JP3324905B2 - Frequency comparison method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION The present invention relates to quadrature amplitude modulation (QA).
M) A receiver for receiving a signal, which demodulates a QAM signal, relates to a frequency comparison method for detecting a frequency difference between a received carrier and a reproduced carrier, and more particularly to a method for detecting this frequency difference in a short time. It was done.

[0002]

2. Description of the Related Art In QAM, a carrier having a different phase of π / 2 is given a change in amplitude, and these signals are combined and transmitted. On the receiving side, the received signal is split into two, one of which is multiplied by the reproduced carrier generated by the oscillator and the other is multiplied by a signal obtained by shifting the phase of the reproduced carrier by π / 2 to perform demodulation. Take the amplitude value of each orthogonal component,
A multi-value represented by a combination of those amplitude values is decoded.

[0005] Each symbol point and received signal point of QAM representing the combination of the amplitude values of the two orthogonal components can be displayed on an IQ plane composed of orthogonal I-axis and Q-axis. The received signal points represent the received signal on the IQ plane, and the symbol points represent points on the IQ plane at which the carrier-to-noise ratio is theoretically the best. FIG. 5 shows the first quadrant of this IQ plane.
Each symbol point in 64QAM is represented by a black circle.
In the following description, only the first quadrant of the IQ plane will be described, but this description does not lose generality even if other quadrants are considered. Further, the distance from the origin 0 of a symbol or a received signal point will be referred to as an amplitude.

When the frequency of the carrier (reception carrier) on the transmitting side does not match the frequency of the reproduced carrier generated by the receiving device, if the same signal is continuously received, as shown in FIG. The signal point is observed to rotate around the origin 0 on the IQ plane. Upon demodulation, the receiving apparatus obtains the frequency difference between the received carrier and the reproduced carrier from the rotation angle and the reception time interval of the signal, and controls the frequency of the reproduced carrier to correct the difference, or calculates the frequency difference. Perform signal processing in consideration of the above.

As shown in FIG. 5, there are two symbol points, one in which another symbol point having the same amplitude exists in the same quadrant (the one in which a plurality of symbol points lie on the circumference). Some symbol points with the same amplitude do not exist in the same quadrant (only one symbol point is on the circumference). The latter symbol point is called a single symbol, and a received signal whose corresponding symbol is a single symbol is called a single signal. In the case of 64QAM, the phase of a single symbol on the IQ plane is π / 4.

As shown in FIG. 11, even when a received signal point is rotated on the IQ plane, if the received signal is a single signal, the amplitude of the received signal is checked to determine which symbol point corresponds to which symbol point. You can know if it is a signal.
However, if the signal is not a single signal, the corresponding symbol point cannot be determined from its amplitude.

Therefore, conventionally, when a frequency difference between a received carrier and a reproduced carrier is obtained, when the received signal is determined to be a single signal from its amplitude, the phase of the signal is determined with reference to the phase of the reproduced carrier. When the received signal that has been stored and subsequently received is a single signal, the phase of the signal is obtained again with reference to the phase of the reproduced carrier, and the difference from the previously stored phase value is obtained. This difference Δθ is the phase change in one symbol time. Therefore, the frequency difference Δf between the reproduced carrier and the received carrier can be obtained by the following equation, where t _sym is the symbol time.

Δf = (1 / 2π) · (Δθ / t _sym ) Conventionally, the frequency difference between the reproduced carrier and the received carrier is obtained by such a frequency comparison method.

[0009]

However, in the conventional frequency comparison method, there is a problem that the frequency comparison between the reproduced carrier and the received carrier cannot be performed unless two or more received signals are continuous signals. For example, in the case of 64QAM, the probability that a single signal continues twice is as small as 9/256 assuming that the signal is received at random, and it is difficult to obtain a sufficient frequency comparison gain.

The present invention has been made to solve such a conventional problem, and has as its object to provide a frequency comparison method capable of comparing the frequencies of a reproduced carrier and a received carrier even when a single signal is not continuous. The purpose is.

[0011]

Therefore, according to the present invention, there is provided a frequency comparison method for determining a frequency difference between a received carrier and a reproduced carrier when demodulating a received quadrature amplitude modulation signal.
The IQ axis is rotated so that the first received signal point coincides with the corresponding first symbol point, and then the distance from the origin of the second received signal point received and the phase from either IQ axis And a second symbol point corresponding to the second received signal point is determined from the frequency difference between the angle formed by the second received signal point, the origin and the second symbol point, and the time interval for receiving the signal. Seeking.

