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CN112073034A - Timing synchronization system based on self-adaptive loop gain adjustment - Google Patents

Timing synchronization system based on self-adaptive loop gain adjustment Download PDF

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CN112073034A
CN112073034A CN202010830973.3A CN202010830973A CN112073034A CN 112073034 A CN112073034 A CN 112073034A CN 202010830973 A CN202010830973 A CN 202010830973A CN 112073034 A CN112073034 A CN 112073034A
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fuzzy subset
fuzzy
membership
output
subset
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CN112073034B (en
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王永庆
申宇瑶
史学森
张春
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Beijing Institute of Technology BIT
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
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Abstract

The invention discloses a timing synchronization system based on self-adaptive loop gain adjustment, which can realize the purpose of adjusting the loop bandwidth by self-adaptively adjusting the loop gain of a loop filter on the basis of a Gardner synchronous loop model, thereby effectively balancing the relation between the timing synchronization tracking precision and the locking time. The system adds a loop gain adjustment LGAA unit on the Gardner timing synchronization loop. The LGA unit is connected between a timing error discriminator on the Gardner timing synchronization loop and a loop filter; the LGA unit takes the identification result of the timing error identifier as input; wherein the normalized value of the p-th discrimination result output by the timing error discriminator is taken
Figure DDA0002637957700000011
Input to a loop filter. In LGA unit, get
Figure DDA0002637957700000012
And
Figure DDA0002637957700000013
normalized to the p-1 th discrimination
Figure DDA0002637957700000014
Difference of (2)
Figure DDA0002637957700000015
And as an input variable of the fuzzy controller, obtaining a fuzzy output result through a set fuzzy rule, and updating the gain of the loop filter.

Description

Timing synchronization system based on self-adaptive loop gain adjustment
Technical Field
The invention relates to the technical field of aerospace measurement and control communication, in particular to a timing synchronization system based on self-adaptive loop gain adjustment.
Background
In the aerospace survey and control communication system, data information is modulated on a carrier wave at a certain code element rate for transmission, a receiving end needs to judge the initial position and the end position of each data bit of a transmission signal, and a local data bit sampling pulse is continuously adjusted to be positioned at the code element peak value moment, so that optimal receiving sampling is realized, and data demodulation is completed. If the local data bit clock is not synchronous with the received signal data bit, the sampling judgment time is not the optimal sampling time any more, the judgment result is likely to be wrong, and the demodulation error rate is improved, so the timing synchronization performance determines the performance of the communication system to a certain extent.
The Gardner synchronous loop can realize timing synchronization under the condition that each data bit sampling point is not less than 2, the requirement on the hardware AD sampling rate is relaxed to a certain extent, and meanwhile, the Gardner synchronous loop is widely applied to the field of aerospace measurement and control due to the advantages of simple structure, high precision, high efficiency and the like. Tracking accuracy and lock time are two important metrics for measuring performance of the Gardner timing synchronization loop. The tracking accuracy marks the stability of the loop, the higher the accuracy, the more stable the timing synchronization and the smaller the synchronization error. The lock time marks the setup time of the loop, and the shorter the lock time, the faster the loop is stable and can adapt to the dynamic changes of the signal.
The loop tracking accuracy is mainly affected by the roll-off coefficient of the shaping filter, the symbol rate, the signal-to-noise ratio and the loop bandwidth. Considering that signal parameters such as information symbol rate, roll-off coefficient of a shaping filter and the like are definite information, signal-to-noise ratio is random variation caused by an external environment, and the condition of the lowest signal-to-noise ratio is considered in loop design. Reducing the loop bandwidth can make the jitter variance smaller, thereby improving tracking accuracy, but the lock time can become longer. While increasing the loop bandwidth may reduce the lock time, it may result in a decrease in tracking accuracy. During timing synchronization, it is difficult to balance the relationship between tracking accuracy and lock time if a fixed loop bandwidth is used.
In contrast, at present, research proposes that different loop bandwidths are adopted at the initial stage and the later stage of loop locking, that is, a larger loop bandwidth is adopted at the initial stage of loop tracking, so as to facilitate quick locking; and a smaller loop bandwidth is adopted in the later stage of loop tracking, so that the tracking precision of the loop is improved. The loop tracking performance can be improved to a certain extent by adopting different loop bandwidths according to the loop tracking state.
