CN111865850B - PCM/FM signal early-late loop frequency synchronization method based on multi-symbol detection - Google Patents

PCM/FM signal early-late loop frequency synchronization method based on multi-symbol detection Download PDF

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CN111865850B
CN111865850B CN202010660213.2A CN202010660213A CN111865850B CN 111865850 B CN111865850 B CN 111865850B CN 202010660213 A CN202010660213 A CN 202010660213A CN 111865850 B CN111865850 B CN 111865850B
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CN111865850A (en
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谢顺钦
陈大海
李湘鲁
周锞
黄治江
范靖
代涛
马国宁
张金荣
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Institute of Electronic Engineering of CAEP
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0014—Carrier regulation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0014—Carrier regulation
    • H04L2027/0044—Control loops for carrier regulation
    • H04L2027/0063—Elements of loops
    • H04L2027/0069—Loop filters

Abstract

The invention belongs to the technical field of broadband signal sampling, and particularly relates to a PCM/FM signal early-late loop frequency synchronization method based on multi-symbol detection.

Description

PCM/FM signal early-late loop frequency synchronization method based on multi-symbol detection
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a PCM/FM signal early-late loop frequency synchronization method based on multi-symbol detection.
Background
In a wireless communication scene with large dynamic, the received PCM/FM signals have large Doppler frequency offset and first-order and second-order Doppler change rates, and show large dynamic characteristics. The demodulation performance of the telemetry signal is affected by the excessive doppler frequency offset, so the receiving end usually needs to estimate the doppler frequency, complete the capture and tracking of the carrier frequency, and then perform subsequent signal demodulation.
The carrier frequency synchronization of existing PCM/FM telemetry signals typically uses estimation methods based on power spectrum characteristics, such as the power spectrum maxima method, the power spectrum medians method, and the power spectrum centroids method. The first two algorithms complete the estimation of the carrier frequency by solving the frequency corresponding to the maximum amplitude of the power spectrum or estimating the center frequency of the power spectrum in the signal bandwidth after performing FFT on the signal, but the estimation accuracy of the two methods is poor because the maximum amplitude of the power spectrum and the estimation of the center frequency are greatly affected by noise. Especially when the signal-to-noise ratio is low, the method is difficult to realize high-performance carrier synchronization; the third algorithm, the power spectrum gravity center method, utilizes the symmetry of the signal power spectrum to realize the estimation of the carrier frequency. When the modulation code elements '0' and '1' at the transmitting end keep relatively balanced quantity, the center of gravity of the PCM/FM signal power spectrum is always at the carrier frequency, and then the algorithm can realize the carrier frequency synchronization with higher precision. In addition, due to the fact that the utilized power spectrum information is increased, the anti-noise performance of the algorithm is greatly improved compared with the former two algorithms, but unfortunately, in practical application, for most PCM/FM transmitters, due to the non-randomness of the data frame structure, the number of modulation symbols of the transmitter is not balanced, so that the center of gravity of the signal power spectrum is not always at the carrier frequency, which causes the estimation deviation of the synchronization method, and therefore, several carrier frequency estimation methods based on the power spectrum characteristics have certain limitations in practical application.
