CN112688716B - Time-frequency difference estimation method for time-frequency aliasing signals - Google Patents
Time-frequency difference estimation method for time-frequency aliasing signals Download PDFInfo
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Abstract
The invention discloses a time-frequency difference estimation method for time-frequency aliasing signals, which relates to the technical field of electronic reconnaissance and is used for carrying out frequency domain cross-correlation operation on input signals to obtain a correlation function; carrying out frequency domain cross-correlation operation on known communication signal components in the input signals to obtain a correlation function of the communication signals; subtracting the correlation function of the communication signal from the correlation function of the aliasing signal to obtain the correlation function of the interference signal; and changing the amplitude of the communication signal correlation function, calculating the peak-to-average ratio of the interference signal correlation peak, and estimating the TDOA and FDOA values of the interference signal under the condition of the maximum peak-to-average ratio. The time difference-frequency difference maximum likelihood estimation method constructs an aliasing signal time difference-frequency difference maximum likelihood estimation model, removes a correlation peak of one path of signal by adopting a linear subtraction method so as to obtain a correlation peak of the other path of signal, estimates a peak value of one path of signal according to the peak-to-average ratio of the final correlation peak, and further obtains a global maximum value of the other path of signal, namely a time difference-frequency difference estimation value.
Description
Technical Field
The invention relates to the technical field of electronic reconnaissance, in particular to a time-frequency difference estimation method for time-frequency aliasing signals.
Background
Passive positioning is one of the main means of satellite-borne positioning, and plays an increasingly important role in battlefield environments, natural disasters and other extreme situations. The main approach adopted by passive positioning is Time-Frequency difference joint positioning, and the estimation accuracy Of two important parameters used by the passive positioning, namely Time Difference Of Arrival (TDOA) and Frequency Difference Of Arrival (FDOA), directly influences the positioning accuracy. Therefore, a high-precision time-frequency difference estimation method is indispensable for improving the positioning precision.
When carrying out normal satellite communication, the other party is often subjected to co-channel interference simultaneously by enemy interference signals or unintentional interference signals. The positioning of the interference source is a very urgent task in the field of electronic countermeasure. How to realize accurate positioning of aliasing interference signals by adopting an effective algorithm under the condition of existence of interfered communication signals is a great problem to be solved urgently at present.
A second-order mutual Ambiguity Function (CAF) is used as a classic time-frequency difference joint estimation algorithm, has the advantage of accurately estimating the TDOA under the condition that the FDOA is not corrected, and has relatively high operation speed; the high-order mutual fuzzy function realizes more accurate estimation than a second-order mutual fuzzy function on the premise of increasing the operation amount and sacrificing the operation speed; another commonly used means, the Maximum estimation accuracy of the fourth-order Maximum Likelihood algorithm (ML) can be achieved in the above algorithms, however, the fourth-order Maximum Likelihood algorithm has huge computation load, and some means are required to reduce the computation load; however, all the functions above do not satisfy the linear additive relationship and cannot be used for separate localization of aliasing signals.
The second-order Frequency-domain Cross-correlation Function (FCF), which is one of the second-order maximum likelihood functions, has an estimation accuracy exceeding a Cross-ambiguity Function, and a computation complexity lower than the fourth-order maximum likelihood algorithm, and satisfies a linear additive relationship of aliasing signals, that is, the sum of the Frequency-domain Cross-correlation functions of the interfered communication signal and the interference signal is equal to the Frequency-domain Cross-correlation Function value of the sum of the two signals, which has an important role in separating the aliasing signals.
Aiming at the TDOA/FDOA joint estimation problem of interference signals in simultaneous same-frequency aliasing signals in the prior art, an aliasing signal time difference-frequency difference maximum likelihood estimation model is constructed, a linear subtraction method is adopted to remove a correlation peak of an interfered communication signal in the aliasing signal, so that the correlation peak of the interference signal to be positioned is obtained, the peak value of the interfered communication signal is estimated according to the peak-to-average ratio of the final correlation peak, and then the global maximum value of the interference signal to be positioned is obtained, namely the time difference-frequency difference estimation value of the interference signal to be positioned.
Disclosure of Invention
The invention aims to provide a time-frequency aliasing signal time-frequency difference estimation method, which constructs an aliasing signal time difference-frequency difference maximum likelihood estimation model, removes a related peak of an interfered communication signal by adopting a linear subtraction method so as to obtain the related peak of the interference signal to be positioned, estimates the peak value of the interfered communication signal according to the peak-to-average ratio of the final related peak, and further obtains the global maximum value of the interference signal to be positioned, namely the time difference-frequency difference estimation value of the interference signal to be positioned.
