JP4129530B2 - Carrier synchronization method - Google Patents

Description

  The present invention relates to a carrier synchronization method in a digital communication system.

  In general, a digital communication system includes a modulator for matching a transmission signal to a transmission path, and a demodulator for returning a modulated wave of a received signal to an original signal. Therefore, it is required as a basic function in a digital communication system. The demodulator constituting the digital communication system includes a carrier synchronization circuit that performs quasi-synchronous detection to obtain a demodulated signal. The carrier synchronization circuit is a circuit that generates a local oscillation signal synchronized with a carrier wave, synthesizes the local oscillation signal and a reception signal, and outputs a detection signal. This local oscillation signal is a signal having the same frequency and phase as the carrier wave, but the carrier synchronization circuit synchronizes the local oscillation signal and the reception signal due to multipath distortion between the modulator and the demodulator. Therefore, it is not always possible to output a high-quality detection signal.

  Conventionally, a carrier synchronization circuit directly and continuously controls a PLL (Phase-Locked Loop) local oscillator (see, for example, Non-Patent Document 1 and Patent Document 1) and quasi-synchronous detection of a known training signal. From the temporary demodulated signal subjected to the quasi-synchronous detection, the frequency offset and the phase offset can be classified discretely for each symbol (see, for example, Patent Document 2), and each has been put to practical use. . Comparing both types, the latter has a larger computation scale than the former, but is superior in operational stability because it handles baseband signals. For this reason, the latter is suitable for processing in DSP (Digital Signal Processor) and LSI implementation, and is considered promising.

Lindsey & Simon, Telecommunication Systems Engineering, Prentice-Hall, 1973 Japanese Patent No. 1536050 JP-A-5-103030

  The latter type of carrier synchronization circuit described above performs frequency offset and phase offset estimation in the time domain. In other words, this carrier synchronization circuit measures as a phase error how far the training signal demodulated by quasi-synchronous detection is from the position where it should originally exist on the complex plane and how much it changes with time. , Estimate frequency offset and phase offset. Further, these offset values are estimated by a least square method, a sequential least square method, or the like. For this reason, there has been a problem that the operation scale becomes large.

  By the way, in a digital communication system, a circuit for performing various synchronizations such as modulation and demodulation is generally processed in the time domain in order to handle a waveform signal. However, the pair of the time signal waveform and the Fourier transformed signal has the same mapping. For this reason, even if circuits such as modulation and demodulation do not handle the time signal waveform but handle the frequency spectrum of the Fourier transformed signal, it is possible to achieve the intended purpose.

  For example, in an earlier application (Japanese Patent Application No. 2005-53393) that was filed by the same applicant and inventor as the present application and has not been published at the time of filing the present application, the time signal after synchronous detection is converted into a discrete Fourier transform (DFT / Discrete Fourier Transform), and a method of demodulating the original signal from the frequency spectrum has been proposed. According to this method, it is possible to realize a demodulator that shares the Fourier transform function, and it is possible to reduce the operation scale. Further, the method of handling the frequency domain signal has an advantage that the uncertainty in the frequency offset estimation does not occur as compared with the method of handling the time domain signal. In the time domain, the frequency offset is estimated by the temporal change of the phase error of the temporary demodulated signal, so if a phase error that exceeds the judgment threshold of the temporary demodulated signal occurs, the polarity of the offset is reversed and an incorrect estimated value is generated. Will be obtained. On the other hand, in the frequency domain, since the spectral component is only shifted to the right or left (high frequency / low frequency) according to the frequency offset, there is no uncertainty of polarity in the estimation. For this reason, the preamble signal {1, -1, 1, -1,...} That has been conventionally used for timing synchronization can be used as a training signal for carrier wave synchronization. In other words, two types of signals that have been transmitted separately for timing synchronization and carrier synchronization can be shared by one type of signal, so there is no need to transmit useless signals and improve signal transmission efficiency. You can expect.

  Therefore, the present invention has been made in view of such problems, and its purpose is to reduce the operation scale and estimate the frequency offset when detecting the received signal to realize carrier wave synchronization. It is an object of the present invention to provide a carrier synchronization system that does not cause uncertainty.

