CN116319209A - Signal detection and time-frequency synchronization method based on symmetric linear frequency modulation signals - Google Patents

Signal detection and time-frequency synchronization method based on symmetric linear frequency modulation signals Download PDF

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CN116319209A
CN116319209A CN202310146961.2A CN202310146961A CN116319209A CN 116319209 A CN116319209 A CN 116319209A CN 202310146961 A CN202310146961 A CN 202310146961A CN 116319209 A CN116319209 A CN 116319209A
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signal
chirp
peak
frequency modulation
time
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赵世铎
袁伟皓
许沐
何入洋
刘欢
韩东
李逸君
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CETC 54 Research Institute
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0014—Carrier regulation
    • 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
    • H04L27/0014—Carrier regulation
    • H04L2027/0024—Carrier regulation at the receiver end
    • H04L2027/0026—Correction of carrier offset
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0014—Carrier regulation
    • H04L2027/0083—Signalling arrangements
    • H04L2027/0097—Adaptive synchronisation signals
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
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    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention provides a signal detection and time synchronization method based on symmetric linear frequency modulation signals, which comprises the steps of transmitting the symmetric linear frequency modulation signals by a transmitting end, calculating correlation results of a receiving end, searching peaks, judging amplitude threshold values, judging two-peak interval threshold values, estimating carrier frequency offset, estimating arrival time and the like. The invention can realize stable signal detection and accurate time and frequency synchronization when the receiving end has larger carrier frequency offset, thereby improving the performance of the communication system. The invention has low calculation complexity, simple and convenient realization and easy engineering realization, and can be applied to various mobile communication systems.

Description

Signal detection and time-frequency synchronization method based on symmetric linear frequency modulation signals
Technical Field
The invention relates to a signal detection and time-frequency synchronization method based on symmetric linear frequency modulation signals, which is particularly suitable for mobile communication systems with larger carrier frequency deviation at the two ends of various receiving and transmitting.
Background
Most of data in modern communication systems has burst characteristics, and there may be carrier frequency deviation at the receiving end caused by clock deviation or relative motion, so that signal arrival detection and accurate time and frequency synchronization are required at the receiving end. The purpose of signal detection is to determine if a signal arrives, and to synchronize time and frequency after determining that a signal arrives. The purpose of time synchronization is to obtain the accurate arrival time of the signal, and the purpose of frequency synchronization is to estimate the carrier frequency offset of the received signal. Signal detection and time-frequency synchronization are the basis for subsequent processing at the receiving end, and the accuracy of the signal detection and time-frequency synchronization directly affects the performance of a communication system.
The signal detection and time synchronization usually use a known preamble signal, then the receiving end correlates the received preamble signal with the local preamble signal, and the signal detection is realized by judging whether the magnitude of the correlation peak is higher than a threshold value, and the time synchronization is realized by the position of the correlation peak. Since the correlation peak of a pseudo random sequence signal (e.g., an m-sequence) is significantly reduced in a large frequency offset environment, the preamble signal is typically selected to be insensitive to frequency offset, such as a chirp signal.
Fig. 1 and fig. 2 are diagrams showing correlation peaks at the receiving end of m-sequences and chirp signals under different normalized carrier frequencies. The normalized carrier frequency offset, i.e., the product of the true frequency offset Δf and the symbol period T, is also equivalent to the ratio of the true frequency offset Δf to the signal bandwidth.
The common simulation parameters of the m-sequence and the chirp signal are as follows: sample rate 100kHz, bandwidth 25kHz, signal point 2048. The chirp rate of the chirp signal is greater than 0. The true arrival time of the signal is set to 0.
As can be seen from fig. 1, the correlation peak of the m-sequence can be significantly reduced or even completely disappeared under the environment of large frequency offset, which can lead to the failure of signal detection and time synchronization. As can be seen from fig. 2, the chirp signal can obtain a higher correlation peak even in a large frequency offset environment, so that signal detection is successfully realized; however, when the frequency offset is large, correlation peaks of the chirp signal deviate from the true arrival position of the signal, thereby causing deviation of time synchronization.
For this problem, a plurality of correlators may be used at the receiving end, the local signal input of each correlator being a copy of the preamble signal to which the frequency offset is applied. Then, the one of the correlators with the largest output peak value is selected for signal detection and time synchronization, and the frequency offset value corresponding to the correlator can be used as the frequency offset estimation. Thus, signal detection and time-frequency synchronization in a large frequency offset environment can be realized. A flow chart of this method is shown in fig. 3. However, the synchronization accuracy of this method depends on the number of correlators, and the computational complexity for obtaining high accuracy is too high.
