CN115811355B - High dynamic carrier capturing method - Google Patents

High dynamic carrier capturing method Download PDF

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CN115811355B
CN115811355B CN202310083862.4A CN202310083862A CN115811355B CN 115811355 B CN115811355 B CN 115811355B CN 202310083862 A CN202310083862 A CN 202310083862A CN 115811355 B CN115811355 B CN 115811355B
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frequency
order
baseband signal
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CN115811355A (en
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倪淑燕
程凌峰
房彦龙
李豪
张书豪
陈世淼
雷拓峰
王海宁
付琦玮
张英健
毛文轩
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Peoples Liberation Army Strategic Support Force Aerospace Engineering University
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Abstract

The invention provides a high-dynamic carrier capturing method, which is used for carrying out multiple compression on a time-frequency analysis result of a high-order synchronous compression method, so that the problem that noise robustness of the high-order synchronous compression method is poor under a low signal-to-noise ratio can be effectively solved, and meanwhile, the energy concentration degree of a time-frequency diagram can be improved; meanwhile, the time-frequency diagram is divided into a plurality of parts, each part independently selects a searching starting point, and performs searching estimation simultaneously in the forward and backward directions, so that the accuracy of instantaneous frequency estimation can be ensured under the condition of low signal-to-noise ratio.

Description

High dynamic carrier capturing method
Technical Field
The invention belongs to the field of communication signal reception, and particularly relates to a high-dynamic carrier capturing method.
Background
The low orbit satellite has the advantages of low orbit satellite orbit height, small transmission delay and small path loss, and the mode of using the low orbit satellite for forwarding the communication signals of the ground station and the air target has become an important communication mode in recent years. However, for high-speed users such as airplanes, missiles and the like, high-speed relative motion is generated when the two parties communicate, and in this case, the received signals can receive a stronger Doppler effect, and the high-speed Doppler frequency offset and the high-order frequency offset change rate are reflected. In the case where the frequency offset variation exceeds the FFT resolution in the time of receiving the signal, the conventional acquisition method has difficulty in effectively estimating the signal. The time-frequency analysis method can effectively observe the time-dependent change of the frequency of the signal, is an ideal tool for dealing with high-dynamic and quick-time-varying signals, but when the high-order synchronous compression method captures the received signal, the problems of time-frequency diagram divergence, poor noise robustness under lower signal-to-noise ratio and the like caused by inaccurate window length values exist.
Disclosure of Invention
In order to solve the problems, the invention provides a high dynamic carrier capturing method which can improve the carrier capturing precision and the precision of a follow-up tracking loop.
A high dynamic carrier acquisition method comprising the steps of:
s1: performing M-order synchronous compression conversion on the time-varying baseband signal to obtain a conversion result
Figure SMS_1
；
S2: for the transformation result
Figure SMS_2
Then N-time compression is carried out to obtain a time-frequency signal +.>
Figure SMS_3
；
S3: time-frequency signal
Figure SMS_4
The corresponding time-frequency diagram is divided into at least three parts, each part independently determines a searching starting point, searches the time-frequency diagram ridge lines from the front to the back of each searching starting point, and then splices the time-frequency diagram ridge lines of each part to obtain an instantaneous frequency track of the time-varying baseband signal, thereby completing carrier capturing.
