JP2005333545A - Modulation/demodulation method and circuit - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a modulation method and circuit in which the arrangement of signal points is compliant to square quadrature amplitude modulation (QAM) and the arrangement of QAM signal points is used to efficiently suppress the deterioration of a BER (Bit Error Rate) characteristic caused by phase noise. <P>SOLUTION: Signal points selected out of signal points in which an in-phase/quadrature component is divided at equal intervals and which do not exceed a maximum amplitude of a multi-level square QAM outside the signal points of the square QAM, so as not to be adjacent to each other are added to the arrangement of signal points of the square QAM. Further, signal points which are on the outer-most periphery of the square QAM and adjacent to four corners or at the second from signal points adjacent to the four corners, and in which order of closeness from four corners is within the number of the added signal points, are deleted. A transmission bit sequence is then mapped to the remaining signal points. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a modulation / demodulation method and circuit for reducing deterioration in bit error rate (BER) characteristics due to phase noise of a transmitter / receiver oscillator in a quadrature amplitude modulation (QAM) system.

  QAM is one of digital modulation systems, and data can be efficiently transferred with a limited bandwidth by expressing information using both amplitude and phase. For this reason, it is widely used in systems capable of ensuring a sufficient carrier-to-noise ratio (C / N) such as FWA (Fixed Wireless Access) and CATV. Various signal point arrangement methods in multi-level QAM have been proposed, but a square QAM in which signal points are arranged in a square in the in-phase direction and in the orthogonal direction regards the in-phase and orthogonal components as independent. There is an advantage that it is easy to mount because it is possible to modulate and demodulate. FIG. 4 is a diagram showing a signal point arrangement of 64-valued square QAM.

One factor that causes deterioration in the BER characteristics of the square QAM is local oscillation frequency fluctuation (phase noise) in the transceiver. The received signal r (t) on which the phase noise Φ (t) is superimposed is expressed by the following equation r (t) using the in-phase / quadrature component modulation signals i (t), q (t), the angular frequency ω, and the time t. = I (t) cos (ωt + Φ (t)) − q (t) sin (ωt + Φ (t))
Given by. Usually, the band of the phase noise Φ (t) is about several tens of kHz, and in high-speed communication with a symbol rate of several MHz or more, an influence appears in the form of gradual phase fluctuations. FIG. 5 is a diagram illustrating a case where phase noise is superimposed on a square QAM signal point. As shown in FIG. 5, the original signal point is spread in the phase direction due to the influence of phase noise.

  In the square QAM, the signal points are uniformly arranged in the in-phase / orthogonal directions, so that the identification margin in the phase direction is not uniform. In particular, since the discriminating margin for the phase tends to decrease as the amplitude of the signal point increases, the deterioration of the BER characteristic due to the phase noise becomes remarkable as the modulation multi-level number increases. Specifically, in the square 64QAM of FIG. 4, at the signal point 401, the phase interval to the adjacent signal point 402 is 0.5π (rad), but at the outer signal point 403, up to the adjacent signal point 404. The phase interval is 0.053π (rad). Therefore, the signal points 401 and 402 are less affected by the phase noise, whereas the signal points 403 and 404 are more affected by the phase noise.

  As a method for removing phase noise, there is an automatic phase control (APC) circuit that calculates and compensates for a phase error of a received signal from a reference signal point in a baseband processing unit of a receiver. The APC circuit realizes highly accurate compensation for gradual phase fluctuations. However, when the phase noise band is wider than the compensation range of the APC circuit, the APC circuit is sufficient for fluctuation of the received signal due to the phase noise. Since no follow-up is possible, phase noise remains in the output of the APC circuit.

  In addition, as a technique that can be used in combination with an APC circuit, a technique for changing a part of square QAM signal points has been proposed (see, for example, Patent Document 1 and Patent Document 2). The modulation method and circuit of Stepped Square QAM (hereinafter referred to as SS-QAM) described in Patent Documents 1 and 2 are a maximum amplitude signal point in square QAM and a high amplitude signal point present in the vicinity thereof. The C / N ratio is improved by moving to a newly created signal point having a small amplitude. The newly created signal point is created by equally dividing the in-phase / quadrature component outside the original signal point within a range not exceeding the maximum amplitude of the original square QAM. FIG. 9 is a diagram illustrating a signal point arrangement of 64-value SS-QAM. As shown in FIG. 9, SS-64QAM is realized by moving signal points 900a to 900d having the maximum power of square type 64QAM to signal points 901a to 901d, respectively. As a result, the C / N at the signal point before movement and the signal point after movement can be improved by about 0.8 dB, and the average C / N of the entire signal can be improved by about 0.2 dB. At the same time, SS-QAM has the advantage that the square QAM carrier synchronization circuit, symbol timing synchronization circuit, etc. can be used without significant changes since the signal point arrangement is equally spaced in the in-phase and orthogonal directions. is there.

