Subspace-constrained grant-free massive-mimo active user and channel joint estimation method

Abstract

A subspace-constrained unlicensed large-scale MIMO active user and channel joint estimation method is proposed. Under the GEC framework, the subspace strategy is integrated, and matrix inversion operations within the subspace are used to replace matrix inversion operations in the full-dimensional space. The low-precision quantized uplink received signal matrix received by the base station is iteratively processed to achieve joint channel estimation and user active state estimation, which greatly reduces the computational complexity of the algorithm. In addition, by modeling the hybrid channel as mutually independent conditional distributions, the channel column correlation is decoupled using cyclic belief propagation (LBP), thereby enabling parallel operation of hybrid channel posterior mean estimation, which greatly reduces the algorithm's running time.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication and signal processing technology, and in particular to a method for joint estimation of active users and channels in subspace-constrained unlicensed massive MIMO, specifically a method for joint estimation of active users and channels in an unlicensed massive MIMO uplink system equipped with a low-precision converter (ADC) at the receiver. Background Technology

[0002] Massive Machine-Type Communication (mMTC) is one of the representative scenarios for sixth-generation mobile communication systems and even future wireless communication systems. The main characteristics of this scenario are a massive number of user equipments within a single cell, but only a small number of potential user equipments are active within the same coherent time interval, and any device accesses the system network in an unlicensed manner. Due to the advantages of channel capacity and spectral efficiency of Massive Multiple-Input Multiple-Output (MIMO) technology, it is typically used to support this scale of massive connections. The core challenge of unweighted massive MIMO systems is the joint estimation of active users and the channel, which is modeled as a multiple measurement vector (MMV) problem.

[0003] To address this joint estimation problem, many novel algorithms have been proposed, such as message passing algorithms and greedy iterative algorithms. Message passing algorithms are inference algorithms based on bidirectional graph models in information theory. This method is known as the cavity method in statistical physics or statistical mechanics, and as the belief propagation algorithm in computational science. Donoho et al. proposed the Approximate Message Passing (AMP) algorithm by simplifying the message updated by the message passing algorithm using Gaussian approximation. This algorithm has been verified to achieve Bayesian optimal performance under independent and identically distributed (iid) Gaussian measurement matrices. Subsequently, many algorithms have extended the AMP algorithm for single-measurement vector problems to the MMV scenario, such as AMP-MMV, hybrid generalized approximate message passing, and generalized AMP-MMV. Although these algorithms inherit the efficient computational complexity and accuracy of the AMP algorithm, they may experience performance degradation or even divergence when the pilot matrix is ​​non-Gaussian, such as the Hadamard and Zadoff-Chu pilot sequences. In contrast, the Vector Approximate Message Passing (VAMP) algorithm is suitable for right-rotation invariant pilot matrices, and its applicability is wider than that of iid Gaussian pilot matrices. VAMP, along with the Expectation Propagation Algorithm, Expectation Consistency Algorithm, and Orthogonal Approximate Message Passing Algorithm, were proposed successively based on different principles, but are essentially equivalent. Rangan, in his paper "S. Rangan, P. Schniter, and AK Fletcher, 'Vector approximate message passing,' IEEE Trans. Inf. Theory, vol. 65, no. 10, pp. 6664–6684, 2019," proposed a vector message update rule, derived the VAMP algorithm, and rigorously analyzed its dynamic performance. Generalized Expectation Consistency Signal Recovery (GEC-SR) further extends VAMP to generalized linear models. However, both GEC-SR and VAMP algorithms involve large-scale matrix inversion operations, resulting in significantly higher computational complexity than the AMP algorithm. In contrast, greedy iterative algorithms, such as matching pursuit, orthogonal matching pursuit, and piecewise orthogonal matching, recover the target signal within a specific subspace. However, greedy iterative algorithms cannot utilize prior information about the signal to improve estimation accuracy. To reduce computational complexity, an intuitive approach is to introduce the subspace strategy into the Generalized Expectation Consistency (GEC) framework, thereby improving the algorithm's practicality by reducing the dimension of matrix inversion.