The invention provides a time-frequency difference estimation method for time-frequency aliasing signals, which comprises the following steps:
s1: performing frequency domain cross-correlation operation on the input aliasing signal to obtain the frequency domain correlation function of the aliasing signal
Where τ represents the time shift, υ represents the frequency shift, X1And X2(τ, ν) is a frequency domain function;
s2: performing frequency domain cross-correlation operation on known communication signal components in the input signal, calculating fading quantity a, time delay quantity tau and frequency offset quantity upsilon of the communication signal, thereby obtaining real TDOA and FDOA values, and solving the correlation function of the communication signal at the moment
Let the actual communication signal correlation peak amplitude be a0And the assumed correlation peak amplitude of the communication signal is λ, and the assumed correlation function of the communication signal is
S3: correlation function of aliased signals
Subtracting the correlation function of the communication signal
Obtaining a correlation function R of the interference signal3(τ,υ)＝R(τ,υ)-R2(τ,υ)；
S4: and changing the amplitude of the related function of the communication signal, calculating the peak-to-average ratio of the related peak of the interference signal under different communication signal amplitudes, and taking the condition of the maximum peak-to-average ratio to obtain the TDOA and FDOA values of the interference signal.
Further, the frequency domain cross-correlation operation described in step S1 is simplified by a fourth-order maximum likelihood algorithm, which is expressed by the formula:
wherein, X1Is the result of a discrete Fourier transform, X, on the first signal2And (tau, upsilon) is a result of performing discrete Fourier transform on a signal subjected to time delay tau and frequency offset upsilon on the second path of signal, and different values of tau and upsilon are taken to obtain different frequency domain cross-correlation function values, wherein the value of tau and the value of upsilon corresponding to the maximum frequency domain cross-correlation function value are estimated values of TDOA and FDOA.
Further, the method for obtaining the real TDOA and FDOA values in step S2 is as follows:
first to x1(n) and x2(n) performing discrete Fourier transform to obtain frequency domain form of two paths of received signals
Let m11＝k-NTsν11，m12＝k-NTsν12，m21＝k-NTsν21，m22＝k-NTsν22The above formula can be simplified to
M in the above formula12Substitution of (2) to m11The following formula can be obtained
Mixing X1(m11) And X2(m11) Conjugate multiplication to obtain a frequency domain cross-correlation function R of
Substituting the time-frequency difference truth value into the formula to obtain R (delta tau)1,Δτ2,Δν1,Δν2) Is composed of
Because the correlation between noise and signal is relatively weak, the noise component in the above formula can be removed to obtain the cross-correlation function R of
From the above equation, the correlation peak (Δ τ) of the cross-correlation function in the frequency domain1,Δν1) And (Δ τ)2,Δν2) The TDOA and FDOA estimated values of the communication signal and the interference signal are obtained at the two positions respectively.
Further, the method for calculating the peak-to-average ratio of the correlation peak of the interference signal in step S4 is as follows:
setting an equivalent fading of a communication signal to
I.e. the amount of fading of the communication signal to both stars is
The cross-correlation function of the communication signals becomes:
the correlation function of the aliased signal minus the correlation function of the communication signal is
As shown in the above formula, exist
Only the autocorrelation component of the communication signal is completely removed, i.e.
Only the TDOA and FDOA estimates of the interfering signal can be further improved;
in the case where the communication signal has not been completely removed, the peak value of the interference signal is approximated as:
|R3|max＝|R3(Δτ2,Δν2)|＝|a21a22S2[m11+NTs(ν11-ν21)]S2[m11+NTs(ν11-ν22)]|
the average of all correlation results can be approximated as the average of all correlation results for different time correction amounts and frequency correction amounts
So that the value of lambda can be deduced
In that
In the case of (2), λ reaches a maximum value λmaxThe TDOA and FDOA estimates for the interfering signals are most accurate.
