CN113765555A - Method for designing non-orthogonal multiple access system codebook based on resource block constellation distance - Google Patents

Method for designing non-orthogonal multiple access system codebook based on resource block constellation distance Download PDF

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CN113765555A
CN113765555A CN202111112782.4A CN202111112782A CN113765555A CN 113765555 A CN113765555 A CN 113765555A CN 202111112782 A CN202111112782 A CN 202111112782A CN 113765555 A CN113765555 A CN 113765555A
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何超
何春
朱立东
王剑
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University of Electronic Science and Technology of China
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • 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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    • H04L27/00—Modulated-carrier systems
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    • 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
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Abstract

The invention provides a method for designing a codebook of a non-orthogonal multiple access system based on constellation distance of resource blocks, which comprises the following steps: firstly, determining parameters J, M, N, K in an SCMA codebook according to user requirements; then according to the Latin criterion, determining the mapping matrix of the associated users and the resource blocks in the codebook
Figure DDA0003274421490000011
(ii) a Construction of an energy-normalized N-dimensional basis constellation S0(ii) a Calculating to obtain the optimal coefficient of the element and the optimal rotation angle according to the criterion of maximizing the sum of the distances of the code words among the constellation points of the resource block by a particle swarm PSO algorithm: finally, the optimal user constellation function is determined by the optimal element coefficient and the optimal rotation angle, the user constellation set corresponding to the optimal user constellation function is rearranged by code words, and the code words before and after rearrangement are distributed to the mapping matrix
Figure DDA0003274421490000012
Thereby obtaining a multi-user codebook for SCMA. The method can obtain larger integer gain and improve the anti-noise performance of the SCMA system under the Gaussian channel.

Description

Method for designing non-orthogonal multiple access system codebook based on resource block constellation distance
Technical Field
The invention relates to the field of wireless communication, in particular to a codebook design scheme of a non-orthogonal multiple access system for maximizing the Euclidean distance square sum between constellation points of a resource block under the condition of codebook resource block energy normalization.
Background
With the rapid development of mobile internet services and internet of things service applications, the mobile internet and the internet of things will become the main driving force for the development of future mobile communication, a fifth generation (5G) mobile communication system puts higher requirements on the number of user connections, experience rate, system capacity and delay index, and creates a severe challenge for the existing OMA scheme represented by OFDMA, and a novel non-orthogonal multiple access (NOMA) technical scheme represented by overlay transmission becomes one of key technologies in 5G mobile communication.
Compared with the OMA technology, Sparse Code Multiple Access (SCMA) has obvious advantages in the aspects of enhancing spectrum efficiency, improving user connection capability, reducing air interface transmission delay and the like, can be suitable for 5G different typical application scenes in the NOMA scheme, can support more user connections on the same time-frequency resource through superposition transmission of multi-user information, and can effectively meet the index requirements of connection of mass equipment of the Internet of things. In addition, the SCMA technology can realize scheduling-free transmission, can effectively simplify a signaling flow compared with orthogonal transmission, greatly reduces air interface transmission delay, and is beneficial to realizing 1ms air interface transmission delay indexes. Finally, SCMA techniques may also utilize multi-dimensional modulation and code domain spreading to achieve higher spectral efficiency. Therefore, by introducing the non-orthogonal multiple access technology, higher system capacity, lower time delay and support of more user connections can be obtained.
The SCMA codebook design is crucial in the SCMA system, because the SCMA coding process can be regarded as joint optimization of multidimensional modulation and sparse spreading, and the number of codewords, the spreading length, the number of nonzero codewords and the like in the codebook are important reasons influencing the SCMA system performance.
The SCMA codebook design scheme was first proposed by hua for the company and a codebook was disclosed in asian innovative design tournament of 2015, but its codebook implementation is unknown.