  In addition, a method of reducing the influence of phase noise without changing the signal point from the square QAM has been proposed (see Non-Patent Document 1, for example). FIG. 10 is a diagram illustrating threshold values of signal points described in Non-Patent Document 1. Conventionally, as shown in FIG. 4, the threshold value of the signal point represented by a straight line on the in-phase / orthogonal plane is set to both thermal noise and phase noise so that the error characteristic of symbol determination with respect to thermal noise becomes the best as shown in FIG. Is replaced with a curve determined to be the best. Here, as shown in FIG. 10, the line representing the threshold value is widened so as to increase the identification margin in the phase direction as the amplitude increases. As a result, the BER characteristics under the environment of thermal noise and phase noise can be optimized, and only the symbol determination circuit needs to be changed from the square QAM, and there is an advantage that the influence of the phase noise can be reduced with a small change.

JP 61-077452 A Japanese Patent Publication No. 06-71278 Kurakake, Nakamura, and Oyamada, “QAM Symbol Judgment Methods for Reducing Phase Noise Effects” 2003 IEICE Communication Society, B-8-8, 2003, p286

  The SS-QAM scheme is intended to obtain gain for all signal points with constant transmission power by lowering the peak C / N with respect to the average C / N. For this reason, it exhibits good characteristics in a thermal noise environment that affects the amplitude direction evenly, but as described above, the compensation effect is insufficient for phase noise in which characteristic deterioration becomes significant at a specific signal point as described above. It is.

  Although the method of Non-Patent Document 1 can reduce the influence of phase noise with a small change from a square QAM modulator / demodulator, the optimum threshold changes due to changes in thermal noise and phase noise, so design is difficult. There is a problem. In addition, regarding the characteristics, there is a trade-off relationship in which the BER characteristics against thermal noise are deteriorated by distorting the threshold value in order to enhance the characteristics against phase noise, and there is a problem that a large improvement effect cannot be obtained.

  Thus, no method has been proposed for sufficiently improving the BER characteristic degradation caused by the phase noise in the square QAM.

  Therefore, the present invention can be used together with an APC circuit, the signal point arrangement conforms to the square QAM, and the modulation method using the QAM signal point arrangement that can efficiently suppress the deterioration of the BER characteristic due to the phase noise. And it aims at providing a circuit.

According to the modulation method of the present invention,
Dividing the in-phase and quadrature components at equal intervals in the signal point arrangement of the multi-valued square QAM, and out of the signal points that do not exceed the maximum amplitude of the square QAM outside the square QAM signal point, Signal points selected so that they are not adjacent to each other are added, and further, the signal points on the outermost periphery of the square QAM and the signal points adjacent to the four corners or every other signal point from the four corners. In addition, signal points within the order of proximity from the four corners within the number of the added signal points are deleted, and a transmission bit sequence is mapped to the remaining signal points.

  That is, among the signal points of the square QAM, the signal points located on the outermost side where the influence of the phase noise is particularly large are selected from every other corner and moved to the signal points outside the square QAM. . Here, the destination signal point is created by equally dividing the in-phase and quadrature components as in SS-QAM, and is determined without exceeding the maximum amplitude of the original square QAM. In the present invention, the destination signal points are determined not to be adjacent to each other. Under a phase noise environment, the larger the amplitude of a signal point, the more identification errors occur between adjacent signal points in the phase direction. Therefore, by removing signal points outside the square QAM alternately, a sufficient phase margin can be obtained. It can be secured. As a result, it is possible to improve the characteristics specialized for phase noise without increasing the maximum amplitude of the square QAM signal point. Further, as with SS-QAM, since it has signal points according to square QAM, there is an advantage that various synchronization processes can use the same as those of square QAM.

