CN107257324A - Time frequency combined synchronizing method and device in a kind of ofdm system - Google Patents
Time frequency combined synchronizing method and device in a kind of ofdm system Download PDFInfo
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- H—ELECTRICITY
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Abstract
The invention discloses time frequency combined synchronizing method and device in a kind of ofdm system.In an ofdm system, converted according to linear frequency modulation (LFM) signal through Radon Wigner produce convergence and peak because when partially and the property that accordingly moves of frequency deviation generation, using LFM signals as training sequence, and detect peak, pair when partially and frequency deviation is estimated and compensated simultaneously.Mainly include the following steps that：The opposite LFM signals addition of two frequency modulation rates, which is chosen, in transmitting terminal is used as training sequence；Radon Wigner conversion is carried out to the training sequence received in receiving terminal, its actual peak-location information is detected；Determine the centre frequency variable quantity of two LFM signals；Inclined and frequency deviation when determining in system；OFDM symbol is compensated with frequency deviation according to inclined during gained.This method and device have good net synchronization capability, particularly in low signal-to-noise ratio, can be obviously improved the estimated accuracy of existing algorithm.
Description
Technical Field
The invention relates to the field of digital communication, in particular to a time-frequency joint synchronization method and a time-frequency joint synchronization device in an OFDM system.
Background
Digital communication systems are systems that transmit information using digital signals, which form the basis of modern communication networks. The digital communication system has the advantages of strong anti-interference capability, high reliability, easy encryption, strong confidentiality, good flexibility, equipment integration and the like which do not exist in analog communication systems. However, while having many advantages, the digital communication system also has the problems of wide occupied frequency band, complex technical requirements, high precision of the synchronization technical requirements and the like.
The most fundamental requirement and target of digital communication is the reliable and high-speed transmission of signals in a channel, and in order to meet the requirement, various novel communication technologies are continuously emerging, and the occurrence of an Orthogonal Frequency Division Multiplexing (OFDM) technology can effectively reduce the influence of fading, interference and noise frequently encountered in the digital communication process on the signals, thereby greatly improving the channel capacity and the transmission rate of a digital communication system. Therefore, OFDM technology is increasingly used in the field of digital communications.
The OFDM technology becomes a core technology of fourth-generation mobile communication because of its advantages of high spectrum utilization, multipath interference resistance, frequency selective fading resistance, low requirement for equalization, and the like. Optical Orthogonal Frequency Division Multiplexing (OOFDM) combined with Optical fiber communication technology also becomes a core technology in the field of Optical fiber communication. However, OFDM digital communication systems (OFDM systems for short) also have their inherent disadvantages, such as high peak-to-average ratio (PAPR), sensitivity to phase noise, frequency offset, and synchronization error. The invention aims to solve the problem of time-frequency synchronization in an OFDM system.
In the OFDM system, on one hand, in order to obtain an accurate fft start position at a receiving end, accurate symbol timing synchronization is required, otherwise, severe inter-symbol interference (ISI) or even inter-carrier interference (ICI) may be caused; on the other hand, if the carrier frequency deviation in the system is not effectively compensated, and the orthogonality between the sub-carriers of the OFDM system is destroyed, many advantages of the system will not exist. Therefore, the more effective synchronization technology is adopted to ensure the communication quality of the system, and the deep research on the symbol timing synchronization and the carrier frequency synchronization of the OFDM system has important significance.
Synchronization algorithms can be divided into two categories according to whether additional data insertion is required in OFDM symbols: data-assisted synchronization algorithms and non-data-assisted synchronization algorithms. The data-assisted synchronization algorithm inevitably increases the redundancy of the system and reduces the effectiveness of the system due to the insertion of additional data, but the algorithm has the advantages of high estimation precision, relatively low calculation complexity and better application prospect in an OFDM system. The algorithms mainly comprise three kinds of synchronization algorithms based on a guard interval, a pilot frequency and a training sequence. The synchronization method based on the training sequence is often applied to burst communication because of the advantages of high synchronization speed, high precision and the like, can obtain good synchronization performance under an Additive White Gaussian Noise (AWGN) channel and a multipath fading channel, and is also a preferred method for realizing time-frequency joint synchronization in an OFDM system. The traditional synchronization algorithm based on the training sequence mainly depends on the correlation of the training sequence to complete the synchronization, so that when the training sequence is designed, certain parts inside the training sequence have strong correlation and can be easily realized.
The most classical of the synchronization algorithms based on training sequences is the Schmidl algorithm proposed in the literature "Robust frequency and timing synchronization for OFDM" (T.M. Schmidl, D.C. Cox.robust frequency and timing synchronization for OFDM [ J ]. Transactions on Communications, 1997, 45(12), pp: 1613-1621), which utilizes the correlation of training sequences for time-frequency estimation of synchronization. Due to the existence of the cyclic prefix, the timing measurement function of the Schmidl algorithm can generate a peak platform, and timing ambiguity is caused. The classical time-frequency synchronization algorithm can respectively calculate time offset and carrier frequency offset only through two steps of operation, not only has higher synchronization processing complexity, but also influences the processing speed, so that a time-frequency joint synchronization method for simultaneously estimating the time offset and the carrier frequency offset appears.