  To achieve the above object, the carrier synchronization system of the present invention is a system for quasi-synchronizing detection of a received signal, quasi-synchronously detecting a timing synchronization preamble signal M symbol added to the head of the received signal, The detection signal is multiplied by a correction signal for correcting the phase rotation amount of the quasi-synchronous detection signal generated due to the frequency offset and phase offset, and NM symbol zeros are added to the correction signal, and then discrete Fourier transform is performed. Generating a demodulated signal in a spectral space, estimating a frequency offset and a phase offset based on the spectrum of the demodulated signal, generating the correction signal based on the estimated frequency offset and phase offset, A correction signal is fed back for the multiplication.

  In the present invention, when the received signal is quasi-synchronously detected, the frequency offset and the phase offset are estimated in the frequency domain, not in the conventional time domain. As a result, it is not necessary to use a least square method, a sequential least square method, or the like, which is necessary when estimating an offset in the time domain. Therefore, the calculation load for offset estimation is reduced.

  Further, according to the present invention, carrier wave synchronization is performed using a preamble signal among received signals. Specifically, the present invention performs quasi-synchronous detection on the preamble signal of the received signal, Fourier-transforms M symbols in the quasi-synchronized detection signal, and an N-dimensional complex vector (N is M or less, N ≧ 2 M ≧ 2), the frequency offset and the phase offset are estimated based on the spectrum data of the N-dimensional complex vector, and the quasi-synchronous detection is corrected using the frequency offset and the phase offset.

  This is because when the frequency offset and phase offset are estimated in the frequency domain, the spectral components only shift according to the offset and no polarity uncertainty occurs, so the polarity of the preamble signal is This is because it is ensured. Thereby, the modulator on the transmission side does not need to transmit a training signal used for carrier wave synchronization. This preamble signal is essentially a signal for timing synchronization. Conventionally, a training signal is transmitted for carrier wave synchronization, and a preamble signal is transmitted for timing synchronization. According to the present invention, one common preamble signal can be used for carrier wave synchronization and timing synchronization.

を用いて行うことが好適である。 Further, the present invention provides a complex N symbol (n = 0, 1) obtained by subjecting Δf to a frequency offset, T to a symbol length, G (n) to N (symbol) by adding zero and N to the correction signal. ,..., N-1), where N is the maximum symbol number and n is the frequency spectrum component number, the frequency offset is estimated using the following frequency offset function formula:

It is suitable to carry out using.

を用いて行うことが好適である。 Further, according to the present invention, the frequency offset is estimated by the following equation instead of the frequency offset function equation.

It is suitable to carry out using.

を用いて行うことが好適である。 Further, the present invention estimates the phase offset by the following formula:

It is suitable to carry out using.

により表される補正信号をフィードバックすることが好適である。 Further, the present invention provides the following formula:

It is preferable to feed back the correction signal represented by:

  According to the present invention, it is possible to provide a carrier synchronization method that reduces the scale of computation and that does not cause uncertainty when estimating a frequency offset.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
In order to facilitate the description of the embodiment of the present invention, it is assumed that the information signal is transmitted by QPSK (Quadrature Phase Shift Keying) as a precondition. Prior to transmission of the information signal, a sufficiently long preamble signal {1 + j, −1−j, 1 + j, −1−j,...} For timing synchronization, that is, the first quadrant and the second QPSK signal. It is assumed that the signals of the signal points in the three quadrants are transmitted alternately and the symbol synchronization is established.

  FIG. 1 is a block diagram showing a configuration of a quasi-synchronous detector that realizes a carrier synchronization system according to an embodiment of the present invention. The quasi-synchronous detector 100 has a frequency / phase offset correction function, and receives a signal transmitted from a modulator on the transmitting side as a receiving side, a quadrature phase detector 3, a local oscillator 4, and a low-pass filter 5. -1,5-2, complex multiplier 9, DFT calculator 6, normalized frequency offset estimator 7, phase offset estimator 8 and output terminal 2 for outputting a spectrum space synchronous detection signal to the outside. .

  The quadrature detector 3 receives a received signal via the receiving end 1 and a local oscillation signal from the local oscillator 4 and performs quasi-synchronous detection. Here, quasi-synchronous detection means phase detection using a carrier wave (local oscillation signal) that is not strictly synchronized.

  The low-pass filters 5-1 and 5-2 remove the second harmonic component from the output signal of the quadrature detector 3 and output a baseband demodulated signal. Here, the low-pass filter 5-1 outputs the in-phase component 10a in the demodulated signal, and the low-pass filter 5-2 outputs the quadrature component 10b in the demodulated signal. Both can be considered as the complex demodulated signal 10 together.