Further, M-order synchronous compression conversion is carried out on the time-varying baseband signal to obtain a conversion result
Figure SMS_5
The method comprises the following steps:
defining M-order frequency modulation factor
Figure SMS_6
Which is the phase of the time-varying baseband signal>
Figure SMS_7
The M-th derivative over time, expressed as:
Figure SMS_8
wherein ,
Figure SMS_9
for taking the real part, the +.>
Figure SMS_10
Phase of time-varying baseband signal>
Figure SMS_11
K-th order term when Taylor series expansion is performed, k is the phase +.>
Figure SMS_12
The order when Taylor series expansion is performed;
wherein the M-order frequency modulation factor is obtained by:
Figure SMS_13
wherein ,
Figure SMS_14
m-th order frequency modulation factor when M-order Taylor series expansion is carried out for the phase of the time-varying baseband signal; />
Figure SMS_15
A kth order frequency modulation factor when performing M-order Taylor series expansion for the phase of the time-varying baseband signal; />
Figure SMS_16
Performing offset corresponding to an M-th order frequency modulation factor when performing M-th order Taylor series expansion on the phase of the time-varying baseband signal; />
Figure SMS_17
Performing offset corresponding to a k-th order frequency modulation factor when performing M-th order Taylor series expansion on the phase of the time-varying baseband signal; />
Figure SMS_18
A backward coefficient corresponding to a kth order frequency modulation factor when performing an M-order taylor series expansion for the phase of the time-varying baseband signal, wherein n=k+1, …, M;
wherein ,
Figure SMS_19
and />
Figure SMS_20
Expressed in iterative form as follows:
Figure SMS_21
wherein ,
Figure SMS_22
represents the offset +.>
Figure SMS_23
Partial derivative with respect to frequency f->
Figure SMS_24
Representing the backward coefficient->
Figure SMS_25
Partial derivative with respect to frequency f->
Figure SMS_26
Representing the backward coefficient->
Figure SMS_27
Partial derivative with respect to frequency f;
Figure SMS_28
and />
Figure SMS_29
The solving starting point of (2) is +.>
Figure SMS_30
and />
Figure SMS_31
And->
Figure SMS_32
And
Figure SMS_33
the definition is as follows:
Figure SMS_34
wherein ,
Figure SMS_35
indicating that the window function is +.>
Figure SMS_36
Is a short-time Fourier transform of->
Figure SMS_37
Indicating that the window function is +.>
Figure SMS_38
Is a short-time Fourier transform of->
Figure SMS_39
For short-time Fourier transform->
Figure SMS_40
The frequency reassignment factor obtained by time bias is expressed as:
Figure SMS_41
wherein ,
Figure SMS_42
representing a short-time Fourier transform +.>
Figure SMS_43
Partial derivative with respect to time t;
based on
Figure SMS_44
Obtaining M-order complex instantaneous frequency redistribution factor +.>
Figure SMS_45
The following are provided: />
Figure SMS_46
Based on
Figure SMS_47
Obtaining transformation result->
Figure SMS_48
The following are provided:
Figure SMS_49
wherein ,
Figure SMS_50
as a pulse function +.>
Figure SMS_51
Is the short-time Fourier transform result.
Further, for the transformation result
Figure SMS_52
Then N-time compression is carried out to obtain a time-frequency signal +.>
Figure SMS_53
The method comprises the following steps:
the transformation result is transformed according to the following formula
Figure SMS_54
Compression is carried out:
Figure SMS_55
wherein ,
Figure SMS_56
for N-1 heavy M order synchronous compression transformation result, < >>
Figure SMS_57
Is a short-time Fourier transform result;
each time compression is performed, the compression is calculated according to the following formula
Figure SMS_58
Order Li Shang:
Figure SMS_59
wherein the order is
Figure SMS_60
；
Judging whether the difference between the current obtained Rayleigh entropy and the Rayleigh entropy obtained by the last compression is smaller than a preset threshold, if so, the current compression result is a final time-frequency signal
Figure SMS_61
If not, substituting the current compression result into a compression formula to compress again until the difference between the Rayleigh entropy obtained by two adjacent compression is smaller than a preset threshold.
Further, the window function in the short-time Fourier transform is
Figure SMS_62
The method comprises the following steps:
Figure SMS_63
wherein ,
Figure SMS_64
the standard deviation is determined as follows:
Figure SMS_65
wherein ,
Figure SMS_66
is the instantaneous frequency of the time-varying baseband signal, and +.>
Figure SMS_67
The calculation method of (2) is as follows:
defining modulation frequency
Figure SMS_68
Wherein: />
Figure SMS_69
wherein ,
Figure SMS_70
representing the frequency estimate +.>
Figure SMS_71
Deviation of time t is determined by->
Figure SMS_72
Representing a time estimate +.>
Figure SMS_73
The time t is biased, and the method comprises the following steps:
Figure SMS_74
wherein ,
Figure SMS_75
representing a short-time Fourier transform +.>
Figure SMS_76
Deviation of time t is determined by->
Figure SMS_77
Representing a short-time Fourier transform +.>
Figure SMS_78
Performing bias guide on the frequency f;
the calculated modulation frequency
Figure SMS_79
Equivalent is instantaneous frequency +.>
Figure SMS_80
Substitution of standard deviation->
Figure SMS_81
In the calculation formula of (a), the standard deviation of the current iteration period i is obtained:
Figure SMS_82
judging standard deviation of current iteration period
Figure SMS_85
Standard deviation from the last iteration period +.>
Figure SMS_87
Whether the difference between them is smaller than the set threshold, if so, the standard deviation of the current iteration period is +.>
Figure SMS_90
For window function->
Figure SMS_84
If not, the standard deviation of the current iteration period is +.>
Figure SMS_88
Corresponding current window function->
Figure SMS_91
Substituted short-time Fourier transform
Figure SMS_93
Obtaining the current short-time Fourier transform +.>
Figure SMS_83
Then the current short-time Fourier transform +.>
Figure SMS_86
Standard deviation solving for the next iteration period is applied, and when the standard deviation of the current iteration period is +.>
Figure SMS_89
Standard deviation from the last iteration period
Figure SMS_92
The iteration is aborted when the difference between them is less than the set threshold.
