JP2022069257A - Determination device for symbol position of symbol used in modulation, and program - Google Patents

Abstract

To provide a technique capable of shortening the time required for determining a symbol position of a symbol used in modulation.SOLUTION: A determination device comprises: first processing means which repeatedly performs first processing of selecting two symbols whose symbol positions are in a selection quadrant of four quadrants of a complex plane out of the plurality of symbols, changing the symbol positions of the two selected symbols and changing symbol positions in other three quadrants on the basis of the symbol position in the selection quadrant after the change of the symbol positions of the two selected symbols, for a prescribed number of times; and second processing means which determines the symbol position of each of the plurality of symbols by selecting two symbols from the plurality of symbols after the first processing means repeats the first processing for the prescribed number of times, and repeating the second processing of changing the symbol positions of the two selected symbols.SELECTED DRAWING: Figure 3

Description

The present invention relates to a technique for determining a position (symbol position) on a complex plane corresponding to a symbol used in modulation.

For example, quadrature amplitude modulation (QAM) is used as the modulation method of the communication system. A QAM that uses N different symbols is called N-QAM. In N-QAM, the bit string corresponding to each of the N symbols and the coordinates (constitutation) on the complex plane (hereinafter, IQ plane) corresponding to each of the N symbols, that is, the symbol positions are determined in advance. .. Then, the modulation device transmits the symbol corresponding to the bit example as a modulation signal. The amplitude and phase of the modulated signal correspond to the amplitude and phase of the vector when the symbol position corresponding to the symbol is a vector on the IQ plane. Probability shaping (PS) and geometric shaping (GS) techniques are used to bring the N-QAM communication capacity closer to the Shannon limit.

PS is a technique for increasing the communication capacity by bringing the amplitude distribution of the modulated signal closer to the Gaussian distribution. Therefore, in PS, the smaller the amplitude, the larger the probability of selection (probability of occurrence). In PS, the correspondence between the bit string and the symbol string is determined in advance in order to increase the probability of occurrence as the amplitude of the symbol becomes smaller. It should be noted that this correspondence relationship is determined so that the smaller the amplitude of the symbol, the higher the probability of occurrence, assuming that the bit string is random. The distribution adaptor (DM) used in PS converts the input bit string into a symbol string based on this predetermined correspondence, and brings the amplitude distribution of the modulated signal closer to the Gaussian distribution.

On the other hand, GS is a technique for increasing the communication capacity by selecting and adjusting the symbol position on the IQ plane corresponding to each symbol of N-QAM according to the characteristics of the transmission line.

Non-Patent Document 1 discloses HPGS (hybrid probability and geometric shaping) in which PS and GS are used in combination. In addition, Non-Patent Document 2 discloses a method called GPO (Generalized Pairwise Optimization) for determining the symbol position of a symbol in HPGS.

Z. Qu, et. al. , "Universal Hybrid Probabilistic-geometry Shipping Based on Two-Dimensional Distribution Machines", 2018 Optical Fiber Corporation, California Corporation, Corporation, California, Corporation 1-3, 2018 S. Zhang, et. al. , "A generallyzed polypropylene optionization for designing multi-dimensional modeling formulas", 2017 Optical Fiber Communications Connections Corporation, California, Technology and Technology. 1-3, 2017

Hereinafter, GPO will be described using 64-QAM shown in FIG. 1 as an example. In the preparatory stage, the signal-to-noise ratio (SNR) of the transmission line and the probability of occurrence of each symbol are determined. The probability of occurrence of each symbol is determined based on the information indicating the correspondence between the bit string and the symbol string used by the DM of PS (hereinafter referred to as correspondence information). In GPO, the total of each vector is 0 when the symbol position of each symbol is a vector, and the average power (obtained by the probability of occurrence of each symbol and its amplitude) is a constant value at a predetermined value. Set conditions.