In satellite communication, a double Chirp signal, namely a positive frequency sweep Chirp signal and a negative frequency sweep Chirp signal which are overlapped in a time domain, is adopted to realize signal detection and time-frequency synchronization. The receiving end is schematically shown in fig. 4. However, under the condition of a certain transmitter power, the transmitting power of the positive frequency sweeping signal and the transmitting power of the negative frequency sweeping signal are lost by half, so that the method has poor performance under the condition of low signal-to-noise ratio. In addition, the method needs to carry out FFT operation twice, and the calculated amount still has an optimization space.
In addition, most of the existing methods only adopt amplitude threshold judgment to detect signals, if a false peak higher than a threshold happens due to interference or noise, false alarm is caused, and an error detection result is caused.
Disclosure of Invention
The technical problem to be solved by the invention is to avoid the defects in the background, and provide a novel signal detection and synchronization method based on symmetric linear frequency modulation signals, which can realize stable signal detection and accurate time-frequency synchronization under the condition of large carrier frequency offset under lower calculation complexity, thereby improving the performance of a communication system.
The invention adopts the technical scheme that:
a signal detection and time-frequency synchronization method based on symmetric linear frequency modulation signals comprises the following steps:
(1) The transmitting terminal transmits symmetrical linear frequency modulation signals, including a first linear frequency modulation signal and a second linear frequency modulation signal;
(2) The receiving end correspondingly calculates the cross correlation between the first linear frequency modulation signal and the second linear frequency modulation signal and the receiving signal by using the first correlator and the second correlator respectively;
(3) Peak search is carried out on the cross-correlation output result of the first correlator and the second correlator, and the amplitude of the peak value in the output of the first correlator is recorded as
Figure BDA0004089451950000021
The peak position is marked +.>
Figure BDA0004089451950000022
The amplitude of the peak in the output of the second correlator is noted +.>
Figure BDA0004089451950000023
The peak position is marked +.>
Figure BDA0004089451950000024
(4) Setting an amplitude threshold A thr Judging whether or not to meet
Figure BDA0004089451950000025
And->
Figure BDA0004089451950000026
If yes, the real signal is detected to arrive, the step (5) is continuously executed, otherwise, no signal is detected to arrive, and the step (2) is returned;
(5) Setting the range of carrier frequency offset delta f, and judging the two peak intervals by combining the frequency modulation slope, duration and protection interval of the first linear frequency modulation signal and the second linear frequency modulation signal
Figure BDA0004089451950000027
Whether the requirements are met, if so, continuing to executeStep (6), otherwise, returning to the step (2);
(6) Calculating carrier frequency offset delta f according to the frequency modulation slope, duration time, guard interval and peak-to-peak distance of the first linear frequency modulation signal and the second linear frequency modulation signal;
(7) And calculating the real arrival time tau of the signal according to the carrier frequency offset and the relation between the position of the first signal correlation peak and the real arrival time of the signal.
Further, the expression of the symmetric chirp signal in step (1) is as follows:
Figure BDA0004089451950000031
in the formula ,x1 (t) is a first linear FM signal, x 2 (T) is the second chirp signal, T is the duration of the first and second chirp signals, T g For the guard interval between the first chirp and the second chirp, T g ≥0；
First chirp signal x 1 The expression of (t) is as follows:
Figure BDA0004089451950000032
wherein ,
Figure BDA0004089451950000033
for the starting frequency, K, of the first linear FM signal 1 A chirp rate that is the first chirp rate;
second chirp signal x 2 The expression of (t) is as follows:
Figure BDA0004089451950000034
wherein ,
Figure BDA0004089451950000035
is the second lineStart frequency of chirped signal, K 2 Is the frequency modulation slope of the second linear frequency modulation signal and has
Figure BDA0004089451950000036
Further, the step (5) specifically comprises:
setting the range of carrier frequency offset delta f as [ -delta f according to prior information max ,Δf max], wherein Δfmax >0；
When K is 1 >0, judging if the peak distance is between two peaks
Figure BDA0004089451950000037
At->
Figure BDA0004089451950000038
If the two peaks are within the range, the two peaks are considered to be related peaks of the real signal, the step (6) is continuously executed, otherwise, at least one peak is considered to be caused by interference or noise, and the step (2) is returned;
when K is 1 <0, judging if the peak distance is between two peaks
Figure BDA0004089451950000039
At->
Figure BDA00040894519500000310
And (3) if the range is within the range, considering that both peaks are correlation peaks of the real signal, continuing to execute the step (6), otherwise, considering that at least one peak is caused by interference or noise, and returning to the step (2).