Further, after completing carrier acquisition, according to the time-frequency signal
Figure SMS_94
Reconstructing a time-varying baseband signal:
Figure SMS_95
wherein ,
Figure SMS_96
reconstructed time-varying baseband signal, ">
Figure SMS_97
Is a window function at time 0.
Further, the time-varying baseband signal acquisition method comprises the following steps:
the local carrier wave is generated in the receiver and multiplied by the received signal, the multiplication result is composed of a carrier wave component close to zero frequency and a high-frequency carrier wave component, the high-frequency carrier wave component is removed by integrating the multiplication result, and the carrier wave component close to zero frequency containing Doppler frequency offset is used as a time-varying baseband signal.
The beneficial effects are that:
1. the invention provides a high-dynamic carrier capturing method, which is used for carrying out multiple compression on a time-frequency analysis result of a high-order synchronous compression method, so that the problem that noise robustness of the high-order synchronous compression method is poor under a low signal-to-noise ratio can be effectively solved, and meanwhile, the energy concentration degree of a time-frequency diagram can be improved; meanwhile, the time-frequency diagram is divided into a plurality of parts, each part independently selects a searching starting point, and performs searching estimation simultaneously in the forward and backward directions, so that the accuracy of instantaneous frequency estimation can be ensured under the condition of low signal-to-noise ratio.
2. The invention provides a high dynamic carrier capturing method, which is used for iterating a Gaussian window length of short-time Fourier transform based on a modulation frequency, so that the determined optimal window length can effectively solve the problem of compromise between frequency resolution and time resolution, namely, higher frequency resolution and time resolution can be obtained at the same time.
3. The invention provides a high-dynamic carrier capturing method, which has the advantage of improving the signal-to-noise ratio of signals based on multiple high-order synchronous compression, and can reconstruct a time-varying baseband signal after the carrier capturing of the signals is completed, thereby improving the precision of a subsequent tracking loop and being applicable to the scene of signal enhancement.
Drawings
Fig. 1 is a flow chart of a method of high dynamic carrier acquisition;
FIG. 2 is a schematic diagram of an N-fold compression process;
FIG. 3 shows the variation of N-level synchronous compressed Rayleigh entropy with the number of iterations under different signal-to-noise ratios;
FIG. 4 (a) is a time-frequency analysis diagram of M-order synchronous compression versus high dynamic signal;
FIG. 4 (b) is a partial enlarged view of the time-frequency analysis of the high dynamic signal by M-order synchronous compression;
FIG. 4 (c) is a time-frequency analysis chart of N-heavy M-order synchronous compression versus high dynamic signal;
FIG. 4 (d) is a partial enlarged view of the time-frequency analysis chart of N heavy M-order synchronous compression versus high dynamic signal;
FIG. 5 is a comparison chart of the Rayleigh entropy of higher-order synchronous compression and N-up-higher-order synchronous compression;
FIG. 6 is a capture probability for a high dynamic capture method;
fig. 7 is a graph showing the contribution of the signal to noise ratio of the reconstructed signal as a function of the number of iterations for a signal processed by the high dynamic capture method.
Detailed Description
In order to enable those skilled in the art to better understand the present application, the following description will make clear and complete descriptions of the technical solutions in the embodiments of the present application with reference to the accompanying drawings in the embodiments of the present application.
As shown in fig. 1, a high dynamic carrier acquisition method includes the following steps:
s1: performing M-order synchronous compression conversion on the time-varying baseband signal to obtain a conversion result
Figure SMS_98
。
The time-varying baseband signal acquisition method comprises the following steps: the local carrier wave is generated in the receiver and multiplied by the received signal, the multiplication result is composed of a carrier wave component close to zero frequency and a high-frequency carrier wave component, the high-frequency carrier wave component is removed by integrating the multiplication result, and the carrier wave component close to zero frequency containing Doppler frequency offset is used as a time-varying baseband signal.
