CN114004336A - Three-dimensional ray reconstruction method based on enhanced variational self-encoder - Google Patents

Abstract

The invention provides a three-dimensional ray reconstruction method based on an enhanced variational self-encoder, which is used for perfecting a neural network training sample set of ray tracing data used for neural network model training for predicting a user channel amplitude_cThe training samples are input into a decoder of a trained enhancement condition variation self-encoder, and the generation of the training samples of the appointed channel amplitude interval can be realized. The invention ensures that the distribution of the generated ray samples more conforms to the characteristics of the real environment, and can effectively reduceThe number of users with high error and the prediction error of the neural network greatly reduce the time overhead of obtaining the channel amplitude.

Description

Three-dimensional ray reconstruction method based on enhanced variational self-encoder

Technical Field

The invention relates to a three-dimensional ray reconstruction method based on enhanced distribution condition variational auto-encoder (CVAE). A new ray sample training set is generated for a high-error user through the enhanced variational auto-encoder based on prior probability distribution, so that the hidden variable distribution influencing ray tracing data is more consistent with the characteristics of the high-error user.

Background

In recent years, neural networks have solved many of the problems in the field of communications and have demonstrated advantages over conventional approaches, such as saving computational time overhead. Document [1] discloses a least square support vector machine algorithm, which is applied to modeling of time-varying channel parameters, learns data characteristics of the channel parameters such as delay spread, horizontal angle spread of a receiving end and vertical angle spread, and realizes accurate prediction. Document [2] proposes a channel state information compression feedback algorithm based on deep learning, which is suitable for single-user and multi-user scenes in Massive MIMO systems, and compared with several classical channel state information compression feedback algorithms, the algorithm has lower computational complexity, higher feedback accuracy and better system performance in Massive MIMO systems.

The method is based on ray tracing data, and finds out that more users with higher prediction errors exist in the process of predicting the channel characteristics of the Massive MIMO system by utilizing the neural network. Through research on training samples of the neural network, the problem that actually measured ray data is missing in the process of a system-level simulation experiment is found. Document [3] proposes that the sampling precision is reasonably set by using an information bottleneck method of a self-adaptive neural network, and the balance between the prediction precision and the calculation complexity is realized. However, the neural network proposed by the paper is complex, the computational complexity is still high, and no targeted solution is proposed for the problem of insufficient training sample set existing in the user with high prediction error. To solve the above problems, it is very important to reconstruct and add new samples to make up for the missing measured ray tracing data. Since the cost of newly adding measured ray data through the three-dimensional map is high, different maps are different, and data redundancy is also caused, newly adding data through other ways is considered.

Generative models have often been investigated in recent yearsWherein the conditional variational self-encoder^[4](CVAE) is currently one of the most popular methods for supervised learning of complex probability distributions. CVAE on-repair completion data^[5]Image synthesis^[6]Prediction error^[7]Network security^[8]And the like, so that the CVAE reconstruction and the addition of new samples can be utilized to make up for missing ray data. In a 3D-UMa channel model of a Massive MIMO system, the characteristics that the angular spread of departure and arrival direction angles of rays are described by adopting Laplace distribution^[9]And the training sample obtained based on the ray tracing data contains the information of ray departure and arrival angle, so that the prior knowledge can be fully utilized to construct a new training sample set for the user with high error.

Reference documents:

[1] zhao Xiongwen, Sun Ningyao, Gunn Susei Yan, Yan Yu, Dufei, time varying channel modeling based on least square support vector machine [ J ]. Beijing university of post and Electricity, 2019,42(5):29-35.

[2]Liao Y,Yao H,Hua Y,et al.CSI Feedback Based on Deep Learning for Massive MIMO Systems[J].IEEE Access,2019,PP(99):1-1.

[3] From Wenxin, Likai, Zhou Mingdu, Lijian, Yang, adaptive neural network [ J ] oriented to three-dimensional channel amplitude prediction, university of Chinese academy of sciences, 2021,38(5): 678-.

[4]Diederik P K,Danilo J R,Shakir M,et al.Semi-Supervised Learning with Deep Generative Models[C]//Advances in Neural Information Processing Systems(NIPS).arXiv,2014.

[5]Turhan C G,Bilge H S.Recent Trends in Deep Generative Models:a Review[C]//2018 3rd International Conference on Computer Science and Engineering(UBMK).IEEE,2018.

[6]Zheng K,Cheng Y,Kang X J,et al.Conditional Introspective Variational Autoencoder for Image Synthesis[J].IEEE Access,2020,PP(99):1-1.

[7]Feng X,Cen Z,Hu J,et al.Vehicle Trajectory Prediction Using Intention-based Conditional Variational Autoencoder[C]//2019IEEE Intelligent Transportation Systems Conference(ITSC).IEEE,2019.

[8] Senxiang, Lu J, Wu J, et al. A Conditional variable automatic encoder for Reconstructing Defect Data of Magnetic Flux Leakage [ C ]// 32 nd China conference for control and decision 2020.

[9]3GPPTR38.901.Studyonchannelmodelforfrequenciesfrom0.5to100GHz(R elease15)[S].2018.

[10] Likay, Xujing, Yan 26104, system level simulation modeling and key technology evaluation in 5G environment [ J ]. Zhongxing communication technology, 2016,22(3):41-46.

[11]Diederik P K,Max W.Auto-Encoding Variational Bayes[C]//International Conference on Learning Representations(ICLR).arXiv，2014.

