A shaping method based on sub-constellation overlapping probability and geometric union

Abstract

The present invention discloses a shaping method based on the probability of sub-constellation overlap and geometric union, which lays out the constellation points in the form of regular triangle unit cells, so that the distance between each constellation point is equal, thereby making the constellation point decision area denser; the probability shaping is performed by overlapping sub-constellations, the information is divided into constellation partitions, the priority is set according to the distance from the origin, and the number of sub-constellation overlaps is determined according to the priority and the modulation order, and the information is transmitted after adding an identification mark. The distance between each symbol point in the constellation diagram designed by the present invention is equal, with a denser decision area, and the overall average power is reduced compared with the traditional square constellation, and the high-order modulation constellation can be compressed. Compared with the traditional probability shaping scheme based on Maxwell Boltzmann distribution, the probability of any symbol point in the constellation diagram can be flexibly changed, and the constellation compression from high-order modulation format to low-order modulation format can be realized.

Description

Technical Field

[0001] The invention belongs to the field of optical fiber communication technology, and in particular relates to a shaping method based on sub-constellation overlapping probability and geometric union. Background Art

[0002] In recent years, with the rapid development of the Internet and the gradual popularization of 5G networks, emerging technologies based on underlying communication technologies such as big data, cloud computing, the Internet of Things, high-definition video, augmented reality, and virtual reality have been increasingly used. In addition, the field of communications is becoming more extensive, with many new spaces to be expanded and many new businesses to be developed. These have put forward higher requirements for communication technology, such as further improving the spectrum rate, further improving the user experience rate, and further improving the communication peak rate. The huge demand for information capacity continues to promote the vigorous development of long-distance backbone optical networks and short-distance optical transmission systems, so the expansion of optical communication systems is an eternal topic.

[0003] At present, in communication systems, using probabilistic shaping technology (PS) to approach the Shannon limit is a research hotspot. The basic idea of ​​probabilistic shaping is to process the probability of generating symbols based on the energy of the symbols. In high-order modulation, the symbols in the outer circle of the constellation diagram require higher transmission energy than the points in the inner circle. If the probability shaping technology is used to increase the probability of sending the inner circle points and reduce the transmission probability of the outer circle points at the same time, the overall average energy of the constellation diagram will be reduced. At this time, under the same transmitted optical power, since the signal requires lower transmission power, it is less affected by noise. Therefore, the probabilistic shaping technology can effectively improve the signal-to-noise ratio and make the system capacity closer to the Shannon limit of the channel. The probabilistic shaping technology can further realize the flexible adjustment of the information entropy of different modulation formats by adjusting the probability distribution of different points, that is, the shaping depth, so as to be suitable for different rate requirements for different users and realize dynamic communication resource allocation. In addition, the constellation geometric shaping technology (GS) optimizes the geometric structure of the mapped constellation diagram so that the average power of the signal is relatively reduced when the minimum Euclidean distance of the constellation points is constant, or a relatively large minimum Euclidean distance is obtained when the average power is the same, thereby improving the performance of the system.

[0004] The constellation shaping algorithms currently launched often choose one of geometric shaping and probabilistic shaping, and rarely combine the two. This is mainly because the constellation distribution after geometric shaping often has additional penalties after probabilistic shaping. Using machine learning and other algorithms to optimize the constellation may obtain better results in simulation, but due to its irregular distribution, the overly complex constellation is difficult to process by the digital signal processing algorithm at the receiving end in actual transmission. In addition, the constellation symbols of the traditional constellation diagram are often distributed in the form of a square, and the Euclidean distance between two adjacent symbol points on the square is less than the two points on the diagonal; this situation leads to the expansion of the constellation decision area. Summary of the invention

[0005] Purpose of the invention: The present invention proposes a shaping method based on sub-constellation overlapping probability and geometric union. Through the scheme of sub-constellation overlapping, the probability-geometric joint shaping of the communication constellation is realized, and the maximum constellation shaping gain is achieved under low complexity conditions.

