A SCMA codebook design method based on joint bounds

Abstract

The present invention relates to codebook design in mobile communications, and in particular to a SCMA codebook design method based on a joint bound, which solves the technical problems that the existing codebook design method cannot guarantee the overall performance of the SCMA system, or takes a long time and has a large amount of calculation. The codebook design method provided by the present invention adopts a one-dimensional complex constellation composed of multiple BPSK constellations, and uses the joint bound of the codebook BER performance as the objective function of the genetic algorithm, with low computational complexity, which well reflects the iterative detection performance of the SCMA system and further improves the codebook BER performance. The present invention adopts a constrained individual vector structure to reduce optimization parameters, and then further optimizes the performance of the obtained codebook using an unconstrained individual vector structure, and adds the Latin matrix as an optimization parameter to the optimization design, generates a permutation matrix to optimize the constellation label, which can reduce computational complexity, reduce computational amount, and improve the codebook BER performance.

Description

Technical Field

[0001] The present invention relates to codebook design in mobile communications, and in particular to a SCMA codebook design method based on a joint bound. Background Art

[0002] Given the stringent requirements of future mobile communication systems, such as ultra-low latency and ultra-high system capacity, conventional orthogonal multiple access (OMA) technologies are currently unable to meet these demands. Driven by these application demands, non-orthogonal multiple access (NMA) technologies have garnered widespread attention due to their superior performance, particularly their ability to support massive user numbers. Thanks to the joint efforts of industry and academia, a series of high-performance NMA technologies have emerged, including low-density spread spectrum (LDS), low-density spread spectrum orthogonal frequency division multiplexing (OFDM), multi-user shared access (MMA), interleaved multiple access (IMA), and sparse code multiple access (SCMA).

[0003] In 2013, H. Nikopour and H. Baligh proposed a novel non-orthogonal multiple access technology based on Low Density Signature (LDS) technology, called Sparse Code Multiple Access (SCMA). Compared to LDS, SCMA retains the original iterative detection algorithm of the LDS receiver, thus ensuring low receiver implementation complexity. Furthermore, SCMA further considers spread spectrum and modulation as a whole, providing greater optimization space for system design, thereby achieving greater constellation forming gain and coding gain, and improving overall system performance.

[0004] Codebook design plays a crucial role in SCMA system design. Codebook performance determines key metrics such as the system's detection performance, detection complexity, and peak-to-average power ratio at the receiver. Therefore, optimizing the design of SCMA codebooks is a highly worthy research topic. Several papers have explored SCMA codebook design, exploring various design criteria, such as the number and capacity of one-dimensional constellations, the symbol error rate (SER) obtained through simulation, and the minimum Euclidean distance between superimposed codewords.

[0005] However, simply maximizing the minimum Euclidean distance between superimposed codewords does not necessarily guarantee SER performance; the distribution of Euclidean distances, especially small Euclidean distances, and their corresponding coefficients significantly impact the overall performance of the codebook. The SER obtained through simulation is used as a design metric, and the SCMA codebook is optimized using a differential evolution algorithm. Although SER performance accurately reflects the actual performance of the system, obtaining accurate SER performance through simulation requires a significant amount of simulation time. Summary of the Invention

[0006] The purpose of the present invention is to solve the technical problems that the existing codebook design methods cannot guarantee the overall performance of the SCMA system, or are time-consuming and computationally intensive, and to provide an SCMA codebook design method based on a joint bound.

[0007] The design idea of ​​the present invention is:

[0008] The uplink SCMA system has J users, and J users multiplex K orthogonal resource blocks. Assume that the number of users superimposed on each resource block is the same, both d f In the uplink SCMA system, each user has a specific codebook, each user's codebook contains N non-zero components, and each resource block has N non-zero components from d f The information of each user is superimposed together. This sparse connection relationship can be represented by a sparse matrix, called a factor graph matrix.

[0009] Leveraging the system's sparse nature, the uplink SCMA receiver can be implemented using a message-passing algorithm. By passing messages between resource and user nodes, local information can be gradually diffused to the entire system. This allows the variable node to gather enough information over multiple iterations to achieve a more accurate detection.

[0010] The codebook design of the SCMA system is a complex multi-dimensional optimization problem. Not only is the codebook design of each user a multi-dimensional design problem, but the codebooks of multiple users need to be jointly optimized to achieve the best system performance.