As shown in FIG. 1, first, two symbols are randomly selected. In FIG. 1, the symbol 90 in the third quadrant and the symbol 91 in the first quadrant are selected. Subsequently, it is considered to move (change) the symbol positions (coordinates) of the symbol 90 and the symbol 91 within the range satisfying the above constraint condition. As shown in FIG. 1, in order to satisfy the above constraint condition, the symbol 90 can be moved on the arc 92 passing through the symbol position of the current symbol 90, and the symbol 90 passes through the symbol position of the current symbol 91. The symbol 91 can be moved on the arc 93.

In the GPO, the destination of the symbol 90 and the symbol 91 is determined based on a predetermined cost function. For example, a function for obtaining the bit error rate (BER) can be a cost function. The BER is obtained based on the SNR of the transmission line and the probability of occurrence of each symbol. In this case, under the condition that the above constraint condition is satisfied, the coordinates on the arc 92 and the arc 93 where the cost function is minimized are the destinations of the symbol 90 and the symbol 91, respectively. The cost function is not limited to the function for obtaining the BER, and for example, the function for obtaining the mutual information amount (MI), the generalized mutual information amount (GMI), and the like can be used as the cost function. MI and GMI can also be obtained based on the SNR of the transmission line and the probability of occurrence of each symbol. When MI or GMI is used as a cost function, the coordinates that maximize the cost function are set as the destination under the above constraints.

In the GPO, the selection of the above two symbols and the movement of the two selected symbols based on the constraints and the cost function are repeated, for example, until the cost function converges.

However, in GPO, the number of repetitions until the cost function converges is very large, and it takes time to determine the symbol position of each symbol.

The present invention provides a technique capable of reducing the time required to determine the symbol position of a symbol used in modulation.

According to one aspect of the present invention, the determination device for determining the symbol position in the complex plane of each of the plurality of symbols used in the modulation is such that the symbol position is within the four quadrants of the complex plane among the plurality of symbols. Select two symbols in the selected quadrant, change the symbol position of the selected two symbols, change the symbol position of the selected two symbols, and then change the symbol position in the selected quadrant to the other. A first processing means that repeats the first processing for changing the symbol positions of the three quadrants a predetermined number of times, and after the first processing means repeats the first processing a predetermined number of times, the two from the plurality of symbols. It is provided with a second processing means for determining the symbol position of each of the plurality of symbols by repeatedly performing the second processing of selecting one symbol and changing the symbol position of the two selected symbols. It is a feature.

According to the present invention, the time required to determine the symbol position of the symbol used in the modulation can be shortened.

Explanatory drawing of GPO. The flowchart of the symbol position determination processing by one Embodiment. Explanatory drawing of 1st process by 1 Embodiment. Explanatory drawing of 1st process by 1 Embodiment. Explanatory drawing of 1st process by 1 Embodiment. The figure which shows the relationship between the number of repetitions and BER. The functional block diagram of the determination apparatus by one Embodiment.

Hereinafter, embodiments will be described in detail with reference to the accompanying drawings. It should be noted that the following embodiments do not limit the invention according to the claims, and not all combinations of features described in the embodiments are essential to the invention. Two or more of the plurality of features described in the embodiments may be arbitrarily combined. In addition, the same or similar configuration will be given the same reference number, and duplicated explanations will be omitted.

FIG. 2 is a flowchart of the symbol position according to the present embodiment, that is, the process of determining the coordinates on the IQ plane corresponding to the symbol. The process of FIG. 2 is executed by the determination device. The determination device can be realized, for example, by having one or more processors of the computer execute an appropriate program. The program is stored in a computer-readable storage medium such as a memory device inside the computer or an external storage device such as an HDD connected to the computer.

In the determination device, the SNR of the communication system to which the determined symbol position is applied (hereinafter, referred to as a target communication system, and the device that performs modulation and demodulation in the target communication system is referred to as a target device) is set in advance. .. Further, the probability of occurrence of each symbol is determined in advance and set in the determination device. The target communication system of this embodiment uses HPGS. PS brings the amplitude distribution of the modulated signal closer to the Gaussian distribution, so it is ideal that the occurrence probabilities of symbols of the same amplitude are equal. However, the probability of occurrence of each symbol is determined by the correspondence information held by the DM. In order for the amplitude distribution of the modulated signal to match the Gaussian distribution, the length of the symbol string in this correspondence information must be increased. However, since the length of the symbol string in the correspondence information cannot be made too large, the probability of occurrence of each symbol cannot be completely idealized by the correspondence information. That is, the probability of occurrence of symbols of the same amplitude is not the same, but they are close to each other.