Compared with the prior art, the invention has the following remarkable advantages:
(1) the TDOA/FDOA estimation method with higher precision is adopted, and the fourth-order maximum likelihood algorithm and the frequency domain cross-correlation algorithm can obtain higher estimation precision than the second-order cross-fuzzy algorithm. The four-order maximum likelihood algorithm and the frequency domain cross-correlation algorithm have higher operation complexity than the second-order cross-fuzzy algorithm. Therefore, the TDOA/FDOA value can be obtained by adopting a second-order frequency domain cross-correlation algorithm. And the second-order frequency domain cross-correlation function meets the linear additive relation of the aliasing signals, namely the sum of the frequency domain cross-correlation functions of the two signals is equal to the frequency domain cross-correlation function value of the sum of the two signals, and the characteristic has important significance in separating the aliasing signals.
(2) The invention is based on the second-order frequency domain cross correlation function, and adopts the linear subtraction means to remove the correlation peak of the interfered communication signal, thereby obtaining the correlation peak of the interference signal to be positioned, and estimates the peak value of the interfered communication signal according to the peak-to-average ratio of the final correlation peak, and further obtains the global maximum value of the interference signal to be positioned, namely the time difference-frequency difference estimation value. The method can improve the estimation precision of the TDOA/FDOA parameters, and can also separate the same-frequency aliasing signals at the same time.
Drawings
Fig. 1 is a positioning scene diagram of aliasing of communication signals and interference signals provided by an embodiment of the present invention;
FIG. 2 is a diagram of a correlation peak of a cross-correlation function of a single signal in the frequency domain under the condition of no aliasing according to an embodiment of the present invention;
FIG. 3 is a diagram of a correlation peak of a frequency domain cross-correlation function of an aliased signal according to an embodiment of the present invention;
FIG. 4 is a diagram of the correlation peak of the cross-correlation function of the frequency domain after the signal peak is subtracted from the alias signal provided by the embodiment of the present invention;
fig. 5 is a peak-to-average ratio curve diagram corresponding to different amplitude correction amounts under a zero noise condition according to an embodiment of the present invention;
FIG. 6 is a graph of the peak-to-average ratio corresponding to different amplitude correction amounts under a signal-to-noise ratio of 10dB according to an embodiment of the present invention;
FIG. 7 is a TDOA estimation performance graph under different SNR provided by an embodiment of the present invention;
FIG. 8 is a graph of FDOA estimated performance for different SNR values provided by an embodiment of the present invention.
Detailed Description
The technical solutions of the embodiments of the present invention are clearly and completely described below with reference to the drawings in the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.
Referring to fig. 1-8, the invention provides a time-frequency difference estimation method for time-frequency aliasing signals, which comprises the following steps:
s1: performing frequency domain cross-correlation operation on the input aliasing signal to obtain the frequency domain correlation function of the aliasing signal
Where τ represents the time shift, υ represents the frequency shift, X1And X2(τ, ν) is a frequency domain function;
for two paths of input scout satellite sampling signals x1(n) and x2(n) performing a frequency domain cross-correlation operation, i.e. x2(n) time shifting τ and frequency shifting υ to obtain x2(n) time and frequency shifted Signal x2-τ，υ(n) then x1(n) and x2-τ，υ(n) separately Fourier transforming to obtain frequency domain function X1And X2(tau, upsilon), and the two frequency domain functions are multiplied by conjugate transposition to obtain the frequency domain cross-correlation function of the aliasing signal
S2: performing a frequency domain cross-correlation operation on known communication signal components in the input signal to obtain a correlation function of the communication signal: the main peak amplitude and shape of the related peak are similar to those of the signals with the same bandwidth, the same carrier frequency, the same modulation mode and the same modulation code. Therefore, under the condition that the position of the communication signal source is known, the fading quantity a, the time delay quantity tau and the frequency deviation quantity upsilon of the communication signal can be calculated, so as to obtain the real TDOA and FDOA values, and the correlation function of the communication signal at the moment
Since the fading amount of the communication signal is unknown, the calculated fading amount is actually a statistical average, and the amplitude of the correlation peak of the actual communication signal is set as a0And assuming the amplitude of the correlation peak of the communication signal to be λ, assuming the correlation function of the communication signal to be
S3: correlation function of aliased signals
Subtracting the correlation function of the communication signal
Obtaining a correlation function R of the interference signal3(τ,υ)＝R(τ,υ)-R2(τ, ν); in addition to the autocorrelation components of the communication signal and the interference signal, there are cross-correlation components of the communication signal and the interference signal. If the interfering signal source is to be located, the cross-correlation component between the communication signal and the interfering signal is reducedInfluence. In addition, the calculated value of the fading quantity is a statistical value, and the real fading quantity of the calculated value changes along with the change of the real channel condition;
s4: and changing the amplitude of the related function of the communication signal, calculating the peak-to-average ratio of the related peak of the interference signal under different communication signal amplitudes, and taking the condition of the maximum peak-to-average ratio to obtain the TDOA and FDOA values of the interference signal.