For the relative motion between the satellite and the aircraft, and between the satellite and the ground station, in order to determine the effects of the relative speed in the radial direction, the rate of change of the relative speed, and the like, the phase of the time-varying baseband signal needs to be expanded by the following approximate Gao Jietai lux:
Figure SMS_99
wherein ,
Figure SMS_100
for the initial phase +.>
Figure SMS_101
Time-varying frequency offset, first-order and second-order transform rates, respectively. />
When the pilot frequency mode is adopted for assisting in capturing, because the data length used by the capturing module is short, the time-varying baseband signal phase usually ignores the influence of the Taylor series third order and above, and when the capturing is carried out by other modes, the reserved order condition can be determined according to the actual relative motion condition, so that the order M of the high-order synchronous compression method is determined, and the estimated high-dynamic fast time-varying signal can be better captured.
Based on the method, M-order synchronous compression conversion is carried out on the time-varying baseband signal to obtain conversion results
Figure SMS_102
The method specifically comprises the following steps:
defining M-order frequency modulation factor
Figure SMS_103
Which is the phase of the time-varying baseband signal>
Figure SMS_104
The M-th derivative over time, expressed as:
Figure SMS_105
wherein ,
Figure SMS_106
for taking the real part, the +.>
Figure SMS_107
Phase of time-varying baseband signal>
Figure SMS_108
K-th order term when Taylor series expansion is performed, k is the phase +.>
Figure SMS_109
The order when Taylor series expansion is performed;
the phase of the time-varying baseband signal cannot be directly mastered, and the order frequency modulation factor is obtained by the following formula:
Figure SMS_110
wherein ,
Figure SMS_111
m-th order frequency modulation factor when M-order Taylor series expansion is carried out for the phase of the time-varying baseband signal; />
Figure SMS_112
A kth order frequency modulation factor when performing M-order Taylor series expansion for the phase of the time-varying baseband signal; />
Figure SMS_113
Performing offset corresponding to an M-th order frequency modulation factor when performing M-th order Taylor series expansion on the phase of the time-varying baseband signal; />
Figure SMS_114
Performing offset corresponding to a k-th order frequency modulation factor when performing M-th order Taylor series expansion on the phase of the time-varying baseband signal; />
Figure SMS_115
A backward coefficient corresponding to a kth order frequency modulation factor when performing an M-order taylor series expansion for the phase of the time-varying baseband signal, wherein n=k+1, …, M;
wherein ,
Figure SMS_116
and />
Figure SMS_117
Expressed in iterative form as follows:
Figure SMS_118
wherein ,
Figure SMS_119
represents the offset +.>
Figure SMS_120
Partial derivative with respect to frequency f->
Figure SMS_121
Representing the backward coefficient->
Figure SMS_122
Partial derivative with respect to frequency f->
Figure SMS_123
Representing the backward coefficient->
Figure SMS_124
Partial derivative with respect to frequency f; />
Figure SMS_125
and />
Figure SMS_126
The solving starting point of (2) is +.>
Figure SMS_127
and />
Figure SMS_128
And->
Figure SMS_129
And
Figure SMS_130
the definition is as follows:
Figure SMS_131
wherein ,
Figure SMS_132
indicating that the window function is +.>
Figure SMS_133
Is a short-time Fourier transform of->
Figure SMS_134
Indicating that the window function is +.>
Figure SMS_135
Is a short-time Fourier transform of->
Figure SMS_136
For short-time Fourier transform->
Figure SMS_137
The frequency reassignment factor obtained by time bias is expressed as:
Figure SMS_138
wherein ,
Figure SMS_139
representing a short-time Fourier transform +.>
Figure SMS_140
Partial derivative with respect to time t;
based on
Figure SMS_141
Obtaining M-order complex instantaneous frequency redistribution factor +.>
Figure SMS_142
The following are provided:
Figure SMS_143
based on
Figure SMS_144
Obtaining M-order synchronous compression transformation result->
Figure SMS_145
The following are provided:
Figure SMS_146
wherein ,
Figure SMS_147
as a pulse function +.>
Figure SMS_148
Is the short-time Fourier transform result.