Also, the distance of the first received signal point from the origin coincides with the distance of the symbol point where at least one symbol point at the same distance from the origin exists in the same quadrant, at least in the initial frequency comparison. Then, the target reception signal is selected.

The position of the first received signal point on the IQ plane is stored, and the next received second received signal point is
When a symbol having the same distance from the origin corresponds to a symbol having only one symbol in the same quadrant, the IQ axis is rotated so that the second received signal point becomes the corresponding second symbol point, From the position of the first received signal point after rotating the IQ axis, a first symbol point corresponding to the received signal point is determined, and the first received signal point, the origin, and the first symbol point are formed. The frequency difference is obtained from the angle and the time interval of the received signal.

Further, the target reception signal is selected such that the distance from the origin at the first and second reception signal points is equal to or greater than a predetermined distance threshold.

The distance between the first and second received signal points from the origin and the line connecting any two of the symbol points at the same distance from the origin and the origin are set in advance. The target received signal is selected so as to match the distance between the symbol points that are equal to or greater than the determined angle threshold.

When the obtained frequency difference becomes equal to or less than a predetermined frequency threshold, the value of the angular threshold is reduced.

[0017]

According to the present invention, the frequency difference between the received carrier and the reproduced carrier is obtained as follows. Immediately after the system is reset, the amplitude of the signal received one after another is monitored, and a single signal is detected based on this amplitude. When the single signal is detected, it obtains its phase difference phi _a of the symbol points corresponding to a single signal phase (in 64QAM π / 4). When the next signal is received, the phase of the received signal is rotated by φ _a , a symbol point having the same amplitude near the rotated signal point is determined as a corresponding symbol point, and the received signal point (rotated signal point ) And the corresponding symbol point with respect to the origin with respect to the angle θa, and _a frequency difference is determined from the angle θa. For the next received signal, φ _a + θ _a is newly set as φ _a , and the frequency difference is obtained by the same method. The same applies to subsequent received signals.

In the present invention, this frequency difference is also obtained by the following method. When a signal is received, its amplitude and phase are stored, and when the next received signal is a single signal, the phase of the single signal and the phase of the symbol point corresponding to the single signal (π / 4 in 64QAM) ) And _b
Then, the phase of the previously stored received signal is rotated by φ _b, and a symbol point having the same amplitude near the signal point at the rotational position is determined as a symbol point corresponding to the received signal. Then, the received signal point (signal point after the rotation) and a symbol point its corresponding determined the angle theta _b forming across the origin, calculating the frequency difference from that angle.

Further, by limiting the received signal used for the frequency comparison to only a signal having a large amplitude, the accuracy of the frequency difference to be obtained can be improved.

Further, by limiting the received signal used for the frequency comparison to a signal having a large minimum phase difference at the corresponding symbol point, even if the frequency difference between the received carrier and the reproduced carrier is large, the frequency difference can be reduced. Can be obtained.

Further, when the frequency difference between the received carrier and the reproduced carrier is reduced, the limitation by the minimum phase difference of the received signal used for frequency comparison is removed, so that the frequency comparison gain can be increased.

[0022]

【Example】

(First Embodiment) First, the principle of the frequency comparison method of the first embodiment will be described with reference to FIG. In this figure, I'Q 'represents an axis based on the phase of the reproduced carrier. First, the single signal (i, q) 31 is converted to its amplitude (√ (i ² + q ² )).
And calculate the phase φ ₁ (= tan ⁻¹ (i / q)). In the case of 64QAM, since the phase of a single symbol is always π / 4, the magnitude θ ₁ of the phase shift of the received signal point 31 of the single signal is obtained as θ ₁ = (π / 4) -φ _1. . This θ ₁ represents a shift angle between the I′Q ′ axis and the IQ axis based on the received carrier phase.

Next, assuming that the signal at the reception signal point 33 is received, the amplitude and phase φ ₂ of the signal point 34 obtained by further rotating the phase of the signal point 33 by θ ₁ are obtained. That is, the phase of the received signal point 33, thereby obtaining the 34 points only magnitude theta ₁ correct the phase shift determined solely signal 31. From the amplitude and phase of the reception signal point 34, a symbol point 35 having the same amplitude near the reception signal point 34 is determined as a symbol point corresponding to the reception signal point 34, and the positions of the signal point 34 and the symbol point 35 are determined. Phase difference θ
Ask for ₂ . Since this θ ₂ is the amount of phase change in one symbol time (t _sym ), the frequency difference Δf between the reproduced carrier and the received carrier is obtained as Δf = (1 / 2π) · (θ ₂ / t _sym ). be able to.