[0011] The user's codebook design involves two factors:

[0012] 1) Select N from K resource blocks as non-zero components;

[0013] 2) Design a complex constellation for each non-zero component, with a total of N complex constellations.

[0014] Specifically, the codebook design for the SCMA system is essentially finding J K-dimensional complex constellations (of which there are only N non-zero components), where each non-zero component corresponds to a complex constellation containing M constellation points. The SCMA codebook design problem can be defined as follows:

[0015]

[0016] Here, the function m(.) represents a design criterion. The above formula shows that the design of the SCMA codebook is actually the joint optimization design of multiple mapping matrices V and multidimensional constellations G.

[0017] Therefore, SCMA codebook design is a multidimensional optimization problem, and its optimal solution is generally difficult to find. To reduce design complexity, a suboptimal multi-stage optimization strategy is often adopted. This involves first optimizing the mapping matrix, or equivalently, the factor graph matrix, and then optimizing the multidimensional constellation. The choice of design metrics and the one-dimensional complex constellation are the main factors affecting codebook performance.

[0018] Each user has its own unique mapping matrix, which determines which resource blocks it shares. Therefore, designing the mapping matrix is ​​equivalent to designing a factor graph matrix. For an SCMA system that occupies K resource blocks, assuming each user shares N of the K resource blocks, to reduce detection complexity, the design generally avoids having two different users share the same set of resource blocks.

[0019] Once the mapping matrix is ​​designed, the SCMA codebook optimization problem is simplified to the joint optimization of multiple multidimensional constellations. Specifically, it is necessary to find J K-dimensional complex constellations, each with only N non-zero components. Each complex constellation contains M constellation points.

[0020] The present invention uses a one-dimensional complex constellation composed of multiple BPSK constellations. The one-dimensional complex constellation contains M constellation points, where M is a power of 2. Each non-element in the factor graph matrix is ​​replaced with a one-dimensional complex constellation, ensuring that no elements are repeated in each row or column of the factor graph matrix.

[0021] In this paper, a joint bound on the BER (bit error probability) performance of the SCMA system is used as a design metric for the joint optimization of multiple multidimensional constellations. The results of the joint bound in the high signal-to-noise ratio region are generally consistent with the simulation results. Therefore, the joint bound is more suitable as a design metric than the minimum Euclidean distance between superimposed codewords. Furthermore, the computational complexity of the joint bound is much lower than that of the SER obtained through simulation, and it can well reflect the iterative detection performance of the SCMA system.

[0022] The present invention uses a genetic algorithm to optimize the design of the SCMA codebook. The genetic algorithm is a global optimization search algorithm that draws on the biological genetic and evolutionary processes. The genetic algorithm gradually improves the adaptability of each individual to the environment through mechanisms such as selection, inheritance, and mutation, and approaches the global optimal solution after multiple rounds of iterations. When the genetic algorithm is used to optimize the SCMA codebook, the vector structure of each individual is specified by d f The one-dimensional complex constellation, Latin matrix structure and labeling rules are determined. According to the genetic algorithm parameters, the initial population is generated according to the individual vector structure, and the genetic algorithm is used to optimize the initial population with the joint bound of the BER performance of the SCMA system as the goal to obtain the optimal codebook.

[0023] To achieve the above object, the technical solution adopted by the present invention is:

[0024] A joint-bound-based SCMA codebook design method includes the following steps:

[0025] Step 1: Determine the factor graph matrix based on the SCMA system parameters and generate L candidate Latin matrices and T permutation matrices of length M, where L, M, and T are all positive integers, T≤M!, and M is the number of constellation points, which is a power of 2.

[0026] The SCMA system parameters include the number of users J, the number of resource blocks K, the multidimensional constellation dimension N, the number of users superimposed on each resource block d f , where J, K, N, d f are all positive integers;

[0027] The multidimensional constellation dimension N means that the multidimensional constellation includes N non-zero vectors; each non-zero vector corresponds to a one-dimensional complex constellation, the one-dimensional complex constellation is an mBPSK constellation, the mBPSK constellation is composed of multiple BPSK constellations, and each one-dimensional complex constellation contains M constellation points;

[0028] Step 2: Determine the individual vector structure, specifically:

[0029]

[0030] in, Represents the two parameters of the i-th BPSK constellation, α i is the amplitude parameter of the i-th BPSK constellation, is the phase parameter of the i-th BPSK constellation; i is a positive integer;

[0031] La is the Latin matrix index, which is used to select a specific Latin matrix from L candidate Latin matrices;

[0032] int jis the permutation matrix index, which is used to specify the permutation form of the BPSK constellation label. A permutation matrix is ​​selected from the T permutation matrices generated in step 1. j is a positive integer.