Besides the estimation method based on frequency domain characteristics, the carrier frequency synchronization of PCM/FM signals also has an estimation method based on frequency discrimination demodulation results, for example, Chinese patent publication No. CN104486288A, published on 2015, 4 months and 1 days, entitled "a carrier frequency offset suppression method suitable for PCM/FM telemetering receiver", discloses a carrier frequency offset suppression method suitable for PCM/FM telemetering receiver, which utilizes the statistical characteristics of formed code elements to perform histogram estimation through frequency discriminated signals to realize modulation frequency estimation corresponding to positive and negative code elements, and further averages the modulation frequency to obtain the estimated value of carrier frequency offset,the method estimates the carrier frequency position f corresponding to the modulation code element '0' and the code element '1' by counting the number of '0' and '1' obtained by judgment in a period of time 0 And f 1 And by looking for f 0 And f 1 The method solves the problem of imbalance of modulation code elements '0' and '1' of the transmitter; however, the estimation accuracy for the decision depends on the accuracy of the decision result, and the decision result of the frequency discrimination demodulation of the PCM/FM signal under the low signal-to-noise ratio is low in reliability, so that the frequency estimation accuracy under the low signal-to-noise ratio is affected. In addition, in engineering practice, after a PCM/FM signal passes through an actual radio frequency channel and a wireless channel, due to the amplitude-frequency response or filter design and the like, it is difficult to ensure that the amplitudes of frequency discrimination results corresponding to positive and negative code elements are equivalent, so that a certain residual frequency offset exists when the method is used for carrier frequency synchronization.
The carrier frequency synchronization based on the early-late gate is the most classical signal synchronization structure, and the signal synchronization of a plurality of modulation systems can realize the carrier frequency synchronization by adopting the thought of the early-late gate. The traditional early-late gate synchronization makes the output results of the early branch and the late branch different, and the carrier frequency estimation is finished iteratively by judging the polarity of the difference and selecting the step of adjusting the frequency towards the positive direction or the negative direction, but the step usually determines the speed of frequency adjustment and the estimation precision of a feedback loop, namely the larger step can realize the faster frequency offset capture, but is not beneficial to the fine tracking of the carrier; a smaller step may enable higher accuracy carrier frequency tracking, but may make the acquisition process in the earlier stage too lengthy.
The adoption of the step-size-changing processing of 'big first and small second' is a concept for solving the problems of acquisition speed and tracking accuracy of an early-late gate, but the complexity of loop control is increased, and particularly when signal interruption needs rapid recapture, the control of carrier synchronization becomes complicated and even the re-compensation fails.
In summary, carrier frequency synchronization of PCM/FM signals needs to overcome the problems of low signal-to-noise ratio, unbalanced modulation symbols "0" and "1", fast acquisition and tracking of large dynamic doppler frequency, and the like, but the current algorithms do not solve these problems well.
Disclosure of Invention
The invention aims to solve the defects and shortcomings in the prior art, realize frequency error estimation by utilizing multi-symbol detection, and realize the PCM/FM signal early-late loop frequency synchronization method for quickly capturing and tracking the carrier frequency of a large dynamic PCM/FM signal by adopting an early-late loop carrier synchronization structure added with a loop filter.
In order to achieve the above object, the present invention discloses a PCM/FM signal early-late loop frequency synchronization method based on multi-symbol detection, which is characterized by comprising the following steps:
step 1, according to the estimated value of the frequency deviation of the current carrier wave
Figure GDA0003710524770000031
Frequency interval value delta of the sum branch and the late branch f Calculating a frequency deviation value, respectively controlling Numerically Controlled Oscillators (NCO) of an early branch (an advanced branch) and a late branch (a lagging branch) according to the frequency deviation value, and respectively carrying out frequency correction on a received signal (a complex baseband after down-conversion) s (t) to obtain an early branch signal s el (t) and signal s of the late branch lt (t)；
The frequency deviation values for controlling the numerical controlled oscillators of the early branch (leading branch) and the late branch (lagging branch) are respectively
Figure GDA0003710524770000032
And
Figure GDA0003710524770000033
i.e. the early branch signal s el (t) signal s of the late branch lt (t) is
Figure GDA0003710524770000035
The frequency interval value delta f The method is optimally selected through an S curve of frequency error estimation, and the selection principle is that the larger the slope at the origin (frequency offset is 0) of the S curve, the higher the estimation accuracy is, so delta leading to the larger slope at the origin of the S curve is to be selected as much as possible f (ii) a In addition, since the intersection (also referred to as the second zero-crossing point) of the S-curve with the frequency offset axis (amplitude of 0) at a position other than the origin determines the fast capture band of the loop, δ leading to the second zero-crossing point (farther from the origin) should be selected to allow for a large loop capture range f Combining the above principles, selecting delta for PCM/FM signal f 0.16Rb (Rb is the symbol rate).