For the problem of efficiency and precision of the conventional Synchronization Algorithm, a document "Joint Timing Synchronization and Frequency Offset Acquisition for MIMO OFDM Systems" (q.liu, b.hu.joint Timing Synchronization and Frequency Offset Acquisition for MIMO OFDM Systems [ J ]. Systems Engineering and electronics.2009, 20(3), pp: 470-478) which studies a time-Frequency Joint Synchronization method proposes to use two linear Frequency modulation signals (LFM) with different modulation frequencies as training sequences, and performs fractional fourier transform (ft) twice at a receiving end to simultaneously calculate the time-Frequency Offset and the Frequency-Frequency Offset in the system, thereby realizing Joint Synchronization.
On the basis of this, the document "Joint timing/frequency offset estimation and correction based on FrFT encoded systems for PDM CO-OFDM systems" (Huibin Zhou, Xiang Li, Ming Tang. Joint timing/frequency offset estimation and correction based on FrFT encoded systems for PDM CO-OFDM systems [ J ]. Optics Express (OE), 2016, 19(3), pp: 2831 and 2845.) proposes a FrFT-based time-frequency Joint synchronization algorithm in a polarization multiplexing coherent light orthogonal frequency division multiplexing system. The receiving end realizes the simultaneous estimation of the time offset and the frequency offset through one-time FrFT, and improves the estimation precision and the estimation range of the existing synchronization algorithm.
However, the time-frequency joint synchronization method based on the FrFT also has certain disadvantages, the suppression effect of the FrFT on noise is limited at low signal-to-noise ratio, the detection performance is reduced, and the FrFT spectra of a plurality of LFM signals have the problem of mutual shading, which has certain influence on the estimation accuracy.
Disclosure of Invention
The invention provides a time-frequency joint synchronization method and a time-frequency joint synchronization device in an OFDM system, which are used for simultaneously estimating time offset and frequency offset existing in the system, improving time-frequency synchronization precision and realizing accurate receiving of OFDM symbols. The time-frequency joint synchronization method provided by the invention is realized based on Radon-Wigner (Radon-Wigner) transformation, and two Linear Frequency Modulation (LFM) signals with opposite modulation frequencies are adopted as training sequences and are inserted in front of a transmitted OFDM data symbol; then, Radon-Wigner transformation is carried out on the received training sequence at the receiving end, and the LFM signal can be accurately detected by detecting the peak position in a Radon-Wigner transformation domain by utilizing the characteristic that the LFM signal can generate impulse after the Radon-Wigner transformation. When there is time offset and frequency offset in the OFDM system, the peak position of the LFM signal after Radon-Wigner transformation moves accordingly. And finally, simultaneously calculating the time offset and the integral multiple frequency offset existing in the OFDM system by using the peak position variation obtained by detection, wherein the decimal frequency offset can be further estimated by using the traditional Schmidl (Schmidl) algorithm, and the decimal frequency offset can be easily calculated because the timing position is determined. Compared with the traditional method for synchronizing by utilizing the correlation of the training sequence, the synchronization algorithm can simultaneously calculate the time offset and the integral multiple frequency offset, improves the synchronization efficiency, and solves the problem that the detection performance of the FrFT on the LFM signal is reduced in low signal-to-noise ratio, so that the synchronization algorithm has better synchronization effect in low signal-to-noise ratio compared with a time-frequency joint synchronization method based on the FrFT, and improves the time-frequency synchronization precision.
The technical scheme adopted by the invention for solving the technical problem is as follows: a time-frequency joint synchronization method and device in an OFDM system.
The time-frequency joint synchronization method in the OFDM system comprises the following steps:
selecting two linear frequency modulation LFM signals with opposite frequency modulation rates at a transmitting end to be added to be used as a training sequence, and inserting the training sequence in front of an OFDM symbol;
carrying out Radon-Wigner transformation on the received training sequence at a receiving end, and detecting the actual peak position information of the two LFM signals in a Radon-Wigner transformation domain;
determining central frequency variation corresponding to the two LFM signals according to theoretical peak position information of the two LFM signals in a Radon-Wigner transformation domain and actual peak position information of the two detected LFM signals in the Radon-Wigner transformation domain;
determining time offset and frequency offset existing in the OFDM system according to the obtained central frequency variation of the two LFM signals and the frequency modulation rates of the two LFM signals;
and compensating the received OFDM symbols according to the determined time offset and frequency offset.
Further, the peak position information includes a frequency modulation rate and a center frequency; and
the determining, according to theoretical peak position information of the two LFM signals in the Radon-Wigner transform domain and detected actual peak position information of the two LFM signals in the Radon-Wigner transform domain, central frequency variation corresponding to the two LFM signals specifically includes:
extracting the central frequency theoretical values of the two LFM signals from the theoretical peak position information of the two LFM signals in a Radon-Wigner transform domain;
extracting the actual values of the center frequencies of the two LFM signals from the actual peak position information of the two detected LFM signals in a Radon-Wigner transform domain;
and determining the central frequency variation corresponding to the two LFM signals according to the central frequency theoretical value and the central frequency actual value of the two LFM signals.
Further, theoretical peak position information of the two LFM signals in a Radon-Wigner transform domain is configured at a receiving end in advance.
Further, the two LFM signals with opposite modulation frequencies selected by the transmitting end are respectively expressed by the following formulas:
wherein-f0Representing the LFM signal Z1Theoretical value of center frequency of (t), μ represents Z1(t) frequency modulation rate; f. of0Representing the LFM signal Z2(t) theoretical value of center frequency, - μ represents Z2(t) frequency modulation rate;
Z1(t)、Z2(t) the theoretical peak position information in Radon-Wigner transform domain is (mu, -f) respectively0)、(-μ，f0)；
Z1(t)、Z2(t) the actual peak position information in the Radon-Wigner transform domain is (μ, f) respectively01)、(-μ，f02)，f01Represents Z1(t) actual value of center frequency, f02Represents Z2(t) actual value of center frequency;
the central frequency variation corresponding to the two LFM signals is determined according to the central frequency theoretical value and the central frequency actual value of the two LFM signals, and is specifically represented by the following formula:
ρ1＝f01-(-f0)
ρ2＝f02-f0
where ρ is1Representing the LFM signal Z1(t) amount of change in center frequency, ρ2Representing the LFM signal Z2(t) amount of change in center frequency.