[0033] Step 3: Determine the joint bound of the codebook BER performance as the genetic algorithm objective function, and set the genetic algorithm parameters; the genetic algorithm parameters include population size, number of elites, crossover probability and evolutionary generations;

[0034] Step 4: Based on the genetic algorithm parameters determined in step 3, an initial population is generated according to the individual vector structure obtained in step 2;

[0035] Step 5: Based on the genetic algorithm objective function determined in step 3, the genetic algorithm is used to optimize the initial population obtained in step 4 to obtain the optimal SCMA codebook.

[0036] Furthermore, the method further includes step 6:

[0037] Step 6: Based on the optimal SCMA codebook obtained in step 5, a genetic algorithm is used for global optimization to obtain a further optimized optimal SCMA codebook, specifically:

[0038] 6.1. Determine the globally optimized individual vector structure, specifically:

[0039]

[0040] 6.2. Determine the genetic algorithm parameters and determine the joint bound of the optimal SCMA codebook BER performance as the genetic algorithm objective function;

[0041] 6.3. Based on the genetic algorithm parameters determined in step 6.2, and the globally optimized individual vector structure determined in step 6.1, a globally optimized initial population is generated based on the optimal SCMA codebook obtained in step 5;

[0042] 6.4. Based on the genetic algorithm objective function determined in step 6.2, the genetic algorithm is used to perform global optimization on the global optimization initial population obtained in step 6.3 to obtain a further optimized optimal SCMA codebook.

[0043] Furthermore, in step 3, the joint bound of the codebook BER performance is:

[0044]

[0045] Among them, v a and v b Represents two different superimposed codewords;

[0046] d 2 (v a ,v b) is the squared Euclidean distance between two superimposed codewords;

[0047] B a,b Indicates v a and v b The number of different bits in the corresponding information packet;

[0048] E s The average symbol energy for each resource block;

[0049] N0 is the unilateral power spectral density of additive white Gaussian noise;

[0050] Q(x) is the tail distribution function of the standard normal distribution, u is the integrand variable.

[0051] Furthermore, in step 1, the number of users superimposed on each resource block is d f Same, d f =JN / K.

[0052] Furthermore, in step 1, the permutation matrix is ​​used to adjust the index of the BPSK constellation in the one-dimensional complex constellation;

[0053] The method for generating the label of the BPSK constellation in the one-dimensional complex constellation is:

[0054] The indices of the BPSK constellations in the first one-dimensional complex constellation are fixed, and the indices of the BPSK constellations in the other N-1 one-dimensional complex constellations are permuted accordingly using N-1 permutation matrices.

[0055] Furthermore, in step 1, generating L candidate Latin matrices is specifically as follows:

[0056] Replace the non-zero components in the factor graph matrix with d f One-dimensional complex constellations, so that the N elements in each column of the factor graph matrix are different, and the d elements in each row are different. f The elements are also different. By choosing different replacement methods, we can obtain L different candidate Latin matrices.

[0057] Compared with the prior art, the present invention has the following beneficial technical effects:

[0058] 1. The joint bound-based SCMA codebook design method provided by the present invention uses the joint bound of the BER performance of the SCMA system as the objective function of the genetic algorithm. It has low computational complexity and can well reflect the iterative detection performance of the SCMA system. It uses a one-dimensional complex constellation composed of multiple BPSK constellations. The constellation design is more flexible and the optimization space is larger than that of existing PAM and Star-QAM constellations, which is beneficial to further improve the BER performance of the codebook.

[0059] 2. The SCMA codebook design method based on the joint boundary provided by the present invention uses an unconstrained individual vector structure to perform global optimization on the codebook based on the constrained individual vector structure, which can further optimize the BER performance of the codebook;

[0060] 3. The SCMA codebook design method based on the joint boundary provided by the present invention generates a permutation matrix to optimize the constellation label, which can narrow the search space, reduce the amount of calculation, and improve the BER performance of the codebook;

[0061] 4. The SCMA codebook design method based on the joint boundary provided by the present invention incorporates the Latin matrix structure as an optimization parameter into the codebook optimization design, which helps to further improve the BER performance of the codebook. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 Figure 1 is a block diagram of an uplink SCMA system with J users.