FIG. 3 shows the initial position of the symbol position of each symbol. As shown in FIG. 3, the initial positions of the symbols are evenly spaced in the same manner as in normal 64-QAM. As described above, since PS is applied, the probability of occurrence of each symbol increases as the amplitude becomes smaller. In the present embodiment, the initial symbol positions of each symbol are evenly spaced on the IQ plane, but if the constraint condition of GPO is satisfied and the amplitude is smaller and the occurrence probability is higher, the initial symbol position of each symbol is set. Does not have to be evenly spaced on the IQ plane.

First, in S10, the determination device initializes the repeat counter I to 1. In S11 and S12, the determination device executes the first process described later, and in S13, the repeat counter I is incremented by 1. continue. In S14, the determination device determines whether or not the repetition counter I is larger than a predetermined threshold value Th. When the repetition counter I is equal to or less than a predetermined threshold value Th, the determination device repeats the process from S11. That is, the determination device repeats the first process a number of times equal to the threshold value Th.

If the repeat counter I is greater than a predetermined threshold Th, the determination device performs a second process in S15. The second processing includes one processing of the GPO processing described with reference to FIG. 1, that is, selection of two symbols and movement processing of the two selected symbols based on constraints and cost functions. After executing the second process, the determination device determines in S16 whether or not the cost function has converged. For example, the determination device can determine that the cost function has converged when the amount of change from the value of the cost function in the previous S16 is not more than or equal to a predetermined value, which is continuous for a predetermined number of times. Alternatively, the determination device can determine that the cost function has converged when the value of the cost function reaches a predetermined target value. If it is determined that the cost function has not converged, the determination device repeats the process from S15. On the other hand, when it is determined that the cost function has converged, the determination device ends the process of FIG. 2, and determines the symbol position at the end time as the determination result. As described above, the iterative processing of S15 and S16 corresponds to the GPO processing.

The determination device may be configured to display the determination result of the symbol position or output the data indicating the determination result to the storage medium. In this case, the user configures the target device based on the determination result. Further, the determination device may be configured to directly output data indicating the determination result of the symbol position to the target device. In this case, the target device constitutes a modulation unit that performs modulation based on the determination result of the symbol position received from the determination device, and a demodulation unit that performs demodulation. Further, the determination device can be incorporated into the target device as a component of the target device.

Subsequently, the first process in S11 and S12 will be described. The movement process of the first process performed in S11 is basically the same as one process of GPO, that is, the second process of S15. However, in the movement process (S11) of the first process, the two symbols to be selected are limited to the symbols whose symbol positions are in the same quadrant. FIG. 3 shows an example in which the two symbols to be selected are limited to the first quadrant. As shown in FIG. 3, the symbol 60 and the symbol 61 in the first quadrant are selected.

The determination device determines the coordinates at which the cost function is minimized at the destination of the symbol 60 and the symbol 61 under the same constraints as the GPO. The arc 62 and the arc 63 connect the candidate coordinates that can be moved to the symbol 60 and the symbol 61 under the constraint condition. Due to the constraint conditions, the destinations of the symbols 60 and 61 are not selected independently from the coordinates on the arc 92 and the arc 93, but if the coordinates of one destination are determined, the destination of the other destination is determined. The coordinates are also determined accordingly.

For example, as shown in FIG. 4, it is assumed that the determination device determines the destinations of the symbols 60 and 61 as shown in FIG. The dotted circles in FIG. 4 indicate the coordinates of the symbol 60 and the symbol 61 before movement. In the copy process of S12, the determination device determines the symbol positions of the other three quadrants based on the symbol positions after the movement of the first quadrant, as shown in FIG.

