A fast mode coupled sparse bayesian multiuser detection method

Abstract

This invention discloses a fast pattern-coupled sparse Bayesian multi-user detection method, comprising the following steps: Step S1: Construct a large-scale IoT uplink system model, convert the multi-timeslot signal measurement model into a single measurement vector model, and assign a pattern-coupled Gaussian prior distribution to the sparse signal to be detected, initializing the hyperparameter set; Step S2: Based on variational inference, derive the relaxed evidence lower bound of the system's logarithmic marginal likelihood function; Step S3: Update the hyperparameter set using the variational expectation maximization method to maximize the relaxed evidence lower bound; Step S4: Determine whether the iteration termination condition is met. If it is, stop the iteration and output the recovered active user signal; otherwise, return to step S3. This invention effectively utilizes the adjacency correlation of each user's transmitted signal through a pattern coupling mechanism, significantly improving detection accuracy; and it can meet the requirements of real-time performance and high reliability in large-scale IoT scenarios.

Description

Technical Field

[0001] This invention relates to a multi-user detection method for uplink unlicensed nonorthogonal multiple access systems, and particularly to a fast mode-coupled sparse Bayesian multi-user detection method. Background Technology

[0002] With the deepening research into sixth-generation mobile communication systems (6G), future wireless networks will evolve from "Internet of Everything" to "Intelligent Internet of Everything." Massive IoT, as one of the core application scenarios of 6G, aims to support millions or even higher density device connections per square kilometer, including smart sensors and environmental monitoring nodes. Significantly different from traditional human-centric communication models, these massive IoT devices typically exhibit characteristics of "extremely high connection density, short data packets, and intermittent bursts of activity." Faced with the enormous spectrum pressure brought by the simultaneous access of massive numbers of devices, traditional orthogonal multiple access technologies are insufficient to support the connection density requirements of 6G. Therefore, unlicensed non-orthogonal multiple access (GF-NOMA) is considered a key technology to solve the bottleneck of massive connectivity, allowing massive numbers of devices to send data directly without complex handshake processes. However, this also brings a core technical challenge: how to efficiently and accurately identify active devices and recover data from severe superimposed interference at the base station—the multi-user detection (MUD) problem.

[0003] In massive Internet of Things (IoT), only a small fraction of devices are active at any given moment. This inherent sparsity makes it possible to reconstruct signals using compressed sensing (CS) theory. While some targeted detection schemes exist, they still face numerous limitations. Traditional linear minimum mean square error (MMSE) detectors and zero-forcing (ZF) detectors perform reasonably well in low-dimensional signals, but in 6G massive connectivity scenarios, the explosive growth in user dimensions leads to a cubic increase in computational complexity due to the high-dimensional matrix inversion operations, resulting in significant signal processing latency and failing to meet real-time requirements. Although OMP detectors outperform traditional linear detection, they require prior knowledge of the number or sparsity of active users. Furthermore, in 6G scheduling-free random access scenarios, the active state of devices is highly random and unknown, making it difficult for base stations to obtain accurate prior information. This causes a sharp decline in the detection performance of such algorithms when prior information is lacking.

[0004] Furthermore, most existing multi-user detection schemes treat the signal in each time slot as an independent process, ignoring the persistent or structured characteristics that IoT devices may exhibit in the time domain. Fully utilizing this hidden structural information and Bayesian statistical properties could significantly improve detection accuracy. Therefore, there is an urgent need for a new multi-user detection method that can adapt to the massive connectivity of 6G, does not require prior knowledge of the number of active users, and has low computational complexity. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a fast mode-coupled sparse Bayesian multi-user detection method. This method transforms the signal matrix model under multi-time slots into a single measurement vector model, uses mode coupling priors to capture the adjacency correlation of user signals, and then finds the optimal solution by maximizing the lower bound of relaxed evidence based on the idea of ​​variational expectation maximization. In this way, the method avoids the computational burden of inverting high-dimensional matrices in traditional methods while effectively extracting user information, significantly reducing the algorithm complexity and realizing efficient and accurate multi-user detection in large-scale IoT scenarios.