[0063] Figure 2 is the factor graph corresponding to the factor graph matrix of the SCMA system;

[0064] Figure 3 Performance comparison chart of SCMA system using Latin matrix and Non-Latin matrix;

[0065] Figure 4 The BER performance comparison of two codebooks using Euclidean distance and joint bound as design indicators in AWGN channel is shown in the figure.

[0066] Figure 5 Schematic diagram of the individual vector structure in step 2 of the embodiment of the SCMA codebook design method based on the joint boundary provided by the present invention;

[0067] Figure 6 Schematic diagram of the globally optimized individual vector structure in step 6 of an embodiment of the SCMA codebook design method based on the joint boundary provided by the present invention;

[0068] Figure 7 This figure compares the BER performance of a codebook designed using the SCMA codebook design method based on the joint boundary provided in an embodiment of the present invention and other existing codebooks in an AWGN channel. DETAILED DESCRIPTION

[0069] In order to make the objects, advantages and features of the present invention more clear, the SCMA codebook design method based on the joint boundary proposed by the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0070] A joint-bound-based SCMA codebook design method includes the following steps:

[0071] Step 1: Determine the factor graph matrix based on the SCMA system parameters and generate L candidate Latin matrices and T permutation matrices of length M, where L, M, and T are all positive integers, T≤M!, M is the number of constellation points, and M is equal to a power of 2. The SCMA system parameters include the number of users J, the number of resource blocks K, the dimension of the multidimensional constellation N, and the number of users superimposed on each resource block d f , where J, K, N, d f are all positive integers. The multidimensional constellation dimension N refers to the number of non-zero vectors in the multidimensional constellation, each of which corresponds to a one-dimensional complex constellation. A one-dimensional complex constellation is an mBPSK constellation, which is composed of multiple BPSK constellations. Each one-dimensional complex constellation contains M constellation points.

[0072] like Figure 1 As shown in Figure 1, a block diagram of an uplink SCMA system with J users multiplexing K orthogonal resource blocks is shown. For the uplink SCMA system, all channel gain vectors in the AWGN channel are all 1 vectors, and the received signal is a K-dimensional complex vector y:

[0073]

[0074] Among them, x j =(x j [1],…,x j [K]) T , x j represents the codeword sent by user j, n is K-dimensional complex Gaussian noise; x j Is a sparse vector with only N non-zero components and the rest are zero components. The N non-zero components indicate that user j sends information to N resource blocks. It is the superposition of J user codewords, called superposition codeword.

[0075] In the uplink SCMA system, each user has a specific codebook. The codebook X of user j is j M sparse codewords are recorded in . The encoding function of user j is expressed as follows:

[0076]

[0077] Among them, u j is log2(M) information bits from user j.

[0078] As mentioned above, each user's codeword contains N non-zero components, and each resource block has N non-zero components. f The information of each user is superimposed together. This sparse connection relationship can be represented by a sparse matrix, called a factor graph matrix.

[0079] In this embodiment, the number of users superimposed on each resource block is d f The same, SCMA system parameters are M = 4, J = 6, K = 4, N = 2, d f =JN / K=3.

[0080] Each row of the factor graph matrix represents a resource block, and each column represents a user. Therefore, in this embodiment, the factor graph matrix has 4 rows and 6 columns, and each column has 2 non-zero components. In this embodiment, the factor graph matrix of the uplink SCMA system is:

[0081]

[0082] By utilizing the sparse characteristics of the system, the receiver of the uplink SCMA system can be implemented through the message passing algorithm. Figure 2 The figure shows the factor graph representation corresponding to the above factor graph matrix. The squares represent resource nodes, and the circles represent user nodes. The iterative receiver is implemented by passing information between the two types of nodes.

[0083] From the factor graph matrix and the corresponding factor graph representation, we can see that the codebook design for user j involves two factors: 1) selecting N non-zero components from K resource blocks; 2) designing a complex constellation for each non-zero component, with a total of N complex constellations.