  The complex multiplier 9 receives the complex demodulated signal 10 from the low-pass filters 5-1 and 5-2, and the correction signal 16 obtained by frequency / phase offset estimation described later from the phase offset estimator 8. The demodulated signal 10 and the correction signal 16 are multiplied. Specifically, the complex multiplier 9 calculates (A + jB) (C + jD) and outputs a time-space synchronous detection signal 11.

  When a signal is identified and reproduced in time space (time domain), the time-space synchronous detection signal 11 output from the complex multiplier 9 is used via an output terminal (not shown). On the other hand, when a signal is identified and reproduced in the spectrum space (frequency domain), a synchronous detection signal in the spectrum space output from the DFT calculator 6 is used via the output terminal 2.

  In order to estimate the frequency offset and the frequency offset in the spectrum space, the output of the complex multiplier 9 is input to the DFT calculator 6. When a signal is input from the complex multiplier 9, the DFT calculator 6 performs a discrete Fourier transform (DFT) on the N-symbol complex time signal, and outputs a synchronous detection signal in the spectrum space via the output terminal 2. Further, the DFT calculator 6 outputs the quasi-synchronous detection signal G (N / 2) 12 in the spectrum space to the phase offset estimator 8, and the quasi-synchronous detection signal G (N / 2 + 1) 13 and the quasi-synchronous detection signal G ( N / 2-1) 14 is output to the normalized frequency offset estimator 7. The quasi-synchronous detection signals G (N / 2) 12, G (N / 2 + 1) 13, and G (N / 2-1) 14 will be described later.

Hereinafter, the processing of the complex multiplier 9, the DFT calculator 6, the normalized frequency offset estimator 7, and the phase offset estimator 8 will be specifically described using mathematical expressions. The DFT computing unit 6 applies NM symbols (k) to the M symbols (k = 0 to M−1) of the frequency offset and the frequency offset compensated (corrected) preamble as shown in the equation (1). = M to N-1) is added with zero (zero padding) to create a signal g ₀ (k) composed of N symbols (k = 0 to N-1). Here, k is a symbol number, and g ₀ (k) is a discrete value at time t = kT (T is a symbol length). For the sake of explanation, the case where the frequency offset and the phase offset are zero is shown. Further, this zero padding is a process at the time of DFT calculation, and does not actually add a signal 0 on hardware.

When the frequency offset and the phase offset of the local oscillation signal output from the local oscillator 4 are Δf and θ ₀ , the signal after quasi-synchronous detection output from the complex multiplier 9 is expressed by the following equation (2). .

ここで、ｎは、準同期検波信号（ｋシンボルからなる信号）をフーリエ変換して得られる周波数スペクトル成分の番号を示し、Ｇ₀（ｎ）は、ｇ₀（ｋ）をＤＦＴして得られたスペクトル空間の信号を示す。正規化周波数オフセット推定器７及び位相オフセット推定器８により、最初に周波数オフセット及び位相オフセットの推定値が得られていない場合に、位相オフセット推定器８は、補正信号１６として１を出力する。前述の（３）式が表すスペクトル空間の信号は、このときのＤＦＴ演算器６による演算結果である。 First, a frequency offset estimation method will be described. When the DFT computing unit 6 performs DFT on the equation (2), the signal in the spectrum space is expressed by the following equation (3).

Here, n indicates the number of a frequency spectrum component obtained by Fourier transform of a quasi-synchronous detection signal (signal consisting of k symbols), and G ₀ (n) is obtained by DFT of g ₀ (k). Shows the signal in the spectral space. When the normalized frequency offset estimator 7 and the phase offset estimator 8 do not initially obtain the estimated values of the frequency offset and the phase offset, the phase offset estimator 8 outputs 1 as the correction signal 16. The signal in the spectrum space represented by the above equation (3) is the calculation result by the DFT calculator 6 at this time.

Comparing equation (2) indicating a time-space signal with equation (3) indicating a spectrum-space signal, if there is a frequency offset and a phase offset, the time-space signal is It is clear that a proportional phase rotation occurs. In contrast, in spectral space, it is clear that a frequency offset causes a constant frequency shift (more precisely, a cyclic frequency shift) in the spectral component, and a phase offset causes a constant phase shift in the spectral component. . In the equation (3), when the frequency offset Δf exists, each component of G ₀ (n) shifts to the right by NΔfT, and when the phase offset θ ₀ exists, the phase component of the frequency spectrum Is shifted by θ ₀ .