Further, the time offset and the frequency offset existing in the OFDM system are determined according to the obtained central frequency variation and the frequency modulation rates of the two LFM signals, and are specifically represented by the following formulas:
f＝-(ρ1+ρ2)/2
t＝(ρ1-ρ2)/2μ
where f denotes a frequency offset present in the OFDM system, t denotes a time offset present in the OFDM system, ρ1Representing the LFM signal Z1(t) amount of change in center frequency, ρ2Representing the LFM signal Z2(t) amount of change in center frequency,. mu.m.1(t) frequency modulation rate.
The invention provides a time-frequency joint synchronization device in an OFDM system, which comprises:
the training sequence inserting module is used for selecting two linear frequency modulation LFM signals with opposite frequency modulation rates at a transmitting end to be added to be used as a training sequence and inserting the training sequence in front of an OFDM symbol;
the transformation detection module is used for carrying out Radon-Wigner transformation on the received training sequence at a receiving end and detecting the actual peak position information of the two LFM signals in a Radon-Wigner transformation domain;
the central frequency variation determining module is used for determining central frequency variations corresponding to the two LFM signals according to theoretical peak position information of the two LFM signals in a Radon-Wigner transformation domain and actual peak position information of the two detected LFM signals in the Radon-Wigner transformation domain;
the offset determining module is used for determining time offset and frequency offset existing in the OFDM system according to the obtained central frequency variation of the two LFM signals and the frequency modulation rates of the two LFM signals;
and the synchronization module is used for compensating the received OFDM symbols according to the determined time offset and frequency offset.
Further, the peak position information includes a frequency modulation rate and a center frequency; and
the center frequency variation determining module specifically includes:
the first extraction submodule is used for extracting the central frequency theoretical values of the two LFM signals from the theoretical peak position information of the two LFM signals in a Radon-Wigner transform domain;
the second extraction submodule is used for extracting the actual central frequency values of the two LFM signals from the actual peak position information of the two detected LFM signals in a Radon-Wigner transform domain;
and the determining submodule is used for determining the central frequency variation corresponding to the two LFM signals according to the central frequency theoretical value and the central frequency actual value of the two LFM signals.
Further, still include:
and the configuration module is used for pre-configuring the theoretical peak position information of the two LFM signals in the Radon-Wigner transform domain at a receiving end.
Further, the two LFM signals with opposite modulation frequencies selected by the transmitting end are respectively expressed by the following formulas:
wherein-f0Representing the LFM signal Z1Theoretical value of center frequency of (t), μ represents Z1(t) frequency modulation rate; f. of0Representing the LFM signal Z2(t) theoretical value of center frequency, - μ represents Z2(t) frequency modulation rate;
Z1(t)、Z2(t) the theoretical peak position information in Radon-Wigner transform domain is (mu, -f) respectively0)、(-μ，f0)；
Z1(t)、Z2(t) the actual peak position information in the Radon-Wigner transform domain is (μ, f) respectively01)、(-μ，f02)，f01Represents Z1(t) actual value of center frequency, f02Represents Z2(t) actual value of center frequency;
the determination submodule is specifically represented by the following formula:
ρ1＝f01-(-f0)
ρ2＝f02-f0
where ρ is1Representing the LFM signal Z1(t) amount of change in center frequency, ρ2Representing the LFM signal Z2(t) amount of change in center frequency.
Further, the offset determining module is specifically represented by the following formula:
f＝-(ρ1+ρ2)/2
t＝(ρ1-ρ2)/2μ
where f denotes a frequency offset present in the OFDM system, t denotes a time offset present in the OFDM system, ρ1Representing the LFM signal Z1(t) amount of change in center frequency, ρ2Representing the LFM signal Z2(t) amount of change in center frequency,. mu.m.1(t) frequency modulation rate.
Compared with the prior art, the invention has the remarkable improvements that:
(1) the invention relates to a time-frequency joint synchronization method and a time-frequency joint synchronization device in an OFDM system. Compared with the traditional timing synchronization and carrier frequency synchronization algorithm, the time-frequency joint synchronization algorithm provided by the invention can simultaneously estimate the time offset and the frequency offset existing in the system by carrying out Radon-Wigner transformation at the receiving end, obtains higher estimation precision, overcomes the defects of the traditional algorithm in efficiency and precision, and realizes the accurate receiving of OFDM signals. And due to the good aggregation characteristic of Radon-Wigner transformation on the LFM signals, the problems that the detection performance of FrFT on the LFM signals is reduced when the signal-to-noise ratio is low and the peak value misjudgment can be caused by mutual shielding of transformation spectrums of a plurality of LFM signals are solved.
(2) Simulation results show that the time-frequency joint synchronization method provided by the invention can effectively improve the estimation precision of the time offset and the frequency offset, and has superior synchronization performance compared with the existing synchronization method especially under the condition of low signal-to-noise ratio.
Drawings
The invention is further illustrated with reference to the following figures and examples.