Aiming at the TDOA/FDOA joint estimation problem of an interference source signal in a simultaneous same-frequency aliasing signal, the time difference-frequency difference maximum likelihood estimation model of the aliasing signal is constructed, the correlation peak of an interfered communication signal in the aliasing signal is removed by adopting a linear subtraction method, so that the correlation peak of the interference signal to be positioned is obtained, the peak value of the interfered communication signal is estimated according to the peak-to-average ratio of the final correlation peak, and then the global maximum value of the interference signal to be positioned is obtained, namely the time difference-frequency difference estimation value.
The invention provides a method for estimating communication signal amplitude, namely a peak-to-average ratio detection method: the main peak amplitude and shape of the related peak are similar to those of the signals with the same bandwidth, the same carrier frequency, the same modulation mode and the same modulation code. Therefore, under the condition that the source position of the communication signal is known, the fading, time delay and frequency offset values of the communication signal are calculated, so that the real TDOA and FDOA values are obtained, the correlation peak of the communication signal is solved, and then the correlation peak of the communication signal is subtracted from the correlation peak of the aliasing signal, so that the correlation peak of the interference signal is obtained. It is noted that in addition to the autocorrelation components of the communication signal and the interference signal, there are cross-correlation components of the communication signal and the interference signal. If the interfering signal source is to be located, the effect of the cross-correlation components of the communication signal and the interfering signal is reduced. In addition, the calculated fading amount is a statistical value, and the real fading amount varies with the real channel condition. And the amount of fading we calculate is not equal to the true amount of fading. The amplitude of the communication signal correlation peak can be changed by means of peak-to-average ratio detection, and the difference between the aliasing signal correlation function and the communication signal correlation function under different communication signal correlation peak amplitudes is obtained, namely the correlation function of the interference signal. And (3) calculating the ratio of the peak value to the average value of the interference signal, and when the peak-to-average ratio is maximum, estimating the amplitude of the communication signal, further calculating the correlation function of the interference signal, and estimating the TDOA value and the FDOA value of the interference signal.
Experiments prove that the method removes the correlation peak of the interfered communication signal by adopting a linear subtraction means on the basis of a second-order frequency domain cross-correlation function so as to obtain the correlation peak of the interference signal to be positioned, estimates the peak value of the interfered communication signal according to the peak-to-average ratio of the final correlation peak, and further obtains the global maximum value of the interference signal to be positioned, namely the time difference-frequency difference estimation value. The method can improve the estimation precision of the TDOA/FDOA parameters, and can also separate the same-frequency aliasing signals at the same time.
Example 1
The frequency domain cross-correlation algorithm described in step S1 is a four-order maximum likelihood algorithm. The fourth order maximum likelihood algorithm is formulated as:
wherein, X1Is the result of a discrete Fourier transform, X, on the first signal2And (tau, upsilon) is the result of performing discrete Fourier transform on the signal after performing time delay tau and frequency offset upsilon on the second path of signal. And (4) taking different tau values and upsilon values to obtain different fourth-order maximum likelihood function values. Wherein, the tau value and the upsilon value corresponding to the maximum four-order maximum likelihood function value are estimated values of TDOA and FDOA;
the frequency-domain cross-correlation algorithm is simplified from the fourth-order maximum likelihood algorithm, and the frequency-domain cross-correlation algorithm in step S1 is formulated as:
wherein, X1Is the result of a discrete Fourier transform, X, on the first signal2(tau, upsilon) is the signal obtained after the time delay tau and the frequency offset upsilon are carried out on the second path of signal and discrete Fourier transform is carried out on the signalThe result of the transformation. And taking different tau values and upsilon values to obtain different frequency domain cross-correlation function values, wherein the tau value and upsilon value corresponding to the maximum frequency domain cross-correlation function value are estimated values of TDOA and FDOA.
The formula of the second-order mutual fuzzy method of the time domain is as follows:
wherein x is1(t- τ) is the signal after the first path signal is delayed by τ, x2(t) is the second signal, and upsilon is the frequency correction amount. And (4) taking different tau values and upsilon values to obtain different mutual fuzzy function values. Wherein the τ and the ν values corresponding to the maximum mutual ambiguity values are estimated values of TDOA and FDOA.