[0084] The complex constellation corresponding to the N non-zero components in the user j codebook is g j , group the information into groups u j Enter the complex constellation and take one of the M constellation points from each complex constellation to form an N-dimensional complex vector g j (u j ). Using the mapping matrix V j , g j (u j ) is projected into the corresponding non-zero components to complete the encoding. Therefore, the encoding function of user j can also be written as:

[0085] x j =f j (u j )= V j g j (u j )

[0086] For convenience, the system structure of the SCMA system can be described as:

[0087]

[0088] Therefore, the design problem of the SCMA codebook can be defined as follows:

[0089]

[0090] Here, the function m(.) represents a design criterion. The SCMA codebook design described above is actually the joint optimization of multiple mapping matrices V and the multidimensional constellation G. Therefore, the SCMA codebook design problem is a multidimensional optimization problem, and its optimal solution is generally difficult to find. To reduce design complexity, a suboptimal multi-stage optimization strategy is often employed. This involves first optimizing the mapping matrix, or equivalently, the factor graph matrix, and then optimizing the multidimensional constellation.

[0091] Each user has its own specific mapping matrix, which determines which resource blocks a user shares. Therefore, the design of the mapping matrix is ​​equivalent to the design of the factor graph matrix. Assume that in the SCMA system, each user shares N of the K resource blocks, while avoiding having two different users share the same set of resource blocks. In this way, the SCMA system can accommodate at most users. In this case, the factor graph matrix is ​​a matrix consisting of all K-dimensional binary vectors containing N 1s. When K = 4 and N = 2, the total number of users is Each resource block is superimposed with d f =JN / K=signals of 3 users.

[0092] Therefore, the optimization problem of the SCMA codebook is simplified to the joint optimization problem of multiple multi-dimensional constellations, namely:

[0093]

[0094] Specifically, we need to find J K-dimensional complex constellations, each of which has only N non-zero components, and each non-zero vector corresponds to a one-dimensional complex constellation. Each complex constellation contains M constellation points.

[0095] The present invention uses a one-dimensional complex constellation composed of multiple BPSK constellations, called a multiple BPSK constellation (mBPSK). The one-dimensional complex constellation contains M constellation points, where M is a power of 2. The mBPSK constellation with parameter M is denoted as mBPSK-M. The mBPSK-M constellation is represented by the constellation points of M / 2 BPSK constellations, specifically:

[0096]

[0097] in, are the two constellation points of the i-th BPSK constellation;

[0098] α i is the amplitude parameter of the i-th BPSK constellation, α i >0;

[0099] is the phase parameter of the i-th BPSK constellation,

[0100] In order to simplify the design complexity, the present invention limits the use of the same three one-dimensional complex constellations on each resource block, denoted as S1, S2, and S3. Each element 1 in the factor graph matrix is ​​replaced with a one-dimensional complex constellation, and the three 1s in each row are replaced with S1, S2, and S3 respectively. The matrix G NLa and G La These are the matrices obtained under two different replacement methods:

[0101]

[0102]

[0103] Matrix G La In a matrix where there are no repeated elements in each row or column, it is called a Latin matrix. Figure 3 As shown, the SCMA system has system parameters J=6, K=4, N=2, d f = 3, the performance comparison of the Latin matrix and the Non-Latin matrix shows that the Latin matrix can achieve better performance than the Non-Latin matrix. The Latin matrix is ​​far superior to the Non-Latin matrix overall. Therefore, the Latin matrix is ​​used in the present invention.

[0104] Replace the non-zero components in the factor graph matrix with d f A one-dimensional complex constellation is selected so that the two elements in each column of the factor graph matrix are different and the three elements in each row are also different. Different replacement methods are selected to obtain 8 different candidate Latin matrices.

[0105] Each user's codebook contains N non-zero components, corresponding to N one-dimensional complex constellations. Each one-dimensional complex constellation contains M constellation points, and each constellation point corresponds to a group of information bits of length log2M. The correspondence between constellation points and information bit groups is called a label. Given N one-dimensional complex constellations, different labels will produce different codebooks. A permutation matrix is ​​used to adjust the labels of the BPSK constellations in the one-dimensional complex constellation. The method for generating the labels of the BPSK constellations in the one-dimensional complex constellation is:

[0106] The indices of the BPSK constellations in the first one-dimensional complex constellation are fixed, and the indices of the BPSK constellations in the other N-1 one-dimensional complex constellations are permuted accordingly using N-1 permutation matrices.

