Deep learning method for outage probability optimization problem

Abstract

The invention discloses a deep learning method for an outage probability optimization problem, and belongs to the field of deep learning. For a downlink transmission scene of the MISO system, modeling is carried out by taking minimization of the total outage probability of all users as an optimization target, an indicative function is introduced, the conditional outage probability of each user in modeling is converted into a conditional expectation form, a sample average method is adopted to approximate a conditional expectation value, and a smooth function is adopted to approximate the indicative function; then, constructing a graph neural network for learning a precoding strategy by using a smoothing function and unsupervised learning, designing an adaptive smoothing function method, modeling parameters of the smoothing function, and solving by using binary search; and then, alternately updating the graph neural network and smooth function parameters until the training achieves convergence. And finally, inputting an estimation channel obtained in real time into the optimized graph neural network, outputting a learned precoding strategy, and ensuring that the total outage probability of all users is minimized. The method is low in calculation complexity.

Description

Technical Field

[0001] The present invention belongs to the field of deep learning, and specifically relates to a deep learning method for interruption probability optimization problem. Background Art

[0002] Existing literature on robust optimization can be divided into three categories: worst-case methods, average methods, and probabilistic methods.

[0003] The worst-case method considers the system's performance under the worst-case scenario. For example, reference [1] studies the precoding optimization problem of maximizing the lower bound of the user rate under the assumption of bounded channel estimation error. The worst-case method focuses on the system's minimum performance, and the optimization strategy is usually overly conservative. Reference [2] considers the system's average performance and optimizes precoding with maximizing the user sum rate as the optimization goal. Compared to the first two methods, the probabilistic method allows for violations of requirements in certain extreme cases, avoiding the high cost of fully meeting the requirements [3].

[0004] Since probability problems are non-convex optimization problems, the calculation of probability requires the known probability distribution of variables and the calculation of the probability integral of the problem. Numerical methods are difficult to solve directly and the computational complexity is high. Deep learning methods can learn precoding strategies from data and effectively reduce the inference complexity [4].

[0005] Because probability calculations involve complex integrals, one of the challenges of deep learning-based interruption probability optimization methods is how to effectively approximate probabilities from samples. Existing literature uses the proportion of samples that meet performance requirements to approximate probabilities, a method known as sample averaging. However, determining whether a sample meets a performance requirement is inherently discontinuous, requiring the system performance to be discretely mapped into a binary result of "satisfied" or "not satisfied." This discretization can lead to vanishing or exploding gradients during backpropagation in neural networks, severely impacting network learning performance.

[0006] To overcome the above problems, smooth function approximation discretization is used during training, such as Sigmoid [3] and piecewise smooth function [5]. Such methods usually introduce a smoothing parameter to control the smoothness of the function. The smoothing parameter affects both the function approximation error and the gradient of the smoothing function, and its value has a significant impact on the learning performance in certain optimization problems. Reference [5] treats the smoothing parameter as a hyperparameter, which remains unchanged throughout the training process, or is simply adjusted using the annealing method.

[0007] However, this type of method uses the same smoothing parameter for all samples and cannot take into account the differences between different samples. In practical applications, it is often necessary to adjust the parameters repeatedly, and it is difficult to select the ideal parameter value, which limits the learning performance of the neural network.

[0008] References are as follows:

[0009] [1]Xu J,Kang C,Xue J,et al.A Fast Deep Unfolding Learning Frameworkfor Robust MU-MIMO Downlink Precoding[J].IEEE Transactions on CognitiveCommunications and Networking,2023,9(2):359-372.doi:10.1109 / TCCN.2023.3235763.

[0010] [2]Yuan Q,Liu H,Xu M,et al.Deep learning-based Hybrid Precoding forTerahertz Massive MIMO Communication With Beam Squint[J].IEEE CommunicationsLetters,2022,27(1):175-179.doi:10.1109 / LCOMM.2022.3211514.

[0011] [3]Vu Q D,Tran L N,Juntti M.On Spectral Efficiency for Multiuser MISOSystems Under Imperfect Channel Information[J].IEEE Transactions on VehicularTechnology,2021,70(2):1946-1951.doi:10.1109 / TVT.2021.3050983.