According to another embodiment of the modulation method of the present invention,
A first step of determining whether or not each signal point of an input signal mapped to a signal point of a multi-valued square QAM is a movement source signal point; A second step of moving the signal point of the signal to a pair of destination signal points, wherein the destination signal point divides the in-phase and quadrature components at equal intervals, and the signal points of the square QAM Are signal points that are selected so as not to be adjacent to each other from among signal points that do not exceed the maximum amplitude of the square QAM, and the source signal points are on the outermost circumference of the square QAM. The signal points are adjacent to the four corners or every other signal point from the signal points adjacent to the four corners, and the order of the proximity from the four corners is within the number of the destination signal points. Features.

  According to another embodiment of the modulation method of the present invention, before the first step, there is a step of mapping a transmission bit sequence to a signal point of a multi-valued square QAM, and the second step It is also preferable to have a step of converting the signal into a signal corresponding to the transmission path and transmitting it after this step.

According to the demodulation method of the present invention,
A signal modulated by any of the modulation methods described above is input, and a transmission bit sequence is output.

According to the modulation circuit of the present invention,
A first determination circuit that uses a signal mapped to a signal point of a multivalued square QAM as an input signal, determines whether the signal point of the input signal is a source signal point, and outputs a determination result; The output of the first determination circuit is the first input signal, the signal mapped to the signal point of the square QAM is the second input signal, and the first input signal notifies that it is the source signal A remapping circuit that moves the signal point of the second input signal to a pair of destination signal points, the destination signal point divides in-phase and quadrature components at equal intervals, and Out of the square QAM signal points, the signal points are selected so as not to be adjacent to each other from the signal points that do not exceed the maximum amplitude of the square QAM, and the source signal points are the square type Signal points on the outermost circumference of the QAM, and four To the signal point of every other from the signal point adjacent to the adjacent or corners, and wherein the order of closeness from the four corners is a signal point within a few of the destination signal point.

According to another embodiment of the modulation circuit of the present invention,
A bit sequence to be transmitted is mapped to a signal point of a multi-valued square QAM, and a mapping circuit input to the first determination circuit and an output signal of the remapping circuit are converted into a signal corresponding to a transmission path and transmitted. It is also preferable to have a transmission circuit that performs the above.

  According to the multitone circuit of the present invention, a signal mapped to the signal point of the received multilevel QAM is used as an input signal, it is determined whether or not the signal point of the input signal is a destination signal point, and the determination result is output. A second determination circuit that outputs the first input signal as an output of the second determination circuit, and a second input signal that is mapped to the signal point of the multi-level QAM, and is moved by the first input signal. A signal point restoration circuit that moves the signal point of the second input signal to a pair of source signal points when notified that the destination signal point is a destination signal point, Signal points selected by dividing orthogonal components into equal intervals and not being adjacent to each other outside the square QAM signal point and not exceeding the maximum amplitude of the square QAM; The source signal point is the outermost periphery of the square QAM. And signal points that are adjacent to the four corners or every other signal point from the signal points adjacent to the four corners, and the order of proximity from the four corners is within the number of the destination signal points. It is characterized by.

According to another embodiment of the demodulation circuit of the present invention,
A receiving circuit that receives a digitally modulated signal from a transmission path; a signal point position of an output signal of the receiving circuit; and a signal point determining circuit that inputs to the second determining circuit and the signal point restoring circuit; It is also preferable to include a symbol determination circuit that performs symbol determination on the output signal of the signal point restoration circuit and reproduces a bit sequence.

According to the modulation and modulation circuit in the present invention,
One of the modulation circuits and one of the demodulation circuits are provided.

  According to the present invention, the influence of phase noise can be reduced by digital signal processing. In general, an oscillator becomes more expensive as the phase noise characteristic is improved. Therefore, the present invention makes it possible to reduce the price of a digital communication system.

  The best mode for carrying out the present invention will be described in detail below with reference to the drawings. In the following description, the case of 64 values will be described as an example, but the present invention can also be applied to M values (M is a power of 2).

  FIG. 3 is a signal point arrangement diagram used by the modulation / demodulation method and circuit of the present invention in the case of 64 values (hereinafter referred to as the signal point arrangement of the present invention).

  The first embodiment of the modulation method according to the present invention is to map the bit sequence to be transmitted to the signal point arrangement of the present invention. The demodulation method embodiment of the present invention maps to the signal point arrangement of the present invention. The converted signal is converted into a transmitted bit sequence. The correspondence between the bit sequence and each signal point of the signal point arrangement of the present invention is determined in advance by an arbitrary method.

  Hereinafter, the signal point arrangement creation method of the present invention will be described with reference to the square QAM signal point arrangement.