[0006] The objective of this invention is achieved through the following technical solution: a fast mode-coupled sparse Bayesian multi-user detection method, in an uplink unlicensed non-orthogonal multiple access system, where there is a base station and For a single-antenna user, set Multiple users share the same channel, and the number of base station receiving antennas is... Each user signal is transmitted and superimposed onto the base station receiver over a continuous period of time. The user-transmitted signal within each time slot is related to its adjacent signals;

[0007] A multi-timeslot measurement model is constructed by stacking the received signals from multiple time slots. The base station received signals within each time slot are denoted as:

[0008] ;

[0009] in, It is the complex channel matrix between the transmitter and receiver, assuming the frame length is less than the channel coherence time. It remains unchanged throughout the entire frame time. , It is the first The received signal of each time slot base station , It is the first All user transmission signals within a time slot noise vector Satisfies Gaussian distribution ;

[0010] The fast-mode coupled sparse Bayesian multi-user detection method includes:

[0011] Step S1: Input known information, including received signal, total number of devices, and equivalent channel matrix. Through matrix vec operation, convert the multi-slot measurement model into a single measurement vector model, and assign a Gaussian prior distribution to the sparse signal to be detected. Initialize all required parameters and complete the setting of the judgment conditions for successful recovery of transmitted signal in the entire system.

[0012] Step S2: Based on the idea of ​​variational reasoning, derive the lower bound of the relaxation evidence for the log marginal likelihood function of the system;

[0013] Step S3: Using the variational expectation maximization method, obtain the approximate posterior distribution of each hyperparameter and update iteratively to maximize the lower bound of relaxed evidence obtained in step S2, thereby obtaining the optimal solution of the transmitted signal hyperparameters;

[0014] Step S4: Determine whether to continue iteration based on the set decision conditions. If the decision conditions are met, output the recovered transmission signal and hyperparameter set. If not, return to step S3 for a new round of iteration.

[0015] The beneficial effects of this invention are: (1) This invention assigns structured Gaussian prior information coupled to the transmission signal mode, and uses the idea of ​​variational expectation maximization to iteratively update parameters by maximizing the lower bound of relaxed evidence. This method allows the algorithm to increase its adaptability and flexibility by not needing to know the actual number of active users, i.e., sparsity, during the iterative calculation process.

[0016] (2) This invention introduces an optimization strategy to maximize the lower bound of relaxed evidence and derives a closed-form parameter iteration update formula. Compared with the traditional Bayesian method, this method does not require inverting the high-dimensional covariance matrix, reducing the computational complexity from cubic to linear, which significantly improves the real-time performance and processing efficiency of multi-user detection in large-scale IoT scenarios.

[0017] (3) This invention utilizes the adjacency correlation of user signals in the time domain to convert the multi-slot signal matrix model into a single measurement vector model. Through mode coupling prior, it significantly improves the detection accuracy and bit error rate performance of the system without adding additional pilot overhead. Attached Figure Description

[0018] Figure 1 This is a flowchart of the method of the present invention;

[0019] Figure 2 This is a graph showing the symbol error rate analysis of various multi-user detection methods under Gaussian channel conditions.

[0020] Figure 3This is a comparison chart of the running times of various multi-user detection methods under different numbers of users. Detailed Implementation

[0021] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description.

[0022] This invention addresses the challenge of unknown and difficult-to-obtain real-time active user numbers in large-scale IoT scenarios. First, it constructs a pattern-coupled structured Gaussian prior model, utilizing the adjacency correlation of signals in the time domain to transform the multi-timeslot signal matrix into a single-measurement vector model for unified representation. Then, based on the variational expectation maximization approach, it derives a closed-form iterative update formula for parameters by maximizing the lower bound of relaxed evidence. This method not only achieves adaptive and accurate detection without requiring prior knowledge of active user sparsity, overcoming the limitations of traditional Bayesian methods that are only applicable to single timeslots or require known priors, but also significantly reduces algorithm complexity by avoiding the inversion operation of high-dimensional covariance matrices. Therefore, it effectively solves the problem of efficient and rapid reconstruction of large-scale user signals in multi-timeslot environments.