Further, the carrier frequency offset Δf in step (6) is calculated in the following manner:
Figure BDA0004089451950000041
further, in the step (7), the actual arrival time τ of the signal is calculated by:
Figure BDA0004089451950000042
the invention carries out signal detection and time-frequency synchronization in a large frequency offset environment by constructing symmetrical linear frequency modulation signals and skillfully utilizing the properties of the symmetrical linear frequency modulation signals. Has the following advantages:
firstly, the invention realizes reliable signal detection through twice amplitude threshold judgment and once two peak-to-peak interval threshold judgment, and reduces the occurrence of false alarms.
Secondly, the invention solves the problem that the linear frequency modulation signal can generate time synchronization error in a large frequency deviation environment by deducing the analysis relation between the carrier frequency deviation and the related peak offset of the linear frequency modulation signal and skillfully designing the transmitting waveform, thereby realizing accurate estimation of the carrier frequency deviation and the arrival time.
Thirdly, the invention only needs to use two correlators, does not need FFT operation, has lower calculation complexity and smaller processing time delay, and is convenient for engineering realization.
Fourth, the signal adopted by the invention has symmetry, only the first linear frequency modulation signal or the second linear frequency modulation signal is generated and stored in the signal in practical application, and then the signal can be read out by controlling the positive sequence or the reverse sequence to send the complete symmetrical linear frequency modulation signal, so that the storage complexity is lower, and the system resource is saved.
Drawings
FIG. 1 is a diagram of correlation peaks at m-sequence receiving ends under different normalized frequency bias;
FIG. 2 is a schematic diagram of correlation peaks at the receiving end of a linear frequency modulation signal under different normalized frequency shifts;
FIG. 3 is a time-frequency synchronization flow chart of the multiple correlation method;
FIG. 4 is a time-frequency synchronization flow chart of a dual Chirp signal receiving end;
FIG. 5 is a schematic diagram of a symmetrical chirp signal time domain waveform;
FIG. 6 is a time-frequency domain schematic diagram of a symmetric chirp signal;
FIG. 7 is a schematic diagram of a time-frequency domain diagram of a first linear FM signal at the receiving and transmitting ends;
FIG. 8 is a diagram of the correlation peak time of a first chirp signal;
FIG. 9 is a flow chart of the receiver processing of the method of the present invention;
FIG. 10 is a simulation diagram of the output results of two correlators at the receiving end;
FIG. 11 is a simulation plot of frequency offset estimation error as a function of signal to noise ratio;
FIG. 12 is a simulation plot of arrival time estimation error as a function of signal to noise ratio;
FIG. 13 is a simulation plot of frequency offset estimation error as a function of signal to noise ratio (after increasing the sampling rate);
FIG. 14 is a graph of arrival time estimation error versus SNR (after increasing sample rate);
fig. 15 is a possible way of applying the invention to a practical communication system.
Detailed Description
The method according to the invention will be further described in connection with specific embodiments.
A signal detection and time-frequency synchronization method based on symmetric linear frequency modulation signals comprises the following steps:
(1) The transmitting end transmits symmetrical linear frequency modulation signals
The expression for symmetric chirp signals is as follows:
Figure BDA0004089451950000051
wherein, is called x 1 (t) is a first linear FM signal, called x 2 And (t) is a second chirp signal. T is the duration of the first chirp signal and the second chirp signal. T (T) g For the guard interval between the first chirp and the second chirp, T g And is more than or equal to 0. The guard interval is used to prevent multipath smearing of the first chirp signal in the multipath channel from affecting the correlation detection of the second chirp signal.
First chirp signal x 1 The expression of (t) is as follows:
Figure BDA0004089451950000052
wherein ,
Figure BDA0004089451950000053
for the starting frequency, K, of the first linear FM signal 1 Is the chirp rate of the first chirp signal.
Since the instantaneous frequency of the signal (in Hz) is the derivative of the instantaneous phase with respect to time divided by 2π, the instantaneous frequency of the first chirp signal can be expressed as
Figure BDA0004089451950000054
It can be seen that it is a line segment in the time-frequency plane.