S2: for the transformation result
Figure SMS_149
Then N-time compression is carried out to obtain a time-frequency signal +.>
Figure SMS_150
；
It should be noted that, although the problem of contradiction between frequency resolution and time resolution is effectively solved based on the higher-order synchronous compression method, a time-frequency diagram with high time-frequency aggregation degree can be obtained, but the noise robustness is poor under a lower signal-to-noise ratio, so that the time-frequency diagram is easy to diverge, the higher-order synchronous compression method is selected to be subjected to multiple compression, thereby improving the noise robustness and also being capable of sending a time-frequency signal
Figure SMS_151
The acquisition method of the method specifically comprises the following steps:
the time-frequency analysis result after N-time compression of the M-order synchronous compression transformation result can be expressed as:
Figure SMS_152
wherein ,
Figure SMS_153
for N-1 heavy M order synchronous compression transformation result, < >>
Figure SMS_154
Is a short-time Fourier transformThe result is exchanged, and the N-fold compression process is shown in FIG. 2;
each time compression is performed, the compression is calculated according to the following formula
Figure SMS_155
Order Li Shang: />
Figure SMS_156
Wherein the order is
Figure SMS_157
Generally taken as 3;
judging whether the difference between the current obtained Rayleigh entropy and the Rayleigh entropy obtained by the last compression is smaller than a preset threshold, if so, the current compression result is a final time-frequency signal
Figure SMS_158
If not, substituting the current compression result into a compression formula to compress again until the difference between the Rayleigh entropy obtained by two adjacent compression is smaller than a preset threshold.
Therefore, the invention introduces Rayleigh entropy as an index for representing time-frequency aggregation capability, and then observes the variation condition of N-heavy M-order synchronous compression transformation Rayleigh entropy along with the iteration times to determine the optimal iteration times, thereby not only ensuring the capture precision, but also reducing the calculated quantity. Specifically, the change condition of the Rayleigh entropy of N-heavy-M-order synchronous compression transformation under different signal-to-noise ratios along with time is shown in fig. 3, the Rayleigh entropy of adjacent iteration times under the same signal-to-noise ratio is compared, and when the difference between the Rayleigh entropy of two times is smaller than a preset threshold, the process can be stopped. Fig. 4 (a) and fig. 4 (b) are respectively a time-frequency analysis diagram and a partial enlarged diagram of M-order synchronous compression on a high dynamic signal, fig. 4 (c) and fig. 4 (d) are respectively a time-frequency analysis diagram and a partial enlarged diagram of N-heavy M-order synchronous compression on a high dynamic signal, and by fig. 4 (a) to fig. 4 (d), it can be intuitively seen that the N-heavy compression improves the M-order synchronous compression, and meanwhile, a representation of the N-heavy M-order synchronous compression quantified by rayleigh entropy relative to the improvement of the M-order synchronous compression is shown in fig. 5.
The short-time fourier transform adopted in the high-order synchronous compression transform and the N-fold synchronous compression transform of the invention is an improved optimal window length short-time fourier transform based on modulation frequency, and the specific description is as follows:
the conventional short-time fourier transform method can be expressed as:
Figure SMS_159
wherein ,
Figure SMS_160
for the input signal, in the present invention a time-varying baseband signal +.>
Figure SMS_161
Is a gaussian window.
At the same time, the result of the transformation
Figure SMS_162
The window function used in the solving process is +.>
Figure SMS_163
The short-time fourier transform of (2) can be expressed as:
Figure SMS_164
the Gaussian window has the smallest time-frequency product, is widely applied in a time-frequency analysis method, and has the expression:
Figure SMS_165
Figure SMS_166
representing a gaussian window function, +.>
Figure SMS_167
Is a standard deviation, also a measure of window lengthQuasi-.
Optimal window length is critical to achieving high-concentration short-time fourier transforms, long window length results in poor time resolution, short window length results in poor frequency resolution, optimal
Figure SMS_168
Can be determined by the following formula:
Figure SMS_169
Figure SMS_170
is the instantaneous frequency of the signal being analyzed, i.e. the modulation frequency.
The method comprises the steps of setting initial window length by adopting modulation frequency factor equivalent instantaneous frequency, and then realizing the solution of the optimal window length by using an iterative instantaneous frequency method.
