Phase noise resistant codebook optimization method and system based on sparse code division multiple access

Abstract

The application discloses a sparse code division multiple access (SCMA) based phase noise resistant codebook optimization method and system, relates to the Internet of Things technology, and comprises the following steps: creating a one-dimensional basic constellation; generating an N-dimensional mother constellation by permutation and combination according to the created one-dimensional basic constellation, so as to form a plurality of sparse codebooks; and optimizing the plurality of sparse codebooks, so that the plurality of sparse codebooks maximize the minimum phase noise distance and improve the performance of the system in the presence of phase noise. The phase noise resistant codebook optimization method can improve the bit error rate performance of the SCMA system in the presence of phase noise.

Description

Technical Field

[0001] The present application relates to the field of Internet of Things technology, and in particular to a method and system for optimizing a phase noise-resistant codebook based on sparse code division multiple access. Background Art

[0002] With the rapid development of the Internet of Things (IoT), traditional orthogonal multiple access (OMA) technologies are no longer able to meet the growing connectivity demands and spectrum resource constraints. To improve spectrum efficiency and user capacity, non-orthogonal multiple access (NOMA) technologies have emerged. Sparse code division multiple access (SCMA), a code-domain NMA technology, has attracted considerable attention due to its unique advantages.

[0003] SCMA technology effectively improves system spectral efficiency by combining high-dimensional modulation with sparse spread spectrum. In SCMA systems, user signals are non-orthogonal in codebook design, allowing multiple users to be served on the same resource block, thereby improving spectrum resource utilization. To further optimize the SCMA codebook, researchers have proposed various methods. For example, by studying the pairwise error probability over Gaussian and Rayleigh fading channels, researchers aim to maximize the minimum Euclidean distance and minimum product distance of the mother constellation or codebook. Following this design principle, researchers have proposed an SCMA codebook design method based on a uniquely decomposable constellation group. This method maximizes the minimum Euclidean distance while maintaining the minimum product distance as large as possible to achieve a power-imbalanced codebook. SCMA codebook design has also been studied in Rician fading channels. Research has proposed new codebooks for both uplink and downlink Rician fading channels. Generally speaking, existing SCMA codebooks are mostly optimized for specific wireless channel conditions, but pay little attention to hardware impairments. For SCMA-based IoT systems, supporting information exchange between low-cost and low-end communication devices is particularly important. Moreover, the traditional SCMA codebook design does not fully consider the impact of phase noise, which is an important hardware damage factor in actual communication systems. Summary of the Invention

[0004] The embodiments of the present application provide a phase noise-resistant codebook optimization method and system based on sparse code division multiple access to improve the bit error rate performance of the SCMA system in the presence of phase noise.

[0005] The present invention provides a method for optimizing a phase noise-resistant codebook based on sparse code division multiple access, including:

[0006] Create a one-dimensional basic constellation diagram;

[0007] Based on the created one-dimensional basic constellation diagram, an N-dimensional mother constellation is generated through permutations and combinations to form multiple sparse codebooks;

[0008] The multiple sparse codebooks are optimized so that the multiple sparse codebooks maximize the minimum phase noise distance and improve the performance of the system in the presence of phase noise.

[0009] An embodiment of the present application also proposes a phase noise-resistant codebook optimization system based on sparse code division multiple access, including a processor and a memory, wherein a computer program is stored on the memory, and when the computer program is executed by the processor, the steps of the aforementioned phase noise-resistant codebook optimization method based on sparse code division multiple access are implemented.

[0010] The phase noise-resistant codebook optimization method of the embodiment of the present application can improve the bit error rate performance of the SCMA system in the presence of phase noise.

[0011] The above description is only an overview of the technical solution of the present application. In order to more clearly understand the technical means of the present application, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Various other advantages and benefits will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiment below. The accompanying drawings are for illustration purposes only and are not to be considered as limiting the present application. The same reference symbols are used throughout the drawings to represent the same components. In the drawings:

[0013] Figure 1 SCMA factor graph (K=4, J=6) of the embodiment of the present application;

[0014] Figure 2 This is a schematic diagram of the basic process of the phase noise-resistant codebook optimization method according to an embodiment of the present application;

[0015] Figure 3 、 4 The anti-phase noise codebook optimization method proposed in this application embodiment and Example;

[0016] Figure 5 This is an illustration of the bit error rate performance of different codebooks under the influence of different phase noises in the application example of this application. DETAILED DESCRIPTION

[0017] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0018] Analysis of the Impact of Phase Noise on Communication Performance

[0019] Consider a K×J SCMA system where J users communicate through K resource nodes (RNs). The overload factor is defined as λ = J / K > 100%. In SCMA, each user is assigned a unique codebook, denoted as Contains M codewords of dimension K. At the base station (BS) side, each SCMA encoder maps log2M binary bits to a sparse complex codeword x of length K. j =[x j,1 ,x j,2 ,…,x j,K ] T , from the codebook Each codeword has only N non-zero elements, and the positions of non-zero elements remain unchanged in the codebook. In this way, a sparse system can be represented by a factor graph that illustrates the sharing of RNs among multiple user nodes (UNs). A SCMA factor graph with K = 4 and J = 6 is shown as Figure 1 shown.