Second chirp signal x 2 The expression of (t) is as follows:
Figure BDA0004089451950000055
wherein ,
Figure BDA0004089451950000061
for the starting frequency of the second chirp signal, K 2 Is the frequency modulation slope of the second linear frequency modulation signal and has
Figure BDA0004089451950000062
According to the second chirp signal expression, it is related to a straight line with the first chirp signal in a rectangular coordinate system
Figure BDA0004089451950000063
Symmetrical.
A schematic diagram of the time domain waveform of the symmetric chirp signal s (t) is shown in fig. 5 (assuming K 1 >0 and take T g ＝T/4，
Figure BDA0004089451950000064
)。
A schematic diagram of a symmetric chirp signal in the time-frequency domain is shown in fig. 6.
The frequency of the transmitting end is f c The signal after up-converting s (t) by carrier frequency of (c) can be expressed as
Figure BDA0004089451950000065
It is assumed that carrier frequency in the received signal is defined by f due to relative motion of the transceiver and time variation of the channel c Becomes f c ′ The receive passband signal may be expressed as
Figure BDA0004089451950000066
Where τ is a time delay, and if the transmission time of the signal is considered to be 0, τ is also a real arrival time of the signal.
(2) Receiving end cross-correlation calculation
The receiving end frequency is f c,r The baseband signal r (t) obtained by down-converting y (t) at the carrier frequency of (2) can be expressed as
Figure BDA0004089451950000067
wherein fc ′ -f c,r Namely, the carrier frequency offset of the receiving end. The carrier frequency offset is marked as delta f, and the random phase is 2 pi f c ′ Where τ is denoted as θ, r (t) may be expressed as
r(t)＝e j(2πΔft-θ) s(t-τ) (8)
The correlator 1 implements the following calculation procedure
Figure BDA0004089451950000068
wherein ,
Figure BDA0004089451950000069
is a convolution operator, (. Cndot.) * Represents conjugate taking, |·| represents modulo taking.
The correlator 2 implements the following calculation procedure
Figure BDA0004089451950000071
(3) Peak search
Amplitude peak search is performed on the outputs of the correlators 1 and 2, and the peak amplitude in the output of the correlator 1 is recorded as
Figure BDA0004089451950000072
The peak position is marked +.>
Figure BDA0004089451950000073
The magnitude of the peak amplitude in the output of the correlator 2 is noted +.>
Figure BDA0004089451950000074
The peak position is marked +.>
Figure BDA0004089451950000075
(4) Amplitude threshold decision
Setting an amplitude threshold A thr Judging if
Figure BDA0004089451950000076
And->
Figure BDA0004089451950000077
And (3) considering that the true signal arrival is detected with high probability, continuing to execute the step (5), otherwise, considering that no signal arrives, and continuing to execute the detection processes of the steps (2) and (3).
(5) Two peak distance threshold decision
The first chirp signal in the received baseband signal may be written as
Figure BDA0004089451950000078
wherein θ′ =2pi Δfτ - θ is a random phase. Its instantaneous frequency is
Figure BDA0004089451950000079
As can be seen from comparison with formula (3), f 1,r (t) is f 1 (t) a result of shifting Δf in the positive direction of the f-axis and then shifting τ in the positive direction of the t-axis on the time-frequency plane. X is as follows 1(t) and x1,r (t) schematic representation in the time-frequency domain is shown in FIG. 7 (assuming K 1 >0)。
It can be seen that if x is used 1 (t) vs. x 1,r (t) performing a correlation operation, the correlation peak will appear at the point at which the two line segments partially coincide, the point being
Figure BDA00040894519500000710
As shown in fig. 8.
Since the correlation between the first chirp signal and the second chirp signal is small, the peak position in the output of the correlator 1 can be regarded as
Figure BDA00040894519500000711
The peak position in the output of the similarly obtainable correlator 2 is
Figure BDA0004089451950000081
Due to K 2 ＝-K 1 ，
Figure BDA0004089451950000082
And can also be written as
Figure BDA0004089451950000083
Thus, the two peak spacing Δt peak Can be expressed as
Figure BDA0004089451950000084
According to the prior information, setting the range of delta f (in Hz) to be [ -delta f max ,Δf max], wherein Δfmax >0. Thus, the range of the peak-to-peak distance is
Figure BDA0004089451950000085
(let K be assumed here 1 >0，K 1 <The case of 0 is not described in detail).