As shown in FIG. 2, an apparatus for implementing such a frequency comparison method is an Ida which is a value of I and Q after detection.
Amplitude determination circuit 21 for obtaining the amplitude of the received signal from ta and Qdata
A phase determining circuit 22 for determining the phase of the received signal with respect to the reproduced carrier from Idata and Qdata, a phase rotating circuit 23 for rotating the value of the phase determining circuit 22, and determining a symbol corresponding to the received signal from the amplitude and phase values. And a phase difference detecting circuit 25 for detecting a phase shift of a received signal with respect to a designated symbol, and a frequency difference detecting circuit 26 for obtaining a frequency difference from a value of the phase shift.

Next, a description will be given of a frequency comparison method according to a first embodiment using this apparatus with reference to FIG. It is assumed that the modulation format is 64 QAM and the signal transmission speed is 1 Mbaud.
Also, a case where signals are received in the order of 31, 33 will be described.

Assuming that the coordinates of the reception signal point 31 are (i, q), the amplitude judgment circuit 21 calculates the amplitude of the reception signal point 31 by calculating √ (i ² + q ² ). The phase determination circuit 22 is tan
The phase φ ₁ of the received signal point 31 is obtained by calculating ⁻¹ (i / q). The phase rotation circuit 23 transmits the value obtained by the phase determination circuit 22 to the symbol determination circuit 24 as it is. The symbol discriminating circuit 24 judges from the value of the amplitude judging circuit 21 that the received signal 31 is a single signal, and notifies the phase difference detecting circuit 25 to that effect regardless of the value of the phase rotating circuit 23. Phase difference detection circuit 25
Is that for 64QAM, the phase of a single symbol must be π /
4, the magnitude θ ₁ of the phase shift of the reception signal point 31
Is obtained by the calculation of θ ₁ = (π / 4) −φ ₁ .

The obtained θ ₁ is sent to the phase rotation circuit 23.

Next, when the received signal point 33 is received, the amplitude judging circuit 21 calculates the amplitude and outputs the calculation result to the symbol judging circuit 24. The phase judging circuit 22 obtains the phase, and The circuit 23 obtains a value φ ₂ obtained by rotating the phase obtained by the phase determination circuit 22 by θ _{1 and}
Output to Therefore, the received signal is
33 will be input as the signal point 34. The symbol determination circuit 24 determines from the amplitude and phase of the signal point 34 that the symbol point 35 having the same amplitude and the approximate phase is the symbol point corresponding to the signal point 34, and notifies the phase difference detection circuit 25. .

The phase difference detection circuit 25 calculates the phase difference θ ₂ between the signal point 34 and the symbol point 35, and calculates the phase difference θ ₂
And the phase rotation circuit 23. The frequency difference detection circuit 26 is 1 symbol time frequency difference Delta] f from the phase changes by _{θ 2 Δf = (1 / 2π} ) · (θ 2 / 1μs) ∴1Mbaud symbol time of obtaining a 1 [mu] s. On the other hand, the phase rotation circuit 23 rotates the phase of the next received signal by θ ₁ + θ ₂ . Similar processing is performed on the subsequent received signals.

As described above, in the frequency comparison method of the first embodiment, once the single signal is received after the initialization of the device, the frequency comparison is performed regardless of the signal corresponding to any symbol point thereafter. Can be.

FIG. 3 shows a phase difference between adjacent symbols in a symbol having the same amplitude in the case of 64QAM. The symbol determination circuit 24, the frequency difference is too large, therefore when the phase difference theta ₂ exceeds the phase difference between adjacent symbols, the signal points 34 symbol points
It becomes impossible to determine whether it corresponds to 35 or to the next symbol point having the same amplitude. For 64QAM,
The minimum value (minimum phase difference) of the phase difference between the adjacent symbols is 16.3 ° and about 0.28 rad as shown in FIG. 3, and therefore, in the frequency comparison method of the first embodiment, (1 / 2π)・ (0.28 / 2) /1μs≒22.6k
Frequency differences up to Hz can be correctly detected.

(Second Embodiment) In the frequency comparison method of the second embodiment, in order to obtain a highly accurate comparison result, the received signal used for comparison is limited to only those having large signal point amplitudes. I have.