Disclosure of Invention

The purpose of the invention is: and constructing a new training sample set for the high-error user by fully utilizing the information of the ray departure and arrival angles contained in the training samples obtained based on the ray tracing data.

In order to achieve the above object, a technical solution of the present invention is to provide a three-dimensional ray reconstruction method based on an enhanced variational self-encoder, which is used for perfecting a neural network training sample set of ray tracing data used for training a neural network model for predicting a user channel amplitude, quantizing angle information of a departure angle horizontal component, a departure angle vertical component, an arrival angle horizontal component, and an arrival angle vertical component in ray tracing data of each user to form a plurality of quantization intervals, and forming a ray tracing data vector input to the neural network model based on the quantization intervals, and the three-dimensional ray reconstruction method is characterized by comprising the following steps:

step 1, dividing the range interval of the absolute values of the channel amplitudes of all training samples in a CVAE training sample set into N subintervals according to a set step length, defining each subinterval as a category and setting a corresponding category label, so that N category labels can be obtained;

step 2, establishing an enhancement condition variational self-encoder, wherein the enhancement condition variational self-encoder comprises a condition variational self-encoder model based on Laplace distribution and a condition variational self-encoder model based on normal distribution, and the condition variational self-encoder model based on Laplace distribution and the condition variational self-encoder model based on normal distribution are trained by using a CVAE training sample set marked with a class label, wherein:

in the training process, the conditional variation is from the input vector X of the coder model_eExpressed as:

X_e＝[X_e1，X_e2，…，X_en]^T (1)

in the formula (1), X_enAn input vector representing the n-th training sample of the encoder, expressed as X_en＝[x_n l]Wherein x is_nThe ray tracing data vector of the nth training sample is obtained, l is a class label vector of the nth training sample, the length is N, and the rest positions except the corresponding class position in l are 0;

output vector Y of encoder of conditional variational self-encoder model_eExpressed as:

Y_e＝[Y_e1，Y_e2，…，Y_en]^T (2)

in formula (2): y is_enAn output vector representing the encoder for the nth training sample:

for a conditional variational autoencoder model based on Laplace distribution, Y_en＝[μ_k λ_k]，μ_kAnd λ_kIs a Laplace distribution parameter, mu_kIs a position parameter and lambda_kIs a scale parameter;

for a normally distributed conditional variant autoencoder model,

and σ_kIn the form of a normal distribution parameter,

is a mean value, σ_kIs the variance;

during the training process, the conditions changeInput vector X of decoder divided from encoder model_dExpressed as:

X_d＝[X_d1，X_d2，…，X_dn]^T (3)

in the formula (3), X_dnRepresenting the input vector, X, of the decoder corresponding to the n-th training sample_dn＝[z l]And z is (mu) output from the encoder based on the Laplace distribution-based conditional variation autoencoder model and the standard normal distribution-based conditional variation autoencoder model using the recomparametric technique_k，λ_k)、

The implicit variable z obtained by sampling is obtained,

z＝μ_k+λ_kε, ε represents the random variables that follow a normal distribution N (0, 1) with a mean of 0 and a variance of 1, or a Laplace distribution L (0, 1) with a location parameter of 0 and a scale parameter of 1;

output vector Y of decoder of conditional variational self-encoder model_dExpressed as:

Y_d＝[Y_d1，Y_d2，…，Y_dn]^T (4)

in formula (4): y is_dnAn output vector representing the n-th training sample of the decoder and having an expression of Y_dn＝y_n，y_nThe nth training sample restored by the decoder;

during training, the training samples generated by the decoder do not contain channel amplitude information, and the channel amplitude of the training sample with the minimum Euclidean distance from a new sample generated by the decoder to all the training samples in a CVAE training sample set is used as the channel amplitude of the new sample by calculating the Euclidean distance between the new sample and the CVAE training samples;

minimizing a loss function L of a conditional variational self-encoder model based on Laplace distribution and a conditional variational self-encoder model based on normal distribution, thereby completing training;

obtaining a prediction set obtained when a neural network model is trained by using an original training sample set, wherein the original training sample set is an imperfect training sample set, traversing each prediction sample in the prediction set, calculating the proximity rho of each prediction sample and other prediction samples, counting the number of all other prediction samples of which the proximity rho with the current prediction sample is not more than a threshold thr, and further obtaining the number of similar samples of each prediction sample;

defining the sparsity Ω (i) of the user in the ray sample space as shown by the following equation:

in the formula (5), M (i)_ρ≤thrTo predict the number of similar samples, Max, possessed by sample i_j∈[1，N](M(j)_ρ≤thr) The number of similar samples in the prediction set is the largest;

calculating the number and sparsity of similar samples of each prediction sample, dividing the prediction samples into M sparsity intervals based on sparsity, dividing a prediction set into M prediction subsets according to the sparsity intervals, simultaneously obtaining a channel amplitude absolute value interval range corresponding to each sparsity interval, defining the channel amplitude absolute value interval range as a large interval, and obtaining K different large intervals, wherein each large interval at least comprises 1 or more than 1 sub-interval in the step 1;

reconstructing each prediction sample in the M prediction subsets by respectively adopting a Laplace distribution-based conditional variational self-encoder model and a normal distribution-based conditional variational self-encoder model which are used for completing training to obtain 2M reconstruction sample sets;