[0012] [4]Peng Y,Guo J,Yang C.Learning Resource Allocation Policy:Vertex-GNNor Edge-GNN?[J].IEEE Transactions on Machine Learning in Communications andNetworking,2024,2:190-209.doi:10.1109 / TMLCN.2024.3354872.

[0013] [5]Iimori H,De Abreu GTF,Taghizadeh O,et al.Stochastic LearningRobust Beamforming for Millimeter-Wave Systems With Path Blockage[J].IEEEWireless Communications Letters,2020,9(9):1557-1561.doi:10.1109 / LWC.2020.2997366. Summary of the Invention

[0014] For downlink multi-user robust precoding, the present invention provides a deep learning method for the interruption probability optimization problem, which provides a solution to the optimization problem with low complexity and solves the problem that the smoothing function in the traditional sample averaging method is difficult to adapt to the differences between different samples.

[0015] The deep learning method for the interruption probability optimization problem has the following specific steps:

[0016] Step 1: For the downlink transmission scenario of the multi-user multiple-input single-output (MISO) system, modeling is performed with the optimization objective P1 of minimizing the total outage probability of all users while satisfying the precoding power constraint.

[0017] The optimization goal is:

[0018]

[0019] Among them, the base station serves K single-antenna users, and the number of base station antennas is N. is the precoding matrix, is the precoding vector of the kth user, For a given Next, about the real channel h k The conditional probability of is the estimated channel vector of the kth user, is the channel vector of the kth user, r k is the transmission rate of the kth user, R k is the minimum transmission rate requirement of the kth user, Tr(·) is the trace of the matrix, P max is the maximum transmit power of the base station.

[0020] Step 2: By introducing the indicator function, the conditional interruption probability of each user in the optimization target P1 is converted into the form of conditional expectation.

[0021] The conditional interruption probability of the kth user is equivalent to the conditional expectation:

[0022]

[0023] Among them, 1(·) is the characteristic function, Indicates a given Next about h k The conditional expectation of R k -r k >0, 1(·)=1; when R k -r k When ≤0, 1(·)=0.

[0024] Step 3: Use the sample averaging method to sample the channel conditional distribution and use the sample mean to approximate the conditional expected value.

[0025] The conditional expectation is approximated to the sample mean as follows:

[0026]

[0027] in, Indicates a given Next is a number of h k The sample set is composed of

[0028] Step 4: Use a smooth function to approximate the characteristic function:

[0029]

[0030] Among them, the smoothing function is expressed as:

[0031]

[0032] β≥0 is a smoothing parameter, and its value is affected by c k impact.

[0033] Step 5: Use smoothing functions and unsupervised learning to build a graph neural network that learns the precoding strategy and transform the optimization objective P1 into an optimization problem P2 that defines the network.

[0034] Step 5.1: Based on the two-dimensional permutation equivariant property of the optimization target P1, construct a heterogeneous graph.

[0035] Heterogeneous graphs include vertex and edge features; antennas and users are two types of vertices, and estimated channels and user rate requirements are edge features;

[0036] Edge features between the kth user vertex and the nth antenna vertex in,

[0037] represents the channel information between the kth user and the nth antenna.

[0038] Step 5.2: Based on heterogeneous graphs, design a graph neural network to learn precoding strategies.

[0039] The input of the graph neural network is designed to be The output is the learned precoding matrix

[0040] in, is the estimated channel matrix, θ is the trainable parameter of the graph neural network, Indicates that each element in the kth column is the rate requirement R of the kth user k Matrix of

[0041] Step 5.3: Using unsupervised learning, define the loss function of the graph neural network:

[0042]

[0043] Step 5.4: Based on the loss function, transform the optimization objective P1 into the optimization problem P2 that defines the network, and obtain:

[0044]

[0045] in, express The sample set is composed of The maximum transmit power constraint is satisfied by designing the output activation function of the neural network, i.e. the normalization layer

[0046] Step 6: Design an adaptive smoothing function method, model the parameter β of the smoothing function in the loss function of the optimization problem P3 as the optimization function P3; use binary search to find the optimal smoothing parameter β;

[0047] The smoothing parameter optimization function is as follows:

[0048]

[0049] in, Gradient requirements. For a given estimated channel Next, the sample set Medium h k The sum of the smooth function approximation errors, is the real channel h k The size of the gradient under the mean condition.

