CN113141326A - Novel SCMA system codebook optimization and codeword distribution method - Google Patents

Novel SCMA system codebook optimization and codeword distribution method Download PDF

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CN113141326A
CN113141326A CN202110430983.2A CN202110430983A CN113141326A CN 113141326 A CN113141326 A CN 113141326A CN 202110430983 A CN202110430983 A CN 202110430983A CN 113141326 A CN113141326 A CN 113141326A
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codebook
matrix
resource block
constellation
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CN113141326B (en
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钱世清
葛文萍
张鹏举
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Xinjiang University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/3405—Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power
    • H04L27/3444—Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power by applying a certain rotation to regular constellations
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting

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Abstract

The invention provides a new method for optimizing a codebook and distributing code words of an SCMA system, which comprises the following steps: the method comprises the following steps: selecting useful points by using a dual threshold method under four-dimensional lattice modulation to obtain a mother constellation of the SCMA
Figure 163941DEST_PATH_IMAGE001
(ii) a Step two: obtaining SCMA according to step one
Figure 12949DEST_PATH_IMAGE002
Using local dimension transformation method pair
Figure 324981DEST_PATH_IMAGE003
Optimizing to obtain an optimal mother constellation
Figure 44676DEST_PATH_IMAGE004
(ii) a Step three: root of herbaceous plantObtained according to the second step
Figure 885593DEST_PATH_IMAGE005
Will be
Figure 736743DEST_PATH_IMAGE006
Is allocated to a time-frequency resource block k, thereby obtaining a code matrix
Figure 524570DEST_PATH_IMAGE007
(ii) a Step four: designing a mapping matrix and an operation factor based on a resource block k; step five: the code word matrix obtained in the third step
Figure 161088DEST_PATH_IMAGE008
Multiplying the k-th row code word in the step (b) with the operation factor and the mapping matrix in the step (c) to obtain a codebook based on the resource block k, and a step (six): according to the fifth step, codebook matrixes of all resource blocks are further obtained, so that the codebook of the user j is separated
Figure 376169DEST_PATH_IMAGE009
. The method of the invention realizes that the BER performance can be obviously improved under different codebook sizes.

Description

Novel SCMA system codebook optimization and codeword distribution method
Technical Field
The invention relates to the technical field of wireless communication, in particular to a novel method for optimizing a codebook and distributing code words of a SCMA system.
Background
With the rapid development of the mobile Internet and Internet of Things (IOT), the 5 th generation wireless communication system (5G) will face a sharp expansion of data services, and the capacity of the mobile communication system will face a huge challenge. In order to deal with the challenges facing the system performance such as high frequency spectrum efficiency, massive connection and low latency in 5G, a Non-Orthogonal Multiple Access (NOMA) technology has been accepted and selected as one of the 5G hollow port candidates.
The SCMA is one of the NOMA technologies, and the codebook design and optimization problem is one of the core problems of the SCMA technology, however, the existing codebook cannot meet the requirement of good error code performance under both small size and large size. Therefore, the invention designs a new method for optimizing the SCMA system codebook and distributing the code words, and the obtained codebook has better BER performance under different codebook sizes.
Disclosure of Invention
The invention aims to provide a novel method for optimizing a codebook and distributing code words of an SCMA system, wherein a parent constellation is designed by using a dual threshold method under the modulation of a 4-dimensional lattice theory, and the problem of constellation point overlapping is solved by optimizing the parent constellation by using local dimension change. Meanwhile, in order to reduce intersymbol interference on the same time frequency resource block (RE); meanwhile, an REs code word allocation method is also designed. Under the improvement of two aspects, BER performance of the designed codebook is greatly improved under different sizes.
