employs global spectral peak search, ngLarge, high complexity; the Capon algorithm presented herein employs a local spectral peak search, nlIs much less than ngAnd the algorithm complexity is greatly reduced.
TABLE 1 comparison table for calculating complexity of each algorithm
Fig. 2 is a graph of frequency offset estimation corresponding to the global search Capon algorithm when SNR is 0 dB. As can be seen from the figure, when the signal-to-noise ratio is low, due to interference of noise, a spectrum peak may be not obvious, even a spectrum peak is absent, so that a large error exists between the frequency offset estimation value obtained according to equation (7) and the actual frequency offset. The frequency offset Δ f is 0.4, the number of subcarriers N is 32, the number of channels P used for transmission is 20, and the number of cyclic prefixes L is 8.
Fig. 3 is a graph of frequency offset estimation corresponding to the global search Capon algorithm when SNR is 20 dB. From the figure, P distinct spectral peaks can be obtained when the signal-to-noise ratio is high. The frequency offset Δ f is 0.4, the number of subcarriers N is 32, the number of channels P used for transmission is 20, and the number of cyclic prefixes L is 8.
Fig. 4 is a graph of frequency offset estimation corresponding to the local search Capon algorithm when SNR is 0 dB. From the figure, under the condition of low signal-to-noise ratio, the local search Capon algorithm can still obtain a relatively accurate frequency offset estimation value through local spectral peak search. The frequency offset Δ f is 0.4, the number of subcarriers N is 32, the number of channels P used for transmission is 20, and the number of cyclic prefixes L is 8.
Fig. 5 is a graph of frequency offset estimation corresponding to the local search Capon algorithm when SNR is 20 dB. The frequency offset Δ f is 0.4, the number of subcarriers N is 32, the number of channels P used for transmission is 20, and the number of cyclic prefixes L is 8.
FIG. 6 is a graph comparing the performance of the local search Capon algorithm, the ESPRIT algorithm, and the PM algorithm herein, from which it can be derived that the estimated performance of the algorithm of the present invention is much higher than the other two algorithms. Wherein, N is 32, P is 20, L is 8, K is 200, and the simulation times is 500.
Fig. 7 to 9 are performance graphs of the local search Capon algorithm under different parameters. Fig. 7 and fig. 8 show the estimation performance of the local search Capon algorithm under different subcarrier numbers N and different fast beat numbers K, respectively, and the estimation performance of CFO improves as K and N increase; fig. 9 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. 10 shows CFO estimation performance for different CFO cases. From the graph, the local search Capon algorithm has very close CFO estimation performance for different CFOs. Where N is 32, P is 20, K is 200, SNR is 20dB and CFO range is [0, ω ], ω is 2 pi/N is normalized subcarrier space.

Claims (2)

  1. The CFO estimation algorithm based on the local search Capon in the OFDM system is characterized by comprising the following steps:
    step 1: establishing a mathematical model of a received signal;
    step 2: calculating an estimated value of a covariance matrix of the received signal;
    and step 3: the CFO estimate is obtained by a local spectral peak search.
  2. 2. The CFO estimation algorithm based on local search Capon as claimed in claim 1, wherein the specific step of step 3 includes:
    step 3.1: constructing a Capon spatial spectrum function;
    Figure FDA0002249159830000011
    in the formula (I), the compound is shown in the specification,
    Figure FDA0002249159830000012
    Figure FDA0002249159830000013
    denotes a local search angle range, P denotes the number of spectral peaks, N denotes the number of subcarriers,
    Figure FDA0002249159830000014
    is a received signal covariance matrix;
    step 3.2: carrying out local spectral peak search on the Capon space spectral function to obtain P spectral peaks;
    step 3.3: calculating to obtain an estimated value of the real frequency offset according to the frequency offset values corresponding to the P spectral peaks;
    Figure FDA0002249159830000015
    in the formula (I), the compound is shown in the specification,
    Figure FDA0002249159830000016
    for local search of the angle corresponding to the ith peak, FLS-CaponRepresenting the estimation value of the true frequency deviation of local search, the range of angle search is [0,2 pi/N]。
CN201911027685.8A 2019-10-28 2019-10-28 CFO estimation algorithm based on local search Capon in OFDM system Pending CN110798416A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201911027685.8A CN110798416A (en) 2019-10-28 2019-10-28 CFO estimation algorithm based on local search Capon in OFDM system

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201911027685.8A CN110798416A (en) 2019-10-28 2019-10-28 CFO estimation algorithm based on local search Capon in OFDM system

Publications (1)

Publication Number Publication Date
CN110798416A true CN110798416A (en) 2020-02-14