[0050] Step 7: Jointly train the graph neural network and optimize the smoothing parameters, alternately updating the parameters θ of the graph neural network and the parameters β of the smoothing function until convergence is reached.

[0051] Initial settings: Network parameters θ and smoothing function β are both random values.

[0052] In the lth iteration of the graph neural network:

[0053] First, input the historical estimated channel value To the graph neural network, get the output of the neural network, that is, the learned precoding matrix Calculate the rate for each user Thus, the smoothing parameter β is obtained.

[0054] For collections For the kth user in the ith sample, the estimated channel and precoding Calculate the rate for each user and According to the set gradient requirements and The smoothing parameter β is obtained by solving the optimization function P3.

[0055] Then, using c at this time k and smoothing parameter β to calculate the loss function in the optimization problem P2 By using the normalization function to satisfy the constraints, the parameters θ of the graph neural network are updated using stochastic gradient descent:

[0056]

[0057] Among them, δ is the learning rate of the graph neural network, is the gradient vector obtained by back propagation.

[0058] When the network converges, the training ends and the network parameters θ are saved.

[0059] Step 8: Input the estimated channel obtained in real time into the optimized graph neural network and output the learned precoding strategy, that is, obtain the solution of the optimization target P1, which minimizes the total interruption probability of all users.

[0060] The advantages of the present invention are:

[0061] This paper proposes a deep learning method for optimizing outage probabilities. This method employs a probabilistic approximation method with adaptive smoothing parameters. During training, the smoothing parameters are dynamically adjusted for each user in each sample based on the network's learned precoding strategy. This method avoids increased outage probabilities caused by abnormal gradients or large function estimation errors. Furthermore, by combining adaptive smoothing parameters with unsupervised learning, a heterogeneous graph-based neural network is proposed, which achieves a low-complexity solution to the optimization problem during actual inference. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a flow chart of a deep learning method for the interruption probability optimization problem of the present invention;

[0063] Figure 2 The present invention simulates and analyzes the impact of rate requirement differences of different methods on the interruption probability;

[0064] Figure 3 The present invention simulates and analyzes the impact of total rate requirements of different methods on the interruption probability;

[0065] Figure 4 The present invention simulates and analyzes the impact of different downlink signal-to-noise ratios on the interruption probability;

[0066] Figure 5 The present invention simulates and analyzes the impact of different uplink signal-to-noise ratios on the interruption probability;

[0067] Figure 6 Simulation analysis of the impact of rate requirement differences of different methods on the interruption probability when the number of users and antennas increases; DETAILED DESCRIPTION

[0068] The following is a complete and detailed description of the embodiments of the present invention in conjunction with the examples and drawings. Obviously, the described embodiments are only some of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0069] The present invention proposes a deep learning method for the interruption probability optimization problem, such as Figure 1 The specific steps are as follows:

[0070] Step 1: For the downlink transmission scenario of a multi-user multiple-input single-output system, modeling is performed with the optimization objective P1 of minimizing the total outage probability of all users while satisfying the precoding power constraint.

[0071] The optimization goal is:

[0072]

[0073] Among them, constraint 1 is the power sum constraint;

[0074] The base station serves K single-antenna users, and the number of base station antennas is N. is the precoding matrix, is the precoding vector of the kth user, For a given Next, about the real channel h k The conditional probability of is the estimated channel vector of the kth user, is the channel vector of the kth user, expressed as is the estimation error, It means that the mean is 0 and the variance is The estimated channel error of the complex Gaussian distribution is, is the transmission rate of the kth user, is the noise variance of the downlink channel, R k is the minimum transmission rate requirement of the kth user, Tr(·) is the trace of the matrix, P max is the maximum transmit power of the base station.

[0075] Step 2: By introducing the indicator function, the conditional interruption probability of each user in the optimization target P1 is converted into the form of conditional expectation.