[0107] Step 2: Determine the individual vector structure. The length of an individual vector structure is (d f M+1+J(N-1)), such as Figure 5 As shown, it contains d f M real-valued parameters, and the remaining (1+J(N-1)) integer parameters, specifically:

[0108]

[0109] in, Represents the two parameters of the i-th BPSK constellation, α i is the amplitude parameter of the i-th BPSK constellation, is the phase parameter of the i-th BPSK constellation, i is a positive integer;

[0110] La is the Latin matrix index, which is used to select a specific Latin matrix from the eight candidate Latin matrices. ζ indicates the selected Latin matrix, and its value space is {0, 1, 2, 3, 4, 5, 6, 7};

[0111] int j is a permutation matrix index, which is used to specify the permutation form of the BPSK constellation label. A permutation matrix is ​​selected from the T permutation matrices generated in step 1. j is a positive integer. Each user has N-1 permutation matrix indices, and there are a total of J(N-1) integer parameters. In this embodiment, 8 different permutations are selected as candidate permutations. Each candidate permutation form is represented by an integer value, namely the permutation matrix index int j The value space is {0,1,2,3,4,5,6,7}.

[0112] This embodiment uses a genetic algorithm to optimize the SCMA codebook, where each individual represents J codebooks. To simplify the representation, J codebooks can be specified by f The one-dimensional complex constellation, Latin matrix structure, and labeling rules are determined. When the codebook size M is determined, each mBPSK-M constellation contains M constellation points, that is, M / 2 BPSK constellations, requiring M / 2 pairs of parameters to describe.

[0113] In this embodiment, each mBPSK-4 constellation is synthesized by two BPSK constellations, and each BPSK constellation needs to specify an amplitude parameter α i and a phase parameter The 3 mBPSK-4 constellations require a total of 12 real-valued parameters, where 0.1≤α i ≤10, An integer parameter ζ is required to indicate the selected Latin matrix. The system has 6 users, and each user requires N-1 permutation matrix indicators. Therefore, in this embodiment, a single individual is represented by a vector of length 19, of which 12 are used to specify the three mBPSK-4 constellations, 1 is used to indicate the Latin matrix, and 6 are permutation matrix indicators, expressed as:

[0114]

[0115] Step 3: Determine the genetic algorithm parameters and use the joint bound of the codebook BER performance as the objective function of the genetic algorithm. The genetic algorithm parameters include population size, number of elites, crossover probability, and number of evolution generations. In this embodiment, the genetic algorithm parameters are set as follows: population size is 400, number of elites is 40, crossover probability is 0.9, maximum number of evolution generations is 300, and other parameters use the default parameters.

[0116] The joint bound of the codebook BER performance is:

[0117]

[0118] Among them, v a and v b Represents two different superimposed codewords;

[0119] d 2 (v a ,v b ) is the squared Euclidean distance between two superimposed codewords;

[0120] B a,b Indicates v a and v b The number of different bits in the corresponding information packet;

[0121] E s The average symbol energy for each resource block;

[0122] N0 is the unilateral power spectral density of additive white Gaussian noise;

[0123] Q(x) is the tail distribution function of the standard normal distribution, u is the integrand variable.

[0124] The Euclidean distance between any two superimposed codewords describes the difficulty of misjudging one superimposed codeword as another superimposed codeword. The smaller the Euclidean distance, the easier it is to misjudge. However, the iterative detection performance of a codebook with a larger minimum Euclidean distance is not necessarily better than that of a codebook with a smaller minimum Euclidean distance. For the AWGN channel, with the minimum Euclidean distance as the design criterion, when the system parameters J = 6, K = 4, N = 2, d f=3, two codebooks of SCMA system are given, denoted as C DE and C GA .

[0125] As shown in Table 1, the distribution of the Euclidean distance of the two codebook superimposed codewords is compared, where d min,i Represents the i-th smallest Euclidean distance. The numbers in parentheses in Table 1 represent the logarithm of codewords with such Euclidean distance. The Euclidean distance here is accurate to the fourth decimal place.