comparing the same prediction subset with channel amplitude error values between two reconstruction sample sets obtained through a condition variational self-encoder model based on Laplace distribution and a condition variational self-encoder model based on normal distribution respectively, selecting the condition variational self-encoder model based on Laplace distribution and corresponding to the reconstruction sample set with small channel amplitude error values and the condition variational self-encoder model based on normal distribution as a condition variational self-encoder model of a large interval where a sparsity interval corresponding to the current prediction subset is located, and completing construction of the enhanced condition variational self-encoder;

step 3, obtaining a neural network training sample set to be completed, designating subintervals, and obtaining designated class label vectors l based on class labels corresponding to the designated subintervals_cThe enhanced conditional variational self-encoder selects the most suitable conditional variational self-encoder model based on the Laplace distribution in the large region corresponding to the appointed subinterval and randomly samples in the conditional variational self-encoder model based on the normal distribution to obtain L hidden variables z, wherein L is the number of new samples of the appointed subinterval to be generated and is a label vector L of the appointed class_cThe training samples are input into the decoder of the trained enhancement condition variation self-encoder together, and the generation of the training samples of the appointed channel amplitude interval can be realized.

Preferably, in step 2, the conditional variational autocorrelation encoder model based on the laplacian distribution is a posterior distribution q (z | x)_k) Is a position parameter of mu_kWith a scale parameter of λ_kL (z; mu) of the Laplace distribution_k，λ_k) Prior distribution p (z) is a laplacian distribution L (z; 0, λ), the loss function L is:

in the formula: l (x)_kY) is the lower bound of the variation of the conditional variation autoencoder model based on the Laplace distribution, y is the training sample restored by the decoder, y_iThe value of the i-th quantization interval, x, of the training sample restored by the decoder_iIs the value of the ith quantization interval of the training sample corresponding to y, J is the dimension of the implicit variable z, D is the number of quantization intervals, μ_jAnd λ_jThe j-th dimension components of the position parameter and the scale parameter of the hidden variable z learned by the encoder are respectively.

Preferably, in step 2, the calculation formula of the proximity ρ is shown as follows:

in the formula (6), T₁And T₂Are both two different prediction samples in the prediction set, t_1iAnd t_2iAre respectively T₁And T₂For the mean value of ray delays of the ith quantization interval of (1), for the predicted sample T₁For all the conditional prediction samples that meet the formula (6) are similar samples.

The invention uses the thought of CVAE generated graphic samples in the field of computer vision for reference, and only supports standard normal distribution in the original CVAE model aiming at the problem of sparse adjacent sample space of a user with high prediction error^[4]The method has the advantages that Laplace distribution is expanded and supported on the basis, three-dimensional ray sample reconstruction based on the enhancement condition variational self-encoder is provided, so that the generated ray sample distribution is more consistent with real environment characteristics, the number of high-error users and the prediction error of a neural network can be effectively reduced, and the time overhead for obtaining the channel amplitude is greatly reduced.

Drawings

Fig. 1 is a 3-dimensional MIMO channel model structure;

FIG. 2 is a schematic diagram of a BP neural network model;

FIG. 3 is a graph of the mean error for each sparsity sample set based on two distributed reconstructions;

FIG. 4 is a diagram of the predicted cosine distance CDF between the user and the training set;

FIG. 5 is a graph of the prediction error CDF of training models based on the original training set and the new training set;

FIG. 6 is a channel amplitude distribution diagram of high-error users in the new/original training set corresponding to the prediction set;

FIG. 7 is a comparison of channel amplitudes obtained for the new BP neural network and the white-box system

Detailed Description

The invention will be further illustrated with reference to the following specific examples. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.

The invention provides a three-dimensional ray reconstruction method based on an enhanced variational self-encoder, which comprises the following technical contents:

one) Massive MIMO channel model

In the invention, the channel model of the Massive MIMO system is a 3-dimensional channel model. The 3-dimensional channel model structure is shown in fig. 1, which is a 3-dimensional MIMO channel model defined by 3GPP38.901^[9]The model includes 3-dimensional characteristics of the departure angle and arrival angle of the base station and the user. The ray tracing model outputs 3-dimensional coordinates of a starting point, an end point and a reflection point of the ray, and information such as an exit angle, an arrival angle, large-scale path loss, time delay and the like of the ray^[9]. The Massive MIMO channel model used by the invention is a new model fusing a ray tracing model and a 3-dimensional MIMO channel model, and can completely describe the characteristics of a wireless channel.

Two) channel feature learning

The ray tracing data used in the present invention is actually measured ray tracing data located in a certain cell of katalto haha, and is used in the document [10]]The 5G wireless simulation platform (hereinafter referred to as a white box system) realized on the basis of the method generates a channel matrix on the basis of the ray tracing data obtained in the previous step and the fusion channel model. The specific calculation process of the channel matrix can refer to 3GPP38.901 related documents^[9]. The white-box system outputs a user channel amplitude that is a statistical average over 100 ms.

According to ray tracing data and user channel amplitude generated by a white box system, a training set and a prediction set of a BP (back propagation) neural network model are obtained. When the amplitude characteristics of the user channel are learned, the spatial characteristics of the channel matrix can be determined by ray departure angle and arrival angle information, and the user channel amplitude has strong correlation with the propagation distance of rays, so that the input of a BP neural network can be designed according to the departure angle, arrival angle, propagation delay and other information of the rays in ray tracing data, and the learning of the complex mapping relation between the ray tracing data and the user channel amplitude is realized.