[0076] The conditional interruption probability of the kth user is equivalent to the conditional expectation:

[0077]

[0078] Among them, 1(·) is the characteristic function, Indicates a given Next about h k The conditional expectation of R k -r k >0, 1(·)=1; when R k -r k When ≤0, 1(·)=0.

[0079] Step 3: Use the sample averaging method to sample the channel conditional distribution and use the sample mean to approximate the conditional expected value.

[0080] Directly calculating the conditional outage probability for each user requires a complex integral calculation of the user rate based on the channel's conditional probability distribution and the precoding strategy. However, the dimensionality of this integral increases with the number of users and antenna size, significantly increasing the computational complexity of traditional numerical integration methods. This incurs extremely high computational overhead in large-scale communication systems. To overcome these difficulties, the sample averaging method adopts a data-driven approach, approximating the probability by counting the proportion of samples that meet specific conditions, thus avoiding complex analytical integral calculations.

[0081] The sample average method is used, assuming that the conditional probability distribution of the channel is known or obtained through an empirical model, and then based on the conditional distribution or empirical model, the For each channel sample collected, calculate whether the achievable rate meets the rate requirement, i.e. 1(R k -r k Finally, for all samples 1(R k -rk ) to calculate the average.

[0082] The conditional expectation is approximated to the sample mean as follows:

[0083]

[0084] in, Indicates a given Next is a number of h k The sample set is composed of

[0085] Step 4: Use a smooth function to approximate the characteristic function:

[0086] When updating neural network parameters using a gradient descent method, the characteristic function can cause gradient vanishing or gradient exploding during backpropagation, thus affecting the learning performance of the neural network. To solve this problem, a smooth function (such as the Sigmoid function) is used to approximate the characteristic function during training:

[0087]

[0088] Among them, the smoothing function is expressed as:

[0089]

[0090] β≥0 is a smoothing parameter, and its value is affected by c k When the smoothing parameter approaches positive infinity, the limit form of the smoothing function is equivalent to the characteristic function.

[0091] Step 5: Use smoothing functions and unsupervised learning to build a graph neural network that learns the precoding strategy and transform the optimization objective P1 into an optimization problem P2 that defines the network.

[0092] Step 5.1: Based on the two-dimensional permutation equivariant property of the optimization target P1, construct a heterogeneous graph.

[0093] A heterogeneous graph includes vertex and edge features. Antennas and users are two types of vertices, and vertices have no features. The estimated channel and user rate requirements are edge features. The rate requirements for all edges of a user vertex are the same.

[0094] Edge features between the kth user vertex and the nth antenna vertex in, represents the channel information between the kth user and the nth antenna.

[0095] When the user dimension and antenna dimension of the estimated channel matrix are permuted, the objective function and constraints remain unchanged, and the precoding strategy remains unchanged. Therefore, the precoding matrix satisfies the two-dimensional permutation equivariance property, and graph neural networks can be used to learn the precoding strategy, that is, learn actions from the features of the graph.

[0096] Step 5.2: Based on heterogeneous graphs, design a graph neural network to learn precoding strategies.

[0097] Based on the literature [7], a graph neural network is designed to solve the outage probability optimization problem, which is used to learn the channel matrix estimated by the base station under a given rate requirement matrix R. The functional relationship between and the precoding matrix V. Different from the literature [7], the input of the graph neural network in this invention is designed to be The output is the learned precoding matrix

[0098] in, is the estimated channel matrix, θ is the trainable parameter of the graph neural network, Indicates that each element in the kth column is the rate requirement R of the kth user k Matrix of

[0099] [7]Guo J, Yang C. Amodel-based GNN for learning precoding[J]. IEEETransactions on Wireless Communications, 2023, 23(7):6983-6999.doi:10.1109 / TWC.2023.3336911.