[0126] Table 1

[0127] <![CDATA[d min ]]> <![CDATA[d min，2 ]]> <![CDATA[d min，3 ]]> <![CDATA[d min，4 ]]> <![CDATA[C DE ]]> 0.7695(16) 0.8732(32) 0.8766(32) 0.9080(4) <![CDATA[C GA ]]> 0.8660(512) 0.8661(2048) 0.8662(32) 0.8666(2112)

[0128] like Figure 4 As shown in the figure, the BER performance of the two codebooks under the message passing decoding algorithm is given. DE The minimum Euclidean distance is less than C GA , but C DE The BER performance is better than C GA As can be seen from Table 1, the codebook C GA The minimum Euclidean distance is greater than C DE The minimum Euclidean distance, but its corresponding coefficient is much larger than C DE The coefficient corresponding to the minimum Euclidean distance. In addition, in C GA The difference between the second smallest and third smallest Euclidean distance and the minimum Euclidean distance is very small, and in C DE The medium and small Euclidean distances are much larger than the minimum Euclidean distance, and their coefficients are all very small. This shows that simply maximizing the minimum Euclidean distance does not necessarily guarantee BER performance; the distribution of Euclidean distances, especially small Euclidean distances, and their corresponding coefficients have a significant impact on the overall performance of the codebook.

[0129] In addition to the minimum Euclidean distance, the SER obtained through simulation can also be directly used as a design metric, and the SCMA codebook can be optimized using a differential evolution algorithm. Although the SER performance can accurately reflect the actual performance of the system, obtaining an accurate SER through simulation requires a considerable amount of simulation time. Therefore, when using the differential evolution algorithm for optimization, a large population size is usually used. In this way, although a global optimization algorithm is used, it is often difficult to obtain a codebook with particularly excellent performance due to the limited population size.

[0130] Therefore, it is particularly important to select design indicators with low computational complexity and that can well reflect the SCMA system. Figure 4 At the same time, the union bound and simulation results of the two codebooks CDE and CGA in AWGN channel are compared. Figure 4It can be seen that in the high signal-to-noise ratio region, the joint bound and the simulation results are basically consistent, indicating that the joint bound is more suitable as a design indicator than the minimum Euclidean distance between superimposed codewords. In addition, the computational complexity of the joint bound is much lower than the computational complexity of the SER obtained by simulation, and it can well reflect the iterative detection performance of the SCMA system. Therefore, in this embodiment, the joint bound of the BER performance of the SCMA system is used as the design indicator.

[0131] Step 4: Based on the genetic algorithm parameters determined in step 3, an initial population is generated according to the individual vector structure obtained in step 2.

[0132] Step 5: Based on the genetic algorithm objective function determined in step 3, the genetic algorithm is used to optimize the initial population obtained in step 4 to obtain the optimal codebook Exp1 as shown below:

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139] Step 6: To further improve the codebook performance, this embodiment uses Exp1 as the initial solution and uses a genetic algorithm for global optimization to obtain a further optimized optimal codebook, specifically:

[0140] 6.1. Determine the globally optimized individual vector structure, specifically:

[0141]

[0142] In this step, each user is allowed to use a different mBPSK-4 constellation, so a total of 12 mBPSK-4 constellations need to be designed. At this time, the vector corresponding to a single individual contains JNM=48 parameters, and the globally optimized individual vector structure is as follows: Figure 6 shown.

[0143] It should be noted that the globally optimized individual vector structure given in this step was not initially adopted because it has far more parameters than the individual vector structure in step 2. Generally speaking, as the number of parameters increases, the required initial population size must also be increased accordingly; otherwise, the optimization results are likely to fall into a local optimum. Therefore, here we first use a constrained codebook individual vector structure to reduce the number of optimized parameters. Then, based on the resulting optimized codebook, we use an unconstrained codebook individual vector structure to further optimize codebook performance.

[0144] 6.2. Determine the parameters of the genetic algorithm and determine the joint bound of the codebook BER performance as the genetic algorithm objective function. The genetic algorithm parameters include population size, number of elites, crossover probability, and evolutionary generations.

[0145] 6.3. Based on the genetic algorithm parameters determined in step 6.2 and the globally optimized individual vector structure determined in step 6.1, a globally optimized initial population is generated on the basis of the optimal codebook obtained in step 5.

[0146] 6.4. Based on the genetic algorithm objective function determined in step 6.2, the genetic algorithm is used to perform global optimization on the global optimization initial population obtained in step 6.3 to obtain the further optimized optimal codebook Exp1i, as shown below:

[0147]

[0148]

[0149]

[0150]

[0151]

[0152]

[0153] Table 2 compares the parameters of two codebooks designed using the codebook design method provided by this embodiment and codebooks in the literature.

[0154] Table 2

[0155]

[0156]

[0157] like Figure 7 As shown in FIG. 1 , a performance comparison diagram of two codebooks designed using the codebook design method provided in this embodiment and a codebook in the literature in an AWGN channel is shown. Figure 7 It can be seen that the performance of the codebook designed using the method of this embodiment is better than other codebooks.