Family

ID=69441409

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201911027685.8A Pending CN110798416A (en) 2019-10-28 2019-10-28 CFO estimation algorithm based on local search Capon in OFDM system

Country Status (1)

Country Link
CN (1) CN110798416A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111464477A (en) * 2020-03-18 2020-07-28 国网重庆市电力公司南岸供电分公司 Low-complexity carrier synchronization method in OFDM power wireless private network
CN113973036A (en) * 2021-12-22 2022-01-25 元智科技集团有限公司 Orthogonal frequency division multiplexing frequency synchronization method for video communication

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20110255864A1 (en) * 2010-04-14 2011-10-20 Nec Laboratories America, Inc. Carrier frequency offset (cfo) estimator with low complexity and high accuracy for orthogonal-frequency-division-multiplexing (co-ofdm) systems
CN107800657A (en) * 2016-09-06 2018-03-13 晨星半导体股份有限公司 Carrier wave frequency deviation estimation device and carrier wave frequency deviation estimation method
CN108537369A (en) * 2018-03-21 2018-09-14 华南理工大学 Improvement population algorithm for distribution network reconfiguration based on local search

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20110255864A1 (en) * 2010-04-14 2011-10-20 Nec Laboratories America, Inc. Carrier frequency offset (cfo) estimator with low complexity and high accuracy for orthogonal-frequency-division-multiplexing (co-ofdm) systems
CN107800657A (en) * 2016-09-06 2018-03-13 晨星半导体股份有限公司 Carrier wave frequency deviation estimation device and carrier wave frequency deviation estimation method
CN108537369A (en) * 2018-03-21 2018-09-14 华南理工大学 Improvement population algorithm for distribution network reconfiguration based on local search

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
马涛等: "电力无线专网中一种OFDM载波同步算法", 《太赫兹科学与电子信息学报》 *

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111464477A (en) * 2020-03-18 2020-07-28 国网重庆市电力公司南岸供电分公司 Low-complexity carrier synchronization method in OFDM power wireless private network
CN113973036A (en) * 2021-12-22 2022-01-25 元智科技集团有限公司 Orthogonal frequency division multiplexing frequency synchronization method for video communication
CN113973036B (en) * 2021-12-22 2022-03-15 元智科技集团有限公司 Orthogonal frequency division multiplexing frequency synchronization method for video communication

Similar Documents

Publication Publication Date Title
CN101204056B (en) Initial parameter estimation in OFDM systems
CN109660478B (en) Timing frequency synchronization method based on improved Park frequency domain training sequence
US8422595B2 (en) Channel estimation for communication systems with multiple transmit antennas
US7286514B2 (en) Method for phase noise suppression for OFDM based WLANs
US7609789B2 (en) Phase noise compensation for MIMO WLAN systems
CN1881970B (en) Method and apparatus for compensating sampling frequency offset and carrier frequency offset in OFDM system
US7099397B2 (en) Receiver of an orthogonal frequency division multiplexing system
CN104836769B (en) A kind of joint timing leading based on conjugated structure and frequency synchronization method
EP1927224A1 (en) A receiver and a method for channel estimation
US8249206B2 (en) Method and apparatus for channel estimation in communication systems, and related computer program product
CN109150772B (en) Underwater acoustic channel time delay estimation method based on orthogonal matching pursuit
CN107222438B (en) Simplified BEM channel estimation method of high-speed mobile SC-FDMA system
CN107454032B (en) OFDM frequency offset estimation method based on amplitude product between subcarriers
CN104836770B (en) It is a kind of based on related average and adding window timing estimation method
CN110798416A (en) CFO estimation algorithm based on local search Capon in OFDM system
CN100486238C (en) Method of low-complexity frequency deviation estimation based on adjustable time frequency training sequence
CN101958872B (en) Method for searching best carrier frequency offset correction value
CN111131119B (en) Method and device for estimating high-precision timing offset of orthogonal frequency division multiplexing system
CN111555993B (en) Channel estimation method based on iterative preprocessing in FBMC system
CN109639602B (en) Low-complexity GFDM channel estimation method for 5G high-speed mobile scene
CN111726308B (en) Orthogonal matching pursuit channel estimation method based on frequency response pre-interpolation
CN111817990B (en) Channel estimation improvement algorithm based on minimum mean square error in OFDM system
CN108989261B (en) Timing synchronization method, device and related equipment of communication system
Manzoor et al. Novel SNR estimation technique in Wireless OFDM systems
Yang et al. Low-complexity channel estimator based on windowed DFT and scalar Wiener filter for OFDM system

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication
RJ01 Rejection of invention patent application after publication

Application publication date: 20200214