[0023] Specifically, in a large-scale IoT uplink unlicensed non-orthogonal multiple access system, there exists a base station and For a single-antenna user, set Multiple users share the same channel, and the number of base station receiving antennas is... Each user signal is transmitted and superimposed onto the base station receiver over a continuous period of time. Each user-transmitted signal within a time slot is correlated with its neighboring signals;

[0024] Therefore, unlike traditional methods that typically assume signals in each time slot are independent and ignore the continuity of user activity over time, this invention aims to uncover the rich prior characteristics of communication signals. It utilizes the temporal correlation of user activity across multiple time slots, stacking the received signals from multiple time slots to construct a multi-time slot measurement (MMV) model. The base station receives signals within each time slot It can be written as:

[0025]

[0026] in, It is the complex channel matrix between the transmitter and receiver, assuming the frame length is less than the channel coherence time. It remains unchanged throughout the entire frame time. , It is the first The received signal of each time slot base station , It is the first All user transmission signals within a time slot noise vector Satisfies Gaussian distribution ;

[0027] It should be noted that the MMV model constructed in this invention is fundamentally different from the traditional Single Measurement Vector (SMV) model. The traditional SMV model only considers the sparse signal recovery problem within a single time slot, assuming that the signals in each time slot are independent, failing to utilize the temporal correlation of user activities. In contrast, the MMV model proposed in this application constructs a signal matrix X with a block-sparse structure by jointly processing the received signals from multiple consecutive time slots. This means that the activity states of the same user in adjacent time slots are correlated, and non-zero elements appear consecutively in "blocks." Based on this unique structural prior, this invention further designs a fast mode-coupled sparse Bayesian multi-user detection method to fully utilize the correlation of user activities between adjacent time slots, thereby improving detection accuracy while reducing computational complexity.

[0028] See appendix Figure 1 A fast pattern-coupled sparse Bayesian multi-user detection method is described below:

[0029] Step 1:

[0030] consider Each user transmits signals to the base station, and each individual time slot can be viewed as a basic SMV model. Within each time slot, only a few users are active, while the majority are inactive. Therefore, the combined matrix... It exhibits a block-sparse structure. Therefore, in order to obtain the structural sparsity characteristics of the transmitted signal, the multi-slot signal measurement matrix is ​​transformed into a single measurement vector model with block-sparse properties:

[0031]

[0032]

[0033] in, Indicates will The long vector obtained by vectorization Each time slot has N observations. Stacking the measurements from T time slots sequentially into an NT×1 vector yields... , Let T be a T×T identity matrix. The Kronecker product with H results in a block diagonal matrix with T H blocks on the diagonal. Off-diagonal blocks are 0, indicating that there is no cross-coupling between measurements in different time slots, and the measurement processes in each time slot are independent of each other. Indicates the Kronecker product. Vectorization operations of representation matrices It is The matrix. To simplify the writing, let's denote it as... Therefore, the problem is transformed into recovering the sparsity from the above model. .

[0034] The key to this invention's ability to significantly improve detection accuracy without increasing pilot overhead lies in its utilization of the temporal adjacency correlation of user signals to construct a mode-coupled prior model, thereby more accurately characterizing the structural properties of the multi-timeslot signal matrix. Specifically, this invention proposes that the prior information of each transmitted signal not only includes its own hyperparameters but also correlates with the hyperparameters of adjacent signals, thus coupling and modeling each user's transmitted signal with the signals in its adjacent time slots. Therefore, it can be assumed that the signal... It follows the following prior distribution:

[0035]

[0036] in, Given a hyperparameter vector At that time, the signal vector The complete prior distribution;

[0037] Given a hyperparameter vector When, vector The i-th signal component The conditional prior distribution; express It follows a mean of 0 and a variance of . Gaussian distribution;

[0038] For the i-th signal component The corresponding non-negative hyperparameters are used to control The prior variance; The prior variance is not independent of It is not decided by, but by and the left and right adjacent , The purpose of this is to make the sparse patterns of adjacent signal components correlated, thereby taking advantage of the block sparse structure of the signal. It is a non-negative hyperparameter related to signal sparsity. K represents the number of signal components in the signal vector; definition , , It is a hyperparameter representing the correlation between a signal and its neighboring signals, and Hyperparameters It satisfies the following Gamma distribution:

[0039]