Defining modulation frequency
Figure SMS_171
, wherein ：
Figure SMS_172
wherein ,
Figure SMS_173
representing the frequency estimate +.>
Figure SMS_174
Deviation of time t is determined by->
Figure SMS_175
Representing a time estimate +.>
Figure SMS_176
The time t is biased, and the method comprises the following steps:
Figure SMS_177
wherein ,
Figure SMS_178
representing a short-time Fourier transform +.>
Figure SMS_179
Deviation of time t is determined by->
Figure SMS_180
Representing a short-time Fourier transform +.>
Figure SMS_181
Performing bias guide on the frequency f;
the calculated modulation frequency
Figure SMS_182
Equivalent is instantaneous frequency +.>
Figure SMS_183
Substitution of standard deviation->
Figure SMS_184
In the calculation formula of (a), the standard deviation of the current iteration period i is obtained:
Figure SMS_185
judging standard deviation of current iteration period
Figure SMS_187
Standard deviation from the last iteration period +.>
Figure SMS_191
Whether the difference between them is smaller than the set threshold, if so, the standard deviation of the current iteration period is +.>
Figure SMS_194
For window function->
Figure SMS_188
If not, the standard deviation of the current iteration period is +.>
Figure SMS_190
Corresponding current window function->
Figure SMS_193
Substituted short-time Fourier transform
Figure SMS_196
Obtaining the current short-time Fourier transform +.>
Figure SMS_186
Then the current short-time Fourier transform +.>
Figure SMS_189
And applying to standard deviation solution of the next iteration period. Standard deviation of current iteration period>
Figure SMS_192
Standard deviation from the last iteration period
Figure SMS_195
The difference between them is less than a set threshold to stop the iteration.
That is, the invention can obtain more concentrated short-time Fourier transform results under the optimal window long condition, the window length iterative process is stopped when the standard deviation obtained by two times is very close and is smaller than the threshold value, and the process can be expressed as:
Figure SMS_197
wherein i is the number of iterations,
Figure SMS_198
for threshold value->
Figure SMS_199
and />
Figure SMS_200
The window lengths for the i-th and i-1 th iterations, respectively.
S3: time-frequency signal
Figure SMS_201
The corresponding time-frequency diagram is divided into at least three parts, each part independently determines a searching starting point, searches the time-frequency diagram ridge lines from the front to the back of each searching starting point, and then splices the time-frequency diagram ridge lines of each part to obtain an instantaneous frequency track of the time-varying baseband signal, thereby completing carrier capturing.
The instantaneous frequency is an important physical quantity of the signal, and the accuracy of the extraction from the time-frequency diagram is of great importance to the study of the non-stationary signal. The energy functional minimization method adds a punishment function to the result of the time-frequency analysis of the signals, selects matching parameters, and calculates an instantaneous frequency curve which is smooth and has the maximum energy. However, the method has higher selection requirement on the starting point of the algorithm, and the incorrect starting point can be caused by larger fluctuation of abnormal conditions under the condition of lower signal-to-noise ratio.
Furthermore, the N-fold M-order synchronous compression method has the effect of improving the signal to noise ratio on the signal, the effect is gradually enhanced along with the increase of the iteration times, the lifting effect tends to be stable when a certain number of times is reached, and the N-fold M-order synchronous compression method can be used as an auxiliary reference for determining the iteration times and can reconstruct and enhance the signal after the time-frequency analysis.
The N-fold M-order synchronous compression method only redistributes the time-frequency coefficient in the frequency direction, and has no information loss, so that perfect signal reconstruction can be realized theoretically.
Figure SMS_202
And so on, can be obtained:
Figure SMS_203
the reconstructed time-varying baseband signal is as follows:
Figure SMS_204
wherein ,
Figure SMS_205
reconstructed time-varying baseband signal, ">
Figure SMS_206
Is a window function at time 0.
As shown in fig. 7, the signal-to-noise ratio of the input signal is 5dB, and it can be clearly seen that the signal-to-noise ratio of the reconstructed signal is obviously improved with the increase of the iteration number, so as to provide convenience for the subsequent tracking link.
In summary, the method carries out iteration to determine the optimal window length on the basis of the Gaussian window length of the short-time Fourier transform by frequency modulation, so that the problem of compromise between frequency resolution and time resolution can be effectively solved; meanwhile, the problem that noise robustness is poor under the condition of low signal-to-noise ratio of the method can be effectively solved by carrying out multiple compression on the time-frequency analysis result of the high-order synchronous compression method, and the energy concentration degree of a time-frequency diagram is improved; when the ridge line is extracted from the time-frequency diagram to obtain instantaneous frequency estimation, the accuracy of frequency estimation cannot be ensured by selecting a starting point from the whole diagram under the condition of lower signal-to-noise ratio, the time-frequency diagram is divided into a plurality of parts, the starting points are independently selected, and the search estimation is carried out in the forward and backward directions at the same time, so that the accuracy is improved; multiple high-order synchronous compression has the advantage of improving the signal-to-noise ratio of signals, can reconstruct the signals after completing the carrier capture of the signals, can improve the precision of subsequent tracking loops, and can be considered for signal enhancement.