The following SCMA codebook optimization scheme promotes the reliability of the algorithm primarily on a distance basis. Taherzadeh.M, Nikopour.H, and the like, propose a design method based on a grid constellation, which is an SCMA codebook design method proposed for the first time and is divided into three steps, wherein the first step is to design a mapping matrix, and the number of layers multiplexed on each resource node is determined by the mapping matrix, so that the complexity of MPA detection is determined, and the more sparse the code word is, the simpler the MPA detection is. Secondly, the constellation points and the multidimensional mother constellation are obtained, the specific operation mode is to construct the multidimensional constellation which maximizes the minimum Euclidean distance, the mother constellation with smaller projection number is obtained under the condition of ensuring that the distance is not changed by methods such as rotation, and the complexity of the corresponding MPA detector is reduced. And finally, performing constellation operation such as phase rotation, power offset and the like based on the mother constellation points to obtain codebooks of different users, wherein the construction methods are used as guidance, the idea of SCMA codebook design problems becomes clear, but the realization complexity is high, and the method is not suitable for high-dimensionality constellations. Cai et al obtain a multidimensional mother constellation by rotating and interleaving a subset of QAM constellations, and then obtain a multi-user codebook by matrix mapping according to the rotated mother constellation points of the constellation operation method in the Taherzadeh paper. Yu et al generates a multidimensional mother constellation through a star-QAM constellation, and then obtains a multi-user codebook by using a constellation operation method in the Taherzadeh paper, wherein the codebook performance of the multi-user codebook exceeds that of the Taherzadeh paper. The above three codebook design methods mainly relate to the construction of multidimensional mother constellation and the determination of constellation operation, and belong to the non-convex Quadratic Constraint Quadratic Programming (QCQP) problem, which is an NP-hard problem, and it is usually difficult to solve one QCQP, even for a small amount of constraints. Beko et al propose a sub-optimal solution to the QCQP problem, which can be solved by a CVX toolbox, by fitting the problem to a convex Second Order Cone Programming (SOCP) problem.
In Gaussian channel, on the basis of QAM in Cai paper, Lianjia et al designs the total constellation of all users on each resource block by using the constellation of QAM, and then generates a user codebook by using a subset partitioning method of trellis coded modulation TCM. Guo Mingkun et al converts the design of the multidimensional codebook constellation in the Taherzadeh paper into a simple process of determining codebook parameters, avoiding solving the QCQP problem, and can obtain a codebook with excellent bit error performance under the condition of reducing the complexity of parameter selection, with the criterion of maximizing the minimum element of the user constellation distance spectrum. Both of the above algorithms are developed based on the distance of the constellation points.
In addition to being based on the distance of the constellation points, there are codebook optimization methods of other angles, such as peak to average power ratio (PAPR) reduction, codeword resource allocation, energy consumption, factor graph matrix, etc. For example, x.ma et al propose an optimization method for PAPR reduction that reallocates high-power constellation points to primarily reduce PAPR and then rotates a jointly optimized user codebook to continue reducing PAPR. Li et al propose an optimization method based on the channel capacity maximization criterion, which dynamically allocates user codewords and energy, eliminating the mutual influence of non-zero elements in the codewords. And S.Yang et al propose a fair rate, power and user code word distribution method, which is based on cooperative game criterion and can ensure the fairness of users under the condition of increasing the rate and power. Bayeth et al propose a codebook optimization method for reducing the complexity of the MPA algorithm at the receiving end, whose design concept is to overlap some constellation points in one dimension, reducing the number of effective constellation points.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for normalizing codebook energy and determining codebook parameters based on the maximized Euclidean distance square sum between constellation points of resource blocks.