[0004] Therefore, in unweighted large-scale MIMO uplink systems equipped with low-precision quantization, in order to reduce the matrix inversion operation of VAMP-like algorithms, it is necessary to combine the GEC framework and subspace strategy to design a joint estimation algorithm for active users and channels. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention aims to provide a method for joint estimation of active users and channels in subspace-constrained unlicensed large-scale MIMO. Under the GEC framework, a subspace strategy is integrated, and matrix inversion within the subspace is used to replace matrix inversion in the full-dimensional space. This iteratively processes the low-precision quantized uplink received signal matrix received by the base station, achieving joint channel estimation and user activity state estimation, significantly reducing the computational complexity of the algorithm. Furthermore, by modeling the hybrid channels as mutually independent conditional distributions and using cyclic belief propagation (LBP) to decouple channel column correlations, parallel computation of the hybrid channel posterior mean estimation is achieved, greatly reducing the algorithm's runtime.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: A subspace-constrained, unlicensed, large-scale MIMO active user and channel joint estimation method includes the following steps: Step 1: Model the unlicensed massive MIMO uplink system and transform it into a multi-measurement vector problem to obtain the minimum mean square error (MMSE) estimate of the channel matrix and the log likelihood ratio (LLR) of active users, which are used to determine the user's active status. Step 2: Using three modules within the GEC framework, the subspace strategy and cyclic belief propagation are integrated to iteratively approximate the MMSE estimation of the target channel matrix and the LLR of active users based on the modeling in Step 1.

[0007] The modeling in step one specifically involves: (1.1) First, the unlicensed massive MIMO uplink system of a single cell and a single base station is modeled as follows:

[0008] in, For complex-valued uniform quantizers, L The pilot length, This refers to the number of base station antennas. It is an additive Gaussian matrix whose elements are independent and follow a mean of 0 and a variance of 0. Gaussian distribution, For the channel matrix, The number of users in the community. For the first Channels for individual users For the first The real channel of each user Indicates the first The activation status of each user, and their activity probability is: The support set of active users is defined as follows: The goal of this modeling is to, given the pilot matrix Under the condition of observation matrix Recovering the channel matrix and support set ; (1.2) Based on the characteristics of sporadic user activity in unlicensed large-scale MIMO scenarios, the channel matrix is... Modeled as a conditionally independent distribution:

[0009] in For Dirac delta function, The channel matrix is ​​a complex Gaussian distribution. The joint distribution is obtained through the independent distribution. The result is obtained by integration; x nm It is the element in the nth row and mth column.

[0010] (1.3) Based on the modeling of (1.1)-(1.2), the channel matrix is ​​estimated within the Bayesian framework to detect the active user support set, that is, the MMSE estimation of the hybrid channel matrix is ​​adopted to achieve the optimal Bayesian MSE performance:

[0011] in Includes multiple integration operations. Indicates except outside The set of the remaining elements in the set, the likelihood function ,in To quantize the Gaussian distribution; The following formula, Log-Likelihood Ratio (LLR), is used to detect active users:

[0012] in and These represent the user being in an active state and the user being in an inactive state, respectively, with marginal probabilities. It can be obtained by marginalizing the joint posterior probability.

[0013] Step two is specifically implemented through three modules: Module A, Module C, and Module B. Module A is The MMSE node module, in which express The The column is based on the approximate prior information provided by module C. Likelihood function of the real model ,implement MMSE estimation of nodes, obtain Then, eliminate external information. ,get Approximate likelihood information of nodes This information will be passed forward to module C as external information, that is... The operation to eliminate external information is defined as follows: ; Module C is a subspace module, based on subspace. Constraints, Solving MMSE of the node ( )or MMSE of the node ( ),in For set The indexed submatrices and vectors, They are respectively The The column uses the estimated support set obtained from the previous iteration. Approximate likelihood information based on module A and approximate prior information of module B. In subspace Solve the following optimization problem under constraints:

[0014] During the forward message passing process, execution Operation, obtain The MMSE of a node, i.e. Then eliminate external information To obtain the approximate likelihood function This information will be passed to module B as external information. During the reverse message passing process, execution will take place. Operation, obtain The MMSE of a node, i.e. Then eliminate external information. To obtain approximate prior information This information will be passed to module A as external information.

