CN113141326A - Novel SCMA system codebook optimization and codeword distribution method - Google Patents
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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(ii) a Step two: obtaining SCMA according to step oneUsing local dimension transformation method pairOptimizing to obtain an optimal mother constellation(ii) a Step three: root of herbaceous plantObtained according to the second stepWill beIs allocated to a time-frequency resource block k, thereby obtaining a code matrix(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 stepMultiplying 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. The method of the invention realizes that the BER performance can be obviously improved under different codebook sizes.
Description
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;
Step two: according to the mother constellation of the SCMA obtained in step one, when M is large,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;
Step three: obtained according to the second stepWill beIs allocated to a time-frequency resource block k, thereby obtaining a code matrix;
Step four: obtaining a mapping matrix based on a resource block k from the perspective of the resource blockAnd an operation factor;
Step five: code word matrixThe k-th row vector ofOperation factorMapping matrixMultiplying 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。
Preferably, in the first step, the mother constellation of the SCMA with dimension N and size M is obtained under the condition of double thresholdingThe following forms:
wherein, 2-dimensional mother constellation constructionThe 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:
wherein,andare respectively asThe power of any column of complex constellation points and the minimum Euclidean distance of the column vector complex constellation points are expressed as follows:
codebook gain of lattice constellation under 4-dimensional lattice theory modulationCan be expressed as:
in order to obtain a good shaping gain and codebook gainSince the lattice constellation points satisfy the dual threshold,the following conditions should be satisfied:
bonding ofCan be prepared by the interior point methodAnd 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:
preferably, in the second step, when the codebook size M is large,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:
the invention provides a method for optimizing local dimension transformationThe optimized optimal 2-dimensional complex mother constellation is represented as follows:
after the transformation, the image is displayed on the screen,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 blockThe number of the individual users is increased by the number of the individual users,is represented as follows:
The factor graph matrix of the Latin structure of 4 time-frequency resource blocks shared by 6 users is represented as follows:
in thatIn the matrix, the position of the jth nonzero element in the kth row is indexed asWherein(ii) a The codeword allocation on a resource block is represented as follows:
combining with the factor graph matrix, under the code word allocation method on the resource block, a code word allocation matrix can be obtained:
in thatThe non-zero vector on the k-th resource block is fromThus, therefore, it isIs a vector of ideas, since the codewords for each user are not the same, hereWill beFurther optimized to the following formula:
preferably, the fourth step includes the steps of:
step four, firstly: matrix according to factor graphA mapping matrix based on the resource block k can be designedExpressed as follows, when k =1, the mapping matrix is expressed as follows:
wherein, the relationship between the mapping matrix and the factor graph matrix can be expressed as:,。
step four and step two: like the code word allocation method, the rotation angle can be adjusted in the same wayIs defined as:
combining the factor graph matrix and the definition of the rotation angle to obtain the rotation matrix meeting the Latin structureCan be expressed as:
to further reduce the complexity of the rotation matrix, the rotation matrix is preferably divided into two partsWhen rotating, the angle is rotatedIs set to 0.
Step four and step three: further obtained is a design operation factor based on resource block 1, expressed as follows:
preferably, in the step five, the code word based on the resource block k may be expressed as:
preferably, the sixth step includes the steps of:
step six: the resource block based codebook matrix is represented as:
step six and two: byThe jth column of (a) is separated to obtain a codebook of the user jThen the codebook of the first userExpressed as:
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.
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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。
wherein, 2-dimensional mother constellation constructionThe 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:
wherein,andare respectively asThe 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 modulationCan be expressed as:
in order to obtain a good shaping gain and codebook gainSince the lattice constellation points satisfy the dual threshold,the following conditions should be satisfied:
bonding ofCan be prepared by the interior point methodAnd 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:
step two: according to the mother constellation of the SCMA obtained in step one, when M is large,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。
When the codebook size M is large,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:
the invention provides a method for optimizing local dimension transformationThe optimized optimal 2-dimensional complex mother constellation is represented as follows:
after the transformation, the image is displayed on the screen,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 stepWill beIs allocated to a time-frequency resource block k, thereby obtaining a code matrix。
If there are K resource blocks and J users, each resource block is connected withThe number of the individual users is increased by the number of the individual users,is represented as follows:
The factor graph matrix of the Latin structure of 4 time-frequency resource blocks shared by 6 users is represented as follows:
in thatIn the matrix, the position of the jth nonzero element in the kth row is indexed asWherein(ii) a The codeword allocation on a resource block is represented as follows:
combining with the factor graph matrix, under the code word allocation method on the resource block, a code word allocation matrix can be obtained:
in thatThe non-zero vector on the k-th resource block is fromThus, therefore, it isIs a vector of ideas, since the codewords for each user are not the same, hereWill beFurther optimized to the following formula:
step four: from the perspective of the resource blockMapping matrix based on resource block kAnd an operation factorThe fourth step comprises the following steps.
Step four, firstly: matrix according to factor graphA mapping matrix based on the resource block k can be designedExpressed as follows, when k =1, the mapping matrix is expressed as follows:
wherein, the relationship between the mapping matrix and the factor graph matrix can be expressed as:,。
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。
According to the method of code word allocation, the rotation angle can be similarly rotatedIs defined as:
Combining the definition of the factor graph matrix and the rotation angle to further obtain the rotation matrix meeting the Latin structureCan be expressed as:
to further reduce the complexity of the rotation matrix, the rotation matrix is preferably divided into two partsWhen rotating, the angle is rotatedIs set to 0.
Therefore, a design operation factor based on resource block 1 can be obtained, which is expressed as follows:
step five: code word matrixThe k-th row vector ofOperation factorMapping matrixMultiplying to obtain a resource-basedThe codebook for block k is as follows:
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。
The resource block based codebook matrix is represented as:
thus, a codebook of user j can be obtainedIs thatColumn j. The codebook of the first userExpressed as:
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 6.6Compared with other schemes, the method is improved by at least one order of magnitude; at a bit error rate ofThe 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 inventionThe error rate of LDS can be achieved(ii) a The result graph with curves can obtain: at a bit error rate ofThe 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 2.13The error rate of constellation rotation is inferior to that of the design scheme of the invention, and the error rate can reach 1.5Compared with other design schemes, the BER performance is improved by at least one order of magnitude; at a bit error rate ofThe 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;
Step two: obtaining SCMA according to said step oneUsing local dimension transformation method toOptimizing to obtain an optimal mother constellation;
Step three: obtained according to the second stepWill beIs allocated to a time-frequency resource block k, thereby obtaining a code matrix;
Step five: obtained in the third stepThe k-th row vector ofAnd an operation factor in said step fourMapping matrixMultiplying to obtain a codebook based on a resource block k;
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:
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:
calculating to obtain the number of users linked on each resource block according to the factor graph matrixAs follows:
step three: to obtain a matrix of codewordsFirst, the code word on resource block k is represented as:
Secondly, the resource block k-based code word allocation method is defined as follows:
wherein,is composed ofRespectively, code words k and j representThe 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:
wherein, inIn (1),is a vector of ideas, which is different according to the code word of each user, and finally ordersWill beFurther optimization is in the form:
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 1Is represented as follows:
wherein, the relationship between the mapping matrix and the factor graph matrix can be expressed as:,;
step four and step two: to obtain an operation factor based on resource block kFirst, the rotation angleIs defined as:
wherein k and i respectively representThe ith non-zero element of the kth row of (1); when in useWhen rotating, the angle is rotatedSetting 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 obtainedComprises the following steps:
finally according toThe operation factor based on resource block 1 design is obtained, and is expressed as follows:
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