[0100] Step 5.3: Using unsupervised learning, we use the proposed sample averaging method based on adaptive smoothing function to define the loss function of the graph neural network:

[0101]

[0102] Step 5.4: Based on the loss function, transform the optimization objective P1 into an optimization problem that defines the network, and obtain:

[0103]

[0104] in, express The sample set is composed of The maximum transmit power constraint is satisfied by designing the output activation function of the neural network, i.e. the normalization layer

[0105] Step 6: Design an adaptive smoothing function method, model the parameter β of the smoothing function in the loss function of the optimization problem P2 as the optimization function P3; use binary search to find the optimal smoothing parameter β;

[0106] In the loss function The smoothing parameter β affects both the approximation error and the gradient of the smoothing function. Improperly selecting the smoothing parameter can lead to excessively large approximation errors or vanishing / exploding gradients. Existing literature typically treats the smoothing parameter as a hyperparameter, either fixed during training or varying with the number of training iterations. However, it is difficult to obtain an appropriate smoothing parameter for all samples in the training set and all feasible strategies during training.

[0107] Based on this, the present invention designs an adaptive smoothing function method based on the characteristics of channel samples and user rate requirements. Based on the precoding strategy of neural network learning, the parameter β of the smoothing function in the loss function of the optimization problem P2 is modeled, and the smoothing parameter optimization function P3 is modeled. The goal is to solve the given c k The smoothing parameter β is used to find the optimal solution using binary search; by dynamically adjusting the smoothing parameter of each user in different samples, the function approximation error is minimized while ensuring gradient stability.

[0108] The process of optimizing the smoothing parameters in the smoothing function includes the following steps:

[0109] Step 6.1: Parameter space design. Considering the diversity of channel samples and the differences in user needs, independent smoothing parameters are designed for different users in each sample to achieve adaptive parameter adjustment.

[0110] Step 6.2: Function approximation error metric. Define the function approximation error metric based on the sample set as: Given the estimated channel Next, the sample set Medium h k The sum of the smooth function approximation errors is As the approximation parameter increases, the total approximation error decreases monotonically.

[0111] Step 6.3: Gradient stability metric. In order to avoid the influence of extreme channel values and make the gradient evaluation robust, the metric is designed to be k The gradient size under the mean condition is defined as

[0112] Step 6.4: Modeling the optimization problem for the smoothing parameter. Based on the parameter space in step 3.1 and the metrics for function approximation error and gradient size in steps 3.2 and 3.3, the optimization problem is modeled as minimizing the function approximation error under the constraint of satisfying the gradient requirement:

[0113] The smoothing parameter optimization function is as follows:

[0114]

[0115] in, Gradient requirements. is the real channel h k The size of the gradient under the mean condition.

[0116] Step 6.5: Optimization algorithm implementation. Using the properties of the objective function and constraint function in problem (P3), the optimal solution can be found through binary search [6].

[0117] [6]Yin M, Han S, Yang C.Learning of Uplink Resource Allocation withMultiuser QoS Constraints[J].arXiv preprint arXiv:2503.06638,2025.

[0118] Step 7: Jointly train the graph neural network and optimize the smoothing parameters, alternately updating the parameters θ of the graph neural network and the parameters β of the smoothing function until convergence is reached.

[0119] The output of the neural network is used to update the smoothing function parameters, and the loss function calculated by the smoothing function parameters is used to update the parameters of the policy network. The smoothing function parameters and network parameters are updated alternately. Initial settings: network parameters θ and smoothing function β are both random values.

[0120] In the lth iteration of the graph neural network, first, the historical estimated channel value is input To the graph neural network, output the learned precoding matrix Using the estimated channel and precoding matrix, the rate for each user can be calculated Since β is about c k function of , thereby obtaining the smoothing parameter β.

[0121] For the kth user in the i-th sample, the estimated channel and precoding Calculation rate and According to the set gradient requirements and The smoothing parameter β is obtained by solving the optimization function P3.

[0122] Then, using c at this time k and smoothing parameter β to calculate the loss function in the optimization problem P2 By using the normalization function to satisfy the constraints, the parameters θ of the graph neural network are updated using stochastic gradient descent:

[0123]

[0124] Among them, δ is the learning rate of the graph neural network, is the gradient vector obtained by back propagation.

[0125] When the network converges, the training ends and the network parameters θ are saved.