Step 2, the receiver receives the ith PCM/FM modulation symbol sent by the transmitter currently, and then the receiver respectively carries out incoherent multi-symbol detection on the signals of the early branch and the late branch to obtain the module value of the matched filtering output result;
the noncoherent multi-symbol detection is to combine the received signals in the ith symbol interval of the two branches of the early branch and the late branch with L groups of local waveforms (matched filter)
Figure GDA0003710524770000036
Performing conjugate correlation symbol by symbol to obtain module value of matched filtering output result
Figure GDA0003710524770000037
The matched filter is a fixed sampling point in each symbol interval and corresponds to the sampling point of the received signal one by one;
Figure GDA0003710524770000038
Figure GDA0003710524770000039
wherein "s (t)" is the conjugate of the complex number s (t),
Figure GDA0003710524770000041
is a matched filter.
The matched filter
Figure GDA0003710524770000042
Is NxT, T is the symbol period of the PCM/FM signal, N is the number of symbols required for one detection, N is>1；
Then, the ith local waveform is:
Figure GDA0003710524770000043
Figure GDA0003710524770000044
wherein the content of the first and second substances,
Figure GDA0003710524770000045
for n symbols to be selected
Figure GDA0003710524770000046
(i is 1,2, …, n and
Figure GDA0003710524770000047
) The constituent symbol vectors, i.e.
Figure GDA0003710524770000048
Kf is the modulation index of PCM/FM and takes 0.7, g (t) is the pre-adjusting filter of PCM/FM signal, usually takes the rectangular shaping filter, that is
Figure GDA0003710524770000049
The matched filter
Figure GDA00037105247700000410
The relation between the number L of (A) and N is that L is 2 n 。
Preferably, in the present invention, N is 3, so L is 8, and the number of matched filters is reduced by 75% compared to N5 (L is 32) which is commonly used for incoherent detection.
Step 3, respectively solving the maximum value of the N MSD measurements obtained by the early branch and the late branch to obtain the maximum measurement of the two branches
Figure GDA00037105247700000411
Every M symbols, respectively calculating the average value of the maximum measurement of the two branches
Figure GDA00037105247700000412
The symbol number M of the accumulation interval determines the granularity of carrier frequency estimation, the larger M is, the more symbols are used for each estimation, so that the higher the precision of single estimation is, the smaller the estimation jitter is, but the larger M can increase the time delay of loop feedback, thereby slowing down the loop capturing speed. In addition, doppler acceleration may cause certain frequency offset changes to occur within multiple symbols, and thus a larger M may reduce the ability of the loop to adapt to doppler acceleration. On the other hand, the smaller M, the larger the jitter of a single estimation, so that an excessively small value of M may reduce the estimation accuracy of the loop in the tracking phase. Therefore, M needs to be chosen according to the specific requirements of the communication system for acquisition time and estimation accuracy.
Step 4, making difference between the maximum measurement cumulant to obtain the estimation result e (k) lambda of the carrier frequency error of this time EL (k)-λ LT (k) Passing e (k) through a second order loop filter shown in FIG. 3 to obtain the frequency estimation result of this time
Figure GDA0003710524770000051
The second-order loop filter can track the Doppler frequency with the second-order change rate not being 0, wherein the loop filter parameters K1 and K2 can be selected according to the system requirement;
step 5, using the frequency estimation result in step 4
Figure GDA0003710524770000052
Updating the carrier frequency offset estimation value in the step 1And repeating the steps 1-5 to complete the frequency synchronization of the early and late loops of the feedback closed loop structure.