Specifically, the determination device determines the symbol position of the second quadrant so that the symbol position of the first quadrant and the symbol position of the second quadrant are line-symmetrical with respect to the Q axis. This operation corresponds to setting the coordinates indicated by the complex number obtained by multiplying the conjugate complex number of the complex number indicating each symbol position of the first quadrant by (-1) as each symbol position of the second quadrant.

Further, the determination device determines the symbol position of the third quadrant so that the symbol position of the second quadrant and the symbol position of the third quadrant are line-symmetrical with respect to the I axis. This operation corresponds to setting the coordinates indicated by the conjugate complex number of the complex number indicating each symbol position of the second quadrant as each symbol position of the third quadrant. In other words, this operation corresponds to setting the coordinates indicated by the complex number obtained by multiplying the complex number indicating each symbol position in the first quadrant by (-1) as each symbol position in the third quadrant.

Further, the determination device determines the symbol position of the fourth quadrant so that the symbol position of the third quadrant and the symbol position of the fourth quadrant are line-symmetrical with respect to the Q axis. This operation corresponds to setting the coordinates indicated by the complex number obtained by multiplying the conjugate complex number of the complex number indicating each symbol position of the third quadrant by (-1) as each symbol position of the fourth quadrant. In other words, this operation corresponds to setting the coordinates indicated by the conjugate complex number of the complex number indicating each symbol position of the first quadrant as each symbol position of the fourth quadrant. As a matter of course, the symbol position of the first quadrant and the symbol position of the fourth quadrant are line symmetric with respect to the I axis.

In the iterative process of S15 and S16 of FIG. 2, only two symbols are moved at each iteration. On the other hand, in the iterative process of S11 to S14 of FIG. 2, eight symbols can be moved at one time. In this way, in the first process, the number of symbols to be moved in one process is larger than that in the second process.

The condition that the total amplitude of the symbol positions is 0 among the above-mentioned constraint conditions is satisfied even after the copy processing of S12 is completed. This is because, as is clear from FIG. 5, when each symbol position is regarded as a vector, each vector always has one corresponding inverse vector. On the other hand, among the above-mentioned constraint conditions, the condition that the average power is constant at a predetermined value may be satisfied after the movement processing of S11, but may not be satisfied after the copy processing of S12. This is because, for example, the probability of occurrence of the symbol 60 in the first quadrant is not always the same as the probability of occurrence of the symbol 70 in the second quadrant corresponding to the symbol 60. However, as described above, the probability of occurrence of the symbol 60 and the probability of occurrence of the symbol 70 are not completely the same, but since they are close to each other, the average power does not differ significantly from the predetermined value. Further, after the repetition of the first process is completed, the normal GPO process is performed, so that there is no problem.

Reference numeral 82 in FIG. 6 shows the relationship between the number of repetitions and the value of the cost function when only GPO processing is performed, that is, when only two symbols are moved at each repetition. In FIG. 6, the function for obtaining the BER is a cost function. Further, in FIG. 6, the time when the BER reaches the target value is the time when the cost function converges. On the other hand, reference numeral 80 and reference numeral 81 in FIG. 6 show the relationship between the number of repetitions by the process of FIG. 2 and the value of the cost function. Reference numeral 80 indicates the relationship between the number of repetitions during the first processing and the value of the cost function after the movement processing in S11 of FIG. 2, and reference numeral 81 indicates the second processing. The relationship between the number of repetitions during the period (number of repetitions of the second process + threshold value Th) and the value of the cost function is shown. By performing the copy process in S12 of FIG. 2, the value of the cost function can change from the value after the move process in S11. Therefore, the connection portion between the curve indicated by the reference numeral 80 and the curve indicated by the reference numeral 81 may actually be discontinuous. However, as described above, the difference in the occurrence probabilities of symbols having similar amplitudes is small, and therefore the change in the value of the cost function due to the copy processing of S12 is also small. The curves shown are displayed as if they were continuous. From FIG. 6, it can be seen that by performing the process of FIG. 2, the number of repetitions until the cost function converges is shorter than that of performing only the GPO process.