In order to achieve the objects and advantages of the present invention, a new method for code book optimization and code word allocation in an SCMA system is provided, which comprises the following steps:
the method comprises the following steps: selecting useful points by using a dual threshold method under four-dimensional lattice modulation to obtain a mother constellation of the SCMA
Figure 690153DEST_PATH_IMAGE001
；
Step two: according to the mother constellation of the SCMA obtained in step one, when M is large,
Figure 17229DEST_PATH_IMAGE002
in the method, constellation points are overlapped, and a local dimension conversion method is used for optimizing the mother constellation to obtain an optimal mother constellation
Figure 98318DEST_PATH_IMAGE003
；
Step three: obtained according to the second step
Figure 510845DEST_PATH_IMAGE003
Will be
Figure 865076DEST_PATH_IMAGE004
Is allocated to a time-frequency resource block k, thereby obtaining a code matrix
Figure 46659DEST_PATH_IMAGE005
；
Step four: obtaining a mapping matrix based on a resource block k from the perspective of the resource block
Figure 501911DEST_PATH_IMAGE006
And an operation factor
Figure 136155DEST_PATH_IMAGE007
；
Step five: code word matrix
Figure 499003DEST_PATH_IMAGE005
The k-th row vector of
Figure 597409DEST_PATH_IMAGE008
Operation factor
Figure 957983DEST_PATH_IMAGE007
Mapping matrix
Figure 361414DEST_PATH_IMAGE006
Multiplying to obtain a codebook based on a resource block k;
step six: according to the fifth step, a K multiplied by J codebook matrix of K resource blocks and J users can be finally obtained, wherein the jth column represents the codebook of the jth user
Figure 527953DEST_PATH_IMAGE009
。
Preferably, in the first step, the mother constellation of the SCMA with dimension N and size M is obtained under the condition of double thresholding
Figure 418549DEST_PATH_IMAGE001
The following forms:
Figure 746762DEST_PATH_IMAGE010
。
wherein, 2-dimensional mother constellation construction
Figure 152335DEST_PATH_IMAGE001
The constellation point is from a 4-dimensional grid space point, and the condition for selecting the constellation point by taking the power of the constellation point and the minimum Euclidean distance as a dual threshold is as follows:
Figure 794669DEST_PATH_IMAGE011
wherein,
Figure 851356DEST_PATH_IMAGE012
and
Figure 553733DEST_PATH_IMAGE013
are respectively as
Figure 446602DEST_PATH_IMAGE014
The power of any column of complex constellation points and the minimum Euclidean distance of the column vector complex constellation points are expressed as follows:
Figure 892627DEST_PATH_IMAGE015
。
codebook gain of lattice constellation under 4-dimensional lattice theory modulation
Figure 288973DEST_PATH_IMAGE016
Can be expressed as:
Figure 224568DEST_PATH_IMAGE017
herein, the
Figure 542417DEST_PATH_IMAGE018
The generator matrix, which is a 4-dimensional lattice, can be expressed as:
Figure 605182DEST_PATH_IMAGE019
herein do, use
Figure 59297DEST_PATH_IMAGE018
Vector of
Figure 165794DEST_PATH_IMAGE020
Generating spatial points
Figure 236518DEST_PATH_IMAGE021
The form is as follows:
Figure 289924DEST_PATH_IMAGE022
in order to obtain a good shaping gain and codebook gain
Figure 129704DEST_PATH_IMAGE016
Since the lattice constellation points satisfy the dual threshold,
Figure 672681DEST_PATH_IMAGE018
the following conditions should be satisfied:
Figure 230702DEST_PATH_IMAGE023
。
bonding of
Figure 822220DEST_PATH_IMAGE018
Can be prepared by the interior point method
Figure 831021DEST_PATH_IMAGE018
And solving to further obtain grid constellation points, thereby obtaining a 4-dimensional real constellation matrix MC of M columns of the maximized MED as follows:
Figure 748161DEST_PATH_IMAGE024
。
generating 2-dimensional complex constellations from MC
Figure 527898DEST_PATH_IMAGE025
The following were used:
Figure 923107DEST_PATH_IMAGE026
。
preferably, in the second step, when the codebook size M is large,
Figure 534217DEST_PATH_IMAGE025
there is a partial constellation point overlap, and assuming that the p-th column element overlaps with the q-th column element, the representation is as follows:
Figure 904150DEST_PATH_IMAGE027
。
the invention provides a method for optimizing local dimension transformation
Figure 905604DEST_PATH_IMAGE002
The optimized optimal 2-dimensional complex mother constellation is represented as follows:
Figure 901242DEST_PATH_IMAGE028
after the transformation, the image is displayed on the screen,
Figure 101279DEST_PATH_IMAGE029
all the elements in the constellation are different, and the design and optimization of the mother constellation are completed.