Compared with the prior art, the technical scheme of the invention utilizes the two-path multi-symbol detector to respectively calculate the maximum measurement for the received signals subjected to different frequency offsets, and uses the measurement difference of the two branches as the estimated value of the carrier frequency error so as to drive the frequency-locked loop comprising the second-order loop filter, thereby completing the fast capture and high-precision tracking of the carrier frequency offset.
In addition, in the scheme, the multi-symbol detector for carrier frequency estimation adopts simplified 3-symbol matched filtering, compared with a 5-symbol MSD detector commonly used for incoherent demodulation, the scale of a matched filter is reduced by 75%, the complexity of hardware realization is reduced, and the loss of the demodulation performance of a PCM/FM signal can be ignored after the carrier synchronization of the invention is carried out; the frequency interval of the early-late branch is optimized by using the S curve of the frequency error estimation, the estimation precision of the loop can be improved and the loop capture range is considered through the optimized frequency interval, and for PCM/FM signals, the optimized frequency interval is 0.16 times of the symbol rate. The multi-symbol detector for estimating the error adopts the idea of block estimation, and each block calculates the frequency error once by using the average value of continuous M times of multi-symbol detection output, thereby reducing the jitter of frequency error estimation and improving the error estimation precision.
In summary, compared with the prior art, the technical scheme of the invention has the following advantages:
1. the technical scheme of the invention combines a multi-symbol detector, adopts the processing process of matched filtering to realize frequency error estimation, thereby fully utilizing modulation information, and in contrast, the frequency offset estimation algorithm based on the power spectrum characteristic generally takes the received signal as the modulation signal of modulation code elements of '0' and '1', and the like, and does not utilize the modulation information, so that the carrier frequency estimation precision of the invention is higher compared with the estimation algorithm based on the power spectrum characteristic.
2. Another advantage of the present invention is that the carrier frequency estimation is performed by using a multi-symbol detector, and the estimation process detects modulation symbols "0" and "1" separately, so that the detection process is not affected no matter how the symbols of the modulation signal are distributed. Therefore, the invention can solve the problem that the estimation performance is influenced by the asymmetry of the power spectrum caused by the uneven number of the modulation symbols '0' and '1'.
3. The technical scheme of the invention is based on multi-symbol detection demodulation, the multi-symbol detection is always acknowledged as an algorithm with the best performance of the incoherent detection of the PCM/FM signal, and the demodulation performance of the multi-symbol detection is improved by about 2.5dB compared with the performance of the algorithm based on frequency discrimination, so that the performance of the multi-symbol detection is better.
4. The technical scheme of the invention adopts the early-late path error estimation combined with the feedback synchronization structure of the loop filter to replace the traditional method that the early-late gate only utilizes the detection error polarity to adjust the frequency stepping (usually fixed stepping) in the forward direction or the reverse direction. The traditional early-late gate takes the polarity of the difference value of the leading branch and the lagging branch, is a 'hard decision' processing mode, and loses part of detection information. The error is processed by the loop filter, and the 'soft decision' information of the error estimation of the early-late branch is utilized, so that the rapid accumulation of the detection error in the capturing stage can be realized, and the capturing speed is accelerated; in the tracking stage, the detection error oscillates around 0, and the jitter of feedback adjustment can be reduced through the loop filter, so that the precision of carrier frequency estimation is improved, and therefore, compared with the carrier frequency synchronization of the traditional early-late gate structure, the method has better frequency acquisition speed and estimation precision.
Drawings
The foregoing and following detailed description of the invention will be apparent when read in conjunction with the following drawings, in which:
FIG. 1 is a schematic circuit diagram of an early-late loop frequency synchronization structure based on multi-symbol detection according to the present invention;
FIG. 2 is a schematic diagram of the frequency error estimation S-curve of different frequency interval values of the early-late branch according to the present invention;
fig. 3 is a schematic diagram of a second-order loop filter circuit structure suitable for the present invention.
Detailed Description
The technical solutions for achieving the objects of the present invention are further illustrated by the following specific examples, and it should be noted that the technical solutions claimed in the present invention include, but are not limited to, the following examples.