The reduction rate of the number of repetitions until the cost function converges by the processing of FIG. 2 with respect to the number of repetitions until the cost function converges when only the GPO processing is performed is, for example, the multivalued degree (value of N), the threshold value Th, and the BER. It may differ depending on the target value and the like. In the experimental results for 64-QAM by the inventor, it was confirmed that the reduction was about 5 to 20%.

Reference numeral 83 in FIG. 6 shows the relationship between the number of repetitions and the value of the cost function when the first processing is continued even after the first processing is repeated by the threshold value Th. The cost function of the reference numeral 83 is a value after the copy process in S12 of FIG. As shown by reference numeral 83, even if the first processing is continued, the decrease of the cost function becomes slow and converges at a value higher than the target value. This limits the selection of two symbols from the same quadrant in the first process, and does not select two symbols from different quadrants, so the optimum symbol position does not match the probability distribution of the symbols. Is considered to be the cause. Therefore, the threshold value Th is determined based on the range in which the cost function is lowered by repeating the first process.

For example, the following equation (1) can be used as a cost function for obtaining BER in N-QAM.

In the formula (1), i and j are integers from 1 to N, and x _i and x _j are the i-th and j-th symbols, respectively. Further, _PX (X = x _i ) and _PX (X = x _j ) are the occurrence probabilities of the symbol x _i and the symbol x _j , respectively. Further, h (x _i x _j ) is a Hamming distance between the symbol x _i and the symbol position (coordinates) of the symbol x _j . Further, M is the number of bits that can be carried by one symbol, and for example, in the case of 64-QAM, M = 6. That is, M = lоg ₂ N. Further, ρ ² is a noise dispersion, which is obtained based on the SNR of the transmission line. Therefore, the BER can be calculated based on the probability of occurrence of the symbol and the SNR of the transmission line.

FIG. 7 is a functional block diagram of the determination device 1 according to the present embodiment. In the holding unit 13, the occurrence probability of each symbol, the SNR of the target transmission line, the multi-valued degree N of the modulation (N is an integer of 2 or more), that is, the number of symbols used in the modulation, and the repetition of the first process. A threshold Th that defines the number of times is set. The initial position determination unit 10 determines the initial position of the symbol position of each of the N symbols based on the above constraint condition and the probability of occurrence of the symbol. The initial position determination unit 10 determines the initial position so that the symbol having a higher probability of occurrence is closer to the origin of the IQ plane. At this time, the initial position determination unit 10 can determine the initial position so that the symbol positions are evenly spaced on the IQ plane.

The first processing unit 11 repeats the above-mentioned first processing as many times as the number of times defined by the threshold value Th with respect to the symbol position determined by the initial position determining unit 10. The first processing unit 11 notifies the second processing unit 12 of the symbol position when the first processing is repeated a number of times defined by the threshold value Th. In the above description, the quadrant (selected quadrant) in which the two symbols are selected in the first process is set as the first quadrant. However, the selected quadrant may be any of the first quadrant to the fourth quadrant. Further, it is not necessary to keep the selected quadrants the same while the first process is repeated. This is because, regardless of the selected quadrant, the symbol positions of the two adjacent quadrants are line-symmetrical with respect to the axis (I-axis or Q-axis) of the boundary between the two quadrants by the copy process of S12 in FIG. Because it becomes. In this case, the first processing unit 11 randomly selects the selected quadrant from the first quadrant to the fourth quadrant or in a predetermined order in each repetition.

The second processing unit 12 repeats the above-mentioned second processing with respect to the symbol position notified from the first processing unit 11. The number of repetitions in the second processing unit 12 is controlled based on the value of the cost function. The cost function can be a function for finding the bit error rate, a function for finding the mutual information amount, or a function for finding the generalized mutual information amount. All of these functions are functions that input SNR and the probability of occurrence of a symbol. When the second processing unit 12 determines that the repetition of the second processing is completed based on the cost function, the second processing unit 12 outputs the symbol position at that time as a determination result.

The determination device according to the present invention can be realized by a program that operates the computer as the determination device when executed by one or more processors of the computer. These computer programs are stored in one or more storage devices (HDD, SSD) of the computer. Alternatively, these computer programs may be stored on a computer-readable storage medium or distributed over a network.