Preferably, in the third step, the invention provides a new code word allocation method, which is a method for automatically allocating code words based on resource blocks, wherein if there are K resource blocks and J users, each resource block is connected with one resource block
Figure 829064DEST_PATH_IMAGE030
The number of the individual users is increased by the number of the individual users,
Figure 380131DEST_PATH_IMAGE030
is represented as follows:
Figure 851563DEST_PATH_IMAGE031
let the sub-constellation over resource block k be denoted as
Figure 420954DEST_PATH_IMAGE032
；
The factor graph matrix of the Latin structure of 4 time-frequency resource blocks shared by 6 users is represented as follows:
Figure 585219DEST_PATH_IMAGE033
in that
Figure 623582DEST_PATH_IMAGE034
In the matrix, the position of the jth nonzero element in the kth row is indexed as
Figure 429864DEST_PATH_IMAGE035
Wherein
Figure 807756DEST_PATH_IMAGE036
(ii) a The codeword allocation on a resource block is represented as follows:
Figure 939660DEST_PATH_IMAGE037
combining with the factor graph matrix, under the code word allocation method on the resource block, a code word allocation matrix can be obtained:
Figure 403002DEST_PATH_IMAGE038
。
in that
Figure 29287DEST_PATH_IMAGE039
The non-zero vector on the k-th resource block is from
Figure 58423DEST_PATH_IMAGE040
Thus, therefore, it is
Figure 564490DEST_PATH_IMAGE041
Is a vector of ideas, since the codewords for each user are not the same, here
Figure 311866DEST_PATH_IMAGE042
Will be
Figure 194372DEST_PATH_IMAGE039
Further optimized to the following formula:
Figure 546856DEST_PATH_IMAGE043
。
preferably, the fourth step includes the steps of:
step four, firstly: matrix according to factor graph
Figure 489404DEST_PATH_IMAGE034
A mapping matrix based on the resource block k can be designed
Figure 976273DEST_PATH_IMAGE006
Expressed as follows, when k =1, the mapping matrix is expressed as follows:
Figure 396890DEST_PATH_IMAGE044
wherein, the relationship between the mapping matrix and the factor graph matrix can be expressed as:
Figure 869460DEST_PATH_IMAGE045
，
Figure 982910DEST_PATH_IMAGE046
。
step four and step two: like the code word allocation method, the rotation angle can be adjusted in the same way
Figure 236036DEST_PATH_IMAGE047
Is defined as:
Figure 460344DEST_PATH_IMAGE048
combining the factor graph matrix and the definition of the rotation angle to obtain the rotation matrix meeting the Latin structure
Figure 521841DEST_PATH_IMAGE049
Can be expressed as:
Figure 619241DEST_PATH_IMAGE050
to further reduce the complexity of the rotation matrix, the rotation matrix is preferably divided into two parts
Figure 766189DEST_PATH_IMAGE051
When rotating, the angle is rotated
Figure 590925DEST_PATH_IMAGE052
Is set to 0.
Step four and step three: further obtained is a design operation factor based on resource block 1, expressed as follows:
Figure 303667DEST_PATH_IMAGE053
。
preferably, in the step five, the code word based on the resource block k may be expressed as:
Figure 227760DEST_PATH_IMAGE054
。
preferably, the sixth step includes the steps of:
step six: the resource block based codebook matrix is represented as:
Figure 924321DEST_PATH_IMAGE055
。
step six and two: by
Figure 224852DEST_PATH_IMAGE056
The jth column of (a) is separated to obtain a codebook of the user j
Figure 572526DEST_PATH_IMAGE057
Then the codebook of the first user
Figure 464258DEST_PATH_IMAGE058
Expressed as:
Figure 585798DEST_PATH_IMAGE059
。
the invention has the beneficial effects that: the problem of parent constellation point overlapping is solved by using a local dimension transformation method, then a codebook based on a resource block is designed from the angle of the resource block, the intersymbol interference of different users on the same time-frequency resource block can be well reduced, when the sizes of the codebooks are different, simulation results are contrasted and displayed, and the BER performance is obviously improved compared with the codebooks designed by other schemes.