However, directly adjusting the loop bandwidth requires recalculation of the coefficients of the loop filter, resulting in high system complexity.
In view of the above problems, how to adjust the loop bandwidth adaptively by adjusting the loop gain coefficient to effectively shorten the loop locking time on the basis of ensuring higher tracking accuracy is a problem to be solved urgently at present.
Disclosure of Invention
In view of this, the present invention provides a timing synchronization system based on adaptive loop gain adjustment, which can achieve the purpose of adjusting the loop bandwidth by adaptively adjusting the loop gain of a loop filter on the basis of a Gardner synchronization loop model, thereby effectively balancing the relationship between the tracking accuracy of timing synchronization and the locking time.
In order to achieve the purpose, the technical scheme of the invention is as follows: a loop gain adjusting LGA unit is added to the Gardner timing synchronization loop based on a timing synchronization system that adaptively adjusts the loop gain.
A loop gain adjusting LGA unit connected between a timing error discriminator on the Gardner timing synchronization loop and a loop filter;
loop gain adjusting LGA unit to timing error discriminator discrimination resultAs an input; wherein the normalized value of the p-th discrimination result output by the timing error discriminator is taken
Figure BDA0002637957680000021
Input to a loop filter.
The loop gain adjustment LGA unit comprises a double-input single-output Mamdani type fuzzy controller; get
Figure BDA0002637957680000031
And
Figure BDA0002637957680000032
normalized to the p-1 th discrimination
Figure BDA0002637957680000033
Difference of (2)
Figure BDA0002637957680000034
To be provided with
Figure BDA0002637957680000035
And
Figure BDA0002637957680000036
as input variables for the fuzzy controller.
Fuzzy controller to input variable
Figure BDA0002637957680000037
And
Figure BDA0002637957680000038
fuzzification is carried out, and the method specifically comprises the following steps:
is provided with
Figure BDA0002637957680000039
The number of fuzzy subsets of (1) is 5, negative large NL, negative small NS, zero ZE, positive small PS, and positive large PL, respectively; get
Figure BDA00026379576800000310
Corresponding fuzziness when corresponding membership is greater than zeroA subset of
Figure BDA00026379576800000311
And (5) fuzzifying the result.
Wherein
Figure BDA00026379576800000312
Membership to fuzzy subset NL of
Figure BDA00026379576800000313
Figure BDA00026379576800000314
Membership functions to the fuzzy subsets NS of
Figure BDA00026379576800000315
Figure BDA00026379576800000316
Membership to the fuzzy subset ZE of
Figure BDA00026379576800000317
Figure BDA00026379576800000318
Membership to the fuzzy subset PS of
Figure BDA00026379576800000319
Figure BDA00026379576800000320
Membership to the fuzzy subset PL of
Figure BDA00026379576800000321
Is provided with
Figure BDA00026379576800000322
Is not blurredThe number of sets is 3, respectively less than zero ZN, equal to zero ZE and greater than zero ZP; get
Figure BDA00026379576800000323
Corresponding to the fuzzy subset corresponding to the membership degree greater than zero is
Figure BDA00026379576800000324
And (5) fuzzifying the result.
Figure BDA0002637957680000041
Membership to the fuzzy subset ZN of
Figure BDA0002637957680000042
Figure BDA0002637957680000043
Membership to the fuzzy subset ZE of
Figure BDA0002637957680000044
Figure BDA0002637957680000045
The degree of membership to the fuzzy subset ZP is
Figure BDA0002637957680000046
By the symbol gpThe output variables of the fuzzy controller are represented, and the fuzzy subset number is 7, which are respectively represented by NL, NM, NS, ZE, PS, PM and PL.
Setting fuzzy control rules of the fuzzy controller comprises the following steps:
Figure BDA0002637957680000047
is subject to the fuzzy subset NL, and
Figure BDA0002637957680000048
die ofWhen the fuzzification result is subordinate to the fuzzy subset ZN, the variable g is outputpBelonging to the fuzzy subset NM.