[0040] Redefining It is the reciprocal of the noise variance, i.e. And noise Satisfies Gaussian distribution And satisfy the hyperparameters , Gamma distribution:

[0041]

[0042] Step 2:

[0043] The observed signal is derived based on the variational expectation maximization (V-EM) approach. The posterior distribution of the hidden variable behind it, let ,Will Approximately a variational distribution , The components in the posterior are independent of each other, thus It can be factored into:

[0044]

[0045] Observation signal The marginal probability can be decomposed into:

[0046]

[0047] in yes and Kullback-Leibler divergence between them

[0048]

[0049] And there always is . The lower bound of evidence is defined as:

[0050]

[0051] in, It is a joint probability distribution. In this case, we need to minimize... To find the best approximation, so that To get as close as possible to the true posterior. And when... hour, Therefore, this process is equivalent to maximizing the lower bound of the evidence. Based on the first-order Taylor expansion of smooth functions and the strong convexity correlation property, the likelihood function can be obtained. A lower bound:

[0052]

[0053] in,

[0054]

[0055] Here, an auxiliary function is introduced. To replace In the original likelihood function, The coefficient of the quadratic term is After relaxation, it becomes a diagonal matrix. Substituting the above formula into... From the definition, we can obtain:

[0056]

[0057] in Ultimately, we can obtain the lower bound of the relaxation evidence:

[0058]

[0059] in It is used to guarantee Normalization terms that satisfy strict distribution.

[0060] Step 3:

[0061] As can be seen from step 2 Therefore, it is necessary to maximize them separately. , , and parameters The lower bound of the relaxation evidence, i.e. .make Next, based on the variational expectation maximization method, we will derive the specific update steps for each parameter.

[0062] (1) Update parameters :

[0063] First, calculate the parameters. Approximate posterior distribution ,

[0064]

[0065] in, It is a diagonal matrix. Clearly, from the above equation, we know... It follows a Gaussian distribution, that is...

[0066]

[0067] And their posterior mean and covariance matrix are respectively:

[0068]

[0069]

[0070] The key to this invention's significant reduction in computational complexity lies in its proposed parameter iteration update rule, which avoids the direct inversion of high-dimensional covariance matrices required in traditional Bayesian methods. Specifically, traditional sparse Bayesian learning algorithms require calculating the following covariance matrix when computing the posterior distribution of a signal:

[0071]

[0072] The dimension of this matrix is ​​related to the total number of users K, and the computational complexity of its inverse operation is O(K). When the number of users reaches hundreds or thousands, this operation becomes insufficient to meet real-time processing requirements. To address this issue, this invention circumvents matrix inversion by introducing an optimization strategy in step 2 that maximizes the lower bound of relaxed evidence. Specifically, the update of the covariance matrix is ​​transformed into a diagonalized form. In the covariance matrix update formula of this invention, I is the identity matrix, and A is the diagonal matrix. The inverse operation of this matrix degenerates into a scalar inversion of the diagonal elements, reducing the computational complexity to O(n). .

[0073] (2) Update parameters :

[0074] Similarly, first calculate the parameters. The approximate posterior distribution,

[0075]

[0076] Let the above expression be ,but .right beg Let the first-order partial derivative of be zero, and assume... Solving the equation, we can obtain the following equation:

[0077]

[0078] in,

[0079]

[0080]

[0081] because Since the parameter is non-negative, we have:

[0082]

[0083] Therefore, we can conclude that

[0084]

[0085] when hour ,when hour, Combining the previous derivation, we can obtain... Theoretical range of values:

[0086]

[0087] The optimal solution can be seen from the above equation. and Proportional. To simplify the calculation and obtain a definite point estimate, a proportionality parameter is introduced here. Therefore, the optimal solution can be expressed in the parameterized form shown below:

[0088]

[0089] Among them, parameters A reasonable value for should fall within the interval defined by its theoretical boundary. Analysis of multiple simulation results shows that when... The value of is in Within the specified range, the system achieves excellent and stable bit error rate performance. Analysis of the above hyperparameters... According to the update rules, when a user is detected to be active in a certain time slot, the probability of its adjacent time slots being identified as active also increases, and vice versa. This adjacent coupling mechanism enables the present invention to more accurately identify active users and their signals, thereby significantly improving the detection accuracy and bit error rate performance of the system without adding additional pilot overhead.