Thirdly) predicting the user channel amplitude by the trained BP neural network

In the invention, a BP neural network model is used for predicting the user channel amplitude. As shown in fig. 2, the BP neural network model is composed of three layers, i.e., an input layer, a hidden layer and an output layer. The number of input layer, hidden layer and output layer nodes is 60, 10 and 1, respectively. The number of input layer nodes 60 corresponds to each ray tracing data vector having 60 values, and the number of output layer nodes 1 corresponds to one output, i.e., user channel amplitude. The activation function used by the hidden layer is a linear rectifying unit (ReLU) function.

1) Inputting a BP neural network model:

the angle information of the horizontal component of Departure Angle (AOD), the vertical component of Departure angle (ZOD), the horizontal component of Arrival angle (AOA), and the vertical component of Arrival angle (ZOA) in the ray tracing data of each user is quantized to form a plurality of quantization intervals. In the invention, the quantization interval of the BP neural network model input vector is 18 degrees, and in the four angle components of the ray tracing data of the user: the AOD and AOA have an angle ranging from-180 DEG, respectively forming 20 quantization intervals; ZOD and ZOA have an angle in the range of [0 °, 180 ° ], which can form 10 quantization intervals, respectively. Then in the present invention, there are 60 quantization intervals in total for each user's ray traced data vector.

And filling the actual time delay of each ray into the corresponding quantization interval by taking the quantization interval as an index. And if a plurality of rays can be filled into the same quantization interval, taking the time delay average value of the rays. If there is no ray distribution in a certain quantization interval, a large delay value is filled.

The input vector of the BP neural network model can be expressed as the following formula (1):

X＝[X₁，X₂，…，X_n]^T (1)

in the formula (1), X_nThe ray tracing data vector representing the nth user is expressed by the following formula (2):

in the formula (2), the reaction mixture is,

representing the time delay of the mth quantization interval of the ray tracing data vector of the nth user.

The output of the BP neural network model can be expressed as the following equation (3):

Y＝[Y₁，Y₂，…，Y_n]^T (3)

in formula (3): y is_nThe output vector representing the nth user is the channel amplitude of the nth user.

The invention measures the difference between the predicted value and the actual value of the channel amplitude output by the BP neural network model by using the relative error, wherein the actual value is the channel amplitude of each user calculated by a white box system. The expression of the relative error is shown in the following formula (4):

in equation (4), e represents a relative error, y represents an actual value of the channel amplitude, and y' represents a predicted value of the channel amplitude.

The training sample number of ray tracing data used for training the BP neural network model is 5900, and the prediction sample number is 1000. However, compared with the actual channel amplitude obtained by the white box system simulation, the predicted channel amplitude obtained by inputting the ray tracing data obtained in real time into the trained BP neural network model has more users with higher prediction errors in a part of amplitude intervals. The reason is that the training set obtained based on the actually measured ray tracing data has the problem of missing training samples, that is, in the amplitude interval, the number of rays of the user position corresponding to the training samples is small, most quantization intervals have no ray distribution, and the ray characteristic difference among the samples is large. From the perspective of perfecting the training set, more samples located in these channel amplitude intervals are required to participate in training the BP neural network model.

Therefore, the invention provides an enhanced CVAE model, and simultaneously generates training samples of a required channel amplitude interval by using a training sample generation algorithm provided by the invention to supplement a training set, and trains a BP neural network model by using the improved training set so as to reduce the number of high-error users and the prediction error thereof and realize rapid and accurate channel amplitude prediction.

Four) conditional variational self-encoder

KL divergence D for CVAE_KLTo measure the posterior distribution q (z | x)_kY) and the difference of the true prior distribution p (z, y)^[4]Wherein z is a hidden variable, x_kIs a sample and y is the label of the sample. CVAE model variation lower bound L (x)_kThe first term in y), i.e., the KL divergence term-D_KL(q(z|x_kY) | p (z, y)), the posterior distribution q (z | x)_kY) and the prior distribution p (z, y) are both in the form of a normal distribution, respectively mean

Standard deviation of σ_kNormal distribution of

And a standard normal distribution N (0, 1), wherein the distribution of the hidden variable z is also the standard normal distribution^[4]。

In respect of VAE^[11]In the research of CVAE, the distribution of hidden variable z adopts standard normal distribution, so the invention explores the hidden variable z adopting different probability distribution and is based on the prior distribution characteristics of three-dimensional ray sample space^[9]The method provides the Laplace distribution to expand the CVAE frame, simultaneously provides a prediction sample classification method of the CVAE to classify the prediction samples, and compares the reconstruction average relative errors of different sample types under the Laplace distribution and the normal distribution to determine each sampleThe sample is reconstructed and added in a most suitable distribution form of the sample category, which specifically comprises the following contents:

1) laplace distribution form of KL divergence term

For convenience of description, the present invention extends to CVAE by deriving formulas in VAE. Reference document [15]]Lower bound of variation L (x) of VAE_k) KL divergence term of (1)_KL(q(z|x_k) | p (z)) is represented by the following formula (5):

obeying the hidden variable z in VAE to the probability density function p (x) of the Laplace distribution, i.e., the n-dimensional Laplace distribution independent of each dimension₁，x₂，…，x_n) Comprises the following steps:

in the formula (6), mu_iIs a position parameter of the i-th dimension, λ_iIs a scale parameter of the ith dimension, x_iIs a sample of the ith dimension, p (x)_n) Is x_nA priori distribution of.