For this reason, the frequency offset estimated value and the phase offset estimated value have an advantage that the frequency offset and the phase offset can be estimated independently without exceeding a threshold value. That is, in the time space, when the demodulated signal is plotted on a two-dimensional plane of amplitude and phase, if there is a frequency offset Δf, the point changes in phase to 2πkΔft with time (rotates on the two-dimensional plane). . Here, when the point exceeds a threshold value (quadrant), it becomes impossible to distinguish between a positive frequency offset and a negative frequency offset. On the other hand, in the spectrum space, there is no equivalent to such a threshold value, so there is no error beyond the threshold value, and there is no uncertainty in estimation. As described above, in time space, the frequency offset and the phase offset appear as the same phase error, whereas in the spectrum space, the frequency offset shifts to the side of the power spectrum component | G (n) | ^2. And the phase offset appears as a shift of the phase component. According to equation (5) indicating a frequency offset function value described later, the square of the absolute value of G (n) is used as an element, and thus the phase component e (jθ ₀ ) of equation (3) is 1. Only the frequency offset can be estimated. That is, the frequency offset and the phase offset can be estimated independently.

また、Ｇ₀（ｎ）及びＧ（ｎ）のｎは、ｎ番目の解析周波数ｎｆ_analysisを示している。プリアンブル信号は、周波数１／２Ｔの余弦波に相当するため、ｎｆ_analysis＝１／２Ｔを満足するｎは、ｎ＝Ｎ／２である。 As a property of DFT, if the number of samplings is N, frequency resolution f _analysis obtained by DFT is expressed by the following equation (4) when normalized by symbol frequency 1 / T.

Further, n in G ₀ (n) and G (n) represents the nth analysis frequency nf _analysis . Since the preamble signal corresponds to a cosine wave having a frequency of 1 / 2T, n satisfying nf _analysis = 1 / 2T is n = N / 2.

この（５）式の周波数オフセット関数はＮ及びＭにより変化するが、Ｍ＝Ｎ／２かつＭが偶数の場合には、（６）式のように、近似することができる。

但し、Ｇ（Ｎ／２±１）のスペクトル成分を利用しているため、推定可能な範囲は以下のとおりである。

したがって、正規化周波数オフセットは、（７）式により推定される。

Equation (5) is defined as a function (frequency offset function) for estimating the normalized frequency offset.

The frequency offset function of the equation (5) varies depending on N and M, but when M = N / 2 and M is an even number, it can be approximated as in the equation (6).

However, since the spectral component of G (N / 2 ± 1) is used, the range that can be estimated is as follows.

Therefore, the normalized frequency offset is estimated by equation (7).

  FIG. 2 is a block diagram showing a configuration of the normalized frequency offset estimator 7 shown in FIG. The normalized frequency offset estimator 7 includes square calculators 71-1 and 71-2, a subtractor 72, a multiplier 73, an inverse sine calculator 74, and a multiplier 75. The quasi-synchronous detection signals G (N / 2 + 1) 13 and G (N / 2-1) 14 in space are input, the normalized frequency offset is estimated, and the normalized frequency offset estimated value signal 15 is converted to the phase offset estimator 8. Output to. The quasi-synchronous detection signals G (N / 2 + 1) 13 and G (N / 2-1) 14 input from the DFT calculator 6 are complex quantities.

The square calculator 71-1 receives the quasi-synchronous detection signal G (N / 2 + 1) 13 and performs a square calculation of | G (N / 2 + 1) | ² . The square calculator 71-2 receives the quasi-synchronized detection signal G (N / 2-1) 14 and performs a square calculation of | G (N / 2-1) | ² . Then, the subtracter 72 subtracts the outputs of the square calculators 71-1 and 71-2 to obtain the frequency offset function value of the above-described equation (5). The multiplier 73 multiplies the 1 / 2M ² to the frequency offset function value, arcsine calculator 74 performs an inverse sine operation on the multiplication result. Thereby, the normalized frequency offset amount can be obtained. The multiplier 75 multiplies the normalized frequency offset amount, which is an inverse sine calculation result, by 2 / M. Thereby, the normalized frequency offset estimated value signal 15 can be obtained. In this way, the normalized frequency offset estimator 7 outputs the value estimated by the above equation (7) as the normalized frequency offset estimated value signal 15.