[0090] (3) Update parameters :

[0091] Similarly, there are

[0092]

[0093] Therefore, parameters It follows the following Gamma distribution:

[0094]

[0095]

[0096] in, .

[0097] (4) Update parameters :

[0098] Based on the previous The obtained parameters Substitute into In the middle, for parameters The update can be achieved through the following optimization methods:

[0099]

[0100] right Seeking information about The derivative of and set it to zero,

[0101]

[0102] Parameters can be obtained The updated version:

[0103]

[0104] Based on the preceding derivation, it can be seen that when updating parameters... It is still necessary to calculate one. The problem involves finding the inverse of a large matrix, but after transformation, the matrix whose inverse is now required is a diagonal matrix. The computational complexity of inverting this matrix is ​​reduced to O(n). And other parameters The updates involve only simple addition and multiplication operations, and their impact on the overall computational complexity of the algorithm is negligible. Therefore, this invention derives a closed-form iterative update formula for all hyperparameters, requiring no computation during the entire iteration process. The inverse of the dimensional matrix is ​​used, thus reducing the overall computational complexity from that of traditional sparse Bayesian methods. Down to This significantly improves the real-time performance of multi-user detection in large-scale IoT scenarios.

[0105] Step 4: In this invention, there are two methods to determine whether the transmitted signal has been successfully recovered. One is that the number of runs reaches a certain threshold. The other is If any of the decision conditions are met, then the last iteration is selected. As a recovery signal, if the condition is not met, return to step 3 to start a new round of iteration.

[0106] In the embodiments of this application, multi-user detection involves separating and determining the original symbols transmitted by each user from the superimposed received signals of multiple users. Therefore, the final output of this detection process is the estimated value of the transmitted signal for each user. Recovering the transmitted signal is the ultimate goal of the multi-user detection method.

[0107] In the embodiments of this application, the feasibility of a fast pattern-coupled sparse Bayesian multi-user detection method is verified through simulation experiments.

[0108] Simulation parameters: This invention considers an additive white Gaussian noise (AWGN) channel, with a binary phase shift keying (BPSK) modulation scheme, and the number of antennas at the base station receiver is [number missing]. The total number of users is User activity factor is Select a time slot length of The maximum number of iterations is The maximum allowable error is .

[0109] Simulation results: Figure 2 The figure shows the SER performance analysis of various multi-user detection methods under different signal-to-noise ratios (SNR). Simulation results show that the method of this invention significantly outperforms traditional linear detectors ZF, MMSE, and the greedy algorithm OMP, exhibiting the lowest SER under both user activity levels. Specifically, the performance curves of the method of this invention and the PCSBL algorithm almost overlap, indicating that their detection accuracy is comparable. Figure 3 This figure compares the running time of various multi-user detection methods under different user numbers, with SNR=15dB, half the number of receiving antennas, and other parameters remaining unchanged. Simulation results show that the running time of the proposed method is significantly lower than that of the SBL and PCSBL algorithms, demonstrating the effectiveness of its low-complexity design.

[0110] The above describes the specific embodiments and simulation verifications of the present invention. It should be noted that those skilled in the art can clearly understand that the above embodiments and simulations of the fast pattern-coupled sparse Bayesian multi-user detection method of the present invention are only used to illustrate and verify the rationality and feasibility of the method, and are not intended to limit the method of the present invention. Although the embodiments effectively illustrate and describe the present invention, many variations exist without departing from the spirit of the present invention. Those skilled in the art can make various corresponding changes or modifications according to the method of the present invention without departing from the spirit and essence of the method, but these corresponding changes or modifications all fall within the protection scope claimed by the method of the present invention.