Figure BDA0002637957680000049
Is subject to the fuzzy subset NL, and
Figure BDA00026379576800000410
when the fuzzification result of (2) is in the fuzzy subset ZE, the variable g is outputpBelonging to the fuzzy subset NM.
Figure BDA00026379576800000411
Is subject to the fuzzy subset NL, and
Figure BDA00026379576800000412
when the fuzzification result of (a) is in the fuzzy subset ZP, the variable g is outputpBelonging to the fuzzy subset NM.
Figure BDA00026379576800000413
Is subject to a fuzzy subset NS, and
Figure BDA00026379576800000414
when the fuzzification result is subordinate to the fuzzy subset ZN, the variable g is outputpMembership to fuzzy subset NL.
Figure BDA00026379576800000415
Is subject to a fuzzy subset NS, and
Figure BDA00026379576800000416
when the fuzzification result of (2) is in the fuzzy subset ZE, the variable g is outputpBelonging to the fuzzy subset NM.
Figure BDA00026379576800000417
Is subject to a fuzzy subset NS, and
Figure BDA00026379576800000418
when the fuzzification result of (a) is in the fuzzy subset ZP, the variable g is outputpBelonging to the fuzzy subset NS.
Figure BDA0002637957680000051
Is subject to a fuzzy subset ZE, and
Figure BDA0002637957680000052
when the fuzzification result is subordinate to the fuzzy subset ZN, the variable g is outputpBelonging to the fuzzy subset PS.
Figure BDA0002637957680000053
Is subject to a fuzzy subset ZE, and
Figure BDA0002637957680000054
when the fuzzification result of (2) is in the fuzzy subset ZE, the variable g is outputpBelonging to the fuzzy subset ZE.
Figure BDA0002637957680000055
Is subject to a fuzzy subset ZE, and
Figure BDA0002637957680000056
when the fuzzification result of (a) is in the fuzzy subset ZP, the variable g is outputpBelonging to the fuzzy subset NS.
Figure BDA0002637957680000057
Is subject to the fuzzy subset PS, and
Figure BDA0002637957680000058
when the fuzzification result is subordinate to the fuzzy subset ZN, the fuzzification result is outputVariable gpBelonging to the fuzzy subset PS.
Figure BDA0002637957680000059
Is subject to the fuzzy subset PS, and
Figure BDA00026379576800000510
when the fuzzification result of (2) is in the fuzzy subset ZE, the variable g is outputpBelonging to the fuzzy subset PM.
Figure BDA00026379576800000511
Is subject to the fuzzy subset PS, and
Figure BDA00026379576800000512
when the fuzzification result of (a) is in the fuzzy subset ZP, the variable g is outputpBelonging to the fuzzy subset PL.
Figure BDA00026379576800000513
Is subject to the fuzzy subset PL, and
Figure BDA00026379576800000514
when the fuzzification result is subordinate to the fuzzy subset ZN, the variable g is outputpBelonging to the fuzzy subset PM.
Figure BDA00026379576800000515
Is subject to the fuzzy subset PL, and
Figure BDA00026379576800000516
when the fuzzification result of (2) is in the fuzzy subset ZE, the variable g is outputpBelonging to the fuzzy subset PM.
Figure BDA00026379576800000517
Is subject to the fuzzification resultFuzzy the subset PL, and
Figure BDA00026379576800000518
when the fuzzification result of (a) is in the fuzzy subset ZP, the variable g is outputpBelonging to the fuzzy subset PM.
According to the output variable g of the fuzzy controllerpThe fuzzification result is subjected to fuzzification to obtain an output variable gpA value of (d), an output gain coefficient GpAs the updated gain of the loop filter is,
Figure BDA00026379576800000519
has the advantages that:
the invention provides a timing synchronization system based on self-adaptive loop gain adjustment. According to the method, a loop gain self-adaptive adjusting unit is added on the basis of a Gardner synchronous loop model, a fuzzy controller is used for generating a loop gain coefficient in a self-adaptive mode according to the output of a Gardner error discriminator, the loop bandwidth of a loop filter is adjusted, the relation between the loop tracking precision and the locking time is effectively considered, and the rapid locking is completed while the higher tracking precision is ensured.