  Note that the frequency offset function value in equation (5) is an amount related to the power spectrum component and does not depend on the phase offset. Therefore, the frequency offset is estimated independently of the phase offset.

  Next, a method for estimating the phase offset will be described. FIG. 3 is a block diagram showing a configuration of the phase offset estimator 8 shown in FIG. The phase offset estimator 8 includes a multiplier 81, a cosine calculator 82, a sine calculator 83, a complex multiplier 84, an adder 85, a one symbol delay circuit 86, a cosine calculator 87, a sine calculator 88, and a complex multiplier. 89, a quasi-synchronous detection signal G (N / 2) 12 in the spectrum space is input from the DFT calculator 6, and a normalized frequency offset estimated value signal 15 is input from the normalized frequency offset estimator 7, respectively. And a control signal (correction signal 16) for correcting the final phase rotation amount is output to the complex multiplier 9.

また、余弦演算器８２からの余弦演算結果は、（８）式におけるｅ^{-j(M-1)πΔfT}の実数部であり、正弦演算器８３からの正弦演算結果は、（８）式におけるｅ^{-j(M-1)πΔfT}の虚数部である。複素乗算器８４は、準同期検波信号Ｇ（Ｎ／２）１２とｅ^{-j(M-1)πΔfT}とを乗算し、準同期検波信号Ｇ（Ｎ／２）１２に含まれる周波数オフセットの成分を複素乗算器９に補正させる。すなわち、複素乗算器８４による乗算後の位相スペクトルΦ（ｎ／２）は、（９）式で表される。

したがって、位相オフセットは（１０）式により推定される。

The multiplier 81 receives the normalized frequency offset estimated value signal 15 from the normalized frequency offset estimator 7 and multiplies (M−1) / 2 to multiply by a constant. The cosine calculator 82 performs a cosine calculation on the multiplication result, and the sine calculator 83 performs a sine calculation on the multiplication result. The complex multiplier 84 inputs the quasi-synchronous detection signal G (N / 2) 12 in the spectrum space from the DFT calculator 6, the cosine calculation result from the cosine calculator 82, and the sine calculation result from the sine calculator 83. . The quasi-synchronous detection signal G (N / 2) 12 is a complex quantity represented by the equation (8).

Further, the cosine calculation result from the cosine calculator 82 is the real part of ^{e -j (M-1)} πΔfT in (8), sine calculation results from the sine calculator 83, e in equation (8) ^{This is} the imaginary part of ^{-j (M-1) πΔfT} . The complex multiplier 84 multiplies the quasi-synchronous detection signal G (N / 2) 12 and e ^{−j (M−1) πΔfT,} and a frequency offset component included in the quasi-synchronous detection signal G (N / 2) 12. Is corrected by the complex multiplier 9. That is, the phase spectrum Φ (n / 2) after multiplication by the complex multiplier 84 is expressed by the equation (9).

Therefore, the phase offset is estimated by equation (10).

On the other hand, the adder 85 receives the normalized frequency offset estimated value signal 15, inputs the output signal of the adder 85 delayed by one symbol by the one symbol delay circuit 86, adds both signals, and depends on the frequency offset A phase rotation amount 2πkΔfT at time t = kT is obtained. The phase rotation amount 2πkΔfT, which is the addition result, is input to the cosine calculator 87, the sine calculator 88, and the one symbol delay circuit 86. The cosine calculator 87 receives the phase rotation amount 2πkΔfT, performs cosine calculation, and ^obtains a real part of e ^−j2πkΔfT . The sine calculator 88 receives the phase rotation amount 2πkΔfT, performs a sine calculation, and ^obtains an imaginary part of e ^−j2πkΔfT .

このように、位相オフセット推定器８は、前記値を補正信号１６として複素乗算器９に出力する。 The complex multiplier 89 ^inputs the phase offset estimation value from the complex multiplier 84, the real part of e ^−j2πkΔfT from the cosine calculator 87, and the imaginary part of e ^−j2πkΔfT from the sine calculator 88, and performs complex multiplication. Then, a control signal (correction signal 16) for correcting the phase rotation amount is obtained. The correction signal 16 is shown below.