[0015] Module B is The node MMSE module and the support set detection module, combined with the approximate likelihood information from module C. implement MMSE estimation, decoupled by LBP By analyzing column correlation, an approximate value of the sparsity of elements can be obtained. Such that the row-independent prior distributions Transformed into an element-independent prior distribution To facilitate parallel computation, this is based on an approximate prior distribution. The approximate likelihood function passed by module C ,calculate MMSE, that is Then, by eliminating external information, it was obtained The approximate prior distribution of the nodes, this information will be passed to module C as external information, i.e. Meanwhile, based on the approximate likelihood function provided by module C... Calculate the LLR of user activity states and obtain an estimate of the support set based on the LLR. ; The algorithm executes in the iterative order of module A -> module C1 -> module B -> module C2 -> module A -> ... until the maximum number of iterations is reached. Alternatively, if the error of the MMSE estimator is less than the preset error, the algorithm stops iterating and outputs the result. and .

[0016] The module C is constrained by the subspace. Next, solve the optimization problem C1 to obtain... The linear minimum mean square error estimate (LMMSE) is specifically expressed as follows:

[0017] Due to submatrix The dimension is The computational complexity of the above formula is . ,in The length of the estimated support set, This reduces computational complexity.

[0018] Module B calculates the LLR of user activity states and obtains an estimate of the support set based on the LLR. The true LLR can be approximated by the following formula:

[0019] LLR is used to determine the user's activity level. At that time, the judgment was When a user is active, At that time, the judgment was The number of users is inactive, thus providing an estimate of the support set. .

[0020] Compared with the prior art, the present invention has at least the following beneficial effects: 1. Step two of this invention utilizes a subspace strategy through three modules, which significantly reduces the computational complexity of the existing GEC-SR-MMV algorithm and improves the algorithm's convergence speed.

[0021] 2. Step two of this invention decouples the column correlation of the channel matrix through LBP iteration, making the obtained approximate prior distribution elements independent, which facilitates the parallel execution of PME estimation of the target channel matrix. Furthermore, LLR is used to determine the user's active state, eliminating the need for manually setting threshold parameters using greedy iterative algorithms.

[0022] In summary, compared with existing AMP-MMV and GAMP-MMV methods, the present invention has a wider range of applications and can be used for the joint estimation of active users and channels under non-Gaussian pilot matrices. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the proposed SC-HyGEC framework.

[0024] Figure 2 A schematic diagram of an unlicensed massive MIMO uplink system.

[0025] Figure 3 The flowchart of the proposed SC-HyGEC algorithm is shown.

[0026] Figure 4 This is a comparison chart of the NMSE of SC-HyGEC and existing algorithms under non-Gaussian pilot conditions.

[0027] Figure 5 Under Gaussian pilot frequencies, with quantization and sparsity Comparison of NMSE values ​​for different SC-HyGEC and GEC-SR-MMV. Detailed Implementation

[0028] The present invention will now be described in detail with reference to the accompanying drawings.

[0029] A subspace-constrained, unlicensed, large-scale MIMO active user and channel joint estimation method includes the following steps: Step 1: Transform the unlicensed massive MIMO uplink system modeling into a multi-measurement vector problem:

[0030] in, L The pilot length, This refers to the number of base station antennas. For complex-valued uniform quantizers, It is an additive Gaussian matrix whose elements are independent and follow a mean of 0 and a variance of 0. Gaussian distribution, For the channel matrix, For the number of users, For the first Channels for individual users For the first The real channel of each user Indicates the first The activation status of each user, and their activity probability is: The support set of active users is defined as follows: The goal of this modeling is to, given the pilot matrix Under the condition of observation matrix Recovering the channel matrix and support set ; The modeling objective is to obtain the minimum mean square error (MMSE) estimate of the channel matrix and the log likelihood ratio (LLR) of active users to determine their activity level. Based on the characteristics of sporadic user activity in unlicensed large-scale MIMO scenarios, the channel matrix will be... Modeled as a conditionally independent distribution:

[0031] in For Dirac delta function, The channel matrix is ​​a complex Gaussian distribution. The joint distribution is obtained through the above independent distributions. The result is obtained by integration; Modeling of unlicensed massive MIMO uplink system and channel matrix Modeling, estimating the channel matrix within a Bayesian framework to detect active user support sets, i.e., using MMSE estimation of the hybrid channel matrix to achieve optimal Bayesian MSE performance:

[0032] in Includes multiple integration operations. Indicates except outside The set of the remaining elements in the set, the likelihood function ,in To quantize the Gaussian distribution; The following formula, Log-Likelihood Ratio (LLR), is used to detect active users:

[0033] in and These represent the user being in an active state and the user being in an inactive state, respectively, with marginal probabilities. It is obtained by marginalization of the joint posterior probability.