Example 1
As a specific implementation scheme of the invention, as shown in FIG. 1, a high-precision carrier frequency synchronization method of PCM/FM telemetering signals is disclosed, wherein a loop filter is added in an early-late loop carrier synchronization structure, and the loop filter is connected between two ends of the early-late loop carrier synchronization structure, so that carrier frequency estimation and correction of PCM/FM signals under high dynamic and low signal-to-noise ratio can be realized, and the method belongs to the field of wireless communication. Specifically, the method comprises the following steps:
step 1, according to the estimated value of the frequency deviation of the current carrier wave
Figure GDA0003710524770000061
Frequency interval value delta of the sum branch and the late branch f Calculating a frequency deviation value, respectively controlling Numerically Controlled Oscillators (NCO) of an early branch (an advanced branch) and a late branch (a lagging branch) according to the frequency deviation value, and respectively carrying out frequency correction on a received signal (a complex baseband after down-conversion) s (t) to obtain an early branch signal s el (t) and signal s of the late branch lt (t)；
Step 2, the receiver receives the ith PCM/FM modulation symbol sent by the transmitter currently, and then the receiver respectively carries out incoherent multi-symbol detection on the signals of the early branch and the late branch to obtain the module value of the matched filtering output result;
step 3, respectively solving the maximum value of the N MSD measurements obtained by the early branch and the late branch to obtain the maximum measurement of the two branches
Figure GDA0003710524770000071
Every M symbols, respectively calculating the average value of the maximum measurement of the two branches
Figure GDA0003710524770000072
The symbol number M of the accumulation interval determines the granularity of carrier frequency estimation, the larger M is, the more symbols are used for each estimation, so that the higher the precision of single estimation is, the smaller the estimation jitter is, but the larger M can increase the time delay of loop feedback, thereby slowing down the loop capturing speed. In addition, doppler acceleration may cause certain frequency offset changes to occur within multiple symbols, and thus a larger M may reduce the ability of the loop to adapt to doppler acceleration. On the other hand, the smaller M, the larger the jitter of a single estimation, so that an excessively small value of M may reduce the estimation accuracy of the loop in the tracking phase. Therefore, M needs to be chosen according to the specific requirements of the communication system for acquisition time and estimation accuracy.
Step 4, taking the difference of the maximum measurement cumulant to obtain the estimation result of the carrier frequency error of the time
e(k)＝λ EL (k)-λ LT (k) Passing e (k) through a second order loop filter shown in FIG. 3 to obtain the frequency estimation result of this time
Figure GDA0003710524770000073
The second-order loop filter can track the Doppler frequency with the second-order change rate not being 0, wherein the loop filter parameters K1 and K2 can be selected according to the system requirement;
step 5, using the frequency estimation result in step 4
Figure GDA0003710524770000074
And updating the carrier frequency offset estimation value in the step 1, and repeating the steps 1-5 to complete the early-late loop frequency synchronization of the feedback closed loop structure.
Example 2
As a preferred implementation of the present invention, on the basis of the technical solution of the above example 1, further, as shown in fig. 1, it is assumed that the current carrier frequency offset estimation value is
Figure GDA0003710524770000075
The working steps are as follows:
by a frequency offset value
Figure GDA0003710524770000076
And
Figure GDA0003710524770000077
respectively controlling Numerically Controlled Oscillators (NCO) of a leading branch (early branch) and a lagging branch (late branch), respectively carrying out frequency correction on a received signal (complex baseband after down-conversion) s (t) to obtain an early branch signal s el (t) and signal s of the late branch lt (t)：
Figure GDA0003710524770000081
Figure GDA0003710524770000082
Wherein, delta f For the frequency interval values of the early branch and the late branch, the parameter is optimally selected by an S-curve of frequency error estimation, and the S-curves at different frequency interval values are shown in fig. 2.