The formula of the second-order mutual fuzzy method of the frequency domain is as follows:
wherein, X1(f) Is the result of the discrete Fourier transform of the first signal, X2(f) Is the result of discrete fourier transform of the second signal, and upsilon is the frequency correction. And (4) taking different tau values and upsilon values to obtain different mutual fuzzy function values. Wherein the τ and the ν values corresponding to the maximum mutual ambiguity values are estimated values of TDOA and FDOA.
As can be seen from the above formula, the TDOA/FDOA estimation is performed by adopting a time domain second-order mutual fuzzy method, and a vector with the same tau and different upsilon can be obtained by performing operation once. TDOA/FDOA estimation is carried out by adopting a frequency domain second-order mutual fuzzy method, and a vector with the same upsilon and different tau can be obtained by carrying out operation once. And the frequency domain cross-correlation algorithm can only obtain one scalar point when performing operation once. The accuracy of the second-order frequency-domain cross-correlation algorithm is higher than that of the second-order cross-ambiguity algorithm.
Example 2
Referring to the communication signal and interference signal aliasing scenario shown in fig. 1. ToiletBoth satellite 1 and satellite 2 receive aliased signals transmitted by the communication station and the interfering station. Suppose that the communication signal source transmits a signal s1(t) the signal emitted by the interfering signal source is s2(t), then the signals received by the two stars can be modeled as
In the formula, ω1(t) and ω2(t) Gaussian white noise received by two satellites, a11、a21、a12And a22Are all the amount of signal fading, τ11、τ21、τ12And τ22Is the amount of time delay, v11、ν21、ν12V and v22Is the amount of frequency shift.
Time difference true value delta tau of communication signal1Sum frequency difference true value delta v1Time difference true value delta tau of interference signal2Sum frequency difference true value delta v2Is composed of
Δτ1＝τ11-τ12
Δν1＝ν11-ν12
Δτ2＝τ21-τ22
Δν2＝ν21-ν22
In an interference localization scenario, the time difference truth value Δ τ of the communication signal is known1Sum frequency difference true value delta v1On the premise of realizing time difference true value delta tau of interference signal2Sum frequency difference true value delta v2Is estimated. However, when the time-frequency difference truth values of the communication signal and the interference signal are unknown, the blind source separation method is required for analysis, which is not in the scope of the discussion.
By TsIs a space, to x1(t) and performing equal-interval sampling to obtain the dispersion of two paths of received signalsIn the form of
n＝0,1,...,N-1
It is difficult to obtain the time-domain cross-correlation function of the time-frequency difference according to the above formula, mainly because of the true value s of the reference signal1(nTs) And s2(nTs) Is unknown. The frequency-domain cross-correlation function of the time-frequency difference can only be derived from the frequency domain.
The method for obtaining the real TDOA and FDOA values in step S2 is as follows:
first to x1(n) and x2(n) performing discrete Fourier transform to obtain frequency domain form of two paths of received signals
Let m11＝k-NTsν11，m12＝k-NTsν12，m21＝k-NTsν21，m22＝k-NTsν22The above formula can be simplified to
M in the above formula12Substitution of (2) to m11The following formula can be obtained
Mixing X1(m11) And X2(m11) Conjugate multiplication to obtain a frequency domain cross-correlation function R of
Substituting the time-frequency difference truth value into the formula to obtain R (delta tau)1,Δτ2,Δν1,Δν2) Is composed of
Because the correlation between noise and signal is relatively weak, the noise component in the above formula can be removed to obtain the cross-correlation function R of
From the above equation, the correlation peak (Δ τ) of the cross-correlation function in the frequency domain1,Δν1) And (Δ τ)2,Δν2) The TDOA and FDOA estimated values of the communication signal and the interference signal are obtained at the two positions respectively.
The main peak amplitude and shape of the related peak are similar to those of the signals with the same bandwidth, the same carrier frequency, the same modulation mode and the same modulation code. Therefore, under the condition that the source position of the communication signal is known, the fading, time delay and frequency offset values of the communication signal are calculated, so that the real TDOA and FDOA values are obtained, the correlation peak of the communication signal is solved, and then the correlation peak of the communication signal is subtracted from the correlation peak of the aliasing signal, so that the correlation peak of the interference signal is obtained.
The communication signal correlation function is shown below.