  Among the signal points of the square type 64QAM in FIG. 4, the signal points to be moved, that is, the signal points to be deleted (hereinafter referred to as the movement source signal points) and the signal points after the movement, that is, the new signal points (hereinafter referred to as the signal points) The destination signal point is determined by the following procedure.

  First, signal points that can be secured outside the square type 64QAM and at positions that do not exceed the maximum amplitude of the square type 64QAM are investigated. From FIG. 6, a total of 16 signal points of signal points 601 a to 601 p can be secured inside the circle 600 representing the maximum amplitude.

  Next, in order to avoid the influence of phase noise, these signal points are selected so that they are not adjacent to each other. FIG. 7 is a diagram illustrating an example of selection. Here, 8 points of 601b, 601c, 601f, 601g, 601j, 601k, 601n and 601o are thinned out, and 8 points of 601a, 601d, 601e, 601h, 601i, 601l, 601m and 601p are adopted as destination signal points. To do.

  Subsequently, the source signal point is determined. As apparent from FIG. 5, since the influence of moving noise increases as the amplitude of the signal point increases, it is a signal point on the outermost periphery of the square QAM and adjacent to the four corners or adjacent to the four corners. A signal point that is every other signal point from the signal point to be processed and whose order counted in the order from the four corners is within the number of destination signal points is selected. Here, since there are eight signal points after movement, eight signal points adjacent to the signal points at the four corners, that is, 300a, 300d, 300e, 300h, 300i, 300l, 300m, and 300p in FIG. Let it be a signal point.

  As described above, the signal point arrangement of the present invention is obtained by adding destination signal points to the square QAM signal point arrangement and deleting the same number of movement source signal points.

  FIG. 2 is a flowchart of a second embodiment of the modulation method and the demodulation method according to the present invention.

  (S201) First, the transmission bit sequence is mapped to multi-valued square QAM.

  (S202, S210, S211) It is determined whether or not the signal point mapped to the square QAM is a source signal point. That is, whether it is a point on the outermost periphery of the square QAM, whether it is adjacent to the four corner signal points or every other signal point from the four corner signal points, the order from the four corners is prepared Judgment is made based on whether the number is within the number of movement destination signal points. In the example of FIG. 3, the signal points 300a, 300d, 300e, 300h, 300i, 300l, 300m, and 300p are determined as the movement source signal points.

  (S203) When it is determined as a movement source signal point by S202, S210, S211, it is moved to a pair of movement destination signal points that are created in advance. The method of determining the pair of the movement source signal point and the movement destination signal point is arbitrary. In the example of FIG. 3, the signal point 300a is moved to 601a, 300d to 601d, 300e to 601e, 300h to 601h, 300i to 601i, 300l to 601l, 300m to 601m, 300p to 601p, respectively. A QAM signal having the signal point arrangement shown in FIG. 3 is obtained.

  (S206) The obtained QAM signal is transmitted to the transmission line (S204) and received on the receiving side (S205), and then it is determined which position is the signal point arrangement of the present invention.

  (S207) It is determined whether or not the position of the determined signal point is a destination signal point. In the example of FIG. 3, it is determined whether or not any of the signal points 601a, 601d, 601e, 601h, 601i, 601l, 601m, and 601p is applicable.

  (S208) If it is determined that the signal point is the destination signal point, the signal is moved to the position of the paired source signal point, that is, the original square QAM signal point. In the example of FIG. 3, the signal point 601a is moved to 300a, 601d to 300d, 601e to 300e, 601h to 300h, 601i to 300i, 601l to 300l, 601m to 300m, and 601p to 300p. The square 64QAM signal is restored.

  (S209) Subsequently, this is determined as a symbol and a bit sequence is reproduced.

  FIG. 1 is a block diagram showing an embodiment of a modulation circuit and a demodulation circuit according to the present invention. The modulation circuit 101 includes a mapping circuit 103, a determination circuit 104, a remapping circuit 105, and a transmission circuit 106. The demodulation circuit 102 includes a reception circuit 107, a signal point determination circuit 108, a determination circuit 109, a signal point restoration circuit 110, and a symbol determination circuit 111.

  The transmission bit sequence is input to the mapping circuit 103. The mapping circuit 103 maps the signal points of the multi-valued square QAM, and the mapped signal is input to the determination circuit 104 and the remapping circuit 105.