[0006] Technical solution: The shaping method based on the sub-constellation overlapping probability and geometric union described in the present invention specifically includes the following steps:

[0007] (1) Clearly define the high-order QAM constellation to be processed and the target constellation order after processing;

[0008] (2) The constellation points are laid out in the form of regular triangle cells, so that the distance between each constellation point is equal, thereby making the constellation point decision area denser;

[0009] (3) Probabilistic shaping is performed by overlapping sub-constellations. The information is divided into constellation partitions, and the priority is set according to the distance from the origin. The number of times the sub-constellation overlaps is determined according to the priority and modulation order. The information is transmitted after adding an identification tag.

[0010] Furthermore, the implementation process of step (1) is as follows:

[0011] Clearly define the constellation order to be processed and determine the symbol point of the target constellation; in the additive white Gaussian noise channel, the gain index of the constellation diagram is expressed as:

[0012]

[0013] Among them, it means C CFM Gain index of the constellation diagram, E b Indicates the average power or average energy value of the signal, d min represents the minimum Euclidean distance, a i It represents the ratio of the Euclidean distance of a constellation point from the origin to the minimum Euclidean distance, and i represents the number of constellation points;

[0014] Constellation Gain Index and d minThere is a direct relationship; the bit error rate of the signal in the communication system is expressed as:

[0015]

[0016] Among them, A and Q are constants related to the modulation format, modulation order, etc. o Represents the noise of the signal; when the gain index C CFM The larger the bit error rate P e The lower.

[0017] Furthermore, the implementation process of step (2) is as follows:

[0018] Based on the equilateral triangle, the constellation points are distributed at the vertices of the equilateral triangle to form a "equilateral triangle unit cell" structure. The constellation gain indexes of the two constellation distribution schemes are calculated respectively:

[0019]

[0020] Among them, d min represents the minimum Euclidean distance, E b Indicates the average power or average energy value of the signal, C 1 The constellation point set representing the square constellation distribution, C 2 Represents the constellation point set of the new constellation distribution proposed in this patent, CFM square Represents the gain index of the square constellation diagram, CFM new Represents the gain index of the new constellation.

[0021] Furthermore, the implementation process of step (3) is as follows:

[0022] The initial high-order constellation is M-QAM, which has M constellation points, each constellation point represents k bits. The target constellation after shaping is N-QAM, which includes N constellation points, each constellation point represents j bits, M>N, k>j; sub-constellation division is performed, that is, some constellation points in the target N-QAM constellation are formed into several sets. In order to improve the constellation gain after shaping, the points with the same distance from the original center of the constellation diagram are formed into a set. Assuming that it is divided into c sub-constellations in total, the number of constellation points in each set is s, then the set is expressed as {s 1 ,s 2 ,s 3 …s c}, assuming that the number of overlaps of each sub-constellation is d, they can also form a set {d 1 ,d 2 ,d 3 …d c}, in order for the shaped constellation to express all the information of the original constellation, it is necessary to satisfy: {s 1 ,s2 ,s 3 …s c}·{d 1 ,d 2 ,d 3 …d c}≥M, and in order to meet the basic requirements of probability shaping, it is necessary to have d 1 ≥d 2 ≥d 3 …≥d c ;

[0023] In order to distinguish the overlapping parts, add labels for the sub-constellations and mark each sub-constellation. Assume that the maximum number of constellation overlaps is d 1 , in order to distinguish the overlapping d 1 constellation points, requiring d 1 Labels are used to mark; and because the label is represented by a binary bit sequence, the number of bits of the label is l, and it must satisfy 2 l ≥d 1 .

[0024] Furthermore, by adjusting the number of times the sub-constellations overlap, a more extreme constellation distribution or one suitable for special scenarios can be achieved.

[0025] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention arranges the constellation points in the form of a regular triangle unit cell. Compared with the traditional square constellation, the distance between each symbol point in the constellation diagram designed by the present invention is equal, with a denser decision area, and the overall average power is lower than that of the traditional square constellation. Furthermore, the present invention can compress the high-order modulation constellation by overlapping sub-constellations. Compared with the traditional probability shaping scheme based on Maxwell Boltzmann distribution, the present invention can flexibly change the probability of any symbol point in the constellation diagram, and can realize constellation compression from high-order modulation format to low-order modulation format. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is a flow chart of the present invention;

[0027] Figure 2 It is the traditional 16QAM constellation diagram;

[0028] Figure 3 It is a regular triangle unit cell constellation diagram;

[0029] Figure 4 Schematic diagram of constellation diagram changes;