The correlation function of the aliased signal minus the correlation function of the communication signal is shown below.
By frequency-domain cross-correlation function R2The TDOA and FDOA estimates of the interfering signal can be determined. It is noted that in addition to the autocorrelation components of the communication signal and the interference signal, there are cross-correlation components of the communication signal and the interference signal. If the interfering signal source is to be located, the effect of the cross-correlation components of the communication signal and the interfering signal is reduced.
In addition, the calculated fading amount is a statistical value, and the real fading amount varies with the real channel condition. And the amount of fading we calculate is not equal to the true amount of fading.
In the case of the above equation, even if the calculated values of the TDOA and FDOA of the communication signal are completely correct, the calculation of the correlation peak of the communication signal has an error due to an error of the fading amount, and thus, the main peak of the communication signal remains after the correlation peak of the alias signal is subtracted from the correlation peak of the communication signal.
From the above equation, it can be seen that only the true TDOA and FDOA of the communication signal can be calculated, but not the true fading amount, which results in a part of the main peak of the communication signal remaining in the correlation peak of the interference signal, causing an error in the estimation of the TDOA and FDOA of the interference signal. The correlation peaks of the communication signal must therefore be removed as thoroughly as possible.
Example 3
The method for calculating the peak-to-average ratio of the correlation peak of the interference signal in step S4 is as follows:
setting an equivalent fading of a communication signal to
I.e. the amount of fading of the communication signal to both stars is
The cross-correlation function of the communication signals becomes:
the correlation function of the aliased signal minus the correlation function of the communication signal is
As shown in the above formula, exist
Only the autocorrelation component of the communication signal is completely removed, i.e.
Only the TDOA and FDOA estimates of the interfering signal can be further improved;
to remove the correlation component of the communication signal more thoroughly, we can introduce a peak-to-average ratio λ, i.e., the peak/average of the correlation peak, when λ takes the maximum value, the communication signal is removed the cleanest.
In the case where the communication signal has not been completely removed, the peak value of the interference signal is approximated as:
|R3|max＝|R3(Δτ2,Δν2)|＝|a21a22S2[m11+NTs(ν11-ν21)]S2[m11+NTs(ν11-ν22)]|
the average of all correlation results can be approximated as the average of all correlation results for different time correction amounts and frequency correction amounts
So that the value of lambda can be deduced
As can be seen from the above equation, as the communication signal is removed, the amplitude of the autocorrelation peak of the interference signal does not change significantly, but the autocorrelation peak of the communication signal gradually decreases and the λ value increases. λ is maximized when the autocorrelation peak of the communication signal is removed to the cleanest. When the autocorrelation peak of the communication signal is continuously subtracted, the autocorrelation peak of the communication signal is increased, and the lambda value is decreased.
Thus, in
In the case of (2), λ reaches a maximum value λmaxThe TDOA and FDOA estimates for the interfering signals are most accurate.
Therefore, the amplitude of the autocorrelation peak of the communication signal can be roughly estimated by using a peak-to-average ratio detection method, and the autocorrelation peak of the interference signal can be obtained by subtracting the autocorrelation function of the communication signal, so that the TDOA and FDOA values of the interference signal can be estimated.
Example 4
The parameter setting of the aliasing interference signal time-frequency difference parameter estimation method based on the peak-to-average detection method is as follows:
parameter setting
And generating 3 paths of BPSK signals modulated by pseudo random codes with the sampling rate of 10MHz, the carrier frequency of 0.5MHz and the bandwidth of 10 KHz. All parameters of the three-path signal are the same, only the modulation code is different, and the added TDOA and FDOA values are different.
Simulation content and results
Simulation 1: the TDOA and FDOA estimates are performed on the received signal by adding different TDOA and FDOA values to BPSK1 and BPSK2, and the TDOA and FDOA can be estimated from the peak values of the correlation peaks.
When the difference between two TDOAs is larger than 1/B (B is the signal bandwidth) or the difference between two FDOAs is larger than 1/T (T is the signal duration for time-frequency difference estimation), the two correlation peaks are independent from each other, and no aliasing condition occurs. A plot of the function of the single peak, as shown in figure 2. When the difference between two TDOAs is less than 1/B (B is the signal bandwidth) and the difference between two FDOAs is less than 1/T (T is the signal duration for time-frequency difference estimation), two related peaks partially overlap, and the time-frequency domain aliasing situation shown in FIG. 3 occurs, which needs to be separated by a frequency domain cross-correlation algorithm.