The technical scheme adopted by the invention for solving the technical problems is that the method for designing the non-orthogonal multiple access system codebook based on the constellation distance of the resource block comprises the following steps:
1) determining J, M, N, K parameters in the SCMA codebook according to user requirements; j is the number of users, M, N represents the constellation function respectively
Figure RE-GDA0003333276970000031
The generated constellation set is M-order N-dimensional, and K is the number of resource blocks;
2) determining a mapping matrix of associated users and resource blocks in a codebook according to the Latin criterion
Figure RE-GDA0003333276970000032
3) Construction of an energy-normalized N-dimensional basis constellation S0；
Figure RE-GDA0003333276970000033
r1Represents the base element of the base constellation,
Figure RE-GDA0003333276970000034
represents the first
Figure RE-GDA0003333276970000035
Coefficient of each element, satisfy
Figure RE-GDA0003333276970000036
dfRepresenting the number of the users superposed on each resource block;
4) p-base constellation S0Rotating the constellation points by the respective rotation angles
Figure RE-GDA0003333276970000037
To obtain dfIndividual user constellation set
Figure RE-GDA0003333276970000038
Figure RE-GDA0003333276970000039
5) Determining a constellation set for a user
Figure RE-GDA00033332769700000310
Code word rearrangement is carried out to obtain
Figure RE-GDA00033332769700000311
Code word repetition ofArranging rules;
6) calculating to obtain the optimal coefficient of the element according to the criterion of maximizing the sum of the code word distances between constellation points of the resource block by a particle swarm PSO algorithm
Figure RE-GDA00033332769700000312
Optimum angle of rotation
Figure RE-GDA00033332769700000313
Figure RE-GDA00033332769700000314
Figure RE-GDA00033332769700000315
Figure RE-GDA00033332769700000316
ssum,i,ssum,j∈Ssum
Wherein S issumIs dfThe constellation set after the superposition of the individual users,
Figure RE-GDA00033332769700000317
ssum,i,ssum,ji ≠ j, which respectively represents the ith constellation point and the j constellation point in the constellation set after the user superposition,
Figure RE-GDA00033332769700000318
the total number of constellation points in the constellation set after the user superposition; e { | | Sk||2Expressing the k-th user constellation set SkThe energy of (a); the rearrangement of the code words only changes the order of the code words, at SsumIn (1)
Figure RE-GDA00033332769700000319
Each element is invariant;
7) coefficient of optimum element
Figure RE-GDA00033332769700000320
Optimum angle of rotation
Figure RE-GDA00033332769700000321
Determining optimal user constellation function
Figure RE-GDA00033332769700000322
Mapping optimal user constellation function
Figure RE-GDA00033332769700000323
The corresponding user constellation set carries out code word rearrangement, and the code words before and after rearrangement are distributed to the mapping matrix
Figure RE-GDA00033332769700000324
Thereby obtaining a multi-user codebook for SCMA.
The method adopted by the invention is similar to that in the Guo Mingkun paper, and the difference is that the codebook energy is normalized, the Euclidean distance square sum among constellation points of a resource block is maximized, and the minimum distance among the constellation points of the minimum user is maximized in the Guo Mingkun paper. The SCMA codebook design is transferred to the optimized partial codebook parameters from the aspect of the construction of the mother constellation and the constellation operation, the optimized parameters meeting the codebook design criterion are obtained by using the PSO algorithm, the problem of solving the QCQP problem of the non-convex quadratic constraint quadratic programming can be avoided, and the complexity of the codebook design is reduced.
The method has the advantages that based on the constellation distance on the resource block, by restricting the rotation angle, the Euclidean distance square sum among the constellation points can be maximized under the condition that the minimum constellation point distance is larger, larger integer gain can be obtained, and the anti-noise performance of the SCMA system under the Gaussian channel can be improved.
Drawings
FIG. 1 is a schematic diagram of codebook resource allocation under four resource blocks and six users;
FIG. 2 is a flow diagram of an embodiment SCMA codebook design;
fig. 3 shows the bit error rate comparison of the codebook with other codebooks at different snrs (additive white gaussian noise channel, J is 6, K is 4, M is 4, and N is 2);
fig. 4 is a constellation diagram of each user and resource block of the codebook for six users and four resource blocks.
Detailed Description
SCMA codebook design problems may be transformed into a mapping matrix by solving a maximum design criterion
Figure RE-GDA0003333276970000041
And constellation function
Figure RE-GDA0003333276970000042
To obtain the optimal mapping matrix
Figure RE-GDA0003333276970000043
And constellation function
Figure RE-GDA0003333276970000044
Figure RE-GDA0003333276970000045
Wherein m is a design criterion;
Figure RE-GDA0003333276970000046
represents the structure of a codebook;
Figure RE-GDA0003333276970000047
representing a mapping matrix which is a user-corresponding column vector VjA set of (a);
Figure RE-GDA0003333276970000048
representing a constellation function, being a user constellation function gjA set of (a); constellation function
Figure RE-GDA0003333276970000049
Generating MjOrder NjA constellation set of dimensions; j stands for codeThe number of independent layers of the device also represents the number of users; m, N respectively represent constellation functions
Figure RE-GDA00033332769700000410
The generated constellation set is M-order N-dimensional, and K is the number of resource blocks.