[0030] Figure 5 Schematic diagram of sub-constellation division;

[0031] Figure 6 Schematic diagram of sub-constellation superposition probability shaping coding;

[0032] Figure 7 Schematic diagram of the constellation after the sub-constellations are superimposed;

[0033] Figure 8 Schematic diagram of the probability distribution of constellation points. DETAILED DESCRIPTION

[0034] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0035] The present invention proposes a shaping method based on the probability of sub-constellation overlap and geometric union. In order to improve the performance of constellation gain, the constellation diagram needs to be redesigned first. Different from the traditional square constellation, the present invention arranges the constellation points in the form of regular triangle cells, so that the distance between each constellation point is equal, so that the constellation point decision area is denser. On this basis, the probability shaping is performed by overlapping sub-constellations, the information is divided into constellations, the priority is set according to the distance from the origin, and the number of sub-constellation overlaps is determined according to the priority and modulation order, and the identification mark is added before transmission. Figure 1 As shown in the figure, it is mainly divided into three parts: constellation diagram design, sub-constellation area division and sub-constellation overlapping probability shaping. First, the high-order quadrature amplitude modulation (QAM) constellation to be processed and the target constellation order after processing are clarified, and the constellation is divided by the power of the constellation point to generate a sub-constellation. Then the bit information is processed, and probability shaping is achieved by superposition of sub-constellations. Finally, the shaped bits are mapped to the constellation symbols. After shaping and filtering, the digital signal is converted into an analog signal through digital-to-analog conversion and input into the channel.

[0036] When designing the constellation diagram, the constellation order to be processed is first clarified. Taking 32QAM as an example, the present invention compresses 32QAM into a 16QAM constellation by overlapping sub-constellations, that is, 32 constellation points are shaped into 16 points. Therefore, the target constellation shaped by the present invention has 16 symbol points, so the geometric shaping involved can be regarded as the geometric shaping of the 16QAM constellation. In the additive white Gaussian noise channel, the gain index of the constellation diagram can be expressed as:

[0037]

[0038] Among them, it means C CFM Gain index of the constellation diagram, E b Indicates the average power or average energy value of the signal, d min represents the minimum Euclidean distance, a iIt represents the ratio of the Euclidean distance of the constellation point from the origin to the minimum Euclidean distance. i represents the number of constellation points. It can be seen that the constellation gain index is related to d min There is a direct relationship. The bit error rate of the signal in the system can be expressed as:

[0039]

[0040] Among them, A and Q are constants related to the modulation format, modulation order, etc. o represents the noise of the signal. It can be seen that when the gain index C CFM The larger it is, the lower the bit error rate is.

[0041] The traditional 16QAM constellation diagram is as follows Figure 2 As shown in FIG. 1 , the constellations are distributed with a square as the primitive. This method causes the Euclidean distance between adjacent constellation points distributed on the two sides of the square to be smaller than the Euclidean distance between two constellation points on the diagonal line, thereby expanding the constellation decision area and making it impossible to distribute the constellation points more densely. Therefore, the present invention re-lays out the constellation points. Since the length of each side of an equilateral triangle is equal, that is, the distance between each vertex is equal, the present invention is based on an equilateral triangle and distributes the constellation points at the vertices of the equilateral triangle to form a "equilateral triangle unit cell" structure, as shown in FIG. Figure 3 shown.

[0042] Using formula (2), the constellation gain index of the two constellation distribution schemes is calculated respectively:

[0043]

[0044] Among them, d min represents the minimum Euclidean distance, E b Indicates the average power or average energy value of the signal, C 1 The constellation point set representing the square constellation distribution, C 2 Represents the constellation point set of the new constellation distribution proposed in this patent, CFM square Represents the gain index of the square constellation diagram, CFM new Represents the gain index of the new constellation.

[0045] It can be seen that the constellation gain of the constellation diagram based on the regular triangle unit cell designed by the present invention is higher than that of the traditional square constellation, so the bit error rate of the system can be effectively reduced. In addition, since the power of the outermost constellation point is higher than that of other points, after the probability shaping is used to suppress the number of outer constellation points, the effect of probability shaping is more obvious than that of the traditional constellation diagram.