[0020] For the downlink SCMA system, the user's data is superimposed at the BS to form a superimposed constellation. Among them is M J Different superimposed code words. Indicates superimposed codewords.

[0021] Considering a Gaussian channel, the received signal affected by unknown phase noise can be expressed as

[0022] r=we jθ +n (1)

[0023] in Represents the received signal vector, n=[n1,...,n K ] T represents a noise vector whose elements Represents the phase error vector, which has zero mean and variance Gaussian distribution, that is By exploiting codebook sparsity, the message passing algorithm (MPA) can be used for low-complexity decoding with error performance close to that of a maximum likelihood receiver.

[0024] For the communication model in formula (1), the likelihood based on the received signal is expressed as:

[0025]

[0026] in represents the received codeword obtained by excluding the kth symbol, and the posterior probability density function of the phase noise is given by Given. Then the maximum likelihood decision of the received superimposed codeword can be expressed as:

[0027]

[0028] In the latter example, an approximate expression for the likelihood (2) is further given to achieve the performance of an approximate maximum likelihood receiver when designing the SCMA codebook.

[0029] The embodiment of the present application proposes a phase noise resistant codebook optimization method based on sparse code division multiple access, such as Figure 2 Shown, including:

[0030] In step S101, a one-dimensional basic constellation diagram is created;

[0031] In step S102, an N-dimensional mother constellation is generated by permutation and combination according to the created one-dimensional basic constellation diagram to form a plurality of sparse codebooks.

[0032] In step S103, the multiple sparse codebooks are optimized so that the multiple sparse codebooks maximize the minimum phase noise distance and improve the performance of the system in the presence of phase noise.

[0033] In the specific example of this application, the sparse codebook design principles when phase noise exists include:

[0034] A. Maximum likelihood decision rule based on phase error

[0035] To derive the maximum likelihood decision, formula (2) is reformulated as follows:

[0036]

[0037] Before calculating formula (4), the approximate expression of the received signal r is proposed as follows:

[0038]

[0039] Wherein step (i) is performed by using the approximation Obtained, r k represents the kth element of vector r, Usually, with The smaller the value of , the better the approximation effect of step (i). In essence, r k It can be expressed as a two-tuple containing real and imaginary parts [μ k ,ν k ],in The probability density function of this binary is a function of w k The bivariate Gaussian distribution pdf conditional on is expressed as

[0040]

[0041] The covariance is

[0042]

[0043] The conditional probability density function of r given w is:

[0044]

[0045] After taking the negative logarithm of (8), the maximum likelihood decision rule is expressed as:

[0046]

[0047] B. Pairwise Error Probability Analysis of SCMA Affected by Phase Noise

[0048] Due to the influence of phase noise and Gaussian noise, it is assumed that the transmitted signal w∈Φ is incorrectly decoded into another codeword use represents w and The pairwise error probability (PEP) between the two, then the average PEP, denoted as P e The upper bound of can be expressed as:

[0049]

[0050] Furthermore, by utilizing the maximum likelihood decision rule derived above, the probability of a pairwise error event can be expressed as:

[0051]

[0052] Formula (11) means that when an error decoding occurs, the performance metric Becomes smaller than L w For the likelihood in formula (9), in the definition after, and The difference between can be expressed as:

[0053]

[0054] Given the transmitted superimposed codeword w, according to equation (5), the real and imaginary parts of the received signal r are expressed as follows:

[0055]

[0056] in, Substituting formula (13) into (12), we can get:

[0057]

[0058] The exact expressions of V1 and V2 can be found in equation (12). The mean values ​​of V1 and V2 are given by:

[0059]

[0060] Therefore, given w k Under the condition η k The mean and covariance of are given as:

[0061]

[0062] in,

[0063]

[0064] Using formula (17), we can get the probability of paired error events:

[0065]

[0066] in, and Gauss Function. Substituting (19) into formula (10), the upper bound of the average PEP is:

[0067]

[0068] (20) The function's parameters can be viewed as a standardized distance metric, called the phase noise distance (similar to the Euclidean distance in additive white Gaussian noise (AWGN)), which can be used to determine the nearest codeword in the presence of phase noise. To construct the optimal codebook, we want to maximize the minimum phase noise distance, i.e.:

[0069]

[0070] This application proposes a phase noise-resistant sparse codebook design based on the proposed minimum phase noise distance metric, including: generating a one-dimensional basic constellation diagram, constructing an N-dimensional mother constellation, and optimizing multiple sparse codebooks by maximizing the minimum phase noise distance.