Example steps are shown in figure 2:
step 1: determining J, M, N, K parameters in SCMA codebook design problem according to the number of users, the number of resources and the constellation dimension of the required codebook;
preferably:
Figure RE-GDA00033332769700000411
Figure RE-GDA00033332769700000412
system overload rate
Figure RE-GDA0003333276970000051
max (0,2N-K) is more than or equal to l and less than or equal to N-1, wherein l represents the number of any column vector overlapping elements in the mapping matrix;
example settings J, M, N, K ═ 6,4,2, 4.
Step 2: determining a mapping matrix of a codebook according to the Latin criterion
Figure RE-GDA00033332769700000516
When J, M, N, K is 6,4,2,4, according to the mapping matrix
Figure RE-GDA00033332769700000517
The resulting factor graph is shown in FIG. 1.
And step 3: constructing an N-dimensional basis constellation S with parameters0Normalizing the constellation energy;
in particular, the method comprises the following steps of,
Figure RE-GDA0003333276970000052
r1represents the base element of the base constellation,
Figure RE-GDA0003333276970000053
represents the first
Figure RE-GDA0003333276970000054
The coefficient of each element is required to meet the energy normalization principle of codebook resource block
Figure RE-GDA0003333276970000055
E{||S0||2Denotes solving the base constellation S0Energy of, i.e. satisfy
Figure RE-GDA0003333276970000056
dfRepresenting the number of the users superposed on each resource block;
and 4, step 4: for N-dimensional base constellation S0Rotating the constellation points, respectively
Figure RE-GDA0003333276970000057
The rotation angle is limited to satisfy the requirement that the minimum Euclidean distance is larger to obtain dfIndividual user constellation
Figure RE-GDA0003333276970000058
dfRepresenting the number of the users superposed on each resource block;
examples of the embodiments
Figure RE-GDA0003333276970000059
Figure RE-GDA00033332769700000510
Can be obtained by a person skilled in the art
Figure RE-GDA00033332769700000511
Other variations of (2) determine the user constellation.
And 5: determining a constellation set for a user
Figure RE-GDA00033332769700000512
Code word rearrangement is carried out to obtain
Figure RE-GDA00033332769700000513
The codeword rearrangement rule of (1);
taking J ═ 6 and M ═ 4 as an example, the principle of codeword rearrangement is to rearrange [ v ═ v1,v2,v3,v4]Is assigned as [ -v ]3,v4,v1,-v2]。
Namely:
Figure RE-GDA00033332769700000514
Figure RE-GDA00033332769700000515
step 6: according to the criterion that the sum of the code word distances among the maximum resource block constellation points is maximum, the base constellation S is solved through a PSO algorithm0And an optimum rotation angle;
codebook design criteria in step 6:
calculating to obtain the optimal coefficient of the element according to the criterion of maximizing the sum of the code word distances between constellation points of the resource block by a particle swarm PSO algorithm
Figure RE-GDA0003333276970000061
Optimum angle of rotation
Figure RE-GDA0003333276970000062
Figure RE-GDA0003333276970000063
Figure RE-GDA0003333276970000064
Figure RE-GDA0003333276970000065
ssum,i,ssum,j∈Ssum
Wherein S issumIs dfThe constellation set after the superposition of the individual users,
Figure RE-GDA0003333276970000066
ssum,i,ssum,ji ≠ j, which respectively represents the ith and j constellation points in the codebook set,
Figure RE-GDA0003333276970000067
the total number of constellation points in the codebook set; e { | | Sk||2Expressing the k-th user constellation set SkThe energy of (a);
coefficient by optimum element
Figure RE-GDA0003333276970000068
Optimum angle of rotation
Figure RE-GDA0003333276970000069
To determine the best user constellation function
Figure RE-GDA00033332769700000610
And 7: mapping optimal user constellation function
Figure RE-GDA00033332769700000611
The corresponding user constellation set carries out code word rearrangement, and the code words before and after rearrangement are distributed to the mapping matrix
Figure RE-GDA00033332769700000612
Thereby obtaining a multi-user codebook for SCMA.