FIG. 1 is a flow chart of a time-frequency synchronization method in an OFDM system according to the present invention;
FIG. 2 is a diagram of a time-frequency synchronization apparatus in an OFDM system according to the present invention;
FIG. 3 is a block diagram of an OFDM signal modulation and demodulation used for time-frequency joint synchronization in an OFDM system according to the present invention;
FIG. 4 is a block diagram of OFDM system synchronization;
FIG. 5 is a Radon-Wigner transform simulation diagram of an LFM signal of a time-frequency joint synchronization algorithm applied to an OFDM system according to the present invention;
fig. 6 shows the position change of the training sequence composed of LFM signals in the presence of different offsets in the system, where fig. 6(a) shows the positions of two signals in the time-frequency plane when no offset exists, fig. 6(b) shows the positions of two signals in the time-frequency plane when frequency offset exists, fig. 6(c) shows the positions of two signals in the time-frequency plane when time offset exists, and fig. 6(d) shows the positions of two signals in the time-frequency plane when both frequency offset and time offset exist;
FIG. 7 is a graph comparing the average timing estimation error of the present invention method and the prior art synchronization algorithm at different SNR;
FIG. 8 is a graph of the average normalized frequency offset estimation error comparison of the present invention method and the prior art synchronization algorithm at different SNR;
fig. 9 is a comparison graph of average estimation errors of the method of the present invention and the prior synchronization algorithm under different normalized frequency offsets.
Detailed Description
The embodiment of the invention provides a time-frequency joint synchronization method and a time-frequency joint synchronization device of an OFDM system, which realize accurate receiving of OFDM symbols.
As shown in fig. 1, an embodiment of the present invention provides a time-frequency joint synchronization method in an OFDM system, including the following steps:
firstly, two Linear Frequency Modulation (LFM) signals with opposite frequency modulation rates are selected at a transmitting end to be added to be used as a training sequence T (t), and the training sequence is inserted before an OFDM symbol.
Namely:
T(t)＝Z1(t)+Z2(t)
wherein Z is1(t) and Z2(t) two LFM signals with opposite modulation frequencies, -f0Indicating LFM signal Z in the absence of offset1Theoretical value of center frequency of (t), μ represents Z1(t) frequency modulation rate; f. of0Indicating LFM signal Z in the absence of offset2(t) center frequency theoretical value, - μmeans Z2(t) frequency modulation rate.
And secondly, carrying out Radon-Wigner transformation on the received training sequence at a receiving end, and detecting the actual peak position information of the two LFM signals in a Radon-Wigner transformation domain.
The receiving end carries out Radon-Wigner transformation on the signal, and the transformation has a convergence effect on the LFM signal, so that the transformed LFM signal can generate a peak value in a Radon-Wigner transformation domain.
(1)The Wigner transformation of (1):
(2)Radon-Wigner transformation of (2):
thus, when there is no offset, Z1(t)、Z2(t) the theoretical peak position information in Radon-Wigner transform domain is (mu, -f) respectively0)、(-μ，f0)。
And thirdly, determining central frequency variation corresponding to the two LFM signals according to theoretical peak position information of the two LFM signals in a Radon-Wigner transformation domain and actual peak position information of the two detected LFM signals in the Radon-Wigner transformation domain.
Two LFM signals f1、f2The frequency plane at which this is done can be expressed as:
f1＝-f0+μt1
f2＝f0-μt2
wherein f is0And-f0Respectively its center frequency, mu and-mu respectively the frequency modulation, f1And f2Is the frequency, t1And t2Is time.
When there is a time offset and a frequency offset:
f1+f＝-f0+μ(t1+t)
f2+f＝f0-μ(t2+t)
namely, it is
f1＝-f0+μ(t1+t)-f
f2＝f0-μ(t2+t)-f
Where t is the time offset present in the system and f is the carrier frequency offset present in the system.
The center frequency f at this time01And f02Is composed of
f01＝-f0+μt-f
f02＝f0-μt-f
After the offset occurs, the frequency modulation rates of the two signals are kept unchanged, the center frequency is changed, and the change amount rho of the center frequency is as follows:
ρ1＝f01-(-f0)
ρ2＝f02-f0
namely, it is
ρ1＝-f+μt
ρ2＝-f-μt
And fourthly, determining the time offset and the frequency offset existing in the OFDM system according to the central frequency variation of the two obtained LFM signals and the modulation frequencies of the two LFM signals.
Calculating the time offset and the frequency offset existing in the system according to the obtained signal center frequency variation and the signal frequency modulation rate, and specifically calculating by the following formula:
f＝-(ρ1+ρ2)/2
t＝(ρ1-ρ2)/2μ
and fifthly, compensating the received OFDM symbols according to the determined time offset and frequency offset.