The derivation of the laplacian distribution form of the KL divergence term in VAE is given below:

suppose a posterior distribution q (z | x)_k) Is a position parameter of mu_kWith a scale parameter of λ_kL (z; mu) of the Laplace distribution_k，λ_k) Prior distribution p (z) is a laplacian distribution L (z; 0, λ) when the first term q (z | x) in the KL divergence terms_k) log ^ p (z) dz has:

in the formula (7), J is the dimension of the hidden variable z, z_jFor the j-th component of the hidden variable z, we can get:

suppose a posterior distribution q (z | x)_k) The j-th dimension of the implicit variable z is a position parameter mu_jWith a scale parameter of λ_jJ1, 2, 1_jAnd λ_jAre respectively mu_kAnd λ_kThe j-th dimension of (1), order

The first term in formula (7) is obtained:

the second term in formula (7):

thus the first term in KL divergence:

from the second term in the KL divergence:

the same as the solution idea of the first term in the KL divergence, the second term in the KL divergence can be obtained:

thus, a posterior distribution q (z | x) can be obtained in which the hidden variable z obeys the Laplace distribution_k) Is a position parameter of mu_kWith a scale parameter of λ_kWhen the prior distribution p (z) is a laplacian distribution with a position parameter of 0 and a scale parameter of λ, the lower bound of the variation of VAE is expressed by the following formula (13):

lower bound of variation L (x) of CVAE_kThe laplacian distribution form of the KL divergence term in y) is the same as in VAE.

Similar to equation (13), the lower bound of the variation of CVAE when the hidden variable z obeys the Laplace distribution, namely the loss function L (x) in the training process of CVAE can be obtained_kAnd y) is:

in the formula (14), the compound represented by the formula (I),

indicating that x is output with the latent variable z obtained_kIs determined.

The Laplace distribution is derived from the ray distribution situation that a large number of rays (> 400) exist in a ray cluster, but the situation that the number of rays is small often occurs in practical application scenes^[9]The CVAE designed to make the hidden variable z obey the laplace distribution may have a large prediction error, so that the standard normal distribution cannot be matched by using the laplace distribution as a unique distribution form. Since in the case of rare data, the data is generally considered to fit a standard normal distribution.

2) Structure of enhancement condition variation self-encoder

In order to realize the generation of the training sample with the channel amplitude in the designated interval, the invention divides the channel amplitude range of the training sample in the training set into an interval according to 10 dB. The absolute value range of the channel amplitude of the training samples in the training set is 80-180dB, so that the training samples can be divided into 10 intervals in total, and the class labels corresponding to the intervals are 0-9 respectively.

The present invention trains a CVAE model based on laplacian distributions and standard normal distributions using a training set labeled with class labels. The encoder and decoder of the CVAE model use four-layer MLPs each containing an input layer, two hidden layers, and an output layer.

The number of input layer, two hidden layer and output layer nodes of the encoder is 70, 310, 300 and 4, respectively. The input layer node number 70 corresponds to 60 values of a training sample input vector obtained based on ray tracing data, and 70 values are added with 10 values of a category label to be used as input of a CVAE model encoder. Output layer node number 4 corresponds to the output of the encoder exclusive to each sample x_kThe normal distribution parameter and the Laplace distribution parameter, wherein the normal distribution parameter is a mean value

Sum variance σ_kThe Laplace distribution parameter is a position parameter mu_kAnd a scale parameter λ_kReference is made to the following document [11 ]]The dimensionality of the hidden variable z selected by the invention is 2-dimensional, so that the position parameter and the scale parameter which are learned by a CVAE model encoder are both 2-dimensional. The activation functions used by the two hidden layers are Exponential Linear Unit (ELU) functions and hyperbolic tangent tanh functions, respectively.

Input vector X of encoder_eCan be expressed as:

X_e＝[X_e1，X_e2，…，X_en]^T (15)

in formula (15), X_enAn input vector representing the n-th training sample of the encoder, expressed as X_en＝[x_n l]Wherein x is_nIs represented by the formula (2). During the training of CVAE model, the quantization interval formed by ray tracing data, namely x_nOf the quantization intervals of (1), the quantization interval having no ray distribution is filled with 0. l is a class label vector of length 10. The positions except the corresponding category position in the l are all 0.

The output vector of the encoder can be represented as:

Y_e＝[Y_e1，Y_e2，…，Y_en]^T (16)

in formula (16): y is_enRepresenting the output vector of the encoder corresponding to the n-th training sample, and dividing the expression into different distributions

Y_en＝[μ_k λ_k]Two kinds.

The number of input layer, two hidden layer and output layer nodes of the decoder is 12, 300 and 60, respectively. The number of input level nodes 12 corresponds to two values of the 2-dimensional hidden variable z, plus 10 values of the class label. The number of output layer nodes 60 corresponds to a training sample vector generated by the decoder having 60 values. The activation functions used by the two hidden layers are the tanh function and the ELU function, respectively. Referring to document [16], the output value range is controlled between (0, 1) by using a sigmoid activation function for the output layer of the decoder.

During the CVAE model training, the input vector of the decoder can be represented as:

X_d＝[X_d1，X_d2，…，X_dn]^T (17)

in the formula (17), X_dnRepresenting the input vector of the decoder corresponding to the n-th training sample, and the expression is X_dn＝[z l]Wherein z is a technique using a heavy parameter^[17]Based on encoder output based on Laplace distribution and normal distribution

(μ_k，λ_k) The sampled implicit variable z is mu_k+σ_kε、z＝μ_k+λ_kε, ε represents a random variable obeying a normal distribution N (0, 1) with a mean of 0 and a variance of 1, or a Laplace distribution L (0, 1) with a location parameter of 0 and a scale parameter of 1, and z has a dimension of 2. Reference document [11 ]]For any distribution such as the "location-scale" type (e.g., normal, laplace, triangular, etc.), a standard distribution with a location of 0 and a scale of 1 may be used for sampling, so that ε follows a normal distribution N (0, 1) with a mean of 0 and a variance of 1. Or the epsilon obedience location parameter is 0 and the scale parameter is1, L (0, 1). l is the same as in the encoder, a class label vector.