As shown in FIG. 4, the apparatus for implementing this method includes an amplitude monitoring circuit 27 for detecting a received signal having an amplitude smaller than a predetermined value. A reset function for stopping the frequency comparison operation on the signal detected by the circuit 27 is provided. Other configurations are the same as those of the first embodiment (FIG. 2).

FIG. 5 is an example in which the coordinates of each symbol point are represented by 8 bits. An "H" attached to a number indicates that the number is a hexadecimal number. The value shown on the arc is the magnitude of the amplitude.

Next, the frequency comparison method of the second embodiment will be described. Here, it is assumed that the amplitude monitoring circuit 27 generates a reset signal to the symbol discrimination circuit 28 when the amplitude of the received signal is equal to or less than E8H. The operation of this embodiment is basically the same as that of the first embodiment. However, when a signal having an amplitude smaller than E8H is received, the amplitude monitoring circuit 27 outputs a reset signal to the symbol discrimination circuit 28, and the symbol discrimination circuit 28 stops the frequency comparison operation and initializes the state.
Thereafter, when a single signal having an amplitude of E8H or more is received, the frequency comparison operation is started again.

Idata and Qdata are 8 as shown in this example.
If the bits are quantized into bits, the accuracy of the representable phase differs between a symbol having a large amplitude and a symbol having a small amplitude. For example, when the I ′ component is changed by 1 LSB between the symbol having the largest amplitude and the symbol having the smallest amplitude, the respective phase changes are 0.11 ° and 0.1 mm.
78 °. Therefore, as in the second embodiment, by excluding low precision symbols from frequency comparison targets,
The accuracy of the comparison result can be improved.

(Third Embodiment) In the frequency comparison method of the third embodiment, a received signal which may correspond to a symbol point having a small phase difference from an adjacent symbol point is excluded from the frequency comparison. As can be seen from FIGS. 3 and 5, 64Q
At an AM symbol point, the minimum phase difference between symbol points whose amplitude is FFH is 16.3 °. If the minimum phase difference between the symbol points is small, as described in the first embodiment, when the frequency difference between the reproduced carrier and the received carrier is large, the frequency comparison between them cannot be performed.

In the apparatus for implementing the frequency comparison method of the third embodiment, as shown in FIG. 6, it is determined whether or not the amplitude of the received signal matches the amplitude of a predetermined symbol point having a small minimum phase difference. The symbol discriminating circuit 28 has a reset function for stopping the frequency comparison operation on the received signal detected by the amplitude discriminating circuit 29. Other configurations of this device are the same as those of the first embodiment (FIG. 2).

Next, the operation of the third embodiment will be described. Here, when the amplitude of each symbol point is represented as shown in FIG. 5, the amplitude selection circuit 29 determines that the amplitude of the received signal is 136H, F
In the case of FH and B8H, it is predetermined to generate a reset signal to the symbol discrimination circuit 28.
The minimum phase difference between the symbols having the amplitudes of 136H, FFH, and B8H is 18.9, as shown in FIG.
°, 16.3 ° and 22.6 °.

The operation of this embodiment is basically the same as that of the first embodiment. However, when a signal having the amplitude indicated above is received, the amplitude selection circuit 29 detects it and outputs a reset signal to the symbol determination circuit 28, and the symbol determination circuit 28 stops the frequency comparison operation. To initialize the state. Thereafter, when the single signal is received, the frequency comparison operation is started again.

As is clear from FIG. 3, when each symbol point is viewed for each amplitude, the minimum phase difference differs depending on the amplitude value. Therefore, the range of comparable frequencies can be widened by targeting only symbols having a large minimum phase difference. In the frequency comparison method of the third embodiment, when the amplitude is 13
By removing the received signals of 6H, FFH, and B8H from the target, the minimum phase difference becomes 28.1 ° (≒ 0.49 rad), so the comparable frequency range is (1 / 2π) · (0.49 / 2) / 1μs ≒ 39kHz
z. This is wider than the comparable frequency range in the first embodiment.

(Fourth Embodiment) In the frequency comparison method of the fourth embodiment, similarly to the third embodiment, a received signal having the same amplitude as a symbol having a small minimum phase difference is excluded from the frequency comparison. This exclusion is stopped when the frequency difference between the reproduction carrier and the reception carrier is reduced.

As shown in FIG. 7, the apparatus for implementing this method includes an amplitude selection circuit 30 that stops the selection of the received signal when the output value of the phase difference detection circuit 25 decreases. Other configurations are the same as those of the third embodiment (FIG. 6).