Judging if the peak distance is between two peaks
Figure BDA0004089451950000086
And (3) if the two peaks are within the range, considering that the two peaks are both related peaks of the real signal, continuing to execute the step (6), otherwise, considering that at least one peak is caused by interference or noise, and continuing to execute the detection processes of the steps (2) to (4).
(6) Carrier frequency offset estimation
The relationship between the distance between two peaks and the carrier frequency offset in the formula (16) can be utilized to obtain the estimated value of delta f as
Figure BDA0004089451950000087
(7) Arrival time estimation
The estimated value of tau can be obtained by using the relation between the correlation peak position of the first linear FM signal and the real arrival time tau of the signal in the formula (13)
Figure BDA0004089451950000088
In summary, a flowchart of the receiving end processing of the method according to the present invention is shown in fig. 9.
Symmetry line selected in this caseThe chirped signal parameters are:
Figure BDA0004089451950000089
K 1 ＝2.4414×10 6 ，
Figure BDA00040894519500000810
K 2 ＝-2.4414×10 6 ，T＝2.048×10 -2 s，T g ＝5.12×10 -3 s. The amplitude detection threshold is set to A thr =1000, the maximum carrier frequency offset is set to Δf max =2500 Hz, the carrier frequency offset range is set to [ -2500,2500]The distance between the two peaks is calculated to be [0.023552,0.027648 ]]。
The signal transmission delay is first set to τ=2×10 -3 s, the carrier frequency offset of the receiving end is set as
Figure BDA0004089451950000091
The corresponding normalized frequency offset is 2e-2 (here set larger for the sake of convenient observation of the shift of the correlation peak with respect to the signal arrival time). The outputs of the two correlators at the receiving end were emulated without noise, and the sampling rate was set to 100kHz. The simulation results are shown in fig. 10. In order to observe the relation between the correlation peak and the signal arrival time, the received signal is also drawn in the figure, and the amplitude normalization processing is performed on the correlator output.
From the figures can be obtained
Figure BDA0004089451950000092
From the normalized pre-correlation peak amplitude
Figure BDA0004089451950000093
Due to the correlation peak amplitude meeting
Figure BDA0004089451950000094
And->
Figure BDA0004089451950000095
The subsequent steps are continued.
Calculating to obtain the interval of two peaks as
Figure BDA0004089451950000096
Due to its range [0.023552,0.027648 ]]And continuing to execute the subsequent steps.
The carrier frequency offset can be estimated by the formulas (17) and (18)
Figure BDA0004089451950000097
The estimate of the moment of arrival is +.>
Figure BDA0004089451950000098
And the time and frequency synchronization under the condition of large carrier frequency offset is successfully realized.
The reason for the small error in the estimate is the discretization error. Specifically, the correlation result of the discrete sampled signal is also discrete in the time domain, so that the continuous carrier frequency offset and arrival time value cannot be accurately estimated by the correlation result, which is also a problem in other existing methods.
Then, a curve of the absolute value of the error of the frequency offset estimation and the arrival time estimation along with the signal to noise ratio is simulated under a Gaussian channel. Under each signal-to-noise ratio, 10000 simulation results are averaged, frequency offset values of each simulation are obtained by random uniform sampling within the range of-1000 Hz to 1000Hz, and signal transmission delay is set to be tau=2×10 -3 s. The simulation results are shown in fig. 11 and 12.
Under the condition of the implementation case, the method provided by the invention can realize reliable time and frequency synchronization when the signal-to-noise ratio is higher than-18 dB, the frequency offset estimation error is about 6Hz, and the arrival time estimation error is about 1e-5s.
In order to illustrate that the error of the method under the high signal-to-noise ratio comes from discretized sampling of the signal, the sampling rate in the simulation is increased from 100kHz to 200kHz, other simulation parameters are kept unchanged, and the simulation results are shown in fig. 13 and 14.
It can be seen that after the sampling rate is doubled, the frequency offset estimation error under high signal-to-noise ratio is reduced from 6Hz to 3Hz, and the arrival time estimation error is reduced from 1e-5s to 5e-6s. And the signal-to-noise ratio gain of about 3dB is obtained as the number of signal samples is doubled.
The simulation result verifies the effectiveness and the robustness of the method.
Finally, one possible way of applying the invention to an actual communication system is shown in fig. 15.