Of course, the present invention is capable of other various embodiments and its several details are capable of modification and variation in light of the present invention by one skilled in the art without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (4)

1. A method for capturing a high dynamic carrier, comprising the steps of:
s1: performing M-order synchronous compression conversion on the time-varying baseband signal to obtain a conversion result
Figure QLYQS_1
The method specifically comprises the following steps:
defining M-order frequency modulation factor
Figure QLYQS_2
Which is the phase of the time-varying baseband signal>
Figure QLYQS_3
The M-th derivative over time, expressed as:
Figure QLYQS_4
wherein ,
Figure QLYQS_5
for taking the real part, the +.>
Figure QLYQS_6
Phase of time-varying baseband signal>
Figure QLYQS_7
K-th order term when Taylor series expansion is performed, k is the phase +.>
Figure QLYQS_8
The order when Taylor series expansion is performed;
wherein the M-order frequency modulation factor is obtained by:
Figure QLYQS_9
wherein ,
Figure QLYQS_10
m-th order frequency modulation factor when M-order Taylor series expansion is carried out for the phase of the time-varying baseband signal; />
Figure QLYQS_11
A kth order frequency modulation factor when performing M-order Taylor series expansion for the phase of the time-varying baseband signal;
Figure QLYQS_12
performing offset corresponding to an M-th order frequency modulation factor when performing M-th order Taylor series expansion on the phase of the time-varying baseband signal; />
Figure QLYQS_13
Performing offset corresponding to a k-th order frequency modulation factor when performing M-th order Taylor series expansion on the phase of the time-varying baseband signal; />
Figure QLYQS_14
A backward coefficient corresponding to a kth order frequency modulation factor when performing an M-order taylor series expansion for the phase of the time-varying baseband signal, wherein n=k+1, …, M;
wherein ,
Figure QLYQS_15
and />
Figure QLYQS_16
Expressed in iterative form as follows:
Figure QLYQS_17
wherein ,
Figure QLYQS_18
represents the offset +.>
Figure QLYQS_19
Partial derivative with respect to frequency f->
Figure QLYQS_20
Representing the backward coefficient->
Figure QLYQS_21
Partial derivative with respect to frequency f->
Figure QLYQS_22
Representing the backward coefficient->
Figure QLYQS_23
Partial derivative with respect to frequency f;
Figure QLYQS_24
and />
Figure QLYQS_25
The solving starting point of (2) is +.>
Figure QLYQS_26
and />
Figure QLYQS_27
And->
Figure QLYQS_28
and />
Figure QLYQS_29
The definition is as follows: />
Figure QLYQS_30
wherein ,
Figure QLYQS_31
indicating that the window function is +.>
Figure QLYQS_32
Is a short-time Fourier transform of->
Figure QLYQS_33
Representing window function as
Figure QLYQS_34
Is a short-time Fourier transform of->
Figure QLYQS_35
For short-time Fourier transform->
Figure QLYQS_36
The frequency reassignment factor obtained by time bias is expressed as:
Figure QLYQS_37
wherein ,
Figure QLYQS_38
representing a short-time Fourier transform +.>
Figure QLYQS_39
Partial derivative with respect to time t;
based on
Figure QLYQS_40
Obtaining M-order complex instantaneous frequency redistribution factor +.>
Figure QLYQS_41
The following are provided:
Figure QLYQS_42
based on
Figure QLYQS_43
Obtaining transformation result->
Figure QLYQS_44
The following are provided:
Figure QLYQS_45
wherein ,
Figure QLYQS_46
as a pulse function +.>
Figure QLYQS_47
Is a short-time Fourier transform result;
s2: for the transformation result
Figure QLYQS_48
Then N-time compression is carried out to obtain a time-frequency signal +.>
Figure QLYQS_49
The method specifically comprises the following steps:
the transformation result is transformed according to the following formula
Figure QLYQS_50
Compression is carried out:
Figure QLYQS_51
wherein ,
Figure QLYQS_52
is identical to N-1 heavy M orderStep compression transform result, < >>
Figure QLYQS_53
Is a short-time Fourier transform result;
each time compression is performed, the compression is calculated according to the following formula
Figure QLYQS_54
Order Li Shang:
Figure QLYQS_55
wherein the order is
Figure QLYQS_56
；
Judging whether the difference between the current obtained Rayleigh entropy and the Rayleigh entropy obtained by the last compression is smaller than a preset threshold, if so, the current compression result is a final time-frequency signal
Figure QLYQS_57
If not, substituting the current compression result into a compression formula to compress again until the difference between the Rayleigh entropy obtained by two adjacent compression is smaller than a preset threshold;