The embodiment shown in fig. 2 shows a time-frequency joint synchronization apparatus diagram in an OFDM system adopted by the method of the present invention:
a training sequence insertion module 21, configured to select two linear frequency modulation LFM signals with opposite frequency modulation rates at a transmitting end, add the two linear frequency modulation LFM signals to serve as a training sequence, and insert the training sequence before an OFDM symbol;
the transformation detection module 22 is configured to perform Radon-Wigner transformation on the received training sequence at the receiving end, and detect actual peak position information of the two LFM signals in a Radon-Wigner transformation domain;
a central frequency variation module 23, configured to determine central frequency variations corresponding to the two LFM signals according to theoretical peak position information of the two LFM signals in a Radon-Wigner transform domain and actual peak position information of the two detected LFM signals in the Radon-Wigner transform domain；
The central frequency variation module 23 may specifically include:
the first extraction submodule 231 is configured to extract theoretical values of center frequencies of the two LFM signals from theoretical peak position information of the two LFM signals in a Radon-Wigner transform domain;
a second extracting submodule 232, configured to extract center frequency actual values of the two LFM signals from actual peak position information of the two detected LFM signals in a Radon-Wigner transform domain;
the determining submodule 233 is configured to determine, according to the theoretical value and the actual value of the center frequency of the two LFM signals, the change amount of the center frequency corresponding to the two LFM signals; the theoretical values of the central frequencies of the two LFM signals can be preset by a configuration module at a receiving end by theoretical peak position information of the two LFM signals in a Radon-Wigner transformation domain;
an offset determining module 24, configured to determine a time offset and a frequency offset existing in the OFDM system according to the obtained central frequency variation of the two LFM signals and the frequency modulation rates of the two LFM signals;
and a synchronization module 25, configured to compensate the received OFDM symbol according to the determined time offset and frequency offset.
The process of modulation and demodulation of an OFDM signal in which synchronization is required is shown in fig. 3. For ease of understanding, the basic principles of the involved OFDM modem process, the system synchronization model, and the involved Radon-Wigner transform are briefly introduced as follows:
(1) the modulation and demodulation process of the OFDM signal used in the method of the present invention is specifically described as shown in fig. 3. With the development of large-scale integrated circuit technology and DSP technology, people successfully utilize Inverse Discrete Fourier Transform (IDFT)/Discrete Fourier Transform (DFT) to modulate/demodulate OFDM signals, which pushes the OFDM technology towards practical application.
Analyzing the modulation/demodulation principle of OFDM signal from the angle of multi-carrier modulation, it can be seen from FIG. 3 that when we take an OFDM symbol as an example and the rate T isSand/N samples s (t) to obtain the m sampling value:
combining the subcarrier orthogonality condition to know
Combining the two formulas, we can get:
wherein,indicating an IDFT. At the receiving end, demodulation can be performed by DFT:
it can be seen that the modulation/demodulation of the OFDM signal can be performed by IDFT/DFT, and in practice, the more rapid and efficient IFFT and FFT are usually used instead, and the number of complex multiplication operations is N2Is reduced toTherefore, not only is the calculation complexity reduced, but also the system cost is saved, and a solid foundation for wide application of the OFDM technology is laid.
(2) OFDM system synchronization model: the invention aims to solve the problem of time-frequency joint synchronization in an OFDM digital communication system, namely, the time offset and the integral multiple carrier frequency offset existing in the system are simultaneously estimated. In OFDM systems, synchronization techniques can be divided into three categories by function: the first type is symbol timing synchronization, the second type is carrier frequency synchronization, and the third type is sample clock synchronization, as shown in fig. 4.
The receiving end of the OFDM system carries out symbol timing synchronization, so that the correct initial position of the OFDM symbol can be obtained, the position of an FFT window is clearly determined, and correct demodulation is finally realized. Because the system adopts coherent detection, and lasers at the transmitting end and the receiving end are influenced by various factors and have certain frequency deviation, the deviation needs to be estimated and compensated by carrier frequency synchronization to restore the signal to a baseband, otherwise, the orthogonality among subcarriers is damaged, and the system performance is also seriously influenced. Due to estimation error, noise and drift of a crystal oscillator at a transmitting end, certain deviation exists in the sampling clock frequency at the receiving end and the transmitting end, which is the problem to be solved for the sampling synchronization.
In an actual system, the sampling frequency deviation is slightly influenced by various factors in a channel, and the optical carrier frequency in the system is far larger than the sampling frequency, so the deviation of the sampling frequency is generally smaller, the influence of the deviation is not serious, and in addition, the timing error and the frequency error caused by partial sampling frequency deviation can be compensated in the timing synchronization and frequency synchronization processes, therefore, the invention mainly analyzes and researches the symbol timing and carrier frequency synchronization.
(3) Basic principle of Radon-Wigner transformation
The Radon transformation is a projection transformation of linear integration, a rectangular coordinate system is rotated by an angle alpha to obtain a new rectangular coordinate system (u, v), and then the rectangular coordinate system is integrated by different u values in parallel with a v axis, and the obtained result is the Radon transformation.
For the time-frequency plane, for any two-dimensional function x (t, f), Radon transform of alpha angle can be expressed as
Radon-Wigner transformation is to do Radon transformation to the time-frequency plane of Wigner-Ville distribution, which is defined as
Intercept f commonly known as y-axis0And the slope mu is a parametric representation of a straight line having f0＝u/sinα，μ＝-cotα，
With the parameters (μ, f)0) Representing the integration path, one can obtain:
the Radon-Wigner transform will be at the corresponding parameters (μ, f)0) Exhibit sharp peaks when the parameters deviate from mu and f0The Radon-Wigner transform value decreases rapidly. For a chirp signalThe Wigner-Ville distribution is
D for Radon-Wigner conversion of LFM signalz(μ, α) represents:
if Z (t) is a parameter of f0And μ, the integral value is maximum; when the parameter deviates from f0And μ, the integral value will decrease rapidly. That is, for a certain LFM signal, its Radon-Wigner transformation will be at the corresponding parameter (mu, f)0) And shows a sharp peak, as shown in fig. 4, which is a simulation of the Radon-Wigner transformation performed on the LFM signal.