Because the frequency domain cross-correlation function satisfies the additivity, the frequency domain cross-correlation function value of the known time-frequency difference signal can be subtracted from the frequency domain cross-correlation function value of the aliasing signal, so that the frequency domain cross-correlation function value of the unknown time-frequency difference signal is obtained. The correlation function after subtracting the known time frequency difference signal is shown in fig. 4.
As can be seen from fig. 4, the autocorrelation peak of the known signal still has a certain residual in addition to the autocorrelation peak of the interference signal. Therefore, the fading amplitude calculated according to the signal fading formula cannot be directly used for removing the correlation peak of the known signal.
Therefore, it is necessary to use a peak-to-average ratio detection method to change the amplitude of the correlation function of the known signal and subtract the correlation function of the known signal with different amplitudes from the correlation function of the aliasing signal to obtain the correlation peak of the interference signal under different conditions. The case of the largest peak-to-average ratio is the case where the amplitude estimation of the known signal is the most accurate and removed cleanly. In this case, the component of the correlation function containing the known signal is the smallest, and the influence of the known signal on the estimation of the time-frequency difference parameter of the interference signal is the smallest. Fig. 5 shows the peak-to-average ratio variation of the correlation function of the interference signal when the aliasing signal correlation function is subtracted by the known signal correlation function with different amplitudes.
It can be seen from fig. 5 that the peak-to-average ratio curve reaches a maximum around 0 dB. In this case, the known communication signal is removed most thoroughly, and the TDOA/FDOA value of the interference signal is estimated most accurately. The peak-to-average ratio at this point is close to that of the pure interference signal.
In the case of relatively large noise, a noise floor of the correlation function rises, resulting in a decrease in detection performance. As shown in fig. 6, the performance of the peak-to-average ratio detection is degraded around the signal-to-noise ratio of 10 dB.
Example 5
Respectively carrying out peak-to-average ratio detection on the aliasing signals under the condition that the received signal-to-noise ratio is 0-20 dB, and estimating the TDOA and FDOA of the interference signals when the peak-to-average ratio is maximum to obtain estimation results.
Simulation 2: and generating 3 paths of BPSK signals modulated by pseudo random codes with the sampling rate of 10MHz, the carrier frequency of 0.5MHz and the bandwidth of 10 KHz. All parameters of the three-path signal are the same, only the modulation code is different, and the added TDOA and FDOA values are different. When the difference between two TDOAs is less than 1/B (B is the signal bandwidth) and the difference between two FDOAs is less than 1/T (T is the signal duration for time-frequency difference estimation), two related peaks are partially overlapped, and the time-frequency domain aliasing situation shown in FIG. 3 occurs, which needs to be separated by using a peak-to-average ratio detection method and a frequency domain cross-correlation algorithm. The TDOA estimation effect is shown in FIG. 7, and the FDOA estimation effect is shown in FIG. 8.
The simulation result analysis shows that the invention can adopt a peak-to-average ratio detection method to estimate the approximate amplitude of the communication signal under the condition that the communication signal and the interference signal are simultaneously aliased at the same frequency, and the correlation function of the aliasing signal is subtracted from the correlation function of the communication signal, thereby obtaining the correlation function of the interference signal. Therefore, TDOA and FDOA estimation of the interference source is realized, and the positioning precision is further improved.
In short, the invention discloses a method for estimating time-frequency difference parameters of simultaneous co-frequency interference signal sources based on a frequency domain cross-correlation algorithm, which mainly solves the problem that the existing TDOA/FDOA estimation method cannot accurately estimate the TDOA/FDOA parameters of strong interference signals in simultaneous co-frequency aliasing signals. Two innovations of the invention are that in the first aspect, the frequency domain cross-correlation function is introduced into time-varying TDOA/FDOA estimation, so that the estimation performance of TDOA and FDOA is improved. And in the second aspect, the peak-to-average ratio detection is carried out on the difference function of the aliasing signal correlation function and the communication signal correlation function, so that the approximate amplitude of the communication signal is estimated, the communication signal correlation function residue is more accurately subtracted, a purer interference signal correlation function is obtained, the TDOA/FDOA estimation of the interference signal is realized, and the engineering application value is high.
The above disclosure is only for a few specific embodiments of the present invention, however, the present invention is not limited to the above embodiments, and any variations that can be made by those skilled in the art are intended to fall within the scope of the present invention.