Drawings
In order to make the objects, technical solutions and advantageous effects of the present invention appear, the present invention is illustrated by the following drawings.
FIG. 1 is a schematic flow diagram of the present invention.
FIG. 2 is a diagram of a codebook generation process of the present invention.
Fig. 3 is a graph of bit error rate performance versus M of 4.
Fig. 4 is a graph of bit error rate performance when M is 8.
Fig. 5 is a graph of bit error rate performance versus M of 16.
Fig. 6 is a graph comparing bit error rate performance with constellation point coincidence under different codebook sizes.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
Defining the size of a user codebook as M, wherein J users share K time-frequency resource blocks and a parent constellation dimension N. In this embodiment, assume that the number of users J is 6, the time-frequency resource K is 4, the codebook size M is 4, 8, and 16, and the mother constellation dimension N = 2. The specific design process is as follows.
Referring to fig. 1, the implementation steps of the present invention are as follows:
the method comprises the following steps: selecting useful points by using a dual threshold method under four-dimensional lattice modulation to obtain a mother constellation of the SCMA
Figure 752337DEST_PATH_IMAGE060
。
Assuming dimension N, mother constellation of size M
Figure 377354DEST_PATH_IMAGE060
Is defined as follows:
Figure 971146DEST_PATH_IMAGE061
wherein, 2-dimensional mother constellation construction
Figure 861873DEST_PATH_IMAGE060
The constellation point is from a 4-dimensional grid space point, and the following conditions are met when the constellation point is selected by a dual threshold method:
Figure 769786DEST_PATH_IMAGE062
wherein,
Figure 577205DEST_PATH_IMAGE012
and
Figure 279582DEST_PATH_IMAGE013
are respectively as
Figure 375714DEST_PATH_IMAGE060
The power of any column of complex constellation points and the minimum Euclidean distance of the column vector complex constellation points.
Codebook gain of lattice constellation under 4-dimensional lattice theory modulation
Figure 87318DEST_PATH_IMAGE016
Can be expressed as:
Figure 952506DEST_PATH_IMAGE063
herein, the
Figure 419259DEST_PATH_IMAGE018
The generator matrix, which is a 4-dimensional lattice, can be expressed as:
Figure 2687DEST_PATH_IMAGE064
。
by using
Figure 252403DEST_PATH_IMAGE018
Vector of
Figure 286611DEST_PATH_IMAGE020
Generating spatial points
Figure 596370DEST_PATH_IMAGE065
The form is as follows:
Figure 667094DEST_PATH_IMAGE066
。
in order to obtain a good shaping gain and codebook gain
Figure 720501DEST_PATH_IMAGE016
Since the lattice constellation points satisfy the dual threshold,
Figure 622598DEST_PATH_IMAGE018
the following conditions should be satisfied:
Figure 103258DEST_PATH_IMAGE067
。
bonding of
Figure 395699DEST_PATH_IMAGE018
Can be prepared by the interior point method
Figure 331425DEST_PATH_IMAGE018
And solving to further obtain grid constellation points, thereby obtaining a 4-dimensional real constellation matrix MC of M columns of the maximized MED as follows:
Figure 25711DEST_PATH_IMAGE068
。
generating 2-dimensional complex constellations from MC
Figure 677272DEST_PATH_IMAGE060
The following were used:
Figure 722589DEST_PATH_IMAGE069
。
step two: according to the mother constellation of the SCMA obtained in step one, when M is large,
Figure 914536DEST_PATH_IMAGE060
in the method, constellation points are overlapped, and a local dimension conversion method is used for optimizing the mother constellation to obtain an optimal mother constellation
Figure 463329DEST_PATH_IMAGE040
。
When the codebook size M is large,
Figure 551371DEST_PATH_IMAGE060
there is a partial constellation point overlap, and assuming that the p-th column element overlaps with the q-th column element, the representation is as follows:
Figure 395567DEST_PATH_IMAGE070
。
the invention provides a method for optimizing local dimension transformation
Figure 594468DEST_PATH_IMAGE060
The optimized optimal 2-dimensional complex mother constellation is represented as follows:
Figure 997767DEST_PATH_IMAGE071
after the transformation, the image is displayed on the screen,
Figure 53448DEST_PATH_IMAGE040
all the elements in the constellation are different, and the design and optimization of the mother constellation are completed.