The embodiment shown in fig. 3 shows a modulation and demodulation diagram of an OFDM signal used in the method of the present invention:
with the development of large-scale integrated circuit technology and DSP technology, people successfully utilize Inverse Discrete Fourier Transform (IDFT)/Discrete Fourier Transform (DFT) to modulate/demodulate OFDM signals, which pushes OFDM technology towards practical application.
Analyzing the modulation/demodulation principle of OFDM signals from the perspective of multi-carrier modulation3It can be seen that when we take an OFDM symbol as an example, and at a rate TSand/N samples s (t) to obtain the m sampling value:
combining the subcarrier orthogonality condition to know
Combining the two formulas, we can get:
wherein,indicating an IDFT. At the receiving end, demodulation can be performed by DFT:
it can be seen that the modulation/demodulation of the OFDM signal can be performed by IDFT/DFT, and in practice, the more rapid and efficient IFFT and FFT are usually used instead, and the number of complex multiplication operations is N2Is reduced toTherefore, not only is the calculation complexity reduced, but also the system cost is saved, and a solid foundation for wide application of the OFDM technology is laid.
The embodiment shown in fig. 4 shows the positions of three synchronizations in the OFDM system:
the invention aims to solve the problem of time-frequency joint synchronization in an OFDM system, namely, the time offset and the carrier frequency offset existing in the system are simultaneously estimated. In OFDM systems, synchronization techniques can be divided into three categories by function: the first type is symbol timing synchronization, the second type is carrier frequency synchronization, and the third type is sampling clock synchronization, as shown in the figure4As shown.
The receiving end of the OFDM system carries out symbol timing synchronization, so that the initial position of the OFDM symbol can be obtained and the position of an FFT window can be determined, and finally correct demodulation is realized. Because the system adopts coherent detection, and lasers at the transmitting end and the receiving end are influenced by various factors, a certain frequency deviation exists, so that the signal can be restored to a baseband by estimating the deviation in carrier frequency synchronization and compensating, otherwise, the system performance can be seriously influenced if the orthogonality among subcarriers is damaged. Due to estimation error, noise and drift of a crystal oscillator at a transmitting end, certain deviation exists in sampling clock frequencies at the transmitting end and the receiving end, and the problem to be solved is sampling synchronization.
In an actual system, the sampling frequency deviation is slightly influenced by various factors in a channel, and the optical carrier frequency in the system is far larger than the sampling frequency, so the deviation of the sampling frequency is generally smaller, the influence of the deviation is not serious, and in addition, the timing error and the frequency error caused by partial sampling frequency deviation can be compensated in the timing synchronization and frequency synchronization processes, therefore, the invention mainly analyzes and researches the symbol timing and carrier frequency synchronization.
The embodiment shown in fig. 5 shows that the Radon-Wigner transform simulation diagram of the LFM signal applied to the time-frequency joint synchronization algorithm in the OFDM system of the present invention: the Radon-Wigner transformation has good aggregation characteristics on the LFM signal, namely the LFM signal can be aggregated to one point through the Radon-Wigner transformation. As can be seen from fig. 5, in the Radon-Wigner domain, the LFM signal has a sharp peak, and the occurrence of the LFM signal can be accurately determined by searching the peak.
The embodiment shown in fig. 6 shows the position change of the training sequence formed by the LFM signal proposed by the method of the present invention when there are different offsets in the system:
FIG. 6(a) is the position of the training sequence in the absence of any offset in the system; when only a frequency offset exists in the system, as shown in fig. 6(b), two LFM signals will move along the frequency axis f simultaneously; when there is only a time offset in the system, as shown in fig. 6(c), the two LFM signals will be simultaneously shifted along the time axis t; when there is both time offset and frequency offset in the system, as shown in fig. 6(d), the two LFM signals will move in the directions of the time axis t and the frequency axis f at the same time, and at this time, Radon-Wigner transformation is performed on the two LFM signals, and the peak value is detected, so that the slopes and the intercepts of the two LFM signals at this time can be obtained, as can be seen from fig. 5, the intercepts of the two signals after the offset change, and the slopes remain unchanged. The time offset and the frequency offset in the system can be calculated according to the method provided by the invention through the change of the slope and the intercept.
The embodiment shown in fig. 7 shows a comparison graph of the average timing estimation error of the method of the present invention and the existing synchronization algorithm under different signal-to-noise ratios:
in order to verify the synchronization performance of the time-frequency synchronization method in OFDM signal transmission, a CO-OFDM system with a base band data transmission rate of 10Gbit/s is built, and the figure shows the comparison of the average timing estimation errors of the time-frequency synchronization method in different optical signal-to-noise ratios with the existing Schmidl algorithm and FrFT-based time-frequency joint synchronization algorithm when signals are transmitted by 50km optical fibers. Each point in the figure is the average result of 1000 simulations. It can be seen that when the optical signal-to-noise ratio is higher than 12dB, the FrFT-based synchronization algorithm has a timing estimation error of one sampling point, which means that the algorithm can better estimate the time offset in the system at this time; however, as the optical signal-to-noise ratio is reduced, the timing estimation error of the method is obviously increased, and the timing synchronization effect is obviously reduced. When the optical signal-to-noise ratio is higher than 4dB, the average timing estimation error of the method is 0, namely the method can accurately estimate the time offset of the system; when the optical signal to noise ratio is reduced to 2dB, the average estimation error of the method is 0.02, and the method still has good time bias estimation performance. The Schmidl algorithm is influenced by the cyclic prefix, and the timing matrix of the Schmidl algorithm appears on a platform and has the worst time offset estimation effect.