  The determination circuit 104 determines whether the signal point of the input signal is a movement source signal point. In the example of FIG. 3, it is determined whether the signal point is 300a, 300d, 300e, 300h, 300i, 300l, 300m, or 300p. The determination result is input to the remapping circuit 105.

  When the determination result from the determination circuit 104 indicates “movement source signal point”, the remapping circuit 105 changes the signal point of the input signal from the mapping circuit 103 to a destination signal point that is a predetermined pair. Move. In the example of FIG. 3, the signal point 300a is moved to 601a, 300d to 601d, 300e to 601e, 300h to 601h, 300i to 601i, 300l to 601l, 300m to 601m, 300p to 601p, respectively. A QAM signal having the signal point arrangement shown in FIG. 3 is obtained.

  The transmission circuit 106 converts the signal mapped to the signal point arrangement of the present invention from the remapping circuit 105 into a signal corresponding to the transmission path, and performs transmission.

  The reception circuit 107 receives a signal from the transmission path, performs quadrature demodulation, and inputs the signal to the signal point determination circuit 108.

  The signal point discriminating circuit 108 determines which position of the signal point arrangement of the present invention the signal point of the input signal from the receiving circuit 107 is. Here, the determination is made to the point with the closest Euclidean distance. The signal after the determination is input to the determination circuit 109 and the signal point restoration circuit 110.

  The determination circuit 109 determines whether or not the signal point of the input signal is the destination signal point, and the determination result is input to the signal point restoration circuit 110.

  When the signal point restoration circuit 110 is notified by the input signal from the determination circuit 109 that it is a “movement destination signal point”, the signal point of the input signal from the signal point determination circuit 108 is used as a pair of movement source. Move to signal point. Thereby, the square QAM is restored. In the example of FIG. 3, the signal point 601a is moved to 300a, 601d to 300d, 601e to 300e, 601h to 300h, 601i to 300i, 601l to 300l, 601m to 300m, and 601p to 300p. The square 64QAM signal represented in FIG. 4 is obtained. The restored square 64QAM signal is input to the symbol determination circuit 111.

  The symbol determination circuit 111 reproduces a transmission bit sequence from the in-phase / quadrature components of the input signal from the signal point restoration circuit 110.

  Alternatively, with respect to a circuit for reproducing a transmission bit sequence from a reception signal, the signal point determination circuit 108, the determination circuit 109, and the signal point restoration circuit 110 hold a memory corresponding to the in-phase / quadrature components of the reception signal, and store this as an address It is also possible to configure with a circuit that returns a corresponding bit.

FIG. 8 shows the results of calculating the BER characteristics under a phase noise environment by computer simulation when the APC circuit using the signal point arrangement and the LMS (Least Mean Square) algorithm of the present invention is applied. However, the carrier C / N of the phase noise is 20 dB, and the cutoff frequency is 35 kHz. For comparison, the BER characteristics are also shown when LMS is adopted for the square type 64QAM. FIG. 8 shows that the BER characteristics can be improved by using the arrangement method according to the present invention. At BER = 10 ⁻⁵ , an improvement effect of about 0.7 dB is obtained compared to the square QAM.

It is a block diagram of a modulation circuit and a demodulation circuit according to the present invention. 6 is a flowchart of a second embodiment of a modulation method according to the present invention; It is a signal point arrangement diagram used by the modulation and demodulation method and circuit of the present invention in the case of 64 values. It is a figure which shows signal point arrangement | positioning of 64-valued square type QAM. It is a figure showing the case where phase noise is superimposed on the signal point of square type QAM. It is a figure showing the new signal point which does not exceed the maximum amplitude of signal point arrangement | positioning of 64 value square type QAM. It is a figure showing the example of the selection performed in order to remove the influence of a phase noise from the new signal point of FIG. It is a BER characteristic figure under a phase noise environment at the time of applying a signal point arrangement and an APC circuit of the present invention. It is a figure which shows the signal point arrangement | positioning of 64-value SS-QAM. It is a figure showing the threshold value change by the conventional method for the influence reduction of a phase noise.