[0046] For the high-order constellation to be processed, assume that the initial high-order constellation is M-QAM, which has M constellation points, each constellation point represents k bits, and the target constellation after shaping is N-QAM, which includes N constellation points, each constellation point represents j bits. Due to the order reduction, it can be known that M>N, k>j. Obviously, the reduced-order constellation cannot fully represent all the symbols of the original constellation, so constellation overlap is required. First, it is necessary to divide the sub-constellation, that is, for the target N-QAM constellation, some of the constellation points are grouped into several sets. In order to improve the gain of the constellation after shaping, the points with the same distance from the original center of the constellation diagram are grouped into a set. Assuming that it is divided into c sub-constellations in total, and the number of constellation points in each set is s, then the set can be expressed as {s 1 ,s 2 ,s 3 …s c}, assuming that the number of overlaps of each sub-constellation is d, they can also form a set {d 1 ,d 2 ,d 3 …d c}, in order for the shaped constellation to express all the information of the original constellation, it is obviously necessary to satisfy: {s 1 ,s 2 ,s 3 …s c}··{d 1 ,d 2 ,d 3 …d c}≥M, and in order to meet the basic requirements of probability shaping, it is necessary to have d 1 ≥d 2 ≥d 3 …≥d c In order to distinguish the overlapping parts, it is necessary to add labels for the sub-constellations and mark each sub-constellation. Assume that the maximum number of constellation overlaps is d 1 , then to distinguish the overlapping d 1 constellation points, requiring d 1 Since the label is represented by a binary bit sequence, assuming that the number of bits in the label is l, then there are 2 l ≥d 1 .

[0047] like Figure 4As shown, the constellation diagram to be processed by the present invention is a square constellation of 32QAM, and the process is to first compress it into 16QAM, and then process it into the final 16PS-GS-QAM through probability-geometry joint shaping. Since the initial constellation to be processed is 32QAM, in which each symbol represents 5 bits, and the constellation after shaping is 16QAM, each symbol has only 4 bits, it is necessary to overlap the constellation points, and the probability shaping of the constellation is also completed in this step. First, the constellation needs to be divided to generate sub-constellations. Here, the area division is performed by the distance from the constellation point to the origin, that is, the transmission power.

[0048] The 16QAM constellation points are divided into four areas, such as Figure 5 As shown. Constellation points with the same number form a sub-constellation. Therefore, the final target constellation of the present invention includes 4 sub-constellations. The set of the number of constellation points in each sub-constellation can be expressed as A = {2, 2, 6, 6}. In order to map each constellation point in the original 32QAM to these 16 points, some sub-constellations must be overlapped. Here, sub-constellation 1 is overlapped 4 times, sub-constellation 2 is overlapped 3 times, sub-constellation 3 is overlapped 2 times, and sub-constellation 4 is not overlapped. In this way, the number of final constellation points is: 4×2+3×2+2×6+1×6=32.

[0049] Overlapping will inevitably lead to judgment problems when the system receives, and the symbols in the overlapping area cannot be distinguished, so it is necessary to further add sub-constellation labels. Since the maximum number of sub-constellations overlap is 4 times, only a binary label with a length of 2 bits is required. Then the encoded constellation symbol consists of a 4-bit original code and a 2-bit label.

[0050] The coding diagram of 32QAM is probabilistically shaped by superimposing sub-constellations and compressed to 16QAM is shown in the following figure. Figure 6 As shown in the figure. The encoding of each constellation point consists of a 4-bit information bit code and a 2-bit label. In the same sub-constellation, the sub-constellation number is determined by different labels, and in different sub-constellation areas, since the information bit code is different, the label can be the same as that of other sub-constellation areas.

[0051] Taking the innermost sub-constellation as an example, there are only two constellation points in the innermost sub-constellation, which are 0000 and 0001 respectively. The 5-bit 00000 in 32QAM is mapped to the first 0000, and 00001 is mapped to 0001. Then these two constellation points are labeled 00. This is the first level of the innermost sub-constellation. Then 00010 and 00011 are still mapped to 0000 and 0001. In order to distinguish the previous constellation points, a new label 01 is needed here. This is the second level of the innermost circle constellation. And so on, the four overlaps of the innermost circle constellation can be achieved. When processing the sub-inner circle constellation, since the first 4 bits are different from those of the innermost circle, the same label can be used. That is to say, the label only distinguishes the different constellation points overlapping in the sub-constellation area, and does not interfere with the sub-constellations and is independent of each other. The schematic diagram of the final overlapping constellation diagram is shown as follows. Figure 7 shown.