During the CVAE model training, the output vector of the decoder can be expressed as:

Y_d＝[Y_d1，Y_d2，…，Y_dn]^T (18)

in formula (18): y is_dnAn output vector representing the n-th training sample of the decoder and having an expression of Y_dn＝y_n，y_nIs expressed as formula (2), and is the nth training sample recovered by the decoder.

Reference [16]]According to the data type of the training sample of the present invention, the lower bound L (x) of variation shown in equation (14)_kY) log p (x) in the second term_k|z_nY) using a Bernoulli distribution, thus log p (x)_k|z_nAnd y) is:

in formula (19): d is a training sample vector x_kLength of (2), in the present invention, is 60, x_iFor training sample vector x_kValue in the i-th quantization interval, y_iTraining sample vector x restored for decoder_kValue in the ith quantization interval. Reference document [11 ]]When the number of samples trained at each step in the CVAE model training process is sufficiently large, the number of times N of sampling the hidden variable z in equation (14) can be made to be 1, and thus equation (14) is used

The goal of the CVAE model is to make the variational lower bound L (x)_kY) maximum, the present invention leads-L (x) when training the CVAE model_kY), therefore, the loss function L of the training process of the CVAE model based on the standard normal distribution and the CVAE model based on the Laplace distribution in the simulation experiment of the invention is as follows:

the loss function L of the CVAE model based on the standard normal distribution is:

in the above formula: j is 2, D is 60, epsilon_jAnd σ_jJ-th dimension components of expectation and variance of the latent variable z learned by the encoder, respectively;

the loss function L based on the laplacian distribution CVAE model is:

in the above formula: j is 2, D is 60, mu_jAnd λ_jThe j-th dimension component of the position parameter and the scale parameter of the latent variable z learned by the encoder, respectively, is given in document [9]And the practical test results show that the lambda is 1.

The invention calculates the Euclidean distance between the new sample generated by the decoder and all training samples in the training set, and takes the channel amplitude of the training sample with the minimum Euclidean distance with the new sample as the channel amplitude of the new sample.

3) Prediction sample classification method

In the simulation experiment of the invention, for different samples, the deviation of the prediction results and the actual results of different distributions is definitely different, and the result of one sample is probably different from that of another sample when the standard normal distribution of the sample is better than that of Laplace distribution. According to the research background, the number of samples in different channel amplitude intervals is different, some interval samples are dense, and some interval samples are sparse. Therefore, the sparsity of the sample set is found, the sample set is divided into different classes according to the sparsity, the samples of the different classes are predicted by using standard normal distribution or Laplace distribution, and the most appropriate distribution form of each sample is found.

The number of samples in a training set used for training a CVAE model based on standard normal distribution and Laplace distribution is 47200, the number of samples in a testing set is 11800, the Euclidean distance between each sample and other samples in the forecasting set is calculated by traversing the whole testing set, setting a threshold thr, and then the ratio of the Euclidean distance to the length of the sample, namely the proximity rho is calculated, the number of similar samples of the sample is obtained based on the proximity rho, and the calculation formula of the proximity rho is shown as the following formula:

in the formula (20), T₁And T₂Two different prediction samples, t, in the prediction set, both of the CVAE model_1iAnd t_2iAre respectively T₁And T₂The average value of ray time delay of the ith quantization interval of (1), thr is a preset threshold value, the threshold value thr set by the invention is 0.1, and the sample meeting the condition is the prediction sample T₁Similar samples of (2).

Based on the proximity, the invention further defines the sparsity Ω (i) of the user in the ray sample space, as shown in the following formula:

in formula (21): m (i)_ρ≤thrTo predict the number of similar samples, Max, possessed by sample i_j∈[1，N](M(j)_ρ≤thr) The number of similar samples in the prediction set with the largest number is obtained.

Calculating the number and sparsity of similar samples of each prediction sample, dividing the samples in corresponding similar sample intervals together, and obtaining a channel amplitude interval in which the samples in each similar sample interval are mainly located, so that the classification of the prediction samples is shown in the following table 1:

TABLE 1 classification of prediction set samples

As shown in table 1, the present invention divides the prediction samples into 7 intervals, each interval representing one sparsity level. Intervals with more similar samples represent denser samples, and conversely, sparser samples. Therefore, the prediction set samples are divided into 7 sample sets with different sparsity, the sample sets with different sparsity are reconstructed by adopting two distributed CVAE models, the channel amplitude errors between the two distributed reconstructed sample sets and the original input sample set are compared, and the optimal distribution form of the sample sets with different sparsity is found. Fig. 3 shows the magnitude-averaged relative error for each sparsity sample set based on two distributed reconstructions.

As shown in fig. 3, the laplacian distribution in the sample set with dilution of 7 is better than the standard normal distribution except that the average channel amplitude error of the reconstructed samples with standard normal distribution is lower than that of the laplacian distribution. With reference to table 1, the sample channel amplitude interval (absolute value) with dilution of 7 is mainly located at 160dB for 110-. In document [15], it is also known that the enhanced CVAE model is constructed by the fact that the laplacian distribution is more satisfied when there are a large number of rays in the ray cluster.