Step three: obtained according to the second step
Figure 355247DEST_PATH_IMAGE040
Will be
Figure 623418DEST_PATH_IMAGE040
Is allocated to a time-frequency resource block k, thereby obtaining a code matrix
Figure 881224DEST_PATH_IMAGE072
。
If there are K resource blocks and J users, each resource block is connected with
Figure 107806DEST_PATH_IMAGE073
The number of the individual users is increased by the number of the individual users,
Figure 818273DEST_PATH_IMAGE073
is represented as follows:
Figure 155713DEST_PATH_IMAGE074
。
let the sub-constellation over resource block k be denoted as
Figure 533605DEST_PATH_IMAGE075
。
The factor graph matrix of the Latin structure of 4 time-frequency resource blocks shared by 6 users is represented as follows:
Figure 905987DEST_PATH_IMAGE076
。
in that
Figure 369330DEST_PATH_IMAGE034
In the matrix, the position of the jth nonzero element in the kth row is indexed as
Figure 979303DEST_PATH_IMAGE035
Wherein
Figure 274018DEST_PATH_IMAGE036
(ii) a The codeword allocation on a resource block is represented as follows:
Figure 514506DEST_PATH_IMAGE077
。
combining with the factor graph matrix, under the code word allocation method on the resource block, a code word allocation matrix can be obtained:
Figure 527462DEST_PATH_IMAGE078
。
in that
Figure 144388DEST_PATH_IMAGE079
The non-zero vector on the k-th resource block is from
Figure 44342DEST_PATH_IMAGE080
Thus, therefore, it is
Figure 721311DEST_PATH_IMAGE081
Is a vector of ideas, since the codewords for each user are not the same, here
Figure 955983DEST_PATH_IMAGE082
Will be
Figure 907758DEST_PATH_IMAGE079
Further optimized to the following formula:
Figure 114749DEST_PATH_IMAGE083
。
step four: from the perspective of the resource blockMapping matrix based on resource block k
Figure 759357DEST_PATH_IMAGE006
And an operation factor
Figure 419008DEST_PATH_IMAGE084
The fourth step comprises the following steps.
Step four, firstly: matrix according to factor graph
Figure 689322DEST_PATH_IMAGE034
A mapping matrix based on the resource block k can be designed
Figure 750818DEST_PATH_IMAGE006
Expressed as follows, when k =1, the mapping matrix is expressed as follows:
Figure 831907DEST_PATH_IMAGE085
wherein, the relationship between the mapping matrix and the factor graph matrix can be expressed as:
Figure 978854DEST_PATH_IMAGE086
，
Figure 272433DEST_PATH_IMAGE087
。
step four and step two: an operation factor is designed based on the resource block k, and the operation factor based on the resource block k can be obtained by combining a factor graph matrix of a Latin structure
Figure 250753DEST_PATH_IMAGE084
。
According to the method of code word allocation, the rotation angle can be similarly rotated
Figure 440426DEST_PATH_IMAGE088
Is defined as:
Figure 887719DEST_PATH_IMAGE089
wherein k and i respectively represent
Figure 188250DEST_PATH_IMAGE034
The ith non-zero element of the kth line of (1).