The invention is not limited to the above embodiment, and various modifications and changes can be made within the scope of the gist of the invention.

10: Initial position determination unit, 11: 1st processing unit, 12: 2nd processing unit, 13: Holding unit

Claims (15)

A determinant that determines the symbol position in the complex plane of each of the multiple symbols used in modulation.
Among the plurality of symbols, two symbols whose symbol positions are within the selected quadrant among the four quadrants of the complex plane are selected, the symbol positions of the selected two symbols are changed, and the selected two symbols are changed. After changing the symbol position of the symbol, the first processing means for changing the symbol position of the other three quadrants based on the symbol position in the selected quadrant is repeated a predetermined number of times, and the first processing means.
After the first processing means repeats the first processing a predetermined number of times, the second processing of selecting two symbols from the plurality of symbols and changing the symbol positions of the two selected symbols is repeated. The second processing means for determining the symbol position of each of the plurality of symbols and
A determination device characterized by being equipped with. The determination device according to claim 1, wherein the first processing means and the second processing means change the symbol positions of the two selected symbols based on a predetermined cost function. The predetermined cost function is a function that uses the signal-to-noise ratio of the transmission line to which the symbol positions of the plurality of symbols determined by the determination device are applied and the occurrence probability of each of the plurality of symbols as inputs. The determination device according to claim 2, wherein the determination device is provided. The modulation uses stochastic shaping and
The determination device according to claim 3, wherein the probability of occurrence of each of the plurality of symbols is determined based on the correspondence between the bit string used in the probability shaping and the symbol string of each of the plurality of symbols. .. Further provided with a determination means for determining the initial symbol position of each of the plurality of symbols based on the probability of occurrence of each of the plurality of symbols.
The determination device according to claim 3 or 4, wherein the first processing means repeatedly performs the first processing with respect to an initial symbol position of each of the plurality of symbols determined by the determination means. The determination means is characterized in that the initial symbol position of each of the plurality of symbols is determined so that the symbol having a higher occurrence probability is closer to the origin of the complex plane and the symbol positions are evenly spaced. The determination device according to claim 5. The second processing means is characterized in that the second processing is repeated until the predetermined cost function converges or the value of the predetermined cost function reaches the target value. The determination device according to any one of the following items. The predetermined cost function is a function for obtaining a bit error rate, and is a function for obtaining a bit error rate.
The first processing means and the second processing means are characterized in that, under predetermined constraints, the symbol positions of the two selected symbols are changed so as to minimize the bit error rate. The determination device according to any one of 2 to 7. The predetermined cost function is a function for obtaining a mutual information amount or a generalized mutual information amount.
The first processing means and the second processing means change the symbol positions of the two selected symbols so as to maximize the mutual information amount or the generalized mutual information amount under predetermined constraints. The determination device according to any one of claims 2 to 7, wherein the determination device is characterized in that. The predetermined constraint condition is characterized in that the sum of the amplitudes of the symbol positions of the plurality of symbols is 0, and the average power of the symbol positions of the plurality of symbols is a predetermined value. The determination device according to claim 8 or 9. The first processing means is based on the symbol positions in the selected quadrant so that the symbol positions of the two adjacent quadrants are line-symmetrical with respect to the axis of the boundary between the two quadrants, and the other three processing means. The determination device according to any one of claims 1 to 10, wherein the symbol position of the quadrant is changed. The determination device according to any one of claims 1 to 11, wherein the selected quadrant is the same in each of the first processes repeated a predetermined number of times. The first processing means according to any one of claims 1 to 11, wherein the selected quadrant is selected from the four quadrants of the complex plane in each of the first processes repeated a predetermined number of times. Decision device. The determination device according to any one of claims 1 to 13, wherein the first processing means and the second processing means randomly select the two symbols. A program according to any one of claims 1 to 14, wherein when executed by the one or more processors of the apparatus having one or more processors, the apparatus functions as the determination apparatus according to any one of claims 1 to 14.

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