Claims

1. A fast pattern-coupled sparse Bayesian multi-user detection method, characterized in that: In an uplink unlicensed nonorthogonal multiple access system, there exists a base station and For a single-antenna user, set Multiple users share the same channel, and the number of base station receiving antennas is... Each user signal is transmitted and superimposed onto the base station receiver over a continuous period of time. The user-transmitted signal within each time slot is related to its adjacent signals; A multi-timeslot measurement model is constructed by stacking the received signals from multiple time slots. The base station received signals within each time slot are denoted as: ； in, It is the complex channel matrix between the transmitter and receiver, assuming the frame length is less than the channel coherence time. It remains unchanged throughout the entire frame time. , It is the first The received signal of each time slot base station , It is the first All user transmission signals within a time slot noise vector Satisfies Gaussian distribution ; The fast-mode coupled sparse Bayesian multi-user detection method includes: Step S1: Input known information, including received signal, total number of devices, and equivalent channel matrix. Through matrix vec operation, convert the multi-slot measurement model into a single measurement vector model, and assign a Gaussian prior distribution to the sparse signal to be detected. Initialize all required parameters and complete the setting of the judgment conditions for successful recovery of transmitted signal in the entire system. Step S2: Based on the idea of ​​variational reasoning, derive the lower bound of the relaxation evidence for the log marginal likelihood function of the system; Step S3: Using the variational expectation maximization method, obtain the approximate posterior distribution of each hyperparameter and update iteratively to maximize the lower bound of relaxed evidence obtained in step S2, thereby obtaining the optimal solution of the transmitted signal hyperparameters; Step S4: Determine whether to continue iteration based on the set decision conditions. If the decision conditions are met, output the recovered transmission signal and hyperparameter set. If not, return to step S3 for a new round of iteration.

2. The fast pattern-coupled sparse Bayesian multi-user detection method according to claim 1, characterized in that: Step S1 includes: S101. Input base station received signal and equivalent channel matrix Set the maximum number of loops. and the maximum permissible error ε; S102. Consider Each user transmits signals to the base station, and each individual time slot is considered as a basic SMV model, which is the Single Measurement Vector Model. Only a few users are active in each time slot, while the majority are inactive; therefore, the combined matrix... It has a block-sparse structure; the multi-slot signal measurement matrix is ​​converted into a single measurement vector model with block sparsity: ； in, Indicates will The long vector obtained by vectorization It is a T×T identity matrix; Indicates the Kronecker product. Vectorization operations of representation matrices It is The matrix, denoted as ; S103. Assuming signal It follows the following prior distribution: ； in, Given a hyperparameter vector At that time, the signal vector The complete prior distribution; Given a hyperparameter vector When, vector The i-th signal component The conditional prior distribution; express It follows a mean of 0 and a variance of . Gaussian distribution; For the i-th signal component The corresponding non-negative hyperparameters are used to control The prior variance; It is a non-negative hyperparameter related to the signal. K represents the number of signal components in the signal vector; It is a hyperparameter representing the correlation between a signal and its neighboring signals, and ;definition It is the reciprocal of the noise variance, i.e. And noise Satisfies Gaussian distribution .

3. The fast pattern-coupled sparse Bayesian multi-user detection method according to claim 1, characterized in that: Step S2 includes: The observed signal is derived based on the variational expectation maximization (V-EM) approach. The posterior distribution of the hidden variable behind it, let ,Will Approximately a variational distribution : Observation signal The marginal probabilities are decomposed into: in The lower bound of evidence is defined as: Based on the first-order Taylor expansion of smooth functions and the strong convexity correlation property, the likelihood function is obtained. A lower bound: in, Substituting the above equation into... The definition yields: in Finally, the lower bound of the relaxation evidence is obtained: in Used to guarantee Normalization terms that satisfy strict distribution.

4. The fast mode-coupled sparse Bayesian multi-user detection method according to claim 1, characterized in that: Step S3 includes: S301. Update parameters : S302. Update parameters : Among them, parameters The value of should fall within the interval formed by its theoretical boundary; S303. Update parameters : Parameters are derived Follows a Gamma distribution: in, ; S304. Update parameters : 。 5. The fast pattern-coupled sparse Bayesian multi-user detection method according to claim 1, characterized in that: In step S4, when the number of runs reaches the maximum number of loops... Or, the L2 norm of the difference between the posterior mean obtained in this iteration and the posterior mean of the previous iteration is less than the maximum permissible error set in step S1. When the loop ends, the result of the last iteration is calculated. As a recovered transmission signal, and as a result of multi-user detection; If the iteration termination condition is not met, let Based on the new set of hyperparameters, return to step S3 for the next iteration.

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