The embodiment shown in fig. 8 shows a comparison graph of the average normalized frequency offset estimation error of the method of the present invention and the existing synchronization algorithm under different signal-to-noise ratios:
in order to evaluate the frequency offset estimation performance of the method under different signal-to-noise ratios, 1000 times of simulation verification are respectively carried out on the algorithm under different optical signal-to-noise ratios, and the average normalized frequency offset estimation error of the algorithm under different optical signal-to-noise ratios is obtained. It can be seen from fig. 7 that, when the optical signal-to-noise ratio is higher than 14dB, the FrFT-based time-frequency synchronization algorithm and the algorithm of the present invention can correctly estimate the integer frequency offset existing in the system. However, as the optical signal-to-noise ratio decreases, the average estimation error based on the FrFT algorithm gradually increases, and the time-frequency synchronization method based on Radon-Wigner transformation provided by the invention has good estimation performance. When the signal-to-noise ratio is as low as 2dB, the estimation error of the method is still obviously lower than that of the algorithm based on FrFT. It can be seen that the frequency offset estimation performance of the time-frequency joint synchronization method provided by the invention under different signal-to-noise ratios is obviously superior to that of the existing FrFT-based algorithm.
Fig. 9 shows an embodiment of a comparison graph of average estimation errors of frequency offsets of the method of the present invention and the existing synchronization algorithm under different normalized frequency offsets.
In order to verify the estimation performance of the synchronization method provided by the invention on different normalized frequency offset values at a low signal-to-noise ratio, the optical signal-to-noise ratio is set to be 5dB, normalized frequency offsets of-20 to 20 are respectively set in a system, and 1000 times of simulation verification is carried out on the frequency offset estimation performance of the synchronization method based on FrFT and the method provided by the invention. Simulation results show that when the optical signal-to-noise ratio is 5dB and the normalized frequency offset is [ -20, 20], the average frequency offset estimation error of the synchronization method based on FrFT is in the range of 0.1 to 0.4, while the average estimation error of the synchronization method based on Radon-Wigner transformation of the invention is kept below 0.1 and is basically kept stable. Therefore, at the optical signal-to-noise ratio of 5dB, the method can obviously improve the frequency offset estimation performance of the existing algorithm and improve the frequency synchronization precision of the system under the normalization frequency offset of [ -20, 20 ].
According to the time-frequency joint synchronization method and device in the OFDM system, provided by the embodiment of the invention, under the condition of low signal-to-noise ratio, the time offset and the frequency offset existing in the OFDM system can be calculated simultaneously, and the time-frequency synchronization efficiency and precision of the OFDM system can be effectively improved.
Claims (10)
1. A time-frequency joint synchronization method in an OFDM system is characterized by comprising the following steps:
two linear frequency modulation LFM signals with opposite frequency modulation rates are selected at a transmitting end and added to be used as a training sequence, and the training sequence is inserted in front of an OFDM symbol;
carrying out Radon-Wigner transformation on the received training sequence at a receiving end, and detecting the actual peak position information of the two LFM signals in a Radon-Wigner transformation domain;
determining central frequency variation corresponding to the two LFM signals according to theoretical peak position information of the two LFM signals in a Radon-Wigner transformation domain and actual peak position information of the two detected LFM signals in the Radon-Wigner transformation domain;
determining time offset and frequency offset existing in the OFDM system according to the obtained central frequency variation of the two LFM signals and the frequency modulation rates of the two LFM signals;
and compensating the received OFDM symbols according to the determined time offset and frequency offset.
2. The method for time-frequency joint synchronization in an OFDM system according to claim 1, wherein the peak position information comprises a frequency modulation rate and a center frequency; and
the determining, according to theoretical peak position information of the two LFM signals in the Radon-Wigner transform domain and detected actual peak position information of the two LFM signals in the Radon-Wigner transform domain, central frequency variation corresponding to the two LFM signals specifically includes:
extracting the central frequency theoretical values of the two LFM signals from the theoretical peak position information of the two LFM signals in a Radon-Wigner transform domain;
extracting the actual values of the center frequencies of the two LFM signals from the actual peak position information of the two detected LFM signals in a Radon-Wigner transform domain;
and determining the central frequency variation corresponding to the two LFM signals according to the central frequency theoretical value and the central frequency actual value of the two LFM signals.
3. The time-frequency joint synchronization method in the OFDM system according to claim 1 or 2, wherein the theoretical peak position information of the two LFM signals in the Radon-Wigner transform domain is pre-configured at a receiving end.
4. The time-frequency joint synchronization method in the OFDM system according to claim 3, wherein the two LFM signals with opposite modulation frequencies selected by the transmitting end are respectively expressed by the following formulas:
<mrow> <msub> <mi>Z</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&pi;</mi> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>f</mi> <mn>0</mn> </msub> <mi>t</mi> <mo>+</mo> <msup> <mi>&mu;t</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </msup> </mrow>
<mrow> <msub> <mi>Z</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&pi;</mi> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mn>0</mn> </msub> <mi>t</mi> <mo>-</mo> <msup> <mi>&mu;t</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </msup> </mrow>
wherein-f0Representing the LFM signal Z1Theoretical value of center frequency of (t), μ represents Z1(t) frequency modulation rate; f. of0Representing the LFM signal Z2(t) theoretical value of center frequency, - μ represents Z2(t) frequency modulation rate;
Z1(t)、Z2(t) the theoretical peak position information in Radon-Wigner transform domain is (mu, -f) respectively0)、(-μ，f0)；
Z1(t)、Z2(t) the actual peak position information in the Radon-Wigner transform domain is (μ, f) respectively01)、(-μ，f02)，f01Represents Z1(t) actual value of center frequency, f02Represents Z2(t) actual value of center frequency;
the central frequency variation corresponding to the two LFM signals is determined according to the central frequency theoretical value and the central frequency actual value of the two LFM signals, and is specifically represented by the following formula:
ρ1＝f01-(-f0)
ρ2＝f02-f0
where ρ is1Representing the LFM signal Z1(t) amount of change in center frequency, ρ2Representing the LFM signal Z2(t) amount of change in center frequency.