Drawings
FIG. 1 shows a schematic diagram of a Gardner synchronization loop architecture;
FIG. 2 is a schematic diagram illustrating a timing synchronization loop structure based on adaptive adjustment of loop gain according to an embodiment of the present invention;
FIG. 3 shows an S-plot of a Gardner discriminator;
FIG. 4 shows a graph of input variable membership functions;
fig. 5 shows a graph of the membership function of the output variable.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The present invention is directed to improvements over the existing Gardner synchronization loop. The Gardner synchronization loop is shown in FIG. 1 and includes a matched filter, a difference filter, a decimator, a timing error discriminator, a loop filter, anda numerically controlled oscillator; the matched filter receives a baseband signal r (t) and outputs a matched and filtered signal y (t); the interpolation filter takes the matched and filtered signal y (t) as input, and takes the sampling signals at two set time points, namely at the time point tkAnd tk-1/2Sampling the kth symbol to obtain a signal y (t)k) And y (t)k-1/2)，y(tk) Output through the extractor; y (t)k) And y (t)k-1/2) The timing error discriminator outputs discrimination result, namely loop error, the loop error contains noise and high frequency component, the noise and part of the high frequency component are filtered by a loop filter to improve the signal quality, the output of the loop filter outputs control words through a numerical control oscillator, and the control words are input to an interpolation filter to control the interpolation position.
The embodiment of the invention aims at the Gardner synchronous loop shown in the figure 1 to carry out the following improvement: a loop gain adjustment LGAA unit is added to the Gardner timing synchronization loop. The loop gain adjustment LGAA unit is connected between a timing error discriminator on the Gardner timing synchronization loop and a loop filter. As shown in particular in fig. 2.
The baseband signal input to the matched filter is represented as
Figure BDA0002637957680000071
Wherein, ciFor the symbol sequence, u (T) is the baseband pulse, T and τ are the symbol period and the received signal delay, respectively, and w (T) is gaussian white noise. The output of the matched filter is
Figure BDA0002637957680000072
Wherein v (t) is raised cosine pulse, and n (t) is narrow-band noise.
The interpolation filter is at time tkAnd tk-1/2Sampling the kth symbol to obtain a signal y (t)k) Wherein
Figure BDA0002637957680000073
Is the delay of the kth symbol.
The output of the timing error discriminator is
ek＝Re[y*(tk-1/2){y(tk)-y(tk-1)}]
Wherein, Re [ ·]For operation of the delivery section, y*(. cndot.) is a conjugation operation.
The loop gain adjusting LGA unit takes the identification result of the timing error identifier as input; wherein the normalized value of the p-th discrimination result output by the timing error discriminator is taken
Figure BDA0002637957680000074
Input to a loop filter.
The S-curve of the error discriminator output is shown in FIG. 3 and is represented as
Figure BDA0002637957680000075
Figure BDA0002637957680000076
Where A is the signal amplitude and U (f) is the Fourier transform of u (t). Gardner discrimination gain
Figure BDA0002637957680000077
In proportion to the signal power, the noise floor in a receiver is usually fixed, and the magnitude of the received signal power can be usually measured by the signal-to-noise ratio. When the signal-to-noise ratio of the signal is high, the signal power is high, the discrimination gain is high, and the signal adjustment is fast, whereas when the signal-to-noise ratio is low, the signal power is low, the discrimination gain is low, not only the signal adjustment speed is slow, but also the discrimination result is likely to be lower than the noise threshold, so that the timing jitter is increased, and the tracking accuracy is reduced. In order to eliminate the influence of signal power, the power normalization processing is carried out on the discrimination result, and the processed discrimination result is
Figure BDA0002637957680000081
Wherein M is the number of peak sampling points.
The basic principle of the LGAA unit is to generate a loop gain coefficient by analyzing a change in timing error, so that a loop adjustment direction converges toward the center of an S-curve.
The LGAA unit in the present invention generates a loop gain by analyzing the output of the error discriminator while using the fuzzy control theory. The LGA unit consists of two parts, namely an error preprocessing module and a fuzzy control module.
The invention adopts a double-input-single-output Mamdani type fuzzy controller, and the core of the loop gain adjusting method based on the fuzzy control is the design of the fuzzy controller, which is mainly divided into three parts: fuzzification, fuzzy reasoning and deblurring.