Thus, the phase offset estimator 8 outputs the value as the correction signal 16 to the complex multiplier 9.

  As described above, according to the quasi-synchronous detector 100, the DFT calculator 6 performs discrete Fourier transform on the signal in time space and outputs a signal in spectral space, and the normalized frequency offset estimator 7 The frequency offset is estimated using the signal on the spectrum space, and the phase offset estimator 8 estimates the phase offset using the signal on the spectrum space. In this case, the normalized frequency offset estimator 7 and the phase offset estimator 8 do not need to use the least square method, the sequential least square method, or the like in order to estimate the offset. Thereby, it is possible to reduce the operation scale for estimating the frequency offset and the phase offset.

  Further, according to the quasi-synchronous detector 100, since the frequency offset generated in the quasi-synchronous detection is estimated on the spectrum space, the spectral component is only shifted to the left and right according to the frequency offset. When the frequency offset is estimated in the time space, the polarity of the offset is inverted, so that there is no uncertainty regarding the polarity of the offset compared to this case.

  In addition, since the quasi-synchronous detector 100 has such advantages, a preamble signal can be used as a carrier synchronization signal for estimating a frequency offset and a phase offset. This preamble signal is originally a signal transmitted for timing synchronization, but can be used as a common signal for timing synchronization and carrier wave synchronization. Accordingly, since it is not necessary to use a training signal that has been transmitted for carrier wave synchronization in the past, the transmitting-side modulator does not need to transmit the training signal. Therefore, the signal transmission efficiency from the transmission side to the reception side can be improved.

It is a block diagram which shows the structure of the quasi-synchronous detector which implement | achieves the carrier-wave synchronous system by embodiment of this invention. It is a block diagram which shows the structure of a normalized frequency offset estimator. It is a block diagram which shows the structure of a phase offset estimator.

Explanation of symbols

1 Receiving end 2 Output end 3 Quadrature phase detector (DET)
4 Local oscillator 5 Low pass filter (LPF)
6 DFT calculator (DFT)
7 Normalized frequency offset estimator (F-EST)
8 Phase offset estimator (P-EST)
9 Complex multiplier (MULT)
10 Complex demodulated signal 11 Time-space synchronous detection signal 12 Spectral space quasi-synchronous detection signal G (N / 2)
13 Quasi-synchronous detection signal G (N / 2 + 1) in spectral space
14 Quasi-synchronous detection signal G (N / 2-1) in spectral space
15 Normalized frequency offset estimated value signal 16 Correction signal 71 Square calculator 72 Subtractor 73, 75, 81 Multiplier 74 Inverse sine calculator 82, 87 Cosine calculator 83, 88 Sine calculator 84, 89 Complex multiplier ( MULT)
85 Adder 86 1-symbol delay circuit 100 Quasi-synchronous detector

Claims (5)

In the method of quasi-synchronous detection of received signals,
Quasi-synchronous detection of the timing synchronization preamble signal M symbol added to the head of the received signal,
Multiplying the quasi-synchronous detection signal by a correction signal for correcting the phase rotation amount of the quasi-synchronous detection signal generated due to the frequency offset and the phase offset;
A NM symbol zero is added to the correction signal, and then a discrete Fourier transform is performed to generate a demodulated signal in a spectral space.
Estimating a frequency offset and a phase offset based on a spectrum of the demodulated signal;
A carrier synchronization method, wherein the correction signal is generated based on the estimated frequency offset and phase offset, and the correction signal is fed back for the multiplication. In the carrier wave synchronization system according to claim 1,
.DELTA.f is a frequency offset, T is a symbol length, G (n) is added to zero, and N symbols are added as complex N symbols (n = 0, 1,... -1), where N is the maximum symbol number and n is the frequency spectrum component number,
The frequency offset is estimated using the following frequency offset function formula:

A carrier wave synchronization system characterized by using the In the carrier wave synchronization system according to claim 2,
The frequency offset is estimated by the following equation instead of the frequency offset function equation:

A carrier wave synchronization system characterized by using the In the carrier wave synchronization system according to claim 2 or 3,
The estimation of the phase offset is given by

A carrier wave synchronization system characterized by using the In the carrier wave synchronization system according to claim 3 or 4,
The following formula

A carrier wave synchronization system characterized by feeding back a correction signal represented by

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