[0034] Step Two: Refer to Figure 1 Through three modules, within the GEC framework, the subspace strategy and cyclic belief propagation are integrated. Based on the modeling in step one, the MMSE estimation of the target channel matrix and the LLR of active users are iteratively calculated.

[0035] The three modules, refer to Figure 1 They are respectively: (1) Module A, is The MMSE node module, in which express The The column is based on the approximate prior information provided by module C. Likelihood function of the real model ,implement MMSE estimation of nodes, obtain Then, eliminate external information. ,get Approximate likelihood information of nodes ,Right now This information will be passed forward to module C as external information, where the operation to eliminate external information is defined as follows: ; (2) Module C is a subspace module, based on subspace Constraints, Solving MMSE of the node ( )or MMSE of the node ( ),in For set The indexed submatrices and vectors, They are respectively The The column uses the estimated support set obtained from the previous iteration. Approximate likelihood information based on module A and approximate prior information of module B. In subspace Solve the following optimization problem under constraints:

[0036] During the forward message passing process, execution Operation, obtain The PME of a node, i.e. Then eliminate external information To obtain the approximate likelihood function This information will be passed to module B as external information. During the reverse message passing process, execution will take place. Operation, obtain The PME of a node, i.e. ; then eliminate external information To obtain approximate prior information This information will be passed to module A as external information; (3) Module B, for The node MMSE module and the support set detection module, combined with the approximate likelihood information from module C. implement PME estimation, decoupled via LBP Column correlation is used to obtain the sparsity of elements. Such that the row-independent prior distributions Transformed into an element-independent prior distribution To facilitate parallel computation, this is based on an approximate prior distribution. The approximate likelihood function passed by module C ,calculate MMSE, that is Then, by eliminating external information, it was obtained Approximate prior distribution of nodes This information will be passed to module C as external information; simultaneously, based on the approximate likelihood function provided by module C... Even if LLR is used, an estimate of the support set can be obtained. ; The algorithm executes in the iterative order of module A -> module C1 -> module B -> module C2 -> module A -> ... until the maximum number of iterations is reached. or When the error of the MMSE estimator is less than the preset error, the algorithm stops iterating and outputs the result. and .

[0037] Example 1 like Figure 2 The system shown is a single-cell, single-base station unlicensed massive MIMO uplink system, equipped with base station equipment. Root antenna service There are 100 smart devices, of which only a small number of user devices are active. Considering the base station is equipped with a low-precision ADC, the received signal matrix can be represented as follows: The transition probability mass function of this system is:

[0038] in express The real part, express The imaginary part. Indicates ADC output The corresponding upper limit value of the input, and Indicates ADC output The corresponding lower limit value of the input. The experiments conducted in this invention mainly examine the normalized mean square error performance of the algorithm, which is defined as... ,in It is the Frobenius norm. Signal-to-noise ratio (SNR) is defined as... .

[0039] like Figure 3 As shown, for an unlicensed massive MIMO uplink system, this implementation method includes the following steps: Step 2.1: Initialization. Nodes and The mean and variance of the approximate prior distribution of the nodes. The mean parameter is set to... The variance parameter is Calculation yields , ,in For measurement rate. For simplicity, it can be set to... The estimated sparsity is initialized to... Parameter initialization only affects the convergence speed of the algorithm, not its NMSE performance at convergence.

[0040] Step 2.2: Based on the external information transmitted by module C calculate PME

[0041] Where the expectation is approximately the posterior probability Take. Based on the properties of exponential family functions, for convenience, use... replace ,calculate achievable

[0042] in , .

[0043] Then calculate external information. ,in

[0044] Step 2.3: Calculation under subspace constraints LMMSE estimation of nodes. This is achieved by solving the following optimization problem.

[0045] achievable

[0046] Due to submatrix The dimension is The computational complexity of the above formula is . ,in The length of the estimated support set. In license-free massive MIMO systems, only a small number of users are active, therefore... The computational complexity is much smaller than that of LMMSE in full-dimensional space, which is O(log n). This reduces the computational complexity of existing generalized expectation consistent signal recovery multi-measurement vector (GEC-SR-MMV) algorithms.