Explanation of symbols

DESCRIPTION OF SYMBOLS 101 Modulation circuit 102 Demodulation circuit 103 Mapping circuit 104,109 Judgment circuit 105 Remapping circuit 106 Transmission circuit 107 Reception circuit 108 Signal point discrimination circuit 110 Signal point restoration circuit 111 Symbol judgment circuit 300a-300p Original signal point 401-404 Square type QAM signal points
600 Line representing maximum amplitude of square QAM 601a to 601p Destination signal point candidates 900a to 900d Source signal points in SS-QAM system 901a to 901d Destination signal points in SS-QAM system

Claims (9)

In the modulation method of digital communication,
For signal point arrangement of multi-valued square type QAM,
In-phase and quadrature components are divided at equal intervals, and signal points selected so as not to be adjacent to each other outside the square QAM signal points that do not exceed the maximum amplitude of the square QAM are obtained. Add
Further, the signal points on the outermost periphery of the square QAM, the signal points adjacent to the four corners or every other signal point from the signal points adjacent to the four corners, and the order of the proximity from the four corners is the added signal. Delete signal points within the number of points,
A modulation method characterized by mapping a transmission bit sequence to remaining signal points. In the modulation method of digital communication,
A first step of determining whether or not each signal point of the input signal mapped to the signal point of the multi-valued square QAM is a source signal point;
A second source step of moving the signal point of the input signal to a pair of destination signal points if the source signal point is a source signal point;
The destination signal points are divided so that the in-phase and quadrature components are equally spaced, and the signal points outside the square QAM signal points are not adjacent to each other among the signal points that do not exceed the maximum amplitude of the square QAM. Is the signal point selected by
The source signal point is a signal point on the outermost circumference of the square QAM, and every other signal point adjacent to or adjacent to the four corners, and in order of proximity from the four corners. Is a signal point within the number of the destination signal points. In the modulation method of digital communication,
Mapping the transmission bit sequence to a signal point of a multi-valued square QAM before the first step;
3. The modulation method according to claim 2, further comprising a step of converting and transmitting a signal corresponding to a transmission path after the second step. In the demodulation method of digital communication,
4. A demodulation method, comprising: inputting a signal modulated by the modulation method according to claim 1; and outputting a transmission bit sequence. In a modulation circuit for digital communication using quadrature amplitude modulation,
A first determination circuit that uses a signal mapped to a signal point of a multivalued square QAM as an input signal, determines whether the signal point of the input signal is a source signal point, and outputs a determination result;
The output of the first determination circuit is the first input signal, the signal mapped to the signal point of the square QAM is the second input signal, and the first input signal notifies that it is the source signal A remapping circuit that moves the signal point of the second input signal to a destination signal point that is a pair,
The destination signal points are divided so that the in-phase and quadrature components are equally spaced, and the signal points outside the square QAM signal points are not adjacent to each other among the signal points that do not exceed the maximum amplitude of the square QAM. Is the signal point selected by
The source signal point is a signal point on the outermost circumference of the square QAM, and every other signal point adjacent to or adjacent to the four corners, and in order of proximity from the four corners. Is a signal point within the number of the destination signal points. A mapping circuit that maps a bit sequence to be transmitted to signal points of a multi-valued square QAM and inputs the signal to the first determination circuit;
The modulation circuit according to claim 5, further comprising: a transmission circuit that converts an output signal of the remapping circuit into a signal corresponding to a transmission path and transmits the signal. In the demodulation circuit for digital communication using the quadrature amplitude modulation method,
A second determination circuit that uses a signal mapped to a signal point of received multilevel QAM as an input signal, determines whether the signal point of the input signal is a destination signal point, and outputs a determination result;
The output of the second determination circuit is the first input signal, the signal mapped to the signal point of the multilevel QAM is the second input signal, and the destination input signal point is notified by the first input signal. A signal point restoration circuit that moves the signal point of the second input signal to the pair of source signal points,
The destination signal points are divided so that the in-phase and quadrature components are equally spaced, and the signal points outside the square QAM signal points are not adjacent to each other among the signal points that do not exceed the maximum amplitude of the square QAM. Is the signal point selected by
The source signal point is a signal point on the outermost circumference of the square QAM, and every other signal point adjacent to or adjacent to the four corners, and in order of proximity from the four corners. Is a signal point within the number of the destination signal points. A receiving circuit for receiving a digitally modulated signal from the transmission path;
A signal point position of an output signal of the receiving circuit is determined; the second determination circuit; and a signal point determination circuit that is input to the signal point restoration circuit;
The demodulation circuit according to claim 7, further comprising: a symbol determination circuit that performs symbol determination on an output signal of the signal point restoration circuit and reproduces a bit sequence. The modulation circuit according to claim 5 or 6,
A modulation / demodulation circuit comprising the demodulation circuit according to claim 7.

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