Next, the operation of the fourth embodiment will be described.
The operation of this embodiment is basically the same as that of the third embodiment. However, when the frequency difference is reduced and the output value of the phase difference detection circuit 25 becomes smaller than a predetermined value, the amplitude selection circuit 30 stops the selection of the received signal, thereby the symbol determination circuit
28 makes all the received signals to be discriminated.

As is apparent from the third embodiment, if the received signal is selected according to the amplitude, the comparable frequency range is widened, but the number of symbols available for comparison is reduced, so that the frequency comparison gain is reduced. . However, in the present embodiment, since the comparison operation is performed using all the received signals when the frequency difference becomes small, there is an advantage that the frequency comparison gain can be increased as in the first embodiment.

(Fifth Embodiment) In the frequency comparison method of the fifth embodiment, a frequency difference is obtained from a received single signal and a signal received before that.

As shown in FIG. 8, an apparatus for implementing this frequency comparison method detects whether a received signal is a single signal from the amplitude of the received signal, and if the signal is a single signal, activates an output of the single signal. A detection circuit 81; a phase difference calculation circuit 82 for obtaining a difference between the phase indicated by the phase determination circuit 22 and π / 4 when the single signal detection circuit 81 detects the single signal; an amplitude determination circuit 21 and a phase determination circuit 22 And a register 83 for temporarily storing the output value of Other configurations are the same as those of the first embodiment (FIG. 2).

Next, the operation of the fifth embodiment will be described.
Upon receiving the signal, the amplitude determination circuit 21 and the phase determination circuit 22
Finds its amplitude and phase and stores those values in register 83. When the next received signal is a single signal, the single signal detection circuit 81 detects it and activates the output, and the phase difference calculation circuit 82 receives the single signal and outputs the single signal obtained by the phase determination circuit 22. The phase difference between the signal phase and π / 4 is calculated, and the value is sent to the phase rotation circuit 23. The phase rotation circuit 23 rotates the phase stored in the register 83 by the phase difference sent from the phase determination circuit 22 and outputs the value to the symbol determination circuit 28 and the phase difference detection circuit 25.

The symbol discriminating circuit 28 is a single signal detecting circuit
In response to the fact that 81 has detected a single signal, the phase rotation circuit 23
The symbol point of the same amplitude located near the signal point having the phase sent from and the amplitude read from the register 83,
Determined as the corresponding symbol point, and the phase difference detection circuit 25
Calculates the phase difference between the phase of the symbol point and the phase sent from the phase rotation circuit 23, and the frequency difference detection circuit 26 calculates the frequency difference based on the phase difference. The operations of the symbol discriminating circuit 28, the phase difference detecting circuit 25 and the frequency difference detecting circuit 26 are the same as in the first embodiment.

As described above, in the frequency comparison method of the fifth embodiment, the signal received immediately before the single signal can be used for frequency comparison. Therefore, after receiving a single signal, frequency comparison can be performed more quickly than when frequency comparison is performed after receiving the next signal.

(Sixth Embodiment) In the frequency comparison method of the sixth embodiment, in implementing the method of the fifth embodiment, the reception signals used for comparison are limited to those having a large amplitude.

As shown in FIG. 9, the apparatus for implementing this method monitors the amplitude of the received signal and outputs a reset signal to the single signal detection circuit 84 and the register 85 when the amplitude is smaller than a predetermined value. The amplitude monitoring circuit 27 is provided, and the single signal detection circuit 84 and the register 85 have a reset function. Other configurations are the same as those of the fifth embodiment (FIG. 8).

The operation of this embodiment is basically the same as that of the fifth embodiment. However, as in the second embodiment, when the amplitude of the received signal is smaller than E8H, the amplitude monitoring circuit 27 generates a reset signal to the single signal detection circuit 84 and the register 85, and stops the frequency comparison operation. I do.

In this frequency comparison method, as in the second embodiment, the accuracy of the comparison result can be improved.

(Seventh Embodiment) In the frequency comparison method of the seventh embodiment, in implementing the method of the fifth embodiment, a received signal whose amplitude matches that of a symbol having a small minimum phase difference is excluded from comparison targets. An apparatus for performing this method is shown in FIG.
As shown in FIG. 7, an amplitude selection circuit 29 for detecting a received signal having the same amplitude as a predetermined symbol point having a small minimum phase difference is provided. When detecting a signal of a predetermined amplitude, the amplitude selection circuit 29 outputs a reset signal to the single signal detection circuit 84 and the register 85.