Combining the definition of the factor graph matrix and the rotation angle to further obtain the rotation matrix meeting the Latin structure
Figure 755498DEST_PATH_IMAGE090
Can be expressed as:
Figure 178389DEST_PATH_IMAGE091
to further reduce the complexity of the rotation matrix, the rotation matrix is preferably divided into two parts
Figure 299928DEST_PATH_IMAGE092
When rotating, the angle is rotated
Figure 200888DEST_PATH_IMAGE052
Is set to 0.
Therefore, a design operation factor based on resource block 1 can be obtained, which is expressed as follows:
Figure 91484DEST_PATH_IMAGE093
。
step five: code word matrix
Figure 671894DEST_PATH_IMAGE005
The k-th row vector of
Figure 77468DEST_PATH_IMAGE094
Operation factor
Figure 985381DEST_PATH_IMAGE095
Mapping matrix
Figure 792800DEST_PATH_IMAGE006
Multiplying to obtain a resource-basedThe codebook for block k is as follows:
Figure 495177DEST_PATH_IMAGE096
。
step six: according to the fifth step, a K multiplied by J codebook matrix of K resource blocks and J users can be finally obtained, wherein the jth column represents the codebook of the jth user
Figure 388047DEST_PATH_IMAGE009
。
The resource block based codebook matrix is represented as:
Figure 568492DEST_PATH_IMAGE097
。
thus, a codebook of user j can be obtained
Figure 981150DEST_PATH_IMAGE098
Is that
Figure 916745DEST_PATH_IMAGE099
Column j. The codebook of the first user
Figure 234594DEST_PATH_IMAGE100
Expressed as:
Figure 281047DEST_PATH_IMAGE101
。
the invention aims to provide a novel method for optimizing a codebook and distributing code words of an SCMA system, wherein a parent constellation is designed by using a dual threshold method under the modulation of a 4-dimensional lattice theory, and the problem of constellation point overlapping is solved by optimizing the parent constellation by using local dimension change. Meanwhile, in order to reduce intersymbol interference on the same time-frequency resource block; meanwhile, a resource block code word based distribution method is also designed. Under the improvement of two aspects, BER performance of the designed codebook is greatly improved under different sizes. At present, a plurality of methods are designed for an SCMA codebook, and the bit error rate performance of the proposed original codebook is poor under large size; low density signature technology (LDS), codebook gain is not ideal; neither constellation rotation codebook BER performance based on QAM modulation is optimal; a codebook (4-D lattice) is generated under the modulation of a 4-dimensional lattice theory, and the BER performance is not ideal under the condition of small size.
In order to verify the superiority of the performance of the codebook designed by the invention, a simulation experiment is carried out on a matlab platform, the BER performance of the codebook provided by the invention is compared with that of an original codebook, LDS, constellation rotation and 4-D grid comparison simulation experiment, and figures 3, 4, 5 and 6.
Fig. 2 is a diagram of the codebook generating process of the present invention, and the codebook generating process mainly includes: firstly, on the basis of a 4-dimensional grid, a two-dimensional mother constellation is obtained; secondly, optimizing a mother constellation by a local dimension transformation method; then designing a code word distribution method based on the resource block, and designing a mapping matrix and an operation factor based on the resource block; and finally, multiplying the code word on the resource block k, the operation factor and the mapping matrix to obtain a codebook matrix.
As shown in fig. 3, when M =4, the bit error rate performance is compared under different codebook design methods, and as shown by the bit error rate-signal to noise ratio curve, a curve result graph can be obtained: when the signal-to-noise ratio is 17dB, the bit error rate under the codebook design scheme provided by the invention can reach 6.6
Figure 742DEST_PATH_IMAGE102
Compared with other schemes, the method is improved by at least one order of magnitude; at a bit error rate of
Figure 107238DEST_PATH_IMAGE103
The signal-to-noise ratio gain is between 0.5-1.82 dB.
As shown in fig. 4, when M =8, the error rate performance under different codebook design methods is compared, and the error rate-snr curve shows that, when the snr is 20dB, the error rate under the codebook design scheme proposed by the present invention can reach the error rate performance under the codebook design scheme proposed by the present invention
Figure 912383DEST_PATH_IMAGE104
The error rate of LDS can be achieved
Figure 746216DEST_PATH_IMAGE105
(ii) a The result graph with curves can obtain: at a bit error rate of
Figure 382733DEST_PATH_IMAGE106
The signal-to-noise ratio gain can be improved by at least 1.22 dB.