Claims (3)
1. A time-frequency difference estimation method of time-frequency aliasing signals is characterized by comprising the following steps:
s1: performing frequency domain cross-correlation operation on the two paths of input reconnaissance satellite aliasing signals, wherein the frequency domain cross-correlation operation is obtained by simplifying a fourth-order maximum likelihood algorithm, and the fourth-order maximum likelihood algorithm is expressed by a formula as follows:
wherein, X1Is the result of a discrete Fourier transform, X, on the first signal2(tau, upsilon) is a result of performing discrete Fourier transform on a signal after a time delay tau and a frequency offset upsilon are performed on the second path of signal, wherein tau represents time shift, and upsilon represents frequency shift;
simplifying the formula of the fourth-order maximum likelihood algorithm shown in the formula, and solving the frequency domain correlation function of the aliasing signal
Taking different tau values and upsilon values to obtain different frequency domain cross-correlation function values, wherein the tau value and the upsilon value corresponding to the largest frequency domain cross-correlation function value are estimated values of TDOA and FDOA;
for two paths of input scout satellite sampling signals x1(n) and x2(n) performing a frequency domain cross-correlation operation on x2(n) time shifting τ and frequency shifting υ to obtain x2(n) time and frequency shifted Signal x2-τ，υ(n) then x1(n) and x2-τ，υ(n) separately Fourier transforming to obtain frequency domain function X1And X2(tau, upsilon), and the two frequency domain functions are multiplied by conjugate transposition to obtain the frequency domain cross-correlation function of the aliasing signal
S2: performing frequency domain cross-correlation operation on known communication signal components in the input signal to obtain true TDOA and FDOA values, wherein the correlation function of the communication signal
Assuming a correlation peak amplitude of the communication signal as λ, assuming a correlation function of the communication signal as
S3: correlation function of aliased signals
Subtracting the correlation function of the communication signal
Obtaining a correlation function R of the interference signal3(τ,υ)＝R(τ,υ)-R2(τ,υ)；
S4: and changing the amplitude of the related function of the communication signal, calculating the peak-to-average ratio of the related peak of the interference signal under different communication signal amplitudes, and taking the condition of the maximum peak-to-average ratio to obtain the TDOA and FDOA values of the interference signal.
2. The method for estimating time-frequency difference of time-frequency aliasing signals according to claim 1, wherein the method for obtaining the true TDOA and FDOA values in step S2 is as follows:
first to x1(n) and x2(n) performing discrete Fourier transform to obtain frequency domain form of two paths of received signals
Let m11＝k-NTsν11，m12＝k-NTsν12，m21＝k-NTsν21，m22＝k-NTsν22The above formula can be simplified to
M in the above formula12Substitution of (2) to m11The following formula can be obtained
Mixing X1(m11) And X2(m11) Conjugate multiplication to obtain a frequency domain cross-correlation function R of
Substituting the time-frequency difference truth value into the formula to obtain R (delta tau)1,Δτ2,Δν1,Δν2) Is composed of
Because the correlation between noise and signal is relatively weak, the noise component in the above formula is removed to obtain the cross-correlation function R of
From the above equation, the correlation peak (Δ τ) of the cross-correlation function in the frequency domain1,Δν1) And (Δ τ)2,Δν2) The TDOA and FDOA estimated values of the communication signal and the interference signal are obtained at the two positions respectively.
3. The method for estimating time-frequency difference of time-frequency aliasing signals according to claim 1, wherein the method for calculating the peak-to-average ratio of the correlation peak of the interference signal in step S4 is as follows:
setting an equivalent fading of a communication signal to
I.e. the fading amounts of the communication signal to the scout satellite 1 and the scout satellite 2 are both
The cross-correlation function of the communication signals becomes:
the correlation function of the aliased signal minus the correlation function of the communication signal is
As shown in the above formula, exist
Only the autocorrelation component of the communication signal is completely removed, i.e.
In the case of (3), the TDOA and FDOA estimated values of the interference signal are further improved;
in the case where the communication signal has not been completely removed, the peak value of the interference signal is approximated as:
|R3|max＝|R3(Δτ2,Δν2)|＝|a21a22S2[m11+NTs(ν11-ν21)]S2[m11+NTs(ν11-ν22)]|
the average of all correlation results is approximated to be
So that the value of lambda can be deduced
In that
In the case of (2), λ reaches a maximum value λmaxThe TDOA and FDOA estimates for the interfering signals are most accurate.
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