s3: time-frequency signal
Figure QLYQS_58
The corresponding time-frequency diagram is divided into at least three parts, each part independently determines a searching starting point, searches the time-frequency diagram ridge lines from the front to the back of each searching starting point, and then splices the time-frequency diagram ridge lines of each part to obtain an instantaneous frequency track of the time-varying baseband signal, thereby completing carrier capturing. />
2. The method of claim 1, wherein the window function in the short-time fourier transform is
Figure QLYQS_59
The method comprises the following steps:
Figure QLYQS_60
wherein ,
Figure QLYQS_61
the standard deviation is determined as follows:
Figure QLYQS_62
wherein ,
Figure QLYQS_63
is the instantaneous frequency of the time-varying baseband signal, and +.>
Figure QLYQS_64
The calculation method of (2) is as follows:
defining modulation frequency
Figure QLYQS_65
, wherein ：
Figure QLYQS_66
wherein ,
Figure QLYQS_67
representing the frequency estimate +.>
Figure QLYQS_68
Deviation of time t is determined by->
Figure QLYQS_69
Representing time estimates
Figure QLYQS_70
The time t is biased, and the method comprises the following steps:
Figure QLYQS_71
wherein ,
Figure QLYQS_72
representing a short-time Fourier transform +.>
Figure QLYQS_73
Deviation of time t is determined by->
Figure QLYQS_74
Representing a short-time Fourier transform +.>
Figure QLYQS_75
Performing bias guide on the frequency f;
the calculated modulation frequency
Figure QLYQS_76
Equivalent is instantaneous frequency +.>
Figure QLYQS_77
Substitution of standard deviation->
Figure QLYQS_78
In the calculation formula of (a), the standard deviation of the current iteration period i is obtained:
Figure QLYQS_79
judging standard deviation of current iteration period
Figure QLYQS_81
Standard deviation from the last iteration period +.>
Figure QLYQS_83
Between which are locatedIf the difference of (2) is smaller than the set threshold, if so, the standard deviation of the current iteration period is +.>
Figure QLYQS_86
For window function->
Figure QLYQS_82
If not, the standard deviation of the current iteration period is +.>
Figure QLYQS_85
Corresponding current window function->
Figure QLYQS_88
Substitution short-term Fourier transform +.>
Figure QLYQS_90
Obtaining the current short-time Fourier transform +.>
Figure QLYQS_80
Then the current short-time Fourier transform +.>
Figure QLYQS_84
Standard deviation solving for the next iteration period is applied, and when the standard deviation of the current iteration period is +.>
Figure QLYQS_87
Standard deviation from the last iteration period +.>
Figure QLYQS_89
The iteration is aborted when the difference between them is less than the set threshold.
3. The method of claim 1, wherein after carrier acquisition is completed, the method is based on time-frequency signals
Figure QLYQS_91
Reconstructing a time-varying baseband signal:
Figure QLYQS_92
wherein ,
Figure QLYQS_93
reconstructed time-varying baseband signal, ">
Figure QLYQS_94
Is a window function at time 0.
4. The method for capturing a high dynamic carrier wave according to claim 1, wherein the method for acquiring the time-varying baseband signal comprises:
the local carrier wave is generated in the receiver and multiplied by the received signal, the multiplication result is composed of a carrier wave component close to zero frequency and a high-frequency carrier wave component, the high-frequency carrier wave component is removed by integrating the multiplication result, and the carrier wave component close to zero frequency containing Doppler frequency offset is used as a time-varying baseband signal.
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CN113009523A (en) * 2021-02-22 2021-06-22 浙江理工大学 Doppler frequency estimation and compensation method and system for long-time coherent integration capture
CN113972951A (en) * 2021-10-22 2022-01-25 金陵科技学院 Comb-shaped searching method for low signal-to-noise ratio and high dynamic signal carrier Doppler frequency offset

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CN111082835A (en) * 2019-12-03 2020-04-28 南京理工大学 Pseudo code and Doppler combined capturing method of direct sequence spread spectrum signal under high dynamic condition
CN111934710A (en) * 2020-07-06 2020-11-13 南京天际砺剑科技有限公司 High-dynamic spread spectrum signal rapid acquisition algorithm
CN113009523A (en) * 2021-02-22 2021-06-22 浙江理工大学 Doppler frequency estimation and compensation method and system for long-time coherent integration capture
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