As shown in fig. 5, when M =16, the bit error rate performance is compared under different codebook design methods, and as shown by the bit error rate-signal to noise ratio curve, a curve result graph can be obtained: when the signal-to-noise ratio is 25dB, the bit error rate under the codebook design scheme provided by the invention can reach 2.13
Figure 597814DEST_PATH_IMAGE107
The error rate of constellation rotation is inferior to that of the design scheme of the invention, and the error rate can reach 1.5
Figure 686993DEST_PATH_IMAGE108
Compared with other design schemes, the BER performance is improved by at least one order of magnitude; at a bit error rate of
Figure 278511DEST_PATH_IMAGE109
The signal-to-noise ratio gain can be improved by at least 1.3 dB.
Fig. 6 is a graph comparing bit error rate performance with constellation point coincidence under different codebook sizes. As can be seen from fig. 6, under the condition of the same codebook power and different codebook sizes, the BER performance is far better than the BER performance with point coincidence under the condition that the parent constellation points are not overlapped by using the local dimension transformation method. When M =4, the BER performance is improved by 0.7 orders of magnitude when the signal-to-noise ratio is 19 dB; when M =8, the BER performance is improved by 1.4 orders of magnitude when the signal-to-noise ratio is 20 dB; at M =8, the BER performance is improved by 1.7 orders of magnitude at a signal-to-noise ratio of 25 dB. Fig. 6 shows that the local dimension transformation method is significantly optimized for BER performance, and the larger the codebook size is, the better the BER effect obtained by the local dimension transformation method is.
In summary, the method of the invention can significantly improve under different codebook sizes, which shows the rationality of the local dimension transformation method in solving the constellation point overlapping, and reduces the scientificity of the intersymbol interference of different users by designing the user codebook based on the resource block, and after the two aspects are improved, the BER of the designed codebook under different sizes is greatly improved.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that features described in different dependent claims and in the invention may be combined in ways other than those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.

Claims (7)

1. A new SCMA system codebook optimization and codeword allocation method is characterized in that the method for designing a codebook comprises the following processes:
the method comprises the following steps: selecting useful points by using a dual threshold method under four-dimensional lattice modulation to obtain a mother constellation of the SCMA
Figure 199345DEST_PATH_IMAGE001
；
Step two: obtaining SCMA according to said step one
Figure 162490DEST_PATH_IMAGE001
Using local dimension transformation method to
Figure 207807DEST_PATH_IMAGE001
Optimizing to obtain an optimal mother constellation
Figure 603016DEST_PATH_IMAGE002
；
Step three: obtained according to the second step
Figure 214126DEST_PATH_IMAGE002
Will be
Figure 302168DEST_PATH_IMAGE002
Is allocated to a time-frequency resource block k, thereby obtaining a code matrix
Figure 569201DEST_PATH_IMAGE003
；
Step four: designing mapping matrix based on resource block k
Figure 315571DEST_PATH_IMAGE004
And an operation factor
Figure 984450DEST_PATH_IMAGE005
；
Step five: obtained in the third step
Figure 243393DEST_PATH_IMAGE003
The k-th row vector of
Figure 794460DEST_PATH_IMAGE006
And an operation factor in said step four
Figure 797051DEST_PATH_IMAGE005
Mapping matrix
Figure 320436DEST_PATH_IMAGE004
Multiplying to obtain a codebook based on a resource block k;
step six: further obtaining codebook matrixes of all resource blocks according to the fifth step, and separating out the codebook of the user j
Figure 810934DEST_PATH_IMAGE007
。