[0071] In some embodiments, creating a one-dimensional base constellation diagram includes:

[0072] Let the length be M, a one-dimensional LP-PAM constellation It consists of T different elements and MT overlapping points. The vector of length T is constructed as follows

[0073] For even number T, T PAM points are generated, and even number T one-dimensional PAM constellation Expressed as:

[0074]

[0075] Among them, ±r x, (x=1,2,…,T / 2) represents the xth group of symmetrical points in the PAM constellation diagram.

[0076] For odd T, generate T-1 PAM points and add the origin to middle;

[0077] Prioritize constellation points with lower energy and ensure that the resulting set Meet the symmetry requirement, so that There are MT points overlapping.

[0078] In some embodiments, generating an N-dimensional mother constellation through permutations and combinations based on the created one-dimensional basic constellation diagram includes:

[0079] Based on the obtained one-dimensional LP-PAM constellation Use the following method to pass to obtain the remaining N-1 dimensions:

[0080] Let π n Represents the permutation mapping of the nth dimension, then the N-dimensional mother constellation satisfy:

[0081]

[0082] The goal is to find N permutations π n , for n=1,2,…,N, to maximize The minimum Euclidean distance of the present invention is obtained by using a binary exchange algorithm. n , n=1,2,…,N, to maximize The minimum Euclidean distance.

[0083] In a specific example, Figure 3 、 Figure 4 The proposed and For example, α1=r2 / r1 is a parameter that needs to be optimized.

[0084] In some embodiments, optimizing the plurality of sparse codebooks includes:

[0085] According to the obtained N-dimensional mother constellation Phase rotation and energy scaling are used to generate multiple sparse codebooks to enhance the distance property of superimposed codewords.

[0086] In some embodiments, according to the obtained N-dimensional mother constellation Generating multiple sparse codebooks using phase rotation and energy scaling includes:

[0087] The sparse codebook of user j is designed as In order to simplify this application, a constellation operation matrix Ψ is defined j =E j R j , where R j and E j Denote the phase rotation matrix and power scaling matrix of user j respectively. For an N=2 E j and R j It can be expressed as:

[0088]

[0089] in, The codebook of user j can be obtained by Generate, where V j It is a binary mapping matrix that maps the N-dimensional dense constellation to the K-dimensional sparse codebook.

[0090] The constellation operation matrix Ψ j and the mapping matrix V j Combine, that is, V j =V j Ψ j ,for Figure 1 In the SCMA system given in , the mapping matrix is ​​designed as follows:

[0091]

[0092] Based on the proposed multi-dimensional codebook construction scheme, the design of the sparse codebook satisfies:

[0093]

[0094] Among them, α m =r m+1 / r1∈(1,+∞),m=1,2,…,T / 2-1.

[0095] Since the objective function is non-convex, in some embodiments, it also includes using a numerical global search method to solve the design of the sparse codebook, that is, solving formula (26).

[0096] This application example numerically evaluates the proposed phase noise-resistant codebooks (PNCBs). In addition to considering the SCMA system with K=4, J=6, a larger-scale SCMA system such as K=5, J=10 is also considered in this example. Given that the proposed standard is designed for high bit energy / noise power density (Eb / N0), this example selects Eb / N0=14dB as the optimization condition. The PNCBs with T=2 and T=3 designed for M=4, λ=150% are named PNCB1 and PNCB2, respectively. The PNCBs with T=4 and T=5 designed for M=8, λ=150% are named PNCB3 and PNCB4, respectively, and the PNCBs with T=2 and T=3 designed for M=4, λ=200% are named PNCB5 and PNCB6, respectively. For comparison, the GAM codebook, StarQAM codebook, and Huawei codebook are further considered.

[0097] The results show that the minimum phase noise distance (MPND) value of the proposed codebook is greater than that of other codebooks. It is worth noting that the codebook with a larger MPND value has an improved bit error rate (BER) performance. The minimum phase noise distance values ​​in Table 1 are Figure 3 The BER performance shown is consistent.

[0098] Table 1 Minimum phase noise distance values ​​for different codebooks

[0099]

[0100] Figure 5 Figure a compares the BER performance of different codebooks under different phase noise levels with M = 4 and λ = 150%. For σ2p = 0.001, the proposed PNCB1 and PNCB2 have the best BER performance at BER = 10 -4 The proposed PNCB2 achieves the best BER performance among all codebooks for a larger phase noise σ2p=0.03, while the proposed PNCB2 achieves the best BER performance over the StarQAM codebook for a larger phase noise σ2p=0.03. Figure 5 Zhongb and Figure 5 Figure c compares the BER performance of different codebooks under different phase noise levels of M=8, λ=150% and M=4, λ=200%. Figure 5 As can be seen in Figure b, the performance of the proposed PNCB3 and PNCB4 is better than other codebooks under σ2p = 0.01 and σ2p = 0.001. Figure 5In middle c, the performance gain of the proposed PNCB5 is more significant, at BER=10 -3 When σ2p = 0.001 and σ2p = 0.01, the performance gains of about 2.5 and 5 dB are achieved respectively compared with the GAM codebook.