Namely, the loop gain adjustment LGA unit comprises a double-input single-output Mamdani fuzzy controller; by symbols
Figure BDA0002637957680000082
Representing the p-th normalized output of the error discriminator with a corresponding timing error of τp(ii) a By symbols
Figure BDA0002637957680000083
To represent
Figure BDA0002637957680000084
And
Figure BDA0002637957680000085
a difference of (i.e.
Figure BDA0002637957680000086
As can be seen from FIG. 2, the loop direction can be adjusted by
Figure BDA0002637957680000087
And
Figure BDA0002637957680000088
the value of (2) is deduced. Therefore, is provided with
Figure BDA0002637957680000089
And
Figure BDA00026379576800000810
are input variables of the fuzzy controller.
Fuzzy controller to input variable
Figure BDA00026379576800000811
And
Figure BDA00026379576800000812
and performing fuzzification, wherein after the input and output variables are mapped to a certain real value on the fuzzy subsets, the membership degree of the real value belonging to each relevant fuzzy subset is calculated. The method specifically comprises the following steps:
is provided with
Figure BDA00026379576800000813
The number of fuzzy subsets of (1) is 5, negative large NL, negative small NS, zero ZE, positive small PS, and positive large PL, respectively; get
Figure BDA00026379576800000814
Corresponding to the fuzzy subset corresponding to the membership degree greater than zero is
Figure BDA00026379576800000815
And (5) fuzzifying the result.
Wherein
Figure BDA00026379576800000816
Membership to fuzzy subset NL of
Figure BDA00026379576800000817
Figure BDA0002637957680000091
Membership functions to the fuzzy subsets NS of
Figure BDA0002637957680000092
Figure BDA0002637957680000093
Membership to the fuzzy subset ZE of
Figure BDA0002637957680000094
Figure BDA0002637957680000095
Membership to the fuzzy subset PS of
Figure BDA0002637957680000096
Figure BDA0002637957680000097
Membership to the fuzzy subset PL of
Figure BDA0002637957680000098
Is provided with
Figure BDA0002637957680000099
The number of fuzzy subsets of (1) is 3, respectively less than zero ZN, equal to zero ZE and greater than zero ZP; get
Figure BDA00026379576800000910
Corresponding to the fuzzy subset corresponding to the membership degree greater than zero is
Figure BDA00026379576800000911
And (5) fuzzifying the result.
Figure BDA00026379576800000912
Membership to the fuzzy subset ZN of
Figure BDA00026379576800000913
Figure BDA00026379576800000914
Membership to the fuzzy subset ZE of
Figure BDA00026379576800000915
Figure BDA00026379576800000916
The degree of membership to the fuzzy subset ZP is
Figure BDA00026379576800000917
Fig. 3 and 4 show schematic diagrams of input variable membership functions.
By the symbol gpThe output variables of the fuzzy controller are represented, and the fuzzy subset number is 7, which are respectively represented by NL, NM, NS, ZE, PS, PM and PL.
gpMembership to fuzzy subset NL of
Figure BDA0002637957680000101
gpMembership to the fuzzy subset NM of
Figure BDA0002637957680000102
gpMembership to the fuzzy subset NS is
Figure BDA0002637957680000103
gpMembership to the fuzzy subset ZE of
Figure BDA0002637957680000104
gpMembership to the fuzzy subset PS of
Figure BDA0002637957680000105
gpMembership to the fuzzy subset PM of
Figure BDA0002637957680000106
gpMembership belonging to the fuzzy subset PL of
Figure BDA0002637957680000107
Fig. 5 shows a graph of the membership function of the output variable.
Fuzzy inference is the theoretical basis of fuzzy controller design, and refers to a process of deducing a possibly inaccurate conclusion from an imprecise premise according to a fuzzy control rule, that is, the fuzzy inference refers to a process of deducing a fuzzy output variable from a fuzzy input variable through a certain inference method according to the fuzzy control rule. The design of the fuzzy rule mainly depends on expert experience knowledge, and the more abundant the experience is, the more accurate the fuzzy control is. The general idea of fuzzy rule design in the invention is to output a larger gain adjustment coefficient when the relative deviation is larger, accelerate the signal adjustment step at the moment, enable the loop to enter the lock rapidly, and input a smaller gain adjustment coefficient when the relative deviation is smaller, so as to enable the loop to keep stable high-precision tracking. The fuzzy control rules for fuzzy reasoning are summarized and summarized by analyzing experimental test data, as shown in table 1.