Fifthly) sample generation algorithm of enhancement condition variation self-encoder based on the obtained preamble

The invention realizes the generation of training samples of an appointed channel amplitude interval by utilizing an enhanced conditional variational self-encoder, after training an enhanced CVAE model obtained by using training set samples, M hidden variables z are obtained by selecting random sampling in the most appropriate distribution of the corresponding channel amplitude interval, wherein M is the number of new samples of an appointed class to be generated and is a class label vector l of the appointed class_cThe training samples are input into the decoder of the trained enhancement condition variation self-encoder together, and the generation of the training samples of the appointed channel amplitude interval can be realized. Thus, when generating training samples, decodingInput vector X of the device_gCan be expressed as:

X_g＝[X_g1，X_g2，…，X_gm]^T (22)

in formula (22): x_gmRepresenting the m-th input vector of the decoder when generating training samples, expressed by X_gm＝[z l_c]Where z is an implicit variable sampled from the selected distribution, and z ═ z₁，z₂]，z₁And z₂For each dimensional component of the hidden variable z, l_cClass label vector for a given class, l_cThe specified category is set to 1 and the remaining categories are set to 0.

Output vector Y of decoder when generating training samples_gCan be expressed as:

Y_g＝[Y_g1，Y_g2，…，Y_gm]^T (23)

in formula (23): y is_gmRepresenting the m-th output vector of the decoder when the training samples are generated, with the expression Y_gm＝y_m，y_mIs expressed as equation (2), for the mth training sample of the specified class generated by the decoder.

The sample generation algorithm based on the enhancement condition variational self-encoder provided by the invention is specifically described as follows:

and (3) comparing the performance of the BP neural network obtained by training the new training set supplemented with the new sample, the BP neural network obtained by training the original training set not supplemented with the new sample and the adaptive neural network in the document [3] by using the BP neural network model, evaluating the effectiveness of reducing the number of high-error users and the prediction error of the high-error users, and improving the performance of the BP neural network after the training set in predicting the channel amplitude.

The number of training samples used for training the enhancement condition variational self-encoder is 59000; the number of samples in the original training set for training the BP neural network model is 5900; the number of training samples generated by the enhancement condition variational self-encoder is 2000, namely, the BP neural network training samples are supplemented to obtain a new training set, and the number of the training samples of the new training set is 7900. The number of prediction set samples used in this example is 1000.

Users with prediction error > 10% are referred to herein as high error users, and users with prediction error ≦ 10% are referred to herein as normal users. By observing the prediction result of the BP neural network model trained by the original training set, the similarity between a high-error user with large prediction error of the BP neural network model and a training sample in the training set is generally low. Therefore, the invention distinguishes high-error users from ordinary users according to the cosine distance between the predicted user and the training set. The specific distance calculation mode is that the cosine distance between the predicted user and the training sample with the minimum cosine distance in the training set is used as the cosine distance between the predicted user and the training set. When 1000 users are predicted by a BP neural network model trained by an original training set according to a Pearson correlation coefficient formula, the correlation coefficient between the normalized cosine distance between the predicted user and the training set and the prediction error is 0.355, which shows that the cosine distance between the predicted user and the training set and the prediction error have a certain degree of correlation. Fig. 4 shows CDF graphs of normalized cosine distances between high-error users and normal users and the training set when the BP neural network trained by the original training set predicts 1000 users.

As shown in fig. 4, the cosine distance between the high-error user and the training set is generally larger, and the cosine distance between the normal user and the training set is generally smaller. Based on the normalized cosine distance threshold, the normalized cosine distance threshold between the prediction user and the training set is selected to distinguish the high-error user from the common user. The threshold value of the normalized cosine distance selected by the invention is 0.075, the predicted user with the normalized cosine distance from the training set larger than 0.075 is a high-error user, and the predicted user with the normalized cosine distance smaller than or equal to 0.075 is a common user. The channel amplitude distribution of training samples in an original training set for training a BP neural network model and the channel amplitude true value distribution of high-error users in a corresponding prediction set of the original training set are shown in a table 2.

TABLE 2 channel amplitude distribution of training samples of the original training set and corresponding high error users

As can be seen from Table 2, the training samples obtained based on the real ray tracing data, i.e. the original training set does have the problem of missing training samples, the absolute value of the channel amplitude is between 80dB and 140dB, and the number of training samples in the interval of 160dB and 180dB is small, and the high-error users predicted by the BP neural network obtained by training the original training set are basically distributed in the two intervals. Aiming at the problem and the phenomenon, the invention utilizes an enhanced condition variational self-encoder to generate a new sample with the channel amplitude value positioned in the interval with less training samples in the original training set, wherein the absolute value of the channel amplitude value is positioned in the 160-180dB interval, i.e. samples with channel amplitudes in the interval of 160-180dB because the number of rays corresponding to the user position is small, that is, most of the quantization intervals of the samples have no ray distribution, and the ray characteristic difference among the samples is large, the self-encoder of the variation of the enhancement condition is difficult to realize the accurate generation of the part of the samples, the present invention thus utilizes the enhanced conditional variational self-encoder to generate class labels of 0-5, namely, the new sample with the channel amplitude absolute value positioned in the 80-140dB interval realizes the sample supplement of the missing interval of the training sample in the original training set, so as to effectively reduce the prediction error of the high-error user. The enhancement condition variation self-encoder realized by the invention generates 2000 new samples with the channel amplitude absolute value in the interval of 80-140dB and supplements the new samples to the original training set. Fig. 5 shows a prediction error CDF diagram of the BP neural network on the prediction set obtained by training the new training set (the original training set is supplemented with the training set after 2000 new samples generated by the enhanced conditional variation autoencoder) and the original training set.