The operation of this embodiment is basically the same as that of the fifth embodiment. However, as in the third embodiment, when the amplitude of the received signal is 136H, FFH, B8H, the amplitude selection circuit 29 generates a reset signal to the phase difference calculation circuit 84 and the register 85, thereby The comparison operation is stopped.

In this frequency comparison method, as in the third embodiment, the frequency comparison range can be widened.

[0058]

As is apparent from the above description of the embodiment, the frequency comparison method of the present invention uses the received single signal and the received signal before or after the received signal to determine the frequency difference between the received carrier and the reproduced carrier. Can be requested. Therefore, it is not necessary to wait for continuous reception of a single signal, and frequency comparison can be performed quickly.

Also, by limiting the received signal to be compared to only those having a large amplitude, a highly accurate frequency difference can be obtained, and the received signal to be compared can be divided between symbols having the same amplitude. By limiting only signals corresponding to symbols having a large minimum phase difference, the comparison frequency range can be expanded.

[Brief description of the drawings]

FIG. 1 is an explanatory diagram of an operation of a frequency comparison method according to a first embodiment of the present invention;

FIG. 2 is a configuration diagram of an apparatus that implements the frequency comparison method of the first embodiment,

FIG. 3 is a diagram showing a phase difference between symbol points of 64QAM.

FIG. 4 is a configuration diagram of an apparatus that performs a frequency comparison method according to a second embodiment of the present invention;

FIG. 5 is a diagram showing the amplitude of each symbol point of 64QAM;

FIG. 6 is a configuration diagram of an apparatus that performs a frequency comparison method according to a third embodiment of the present invention;

FIG. 7 is a configuration diagram of an apparatus that performs a frequency comparison method according to a fourth embodiment of the present invention;

FIG. 8 is a configuration diagram of an apparatus that performs a frequency comparison method according to a fifth embodiment of the present invention;

FIG. 9 is a configuration diagram of an apparatus that performs a frequency comparison method according to a sixth embodiment of the present invention;

FIG. 10 is a configuration diagram of an apparatus that performs a frequency comparison method according to a seventh embodiment of the present invention;

FIG. 11 is a diagram showing transition of a reception signal point.

[Explanation of symbols]

 21 Amplitude judgment circuit 22 Phase judgment circuit 23 Phase rotation circuit 24, 28 Symbol judgment circuit 25 Phase difference detection circuit 26 Frequency difference detection circuit 27 Amplitude monitoring circuit 29, 30 Amplitude selection circuit 81, 84 Single signal detection circuit 82 Phase difference calculation circuit 83, 85 registers

Claims (6)

(57) [Claims] When demodulating a received quadrature amplitude modulated signal,
In a frequency comparison method for determining a frequency difference between a received carrier and a reproduced carrier, an IQ axis is rotated so that a first received signal point coincides with a corresponding first symbol point. Distance and IQ from signal point origin
A second symbol point corresponding to the second received signal point is determined from a phase from either axis, and an angle formed between the second received signal point, the origin, and the second symbol point, and a signal A frequency comparison method for determining the frequency difference from a time interval at which the frequency is received. 2. The distance of the first received signal point from the origin, at least in the initial frequency comparison, coincides with the distance of a symbol point where there is only one symbol point at the same distance from the origin in the same quadrant. The frequency comparison method according to claim 1, wherein a target reception signal is selected so as to perform the operation. 3. When demodulating a received quadrature amplitude modulation signal,
In a frequency comparison method for obtaining a frequency difference between a received carrier and a reproduced carrier, a position of a first received signal point on an IQ plane is stored, and a second received signal point received next is a distance from the origin. When the symbol having the same value corresponds to a symbol having only one in the same quadrant, the IQ axis is rotated so that the second received signal point becomes the corresponding second symbol point, and the IQ axis is rotated. A first symbol point corresponding to the received signal point is determined from the position of the first received signal point after being made, and an angle formed by the first received signal point, the origin, and the first symbol point And calculating the frequency difference from a time interval of a received signal. 4. The target reception signal is selected such that the distance from the origin at the first and second reception signal points is equal to or greater than a predetermined distance threshold. Or the frequency comparison method according to 3. 5. An angle between a line connecting any two of the symbol points at the same distance from the origin and the origin in the first and second reception signal points is set in advance. 4. The frequency comparison method according to claim 1, wherein a target reception signal is selected so as to match the distance of a symbol point that is equal to or larger than an angle threshold. 6. The frequency comparison method according to claim 5, wherein when the obtained frequency difference is equal to or less than a preset frequency threshold, the value of the angular threshold is reduced.