[0047] Then the approximate likelihood function is calculated. This message will be passed to module B as external information, where

[0048] Note that we used a full-dimensional matrix here. , and not the subspace matrix .

[0049] Step 2.4: Based on the sparsity obtained from LBP iteration ,implement PME calculation

[0050] Among them, the expected value Take. According to Gauss's multiplication lemma, for any... , Calculation yields

[0051] Then the approximate prior distribution is calculated. ,in

[0052] Step 2.5: Based on the prior information provided in Step 4 and the likelihood information provided in step 2. In subspace Solving the optimization problem under constraints , can be obtained

[0053] Then the approximate prior distribution is calculated. ,in

[0054] Step 2.6: LBP Iteration. Definition as well as ,in Represents variable nodes To factor node The news This is the message in the opposite direction. In this case, the LBP loop can be written as follows:

[0055] The algorithm in step 2.6 determines the user's activity status based on the user's LLR (Local Level Response). At that time, the judgment was When a user is active, At that time, the judgment was One user is inactive. This leads to an estimate of the support set. .

[0056] Meanwhile, the LBP module of the SC-HyGEC algorithm provides an approximation of the sparsity rate, the specific expression of which is:

[0057] Since the true channel matrix shares a sparse factor, it exhibits column correlation. Therefore, execution within the generalized expectation consistency framework... The MMSE estimation requires row-by-row computation, which is not conducive to parallel computation of the algorithm. The above formula decouples this column correlation by calculating the approximate sparsity rate, making... The approximate prior distribution is in the form of element-independent operations, which allows the original row-by-row operations to be performed in parallel with each element, thus facilitating parallel computation and reducing program execution time.

[0058] Step 2.7: Detect the support set and determine the user's activity status based on the LLR provided in Step 6.

[0059] The estimated support set will provide subspace constraints for steps 2.3 and 2.5.

[0060] To test the advantages of SC-HyGEC over existing algorithms, this invention tests two cases: non-Gaussian pilots and iid Gaussian pilots. Figure 4 In the middle, the pilot matrix is ​​generated based on the Kronecker correlation. ,in , , The correlation coefficient is... It is a Gaussian matrix, and The parameters are set as follows: It can be seen that when the correlation is low, such as... SC-HyGEC can converge to the same NMSE performance as GEC-SR-MMV and GAMP-MMV, regardless of still Furthermore, the SC-HyGEC algorithm converges significantly faster than GEC-SR-MMV, with GAMP-MMV exhibiting the slowest convergence speed. In cases of high correlation, such as... The GAMP-MMV algorithm diverges, while SC-HyGEC and GEC-SR-MMV converge normally, showing better performance compared to GAMP-MMV. There is a slight attenuation at that time.

[0061] exist Figure 5 In this paper, the NMSE performance of the SC-HyGEC and GEC-SR-MMV algorithms under the Gaussian pilot matrix is ​​compared in detail. Figure 5 This indicates that in low quantification Below, such as At that time, SC-HyGEC did not offer an advantage in convergence speed compared to GEC-SR-MMV. With quantization... With the increase of [unclear], it can be found that SC-HyGEC converges faster than GEC-SR-MMV. This advantage increases with quantization. and sparsity The increase is even more pronounced.

Claims

1. A method for joint estimation of active users and channels in subspace-constrained unlicensed large-scale MIMO, characterized in that: Includes the following steps: Step 1: Model the unlicensed massive MIMO uplink system and transform it into a multi-measurement vector problem to obtain the minimum mean square error (MMSE) estimate of the channel matrix and the log likelihood ratio (LLR) of active users to determine the user's active status. Step 2: Using three modules within the GEC framework, the subspace strategy and cyclic belief propagation are integrated to iteratively approximate the MMSE estimation of the target channel matrix and the LLR of active users based on the modeling in Step 1.