The selection principle is as follows: the larger the slope of the S-curve at the origin (frequency offset is 0), the higher the estimation accuracy, so δ should be selected as much as possible to result in a larger slope of the S-curve at the origin f (ii) a In addition, since the intersection (also referred to as the second zero-crossing point) of the S-curve with the frequency offset axis (amplitude of 0) at a position other than the origin determines the fast capture band of the loop, δ leading to the second zero-crossing point (farther from the origin) should be selected to allow for a large loop capture range f 。
Combining the above principles, selecting delta for PCM/FM signal f 0.16Rb (Rb is the symbol rate).
Then, at the ith symbol received, the signals of the two branches are respectively subjected to non-coherent Multi-symbol Detection (MSD), i.e. are respectively matched with L groups of local waveforms
Figure GDA0003710524770000083
(i.e. matched filter) making complex correlation to obtain module value of matched filter output result:
Figure GDA0003710524770000084
Figure GDA0003710524770000085
where "s x (t)" is the conjugate of the complex number s (t), matched filters
Figure GDA0003710524770000086
Is NxT, T is the symbol period of PCM/FM signal, N is the number of symbols required for one detection, generally N>1。
Then, the ith local waveform is:
Figure GDA0003710524770000087
Figure GDA0003710524770000088
wherein the content of the first and second substances,
Figure GDA0003710524770000089
for n symbols to be selected
Figure GDA00037105247700000810
(i is 1,2, …, n and
Figure GDA00037105247700000811
) The constituent symbol vectors, i.e.
Figure GDA00037105247700000812
Kf is the modulation index of PCM/FM and takes 0.7, and g (t) is a rectangular formed pre-adjusting filter
Figure GDA0003710524770000091
The relation between the number L of matched filters and n is L-2 n 。
In this embodiment, if N is 3, L is 8, and the number of matched filters is reduced by 75% compared to N is 5(L is 32) which is commonly used for incoherent detection.
Further, the maximum values of the N MSD measurements obtained by the early branch and the late branch are respectively obtained to obtain the maximum measurements of the two branches
Figure GDA0003710524770000092
Every M symbols, respectively calculating the average value of the maximum measurement of the two branches
Figure GDA0003710524770000093
The number of accumulated interval symbols M determines the granularity of carrier frequency estimation, and the larger M is, the more symbols are used for each estimation, so that the higher the precision of single estimation is, the smaller the estimation jitter is.
But too large M increases the delay of the loop feedback, slowing down the loop acquisition speed. In addition, doppler acceleration may cause certain frequency offset changes to occur within multiple symbols, and thus a larger M may reduce the ability of the loop to adapt to doppler acceleration.
On the other hand, the smaller M, the larger the jitter of a single estimation, so that an excessively small value of M may reduce the estimation accuracy of the loop in the tracking phase.
Therefore, M needs to be chosen according to the specific requirements of the communication system for acquisition time and estimation accuracy.
The maximum measurement cumulant is differed to obtain the estimation result e (k) of the carrier frequency error at this time EL (k)-λ LT (k) Passing e (k) through a loop filter as shown in FIG. 3 to obtain the frequency estimation result of this time
Figure GDA0003710524770000094
The second order loop filter can track the Doppler frequency with the second order change rate different from 0, wherein the loop filter parameters K1 and K2 can be selected according to the system requirement.
Finally, utilize
Figure GDA0003710524770000095
And updating the carrier frequency offset estimation value in the step 1, and repeating the steps 1-5 to complete the early-late loop frequency synchronization of the feedback closed loop structure.