Table 1: fuzzy control rule
Figure BDA0002637957680000111
The fuzzy control rule set for the fuzzy controller in the embodiment of the invention comprises the following rules:
Figure BDA0002637957680000112
is subject to the fuzzy subset NL, and
Figure BDA0002637957680000113
when the fuzzification result is subordinate to the fuzzy subset ZN, the variable g is outputpBelonging to the fuzzy subset NM.
Figure BDA0002637957680000114
Is subject to the fuzzy subset NL, and
Figure BDA0002637957680000115
when the fuzzification result of (2) is in the fuzzy subset ZE, the variable g is outputpBelonging to the fuzzy subset NM.
Figure BDA0002637957680000116
Is subject to the fuzzy subset NL, and
Figure BDA0002637957680000117
when the fuzzification result of (a) is in the fuzzy subset ZP, the variable g is outputpBelonging to the fuzzy subset NM.
Figure BDA0002637957680000118
Is subject to a fuzzy subset NS, and
Figure BDA0002637957680000119
when the fuzzification result is subordinate to the fuzzy subset ZN, the variable g is outputpMembership to fuzzy subset NL.
Figure BDA00026379576800001110
Is subject to a fuzzy subset NS, and
Figure BDA00026379576800001111
when the fuzzification result of (2) is in the fuzzy subset ZE, the variable g is outputpBelonging to the fuzzy subset NM.
Figure BDA00026379576800001112
Is subject to a fuzzy subset NS, and
Figure BDA00026379576800001113
when the fuzzification result of (a) is in the fuzzy subset ZP, the variable g is outputpBelonging to the fuzzy subset NS.
Figure BDA0002637957680000121
Is subject to a fuzzy subset ZE, and
Figure BDA0002637957680000122
when the fuzzification result is subordinate to the fuzzy subset ZN, the variable g is outputpBelonging to the fuzzy subset PS.
Figure BDA0002637957680000123
Is subject to a fuzzy subset ZE, and
Figure BDA0002637957680000124
when the fuzzification result of (2) is in the fuzzy subset ZE, the variable g is outputpMembership to the fuzzy subset ZE;
Figure BDA0002637957680000125
is subject to a fuzzy subset ZE, and
Figure BDA0002637957680000126
when the fuzzification result of (a) is in the fuzzy subset ZP, the variable g is outputpBelonging to the fuzzy subset NS.
Figure BDA0002637957680000127
Is subject to the fuzzy subset PS, and
Figure BDA0002637957680000128
when the fuzzification result is subordinate to the fuzzy subset ZN, the variable g is outputpBelonging to the fuzzy subset PS.
Figure BDA0002637957680000129
Is subject to the fuzzy subset PS, and
Figure BDA00026379576800001210
when the fuzzification result of (2) is in the fuzzy subset ZE, the variable g is outputpBelonging to the fuzzy subset PM.
Figure BDA00026379576800001211
Is subject to the fuzzy subset PS, and
Figure BDA00026379576800001212
when the fuzzification result of (a) is in the fuzzy subset ZP, the variable g is outputpBelonging to the fuzzy subset PL.
Figure BDA00026379576800001213
Is subject to the fuzzy subset PL, and
Figure BDA00026379576800001214
when the fuzzification result is subordinate to the fuzzy subset ZN, the variable g is outputpBelonging to the fuzzy subset PM.
Figure BDA00026379576800001215
Is subject to the fuzzy subset PL, and
Figure BDA00026379576800001216
when the fuzzification result of (2) is in the fuzzy subset ZE, the variable g is outputpBelonging to the fuzzy subset PM.
Figure BDA00026379576800001217
Is subject to the fuzzy subset PL, and
Figure BDA00026379576800001218
when the fuzzification result of (a) is in the fuzzy subset ZP, the variable g is outputpBelonging to the fuzzy subset PM.
According to the output variable g of the fuzzy controllerpThe fuzzification result is subjected to fuzzification to obtain an output variable gpA value of (d), an output gain coefficient GpAs the updated gain of the loop filter.