Taking J ═ 6 and M ═ 4 as an example, one mapping matrix is:
Figure RE-GDA00033332769700000613
the specific form of the SCMA codebook is as follows:
Figure RE-GDA00033332769700000614
Figure RE-GDA00033332769700000615
Figure RE-GDA0003333276970000071
Figure RE-GDA0003333276970000072
Figure RE-GDA0003333276970000073
Figure RE-GDA0003333276970000074
after the optimal parameters are determined, when M is 4, the coefficients of the elements are only
Figure RE-GDA0003333276970000075
The SCMA codebook determined is as follows:
Figure RE-GDA0003333276970000076
Figure RE-GDA0003333276970000077
Figure RE-GDA0003333276970000078
Figure RE-GDA0003333276970000079
Figure RE-GDA0003333276970000081
Figure RE-GDA0003333276970000082
the comparison of the bit error rate of the codebook with that of other codebooks under different snr (additive white gaussian noise channel, J is 6, K is 4, M is 4, and N is 2) is shown in fig. 3; the constellation of each user and resource block of the codebook is shown in fig. 4.

Claims (3)

1. A method for designing a codebook of a non-orthogonal multiple access system based on constellation distance of resource blocks is characterized by comprising the following steps:
1) determining J, M, N, K parameters in the SCMA codebook according to user requirements; j is the number of users, M, N represents the constellation function respectively
Figure FDA0003274421460000011
The generated constellation set is M-order N-dimensional, and K is the number of resource blocks;
2) determining a mapping matrix of associated users and resource blocks in a codebook according to the Latin criterion
Figure FDA0003274421460000012
3) Construction of an energy-normalized N-dimensional basis constellation S0；
Figure FDA0003274421460000013
r1Represents the base element of the base constellation,
Figure FDA0003274421460000014
represents the first
Figure FDA0003274421460000015
Coefficient of each element, satisfy
Figure FDA0003274421460000016
dfRepresenting the number of the users superposed on each resource block;
4) p-base constellation S0Rotating the constellation points by the respective rotation angles
Figure FDA00032744214600000122
To obtain dfIndividual user constellation set
Figure FDA00032744214600000123
Figure FDA0003274421460000017
5) Determining a constellation set for a user
Figure FDA00032744214600000124
Code word rearrangement is carried out to obtain
Figure FDA00032744214600000125
The codeword rearrangement rule of (1);
6) calculating to obtain the optimal coefficient of the element according to the criterion of maximizing the sum of the code word distances between constellation points of the resource block by a particle swarm PSO algorithm
Figure FDA00032744214600000110
Optimum angle of rotation
Figure FDA00032744214600000111
Figure FDA00032744214600000112
Figure FDA00032744214600000113
Figure FDA00032744214600000114
ssum,i,ssum,j∈Ssum
Wherein S issumIs dfThe constellation set after the superposition of the individual users,
Figure FDA00032744214600000115
ssum,i,ssum,ji ≠ j, which respectively represents the ith constellation point and the j constellation point in the constellation set after the user superposition,
Figure FDA00032744214600000116
the total number of constellation points in the constellation set after the user superposition; e { | | Sk||2Expressing the k-th user constellation set SkThe energy of (a);
7) coefficient of optimum element
Figure FDA00032744214600000117
Optimum angle of rotation
Figure FDA00032744214600000118
Determining optimal user constellation function
Figure FDA00032744214600000119
Mapping optimal user constellation function
Figure FDA00032744214600000120
The corresponding user constellation set carries out code word rearrangement, and the code words before and after rearrangement are distributed to the mappingMatrix array
Figure FDA00032744214600000121
Thereby obtaining a multi-user codebook for SCMA.
2. The method as claimed in claim 1, wherein the parameter J, M, N, K in the SCMA codebook in step 1) satisfies:
Figure FDA0003274421460000021
Figure FDA0003274421460000022
3. the method of claim 1, wherein step 4) is performed on the base constellation S0Performing rotation of constellation points
Figure FDA0003274421460000026
To obtain dfIndividual user constellation set
Figure FDA0003274421460000027
Figure FDA0003274421460000025
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