[0126] Step 8: Input the estimated channel obtained in real time into the optimized graph neural network and output the learned precoding strategy, that is, obtain the solution of the optimization target P1, which minimizes the total interruption probability of all users.

[0127] Deep learning consists of two parts. One is the training process of network parameters, which is to alternately update them until the results converge; the other is the network decision-making process, which uses the network parameters at the time of convergence as the parameters for decision-making. At this time, for random channel inputs to the network, the corresponding precoding strategy can be obtained, and the interruption probability is minimized.

[0128] In the actual inference process, the estimated channel is input into the graph neural network to obtain the learned precoding strategy. The smoothing function and adaptive smoothing function methods are only used in the training process and are not required in the inference process.

[0129] The following uses the problem of outage probability optimization as an example to illustrate the technical effects of the present invention and compares the method proposed in the present invention with four existing solutions.

[0130] Considering the MU-MISO system, the channel model is a zero-mean complex Gaussian channel, and the error variance of the channel estimation is The noise variance of the uplink channel can be To calculate, the relationship between the two satisfies

[0131] Based on the graph neural network structure in reference [7], the network contains three hidden layers, each with 4,000 neurons. Leaky ReLU is used as the activation function, and the output layer uses a normalization function to meet the power constraint. The optimization algorithm uses Adam, with an initial learning rate of 0.005 and an exponential decay strategy with a decay coefficient of 0.99, which decays once every epoch. The number of samples in the training set is 30,000, and the number of samples in the test set is 100. Each sample includes an estimated channel matrix and 100 sets of true channel matrices generated according to the channel error model under the estimated channel. The training process uses small batches to update the trainable parameters of the neural network, with each batch containing 30 samples. The neural network training is carried out for a total of 80 epochs.

[0132] ●Grid search: This method exhaustively searches for precoding strategies. Since the complexity of the algorithm is related to the number of grids, it is necessary to

[0133] A trade-off is found between performance and computational time. This method initializes with a weighted minimum mean square error strategy, a search radius of 1, and a search interval of 0.1. Due to its high time complexity, this algorithm is only used as a benchmark in some simulations.

[0134] ●Average and rate [8] :This method takes into account the CSI error and optimizes the pre-coding by maximizing the total average sum rate of all users.

[0135] Code strategy.

[0136] ●Through Estimator [9] :This method considers the optimization of interruption probability and uses the sample average method to approximate probability, using the linear function

[0137] This method is simple to implement, but the function approximation error is large.

[0138] Fixed parameters

[10] :This method also optimizes the outage probability and approximates the probability using the sample average method. Using the smooth function approximation

[0139] The indicative function is β, where the smoothing parameter β is a hyperparameter. During the training process, the smoothing parameter is the same for all samples. Through multiple adjustments and attempts, different smoothing parameters are designed under different parameters.

[0140] [8]Lu Q, Lin T, Zhu Y.Channel Estimation and Hybrid Precoding for Millimeter Wave Communications: A Deep Learning-Based Approach[J]. IEEE Access, 2021,9:120924-120939.doi:10.1109 / ACCESS.2021.3108625.

[0141] [9]Tjandra A, Sakti S, Nakamura S. End-to-end Feedback Loss in SpeechChain Framework via Straight-through Estimator[C].ICASSP 2019-2019IEEEInternational Conference on Acoustics, Speech and Signal Processing(ICASSP), Brighton, UK, 2019: 6281-6285.

[0142]

[10] Vu QD, Tran LN, Juntti M.On Spectral Efficiency for MultiuserMISO Systems Under Imperfect Channel Information[J]. IEEE Transactions onVehicular Technology, 2021,70(2):1946-1951.doi:10.1109 / TVT.2021.3050983.