Claims

1. A SCMA codebook design method based on joint bounds, characterized in that: The following steps are involved: Step 1: Determine the factor graph matrix based on the SCMA system parameters and generate L candidate Latin matrices and T permutation matrices of length M, where L, M, and T are all positive integers, T≤M!, and M is the number of constellation points, which is a power of 2. The SCMA system parameters include the number of users J, the number of resource blocks K, the multidimensional constellation dimension N, the number of users superimposed on each resource block d f , where J, K, N, d f are all positive integers; The multidimensional constellation dimension N means that the multidimensional constellation includes N non-zero vectors; each non-zero vector corresponds to a one-dimensional complex constellation, the one-dimensional complex constellation is an mBPSK constellation, the mBPSK constellation is composed of multiple BPSK constellations, and each one-dimensional complex constellation contains M constellation points; Step 2: Determine the individual vector structure, specifically: in, Represents the two parameters of the i-th BPSK constellation, α i is the amplitude parameter of the i-th BPSK constellation, is the phase parameter of the i-th BPSK constellation, i is a positive integer; La is the Latin matrix index, which is used to select a specific Latin matrix from L candidate Latin matrices; int j is the permutation matrix index, which is used to specify the permutation form of the BPSK constellation label. Select a permutation matrix from the T permutation matrices generated in step 1. j is a positive integer. Step 3: Determine the joint bound of the codebook BER performance as the genetic algorithm objective function, and set the genetic algorithm parameters; the genetic algorithm parameters include population size, number of elites, crossover probability and evolutionary generations; Step 4: Based on the genetic algorithm parameters determined in step 3, an initial population is generated according to the individual vector structure obtained in step 2; Step 5: Based on the genetic algorithm objective function determined in step 3, the genetic algorithm is used to optimize the initial population obtained in step 4 to obtain the optimal SCMA codebook.

2. The SCMA codebook design method based on joint bounds according to claim 1, characterized in that Also includes step 6: Step 6: Based on the optimal SCMA codebook obtained in step 5, a genetic algorithm is used for global optimization to obtain a further optimized optimal SCMA codebook, specifically: 6.

1. Determine the globally optimized individual vector structure, specifically: 6.

2. Determine the genetic algorithm parameters and determine the joint bound of the optimal SCMA codebook BER performance as the genetic algorithm objective function; 6.

3. Based on the genetic algorithm parameters determined in step 6.2, and the globally optimized individual vector structure determined in step 6.1, a globally optimized initial population is generated based on the optimal SCMA codebook obtained in step 5; 6.

4. Based on the genetic algorithm objective function determined in step 6.2, the genetic algorithm is used to perform global optimization on the global optimization initial population obtained in step 6.3 to obtain a further optimized optimal SCMA codebook.

3. The SCMA codebook design method based on joint bounds according to claim 1 or 2, characterized in that In step 3, the joint bound of the codebook BER performance is: Among them, v a and v b Represents two different superimposed codewords; d 2 (v a ,v b ) is the squared Euclidean distance between two superimposed codewords; B a,b Indicates v a and v b The number of different bits in the corresponding information packet; E s The average symbol energy for each resource block; N0 is the unilateral power spectral density of additive white Gaussian noise; Q(x) is the tail distribution function of the standard normal distribution, u is the integrand variable.

4. The SCMA codebook design method based on joint bounds according to claim 3, characterized in that In step 1, the number of users superimposed on each resource block is d f Same, d f =JN / K.

5. The SCMA codebook design method based on joint bounds according to claim 4, characterized in that In step 1, the permutation matrix is ​​used to adjust the index of the BPSK constellation in the one-dimensional complex constellation; The method for generating the label of the BPSK constellation in the one-dimensional complex constellation is specifically as follows: The indices of the BPSK constellations in the first one-dimensional complex constellation are fixed, and the indices of the BPSK constellations in the other N-1 one-dimensional complex constellations are permuted accordingly using N-1 permutation matrices.

6. The SCMA codebook design method based on joint bounds according to claim 5, characterized in that In step 1, the generation of L candidate Latin matrices is specifically as follows: Replace the non-zero components in the factor graph matrix with d f One-dimensional complex constellation, so that the N elements in each column of the factor graph matrix are different, and the d elements in each row are different. f The elements are also different. By choosing different replacement methods, we can obtain L different candidate Latin matrices.

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