2. The method according to claim 1, wherein the step of obtaining the mother constellation by the dual threshold method in the first step comprises the steps of firstly using the power of the constellation point and the minimum euclidean distance as the dual threshold, secondly selecting the point in the lattice space as the constellation point of the mother constellation, and finally constructing the mother constellation as follows:
Figure 52560DEST_PATH_IMAGE008
。
3. the method as claimed in claim 1, wherein the obtained best mother star in step two is as follows:
Figure 593263DEST_PATH_IMAGE009
。
4. the method of claim 1, wherein the third step comprises the following steps:
step three, firstly: the factor graph matrix of the Latin structure of which 6 users share 4 time-frequency resource blocks is given as follows:
Figure 971154DEST_PATH_IMAGE010
，
calculating to obtain the number of users linked on each resource block according to the factor graph matrix
Figure 634217DEST_PATH_IMAGE011
As follows:
Figure 97559DEST_PATH_IMAGE012
；
step three: to obtain a matrix of codewords
Figure 441953DEST_PATH_IMAGE003
First, the code word on resource block k is represented as:
Figure 752980DEST_PATH_IMAGE013
，
wherein,
Figure 259047DEST_PATH_IMAGE006
the elements in (A) are from
Figure 475265DEST_PATH_IMAGE002
；
Secondly, the resource block k-based code word allocation method is defined as follows:
Figure 420087DEST_PATH_IMAGE014
，
wherein,
Figure 772571DEST_PATH_IMAGE015
is composed of
Figure 449540DEST_PATH_IMAGE002
Respectively, code words k and j represent
Figure 199059DEST_PATH_IMAGE016
The jth non-zero element on the kth resource block;
then, combining the factor graph matrix and the code word allocation method, the code word allocation matrix is obtained as follows:
Figure 885256DEST_PATH_IMAGE017
;
wherein, in
Figure 92246DEST_PATH_IMAGE018
In (1),
Figure 205696DEST_PATH_IMAGE019
is a vector of ideas, which is different according to the code word of each user, and finally orders
Figure 193243DEST_PATH_IMAGE020
Will be
Figure 417551DEST_PATH_IMAGE018
Further optimization is in the form:
Figure 744627DEST_PATH_IMAGE021
。
5. the method of claim 1, wherein step four comprises the steps of:
step four, firstly: combining with the factor graph matrix of the Latin structure to obtain a mapping matrix based on the resource block 1
Figure 842027DEST_PATH_IMAGE022
Is represented as follows:
Figure 988975DEST_PATH_IMAGE023
，
wherein, the relationship between the mapping matrix and the factor graph matrix can be expressed as:
Figure 16974DEST_PATH_IMAGE024
，
Figure 260873DEST_PATH_IMAGE025
；
step four and step two: to obtain an operation factor based on resource block k
Figure 716125DEST_PATH_IMAGE005
First, the rotation angle
Figure 615948DEST_PATH_IMAGE026
Is defined as:
Figure 182059DEST_PATH_IMAGE027
，
wherein k and i respectively represent
Figure 532662DEST_PATH_IMAGE028
The ith non-zero element of the kth row of (1); when in use
Figure 158816DEST_PATH_IMAGE029
When rotating, the angle is rotated
Figure 280355DEST_PATH_IMAGE030
Setting to 0; secondly, the definition of the factor graph matrix and the rotation angle is combined, and the rotation matrix of the Latin structure is further obtained
Figure 712474DEST_PATH_IMAGE031
Comprises the following steps:
Figure 868648DEST_PATH_IMAGE032
；
finally according to
Figure 665703DEST_PATH_IMAGE031
The operation factor based on resource block 1 design is obtained, and is expressed as follows:
Figure 274539DEST_PATH_IMAGE033
。
6. the method of claim 1, wherein the codebook based on resource block k in step five is represented as:
Figure 995502DEST_PATH_IMAGE034
。
7. the method of claim 1, wherein step six comprises the following steps:
step six: the resource block based codebook matrix is represented as:
Figure 6183DEST_PATH_IMAGE035
；
step six and two: in that
Figure 974139DEST_PATH_IMAGE036
In (2), take out the j column element
Figure 132588DEST_PATH_IMAGE007
Is the codebook of the jth user, so the codebook of user 1
Figure 844192DEST_PATH_IMAGE037
Expressed as:
Figure 974959DEST_PATH_IMAGE038
。
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