[0143] like Figure 2 As shown in the figure, simulations compare the impact of different rate requirement differences, |R1-R2|, on the probability of satisfaction. The simulation scenario involves two users and two antennas, an uplink signal-to-noise ratio of 10 dB, a downlink signal-to-noise ratio of 20 dB, and a total rate requirement of 6 bps / Hz. The horizontal axis represents the rate requirement difference, and the vertical axis represents the total outage probability for each user's rate requirement. Simulation results show that while the grid search method can achieve the optimal total outage probability, its computational complexity increases exponentially with search accuracy, making it difficult to apply in practical systems. The average sum rate method, because it does not incorporate the rate satisfaction probability into the optimization objective, results in a network-learned strategy with poor outage probability. While the direct estimator method considers probabilistic optimization, it suffers from large function approximation errors, resulting in comparable performance to the average sum rate method. While the fixed parameter method outperforms the direct estimator method by utilizing a smooth function with smaller approximation errors, its performance is significantly worse than the grid search method when |R1-R2| is large. In contrast, the method proposed in this invention effectively solves this problem by dynamically adjusting the smoothing parameters. It outperforms the fixed parameter method under different |R1-R2| values. In particular, the performance is significantly improved when |R1-R2| is large, and the maximum satisfaction probability can be increased by about 13%.

[0144] like Figure 3As shown in Figure 2, simulations compared the impact of different total rate requirements on the total outage probability. The simulation scenario involved two users and two antennas, an uplink signal-to-noise ratio of 10dB, a downlink signal-to-noise ratio of 20dB, and a rate requirement ratio of 5:1. When R1+R2 is large, the performance of the fixed parameter method is significantly lower than that of the grid search method, but the proposed method can effectively compensate for this performance shortcoming.

[0145] like Figure 4 As shown in the figure, the simulation compares the impact of the downlink signal-to-noise ratio. The simulation scenario is 2 users and 2 antennas, the uplink signal-to-noise ratio is 20dB, and the rate requirement ratio is 5:1. The weighted minimum mean square error algorithm is used to calculate the corresponding maximum achievable rate sample mean under ideal channel conditions under each signal-to-noise ratio as the rate requirement R1. As the downlink signal-to-noise ratio increases, the gain of the method proposed in this invention is more obvious than that of the fixed parameter method.

[0146] like Figure 5 As shown, simulations compare the impact of uplink signal-to-noise ratio (SNR). The simulation scenario involves two users and two antennas, a downlink SNR of 20dB, a required rate ratio of 5:1, and R1 = 5bps / Hz. When the uplink SNR is very low, estimation error has a greater impact on performance. In this case, both the fixed parameter method and the proposed method perform poorly. As the uplink SNR increases, the gain of the proposed method compared to the fixed parameter method first increases and then decreases.

[0147] like Figure 6 As shown in the figure, the simulation compares the performance of different rate requirements in a 4-user 4-antenna scenario. The uplink signal-to-noise ratio is 20dB, the downlink signal-to-noise ratio is 20dB, the total rate requirement is 8bps / Hz, and the rate requirement difference between users is defined as Simulation results show that in a 4-user 4-antenna scenario, as the rate difference increases, the performance of the fixed parameter method decreases, and the performance gain of the method proposed in the present invention is obvious.

[0148] In summary, comparing the outage probabilities of the four schemes and the method proposed in the present invention in the test set, the outage probability given by the method proposed in the present invention is closer to the grid search solution compared with the average sum rate method, the direct estimator method and the fixed parameter method. This is because the method considers the differences in channel samples and user rate requirements during the training process, designs an adaptive smoothing function, achieves smaller function approximation error and appropriate gradient size, and thus improves the performance of network learning.

[0149] This document describes the principles and implementation methods of the present invention with reference to specific examples. The above examples are intended only to help understand the methods and core concepts of the present invention. For those skilled in the art, variations may occur in the specific implementation and application based on the concepts of the present invention. In summary, this specification should not be construed as limiting the present invention.