[0052] After the sub-constellations overlap, the probability distribution of each constellation point of 16PS-GS-QAM is finally obtained as follows: Figure 8 As shown, unlike the traditional Maxwell-Boltzmann distribution, the probability difference between the sub-constellations is more obvious, and a more extreme constellation distribution or one suitable for special scenarios can be achieved by adjusting the number of times the sub-constellations overlap.

Claims

1. A shaping method based on sub-constellation overlapping probability and geometric union, It is characterized in that The following steps are involved: (1) Clearly define the high-order QAM constellation to be processed and the target constellation order after processing; (2) The constellation points are laid out in the form of regular triangle cells, so that the distance between each constellation point is equal, thereby making the constellation point decision area denser; (3) Probabilistic shaping is performed by overlapping sub-constellations, where the information is divided into constellation partitions, priorities are set based on the distance from the origin, and the number of times the sub-constellations overlap is determined based on the priority and modulation order, and then transmitted after adding identification tags; The implementation process of step (3) is as follows: The initial high-order constellation is M-QAM, which has M constellation points, each constellation point represents k bits. The target constellation after shaping is N-QAM, which includes N constellation points, each constellation point represents j bits, M>N, k>j; sub-constellation division is performed. In order to improve the constellation gain after shaping, the points with the same distance from the original center of the constellation diagram are grouped into a set. Assuming that it is divided into c sub-constellations in total, the number of constellation points in each set is s, then the set is expressed as {s 1 ,s 2 ,s 3 …s c }, assuming that the number of overlaps of each sub-constellation is d, they can also form a set {d 1 ,d 2 ,d 3 …d c }, in order for the shaped constellation to express all the information of the original constellation, it is necessary to satisfy: {s 1 ,s 2 ,s 3 …s c }·{d 1 ,d 2 ,d 3 …d c }≥M, and in order to meet the basic requirements of probability shaping, it is necessary to have d 1 ≥d 2 ≥d 3 …≥d c ; In order to distinguish the overlapping parts, add labels for the sub-constellations and mark each sub-constellation. Assume that the maximum number of constellation overlaps is d 1 , in order to distinguish the overlapping d 1 constellation points, requiring d 1 Labels are used to mark; and because the label is represented by a binary bit sequence, the number of bits of the label is l, and it must satisfy 2 l ≥d 1 .

2. A shaping method based on sub-constellation overlap probability and geometric union according to claim 1, It is characterized in that The implementation process of step (1) is as follows: Clearly define the constellation order to be processed and determine the symbol point of the target constellation; in the additive white Gaussian noise channel, the gain index of the constellation diagram is expressed as: Among them, it means C CFM Gain index of the constellation diagram, E b Indicates the average power or average energy value of the signal, d min represents the minimum Euclidean distance, a i It represents the ratio of the Euclidean distance of a constellation point from the origin to the minimum Euclidean distance, and i represents the number of constellation points; Constellation Gain Index and d min There is a direct relationship; the bit error rate of the signal in the communication system is expressed as: Among them, A, Q are constants, which are related to the modulation format and modulation order, and N o Represents the noise of the signal; when the gain index C CFM The larger the bit error rate P e The lower.

3. A shaping method based on sub-constellation overlap probability and geometric union according to claim 1, It is characterized in that The implementation process of step (2) is as follows: Based on the equilateral triangle, the constellation points are distributed at the vertices of the equilateral triangle to form an "equilateral triangle unit cell" structure. The constellation gain indexes of the two constellation distribution schemes are calculated respectively: Among them, d min represents the minimum Euclidean distance, E b Indicates the average power or average energy value of the signal, C 1 The constellation point set representing the square constellation distribution, C 2 The constellation point set representing the new constellation distribution, CFM square Represents the gain index of the square constellation diagram, CFM new Represents the gain index of the new constellation.

4. The shaping method based on sub-constellation overlap probability and geometric union according to claim 1, It is characterized in that The constellation distribution is achieved by adjusting the number of times the sub-constellations overlap.

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