5. The method according to claim 4, wherein the time offset and the frequency offset existing in the OFDM system are determined according to the obtained central frequency variation and the frequency modulation rates of the two LFM signals, and are expressed by the following formulas:
f＝-(ρ1+ρ2)/2
t＝(ρ1-ρ2)/2μ
where f denotes a frequency offset present in the OFDM system, t denotes a time offset present in the OFDM system, ρ1Representing the LFM signal Z1(t) amount of change in center frequency, ρ2Representing the LFM signal Z2(t) amount of change in center frequency,. mu.m.1(t) frequency modulation rate.
6. A time-frequency joint synchronization device in an OFDM system is characterized by comprising:
the training sequence insertion module is used for selecting two linear frequency modulation LFM signals with opposite frequency modulation rates at a transmitting end to be added to be used as a training sequence and inserting the training sequence in front of an OFDM symbol;
the transformation detection module is used for carrying out Radon-Wigner transformation on the received training sequence at a receiving end and detecting the actual peak position information of the two LFM signals in a Radon-Wigner transformation domain;
the central frequency variation determining module is used for determining central frequency variations corresponding to the two LFM signals according to theoretical peak position information of the two LFM signals in a Radon-Wigner transformation domain and actual peak position information of the two detected LFM signals in the Radon-Wigner transformation domain;
the offset determining module is used for determining time offset and frequency offset existing in the OFDM system according to the obtained central frequency variation of the two LFM signals and the frequency modulation rates of the two LFM signals;
and the synchronization module is used for compensating the received OFDM symbols according to the determined time offset and frequency offset.
7. The device for time-frequency joint synchronization in an OFDM system according to claim 6, wherein said peak position information comprises a frequency modulation rate and a center frequency; and
the center frequency variation determining module specifically includes:
the first extraction submodule is used for extracting the central frequency theoretical values of the two LFM signals from the theoretical peak position information of the two LFM signals in a Radon-Wigner transform domain;
the second extraction submodule is used for extracting the actual central frequency values of the two LFM signals from the actual peak position information of the two detected LFM signals in a Radon-Wigner transform domain;
and the determining submodule is used for determining the central frequency variation corresponding to the two LFM signals according to the central frequency theoretical value and the central frequency actual value of the two LFM signals.
8. The device for time-frequency joint synchronization in OFDM system according to claim 6 or 7, further comprising:
and the configuration module is used for pre-configuring the theoretical peak position information of the two LFM signals in the Radon-Wigner transform domain at a receiving end.
9. The time-frequency joint synchronization device in the OFDM system according to claim 8, wherein the two LFM signals with opposite modulation frequencies selected by the transmitting end are respectively expressed by the following formulas:
<mrow> <msub> <mi>Z</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&pi;</mi> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>f</mi> <mn>0</mn> </msub> <mi>t</mi> <mo>+</mo> <msup> <mi>&mu;t</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </msup> </mrow>
<mrow> <msub> <mi>Z</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&pi;</mi> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mn>0</mn> </msub> <mi>t</mi> <mo>-</mo> <msup> <mi>&mu;t</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </msup> </mrow>
wherein-f0Representing the LFM signal Z1Theoretical value of center frequency of (t), μ represents Z1(t) frequency modulation rate; f. of0Representing the LFM signal Z2(t) theoretical value of center frequency, - μ represents Z2(t) frequency modulation rate;
Z1(t)、Z2(t) the theoretical peak position information in Radon-Wigner transform domain is (mu, -f) respectively0)、(-μ，f0)；
Z1(t)、Z2(t) the actual peak position information in the Radon-Wigner transform domain is (μ, f) respectively01)、(-μ，f02)，f01Represents Z1(t) actual value of center frequency, f02Represents Z2(t) actual value of center frequency;
the determination submodule is specifically represented by the following formula:
ρ1＝f01-(-f0)
ρ2＝f02-f0
where ρ is1Representing the LFM signal Z1(t) amount of change in center frequency, ρ2Representing the LFM signal Z2(t) amount of change in center frequency.
10. The device for time-frequency joint synchronization in an OFDM system according to claim 9, wherein the offset determining module is specifically represented by the following formula:
f＝-(ρ1+ρ2)/2
t＝(ρ1-ρ2)/2μ
where f denotes a frequency offset present in the OFDM system, t denotes a time offset present in the OFDM system, ρ1Representing the LFM signal Z1(t) amount of change in center frequency, ρ2Representing the LFM signal Z2(t) amount of change in center frequency,. mu.m.1(t) frequency modulation rate.
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| CN116015372A (en) * | 2022-12-29 | 2023-04-25 | 国家工业信息安全发展研究中心 | Large-scale MIMO digital information transmission method, system, equipment and medium |
| CN116015372B (en) * | 2022-12-29 | 2023-09-12 | 国家工业信息安全发展研究中心 | Large-scale MIMO digital information transmission method, system, equipment and medium |
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