[0101] This application proposes the minimum phase noise distance as a new distance metric for optimizing SCMA codebook design in the presence of phase noise. A low-projection mother constellation (LP-MC) based on pulse amplitude modulation (PAM), called LP-PAM, is used to design a phase noise-resistant codebook.

[0102] This application obtains a new type of sparse codebook that is resistant to phase noise by maximizing the proposed minimum phase noise distance.

[0103] An embodiment of the present application also proposes a phase noise-resistant codebook optimization system based on sparse code division multiple access, including a processor and a memory, wherein a computer program is stored on the memory, and when the computer program is executed by the processor, the steps of the aforementioned phase noise-resistant codebook optimization method based on sparse code division multiple access are implemented.

[0104] It should be noted that, in the various embodiments of the present application, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or apparatus comprising the element.

[0105] The serial numbers of the above embodiments of the present application are for description only and do not represent the advantages or disadvantages of the embodiments.

[0106] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus the necessary general hardware platform, and of course can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk), and includes a number of instructions for enabling a terminal (which can be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in each embodiment of the present application.

[0107] The embodiments of the present application are described above in conjunction with the accompanying drawings, but the present application is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of this application, ordinary technicians in this field can also make many forms without departing from the purpose of this application and the scope of protection of the claims, all of which are protected by this application.

Claims

1. A phase noise-resistant codebook optimization method based on sparse code division multiple access, characterized in that: include: Create a one-dimensional basic constellation diagram; Based on the created one-dimensional basic constellation diagram, an N-dimensional mother constellation is generated through permutations and combinations to form multiple sparse codebooks; Optimizing multiple sparse codebooks so that the multiple sparse codebooks maximize the minimum phase noise distance and improve the performance of the system in the presence of phase noise; According to the obtained N-dimensional mother constellation , using phase rotation and energy scaling to generate multiple sparse codebooks includes: The sparse codebook of user j is designed as , define the constellation operation matrix ,in and denote the phase rotation matrix and power scaling matrix of user j respectively; The constellation operation matrix and the mapping matrix Combine, that is ; Then the design of the sparse codebook satisfies: in, ; represents the power scaling factor in the i-th dimension, represents the phase rotation angle in the i-th dimension; Where MPND(X) represents the minimum phase noise distance, represents the codebook size, K represents the number of resource nodes, Indicates that a given codeword is sent Mistakenly judged as Under the condition of The conditional expectation of Indicates that a given codeword is sent Mistakenly judged as Under the condition of The conditional variance of 、 Represents a superposition codeword, belonging to the superposition constellation set Two different code words in .

2. The method for optimizing a phase noise-resistant codebook based on sparse code division multiple access according to claim 1, wherein: Creating a basic one-dimensional constellation diagram involves: Let the length be M, a one-dimensional LP-PAM constellation It consists of T different elements and MT overlapping points. The vector of length T is constructed as follows ; For even T, T PAM points are generated. For even T, a one-dimensional PAM constellation Expressed as: in, Indicates the first Group symmetry points; For odd T, generate T-1 PAM points and add the origin to middle; Prioritize constellation points with low energy and ensure that the result set Meet the symmetry requirement, so that There are MT points overlapping.

3. The method for optimizing a phase noise-resistant codebook based on sparse code division multiple access according to claim 2, wherein: Based on the created one-dimensional basic constellation diagram, the N-dimensional mother constellation is generated through permutations and combinations including: Based on the obtained one-dimensional LP-PAM constellation , using the following method through to obtain the remaining N-1 dimensions: set up Represents the permutation mapping of the nth dimension, then the N-dimensional mother constellation satisfy: Using the binary exchange algorithm, find N permutations , , to maximize The minimum Euclidean distance.

4. The method for optimizing a phase noise-resistant codebook based on sparse code division multiple access according to claim 2, wherein: Optimizing multiple sparse codebooks includes: According to the obtained N-dimensional mother constellation ,phase rotation and energy scaling are used to generate multiple sparse codebooks to enhance the distance characteristics of superimposed codewords.

5. The method for optimizing a phase noise-resistant codebook based on sparse code division multiple access according to claim 1, wherein: It also includes the design of sparse codebook using numerical global search methods.

6. A phase noise-resistant codebook optimization system based on sparse code division multiple access, characterized in that: The method comprises a processor and a memory, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the anti-phase noise codebook optimization method based on sparse code division multiple access are implemented as described in any one of claims 1 to 5.

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