Deblurring is the process of equating a fuzzy set output through fuzzy inference to a distinct value, also called as sharpening. And performing deblurring processing by adopting an area center method. The area-centric method is to find the fuzzy set membership function curve and the center of the area surrounded by the abscissa, and then to take the abscissa of the center as the output value. The calculation principle of the area center method is
Figure BDA0002637957680000131
Wherein u is an output variable, and U (u) is a fuzzy domain NuA membership function of the fuzzy set U.
The change of the gain coefficient is essentially equivalent to the change of the loop bandwidth, the gain coefficient is increased when the relative error is large, the loop bandwidth is increased, the loop is locked quickly, the gain coefficient is reduced when the relative error is small, the loop bandwidth is reduced, and the loop high-precision tracking is realized. However, too frequent changes in the loop bandwidth can add jitter to the authentication error and, in severe cases, can cause the loop to lose lock. In summary, the gain factor G is consideredpAnd fuzzy controller output gpThe corresponding relation of (A) is an exponential function, i.e.
Figure BDA0002637957680000132
In conventional Gardner loop design, the equivalent loop bandwidth of the loop filter when considering the loop gain is expressed as
Figure BDA0002637957680000133
Wherein H (j2 π f) is the transfer function of the loop filter, a and b are the damping coefficients of the loop filter, wnIs angular frequency, GpIs a loop gain coefficient, GpK is the actual loop gain. The above formula shows that the purpose of adjusting the loop bandwidth can be achieved by adjusting the loop gain factor.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. A timing synchronization system based on self-adaptive loop gain adjustment is characterized in that a loop gain adjustment LGAA unit is added on a Gardner timing synchronization loop;
the loop gain adjusting LGA unit is connected between a timing error discriminator and a loop filter on the Gardner timing synchronization loop;
the loop gain adjusting LGA unit takes the discrimination result of the timing error discriminator as input; wherein the normalized value of the p-th discrimination result output from the timing error discriminator is obtained
Figure FDA0002637957670000011
Inputting to a loop filter;
the loop gain adjusting LGA unit comprises a double-input single-output Mamdani type fuzzy controller; get
Figure FDA0002637957670000012
And
Figure FDA0002637957670000013
normalized to the p-1 th discrimination
Figure FDA0002637957670000014
Difference of (2)
Figure FDA00026379576700000119
To be provided with
Figure FDA00026379576700000121
And
Figure FDA00026379576700000122
as an input variable of the fuzzy controller;
the fuzzy controller is used for inputting variables
Figure FDA0002637957670000018
And
Figure FDA0002637957670000019
fuzzification is carried out, and the method specifically comprises the following steps:
is provided with
Figure FDA00026379576700000110
The number of fuzzy subsets of (1) is 5, negative large NL, negative small NS, zero ZE, positive small PS, and positive large PL, respectively; get
Figure FDA00026379576700000111
Corresponding to the fuzzy subset corresponding to the membership degree greater than zero is
Figure FDA00026379576700000112
Fuzzified results;
wherein
Figure FDA00026379576700000113
Membership to fuzzy subset NL of
Figure FDA00026379576700000114
Figure FDA00026379576700000115
Membership functions to the fuzzy subsets NS of
Figure FDA00026379576700000116
Figure FDA00026379576700000117
Membership to the fuzzy subset ZE of
Figure FDA00026379576700000118
Figure FDA0002637957670000021
Membership to the fuzzy subset PS of
Figure FDA0002637957670000022
Figure FDA0002637957670000023
Membership to the fuzzy subset PL of
Figure FDA0002637957670000024
Is provided with
Figure FDA0002637957670000025
The number of fuzzy subsets of (1) is 3, respectively less than zero ZN, equal to zero ZE and greater than zero ZP; get
Figure FDA0002637957670000026
Corresponding to the fuzzy subset corresponding to the membership degree greater than zero is
Figure FDA0002637957670000027