Claims

1. A deep learning method for the outage probability optimization problem, characterized in that: The following steps are involved: Step 1: For the downlink transmission scenario of the multi-user multiple-input single-output (MISO) system, modeling is performed with the optimization objective P1 of minimizing the total outage probability of all users while satisfying the precoding power constraint. The optimization goal is: Among them, the base station serves K single-antenna users, and the number of base station antennas is N. is the precoding matrix, is the precoding vector of the kth user, For a given Next, about the real channel h k The conditional probability of is the estimated channel vector of the kth user, is the channel vector of the kth user, r k is the transmission rate of the kth user, R k is the minimum transmission rate requirement of the kth user, Tr(·) is the trace of the matrix, P max is the maximum transmit power of the base station; Step 2: By introducing the characteristic function, the conditional interruption probability of each user in the optimization target P1 is converted into the form of conditional expectation. The sample average method is used to approximate the conditional expectation value using the sample mean. The smoothing function is used to approximate the characteristic function: Step 3: Use smoothing functions and unsupervised learning to build a graph neural network that learns the precoding strategy, and transform the optimization objective P1 into an optimization problem P2 that defines the network. Step 5.1: Construct a heterogeneous graph based on the two-dimensional permutation equivariant property of the optimization target P1; Heterogeneous graphs include vertex and edge features; antennas and users are two types of vertices, and estimated channels and user rate requirements are edge features; Edge features between the kth user vertex and the nth antenna vertex in, Represents the channel information between the kth user and the nth antenna; Step 5.2: Design a graph neural network to learn the precoding strategy based on the heterogeneous graph; The input of the graph neural network is designed to be The output is the learned precoding matrix in, is the estimated channel matrix, θ is the trainable parameter of the graph neural network, Indicates that each element in the kth column is the rate requirement R of the kth user k Matrix of Step 5.3: Using unsupervised learning, define the loss function of the graph neural network: Step 5.4: Based on the loss function, transform the optimization objective P1 into an optimization problem that defines the network, and obtain: in, express The sample set is composed of The maximum transmit power constraint is satisfied by designing the output activation function of the neural network, i.e. the normalization layer Step 4: Design an adaptive smoothing function method, model the parameter β of the smoothing function in the loss function of the optimization problem P2 as the optimization function P3; use binary search to find the optimal smoothing parameter β; Step 5: Train the graph neural network, alternately updating the parameters θ of the graph neural network and the parameters β of the smoothing function until convergence is achieved. Step 6: Input the estimated channel obtained in real time into the optimized graph neural network and output the learned precoding strategy, that is, obtain the solution of the optimization target P1, which minimizes the total interruption probability of all users.

2. A deep learning method for the interruption probability optimization problem according to claim 1, characterized in that: In step 2, the conditional interruption probability of the kth user is equivalent to the conditional expectation: Among them, 1(·) is the characteristic function, Indicates a given The conditional expectation of hk is: k -r k >0, 1(·)=1; when R k -r k When ≤0, 1(·)=0.

3. A deep learning method for the interruption probability optimization problem according to claim 1 or 2, characterized in that: The conditional expectation is approximated to the sample mean as follows: in, Indicates a given Next is a number of h k The sample set is composed of 4. The deep learning method for the interruption probability optimization problem according to claim 1, characterized in that: In the step 2, the smoothing function is expressed as: β≥0 is a smoothing parameter, and its value is affected by c k impact.

5. The deep learning method for the interruption probability optimization problem according to claim 1, characterized in that: In step 4, the smoothing parameter optimization function is as follows: in, is the gradient requirement; For a given estimated channel Next, the sample set Medium h k The sum of the smooth function approximation errors, is the real channel h k The size of the gradient under the mean condition.

6. The deep learning method for the interruption probability optimization problem according to claim 1, characterized in that: In the step 5, the initial settings are: the network parameter θ and the smoothing function β are both random values; In the lth iteration of the graph neural network: First, input the historical estimated channel value To the graph neural network, get the output of the neural network, that is, the learned precoding matrix Calculate the rate c of each user k ; Thus we get the smoothing parameter β; For the kth user in the i-th sample, the estimated channel and precoding Calculate the rate c of each user k and According to the set gradient requirements and The smoothing parameter β is obtained by solving the optimization function P2; Then, using c at this time k and smoothing parameter β to calculate the loss function in the optimization problem P3 By using the normalization function to satisfy the constraints, the parameters θ of the graph neural network are updated using stochastic gradient descent: Among them, δ is the learning rate of the graph neural network, is the gradient vector obtained by back propagation; When the network converges, the training ends and the network parameters θ are saved.

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