As shown in fig. 15, the present invention can be flexibly applied to various communication systems, and only the transmitting end transmits symmetrical chirp signals, and the receiving end adopts the method of the present invention to detect signals and synchronize time and frequency. The implementation flow of the specific system can be changed according to the actual application requirement.

Claims (5)

1. A signal detection and time-frequency synchronization method based on symmetric linear frequency modulation signals is characterized by comprising the following steps:
(1) The transmitting terminal transmits symmetrical linear frequency modulation signals, including a first linear frequency modulation signal and a second linear frequency modulation signal;
(2) The receiving end correspondingly calculates the cross correlation between the first linear frequency modulation signal and the second linear frequency modulation signal and the receiving signal by using the first correlator and the second correlator respectively;
(3) Peak search is carried out on the cross-correlation output result of the first correlator and the second correlator, and the amplitude of the peak value in the output of the first correlator is recorded as
Figure FDA0004089451940000011
The peak position is marked +.>
Figure FDA0004089451940000012
The amplitude of the peak in the output of the second correlator is noted +.>
Figure FDA0004089451940000013
The peak position is marked +.>
Figure FDA0004089451940000014
(4) Setting an amplitude threshold A thr Judging whether or not to meet
Figure FDA0004089451940000015
And->
Figure FDA0004089451940000016
If yes, the real signal is detected to arrive, the step (5) is continuously executed, otherwise, no signal is detected to arrive, and the step (2) is returned;
(5) Setting the range of carrier frequency offset delta f, and judging the two peak intervals by combining the frequency modulation slope, duration and protection interval of the first linear frequency modulation signal and the second linear frequency modulation signal
Figure FDA0004089451940000017
If the requirements are met, continuing to execute the step (6), otherwise, returning to the step (2);
(6) Calculating carrier frequency offset delta f according to the frequency modulation slope, duration time, guard interval and peak-to-peak distance of the first linear frequency modulation signal and the second linear frequency modulation signal;
(7) And calculating the real arrival time tau of the signal according to the carrier frequency offset and the relation between the position of the first signal correlation peak and the real arrival time of the signal.
2. The method for signal detection and time-frequency synchronization based on symmetric chirp signals according to claim 1, wherein the expression of the symmetric chirp signals in step (1) is as follows:
Figure FDA0004089451940000018
in the formula ,x1 (t) is a first linear FM signal, x 2 (T) is the second chirp signal, T is the duration of the first and second chirp signals, T g For the guard interval between the first chirp and the second chirp, T g ≥0；
First chirp signal x 1 The expression of (t) is as follows:
Figure FDA0004089451940000021
wherein ,
Figure FDA0004089451940000022
for the starting frequency, K, of the first linear FM signal 1 A chirp rate that is the first chirp rate;
second chirp signal x 2 The expression of (t) is as follows:
Figure FDA0004089451940000023
wherein ,
Figure FDA0004089451940000024
for the starting frequency of the second chirp signal, K 2 Is the frequency modulation slope of the second linear frequency modulation signal and has
Figure FDA0004089451940000025
3. The method for signal detection and time-frequency synchronization based on symmetric chirp signals according to claim 2, wherein step (5) specifically comprises:
setting the range of carrier frequency offset delta f as [ -delta f according to prior information max ,Δf max], wherein Δfmax >0；
When K is 1 >0, judging if the peak distance is between two peaks
Figure FDA0004089451940000026
At->
Figure FDA0004089451940000027
If the two peaks are within the range, the two peaks are considered to be related peaks of the real signal, the step (6) is continuously executed, otherwise, at least one peak is considered to be caused by interference or noise, and the step (2) is returned;
when K is 1 <0, judging if the peak distance is between two peaks
Figure FDA0004089451940000028
At->
Figure FDA0004089451940000029
And (3) if the range is within the range, considering that both peaks are correlation peaks of the real signal, continuing to execute the step (6), otherwise, considering that at least one peak is caused by interference or noise, and returning to the step (2).
4. The method for detecting and synchronizing time and frequency signals based on symmetric chirp signals as claimed in claim 3, wherein the carrier frequency offset Δf in step (6) is calculated by:
Figure FDA00040894519400000210
5. the method for signal detection and time-frequency synchronization based on symmetric chirp signals as claimed in claim 4, wherein the actual arrival time τ of the signal in step (7) is calculated by:
Figure FDA00040894519400000211
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