Fuzzified results;
Figure FDA0002637957670000028
membership to the fuzzy subset ZN of
Figure FDA0002637957670000029
Figure FDA00026379576700000210
Membership to the fuzzy subset ZE of
Figure FDA00026379576700000211
Figure FDA00026379576700000212
The degree of membership to the fuzzy subset ZP is
Figure FDA00026379576700000213
By the symbol gpOutput variables representing the fuzzy controller, the fuzzy subset number of which is 7, and are respectively shown as NL, NM, NS, ZE, PS, PM and PL;
setting the fuzzy control rule of the fuzzy controller comprises the following steps:
Figure FDA00026379576700000214
is subject to the fuzzy subset NL, and
Figure FDA00026379576700000215
when the fuzzification result is subordinate to the fuzzy subset ZN, the variable g is outputpMembership to a fuzzy subset NM;
Figure FDA00026379576700000216
is subject to the fuzzy subset NL, and
Figure FDA00026379576700000217
when the fuzzification result of (2) is in the fuzzy subset ZE, the variable g is outputpMembership to a fuzzy subset NM;
Figure FDA00026379576700000218
is subject to the fuzzy subset NL, and
Figure FDA00026379576700000219
when the fuzzification result of (a) is in the fuzzy subset ZP, the variable g is outputpMembership to a fuzzy subset NM;
Figure FDA0002637957670000031
is subject to a fuzzy subset NS, and
Figure FDA0002637957670000032
when the fuzzification result is subordinate to the fuzzy subset ZN, the variable g is outputpMembership to fuzzy subset NL;
Figure FDA0002637957670000033
is subject to a fuzzy subset NS, and
Figure FDA0002637957670000034
when the fuzzification result of (2) is in the fuzzy subset ZE, the variable g is outputpMembership to a fuzzy subset NM;
Figure FDA0002637957670000035
is subject to a fuzzy subset NS, and
Figure FDA0002637957670000036
when the fuzzification result of (a) is in the fuzzy subset ZP, the variable g is outputpMembership to the fuzzy subset NS;
Figure FDA0002637957670000037
is subject to a fuzzy subset ZE, and
Figure FDA0002637957670000038
when the fuzzification result is subordinate to the fuzzy subset ZN, the variable g is outputpMembership to the fuzzy subset PS;
Figure FDA0002637957670000039
is subject to a fuzzy subset ZE, and
Figure FDA00026379576700000310
when the fuzzification result of (2) is in the fuzzy subset ZE, the variable g is outputpMembership to the fuzzy subset ZE;
Figure FDA00026379576700000311
is subject to a fuzzy subset ZE, and
Figure FDA00026379576700000312
when the fuzzification result of (a) is in the fuzzy subset ZP, the variable g is outputpMembership to the fuzzy subset NS;
Figure FDA00026379576700000313
is subject to the fuzzy subset PS, and
Figure FDA00026379576700000314
when the fuzzification result is subordinate to the fuzzy subset ZN, the variable g is outputpMembership to the fuzzy subset PS;
Figure FDA00026379576700000315
is subject to the fuzzy subset PS, and
Figure FDA00026379576700000316
when the fuzzification result of (2) is in the fuzzy subset ZE, the variable g is outputpMembership to a fuzzy subset PM;
Figure FDA00026379576700000317
is subject to the fuzzy subset PS, and
Figure FDA00026379576700000318
when the fuzzification result of (a) is in the fuzzy subset ZP, the variable g is outputpMembership to the fuzzy subset PL;
Figure FDA00026379576700000319
is subject to the fuzzy subset PL, and
Figure FDA00026379576700000320
when the fuzzification result is subordinate to the fuzzy subset ZN, the variable g is outputpMembership to fuzzy subsets PM
Figure FDA00026379576700000321
Is subject to the fuzzy subset PL, and
Figure FDA00026379576700000322
when the fuzzification result of (2) is in the fuzzy subset ZE, the variable g is outputpMembership to a fuzzy subset PM;
Figure FDA0002637957670000041
is subject to the fuzzy subset PL, and
Figure FDA0002637957670000042
when the fuzzification result of (a) is in the fuzzy subset ZP, the variable g is outputpMembership to a fuzzy subset PM;
according to the output variable g of the fuzzy controllerpThe fuzzification result is subjected to fuzzification to obtain an output variable gpA value of (d), an output gain coefficient GpAs the updated gain of the loop filter is,
Figure FDA0002637957670000043
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