2. The method for joint estimation of active users and channels in subspace-constrained unlicensed large-scale MIMO according to claim 1, characterized in that, The modeling in step one specifically involves: (1.1) First, the unlicensed massive MIMO uplink system of a single cell and a single base station is modeled as follows: in, L The pilot length, This refers to the number of base station antennas. For complex-valued uniform quantizers, It is an additive Gaussian matrix whose elements are independent and follow a mean of 0 and a variance of 0. Gaussian distribution, For the channel matrix, For the number of users, For the first Channels for individual users For the first The real channel of each user Indicates the first The activation status of each user, and their activity probability is: The support set of active users is defined as follows: The goal of this modeling is to, given the pilot matrix Under the condition of observation matrix Recovering the channel matrix and support set ; (1.2) Based on the characteristics of sporadic user activity in unlicensed large-scale MIMO scenarios, the channel matrix is... Modeled as a conditionally independent distribution: in For Dirac delta function, The channel matrix is ​​a complex Gaussian distribution. The joint distribution is obtained through the independent distribution. The integral is obtained. x nm The element in the nth row and mth column; (1.3) Based on the modeling of (1.1)-(1.2), the channel matrix is ​​estimated within the Bayesian framework to detect the active user support set, that is, the MMSE estimation of the hybrid channel matrix is ​​adopted to achieve the optimal Bayesian MSE performance: in Includes multiple integration operations. Indicates except outside The set of the remaining elements in the set, the likelihood function ,in To quantize the Gaussian distribution; The following formula, Log-Likelihood Ratio (LLR), is used to detect active users: in and These represent the user being in an active state and the user being in an inactive state, respectively, with marginal probabilities. It can be obtained by marginalizing the joint posterior probability.

3. The method for joint estimation of active users and channels in subspace-constrained unlicensed large-scale MIMO according to claim 1, characterized in that, Step two is specifically implemented through three modules: Module A, Module C, and Module B. Module A is The MMSE node module, in which express The The column is based on the approximate prior information provided by module C. Likelihood function of the real model ,implement MMSE estimation of nodes, obtain Then, eliminate external information. ,get Approximate likelihood information of nodes ,Right now The operation to eliminate external information is defined as follows: This information will be passed forward to module C as external information; Module C is a subspace module, based on subspace. Constraints, Solving MMSE of the node ( )or MMSE of the node ( ),in For set The indexed submatrices and vectors are obtained. They are respectively The The column uses the estimated support set obtained from the previous iteration. Approximate likelihood information based on module A and approximate prior information of module B. In subspace Solve the following optimization problem under constraints: During the forward message passing process, execution Operation, obtain The PME of a node, i.e. Then eliminate external information To obtain the approximate likelihood function This information will be passed to module B as external information. During the reverse message passing process, execution... Operation, obtain The MMSE of a node, i.e. ; then eliminate external information To obtain approximate prior information This information will be passed to module A as external information; Module B is The node MMSE module and the support set detection module, combined with the approximate likelihood information from module C. implement MMSE, decoupled through LBP Column correlation is used to obtain the sparsity of elements. Such that the row-independent prior distributions Transformed into an element-independent prior distribution To facilitate parallel computation, this is based on an approximate prior distribution. The approximate likelihood function passed by module C ,calculate MMSE, that is Then, by eliminating external information, it was obtained Approximate prior distribution of nodes This information will be passed to module C as external information; simultaneously, based on the approximate likelihood function provided by module C... Calculate the LLR of user activity states and obtain an estimate of the support set based on the LLR. ; The algorithm executes in the iterative order of module A -> module C1 -> module B -> module C2 -> module A -> ... until the maximum number of iterations is reached. Alternatively, if the error of the MMSE estimator is less than the preset error, the algorithm stops iterating and outputs the result. and .

4. The method for joint estimation of active users and channels in subspace-constrained unlicensed large-scale MIMO according to claim 3, characterized in that, The module C is constrained by the subspace. Next, solve the optimization problem C1 to obtain... The linear minimum mean square error estimate (LMMSE) is specifically expressed as: Due to submatrix The dimension is The computational complexity of the above formula is O(n). ,in The length of the estimated support set, This reduces computational complexity.

5. The method for joint estimation of active users and channels in subspace-constrained unlicensed large-scale MIMO according to claim 3, characterized in that, Module B calculates the LLR of user activity states and obtains an estimate of the support set based on the LLR. The true LLR can be approximated by the following formula: LLR is used to determine the user's activity level. At that time, the judgment was When a user is active, At that time, the judgment was The number of users is inactive, thus providing an estimate of the support set. .

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