Claims (4)

1. A PCM/FM signal early-late loop frequency synchronization method based on multi-symbol detection is characterized by comprising the following steps:
step 1, according to the estimated value of the frequency deviation of the current carrier wave
Figure FDA0003710524760000011
Frequency interval value delta of the sum branch and the late branch f Calculating a frequency deviation value, respectively controlling Numerically Controlled Oscillators (NCO) of an early branch (an advanced branch) and a late branch (a lagging branch) according to the frequency deviation value, and respectively carrying out frequency correction on a received signal (a complex baseband after down-conversion) s (t) to obtain an early branch signal s el (t) and signal s of the late branch lt (t); the frequency offset values for controlling the numerically controlled oscillators of the early branch (leading branch) and the late branch (lagging branch) are respectively
Figure FDA0003710524760000012
And
Figure FDA0003710524760000013
i.e. the early branch signal s el (t) signal s of the late branch lt (t) is
Figure FDA0003710524760000014
Figure FDA0003710524760000015
The frequency interval value delta f Is optimally selected by an S curve of frequency error estimation, and delta is selected f Rb is symbol rate 0.16 Rb;
step 2, the receiver receives the ith PCM/FM modulation symbol sent by the transmitter currently, and then the receiver respectively carries out incoherent multi-symbol detection (MSD) on the signals of the early branch and the late branch to obtain the module value of the matched filtering output result;
step 3, respectively solving the maximum value of the N MSD measurements obtained by the early branch and the late branch to obtain the maximum measurement of the two branches
Figure FDA0003710524760000016
Every M symbols, respectively calculating the average value of the maximum measurement of the two branches
Figure FDA0003710524760000017
Obtaining 1 set of values, λ, for every M symbols EL (k) And λ LT (k) Respectively representing the measurement mean values of the kth group of early branches and late branches;
the number M of the symbols of the accumulation interval is selected according to the specific requirements of the communication system on acquisition time and estimation precision, and N and M are positive integers;
step 4, making difference between the maximum measurement cumulant to obtain the estimation result e (k) lambda of the carrier frequency error of this time EL (k)-λ LT (k) E (k) is processed by a second order loop filter to obtain the frequency estimation result of this time
Figure FDA0003710524760000021
The selection of the loop filter parameters K1 and K2 can be set according to the system requirements;
step 5, using the frequency estimation result in step 4
Figure FDA0003710524760000022
And updating the carrier frequency offset estimation value in the step 1, and repeating the steps 1-5 to complete the early-late loop frequency synchronization of the feedback closed loop structure.
2. The method of claim 1 for multi-symbol detection based early-late loop frequency synchronization of PCM/FM signals, wherein: the step 2 of incoherent multi-symbol detection is to receive the ith symbol interval of the two branches of the early branch and the late branchSignals are respectively associated with L groups of local waveforms
Figure FDA0003710524760000023
Performing conjugate correlation symbol by symbol to obtain module value of matched filtering output result
Figure FDA0003710524760000024
Figure FDA0003710524760000025
Figure FDA0003710524760000026
Wherein "s (t)" is the conjugate of the complex number s (t),
Figure FDA0003710524760000027
is a matched filter.
3. The method of claim 2, wherein the PCM/FM signal early-late loop frequency synchronization based on multi-symbol detection comprises: the matched filter
Figure FDA0003710524760000028
Is NxT, T is the symbol period of the PCM/FM signal, N is the number of symbols required for one detection, N is>1；
Then, the ith local waveform is:
Figure FDA0003710524760000029
Figure FDA00037105247600000210
wherein the content of the first and second substances,
Figure FDA00037105247600000211
for n symbols to be selected
Figure FDA00037105247600000212
(i is 1,2, …, n and
Figure FDA00037105247600000213
) The constituent symbol vectors, i.e.
Figure FDA00037105247600000214
Kf is the modulation index of PCM/FM and takes 0.7, and g (t) is the pre-adjusting filter of PCM/FM signal
Figure FDA00037105247600000215
The matched filter
Figure FDA00037105247600000216
The number L of (A) is in a relationship of L-2 with N n 。
4. The method of claim 3 for multi-symbol detection based early-late loop frequency synchronization of PCM/FM signals, wherein: the number n of the symbols to be selected is equal to 3, so the matched filter
Figure FDA00037105247600000217
The number L of (c) is 8.
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