As shown in fig. 5, when the error is less than 0.04, the prediction phase difference between the old training set model and the new training set model is not obvious; when the error is larger than 0.04, the error of the new training set model prediction is obviously lower than that of the old training set. The performance pair ratio of both parties on the prediction set is shown in table 3.

TABLE 3 Performance Pair of BP neural network on prediction set corresponding to new/original training set

As can be seen from table 3, compared with the original BP neural network model, the number of high-error users predicted by the new BP neural network model supplemented with the training samples is significantly reduced, the number of high-error users with prediction errors larger than 10% is reduced by about 29.8%, and users with prediction errors larger than 20% can be basically eliminated; the average error of the new BP neural network model on the prediction set is obviously reduced compared with the original BP neural network model, the average prediction error of the prediction set is reduced from 4.5% to 4.15%, and the average error is reduced by about 8.2% compared with the original average error. Fig. 6 shows a specific distribution histogram of the true values of the channel amplitudes of the high-error users in the prediction set corresponding to the new training set and the original training set.

As shown in FIG. 6, the enhancement condition variational self-encoder is used for supplementing training samples in the 80-140dB interval in the original training set, so that the number of high-error users in the 80-140dB interval predicted by the BP neural network model can be effectively reduced. The average error of the high-error users in the 80-140dB interval predicted by the BP neural network model is reduced from 7.1% to 5.9%, which shows that the number of the high-error users in the corresponding interval and the average prediction error can be effectively reduced by supplementing the training samples in the interval where the training samples are missing in the original training set. FIG. 7 is a graph comparing the predicted user channel amplitude of the BP neural network obtained by training the new training set with the user channel amplitude calculated by the white-box system.

As shown in fig. 7, the user channel amplitude predicted by the BP neural network model obtained by training the new training set is highly consistent with the user channel amplitude obtained by the white-box system through system-level simulation calculation, and the average error of the prediction set is 4.36%. The time overhead for training the new BP neural network with the new training set was 68.59s, and the time overhead for the new BP neural network to predict the channel amplitudes for 1000 users was 0.057 s. Table 4 shows a comparison of the performance of the new BP neural network and the adaptive neural network.

TABLE 4 comparison of Performance of adaptive neural network and New BP neural network

As can be seen from table 4, compared with the adaptive neural network, under the condition of obtaining approximately the same prediction error, the time overhead of predicting the channel amplitudes of 1000 users by the new BP neural network is reduced, which indicates that the BP neural network after completing the training set can predict the channel amplitudes more quickly and accurately.

Claims (3)

1. A three-dimensional ray reconstruction method based on an enhanced variational self-encoder is used for perfecting a neural network training sample set of ray tracing data used for neural network model training for predicting user channel amplitude, quantizing angle information of a departure angle horizontal component, a departure angle vertical component, an arrival angle horizontal component and an arrival angle vertical component in the ray tracing data of each user to form a plurality of quantization intervals, and forming ray tracing data vectors input into a neural network model based on the quantization intervals, and is characterized by comprising the following steps of:

step 1, dividing the range interval of the absolute values of the channel amplitudes of all training samples in a CVAE training sample set into N subintervals according to a set step length, defining each subinterval as a category and setting a corresponding category label, so that N category labels can be obtained;

step 2, establishing an enhancement condition variational self-encoder, wherein the enhancement condition variational self-encoder comprises a condition variational self-encoder model based on Laplace distribution and a condition variational self-encoder model based on normal distribution, and the condition variational self-encoder model based on Laplace distribution and the condition variational self-encoder model based on normal distribution are trained by using a CVAE training sample set marked with a class label, wherein:

in the training process, the conditional variation is from the input vector X of the coder model_eExpressed as:

X_e＝[X_e1，X_e2，…，X_en]^T (1)

in the formula (1), X_enAn input vector representing the n-th training sample of the encoder, expressed as X_en＝[x_n l]Wherein x is_nThe ray tracing data vector of the nth training sample is obtained, l is a class label vector of the nth training sample, the length is N, and the rest positions except the corresponding class position in l are 0;

output vector Y of encoder of conditional variational self-encoder model_eExpressed as:

Y_e＝[Y_e1，Y_e2，…，Y_en]^T (2)

in formula (2): y is_enAn output vector representing the encoder for the nth training sample:

for a conditional variational autoencoder model based on Laplace distribution, Y_en＝[μ_k λ_k]，μ_kAnd λ_kIs a Laplace distribution parameter, mu_kIs a position parameter and lambda_kIs a scale parameter;

for a normally distributed conditional variant autoencoder model,

and σ_kIn the form of a normal distribution parameter,

is a mean value, σ_kIs the variance;

in the training process, the conditional variation is from the input vector X of the decoder of the coder model_dExpressed as:

X_d＝[X_d1，X_d2，…，X_dn]^T (3)

in the formula (3), X_dnIndicating that the decoder corresponds to the n-thInput vector of training sample, X_dn＝[z l]And z is (mu) output from the encoder based on the Laplace distribution-based conditional variation autoencoder model and the standard normal distribution-based conditional variation autoencoder model using the recomparametric technique_k，λ_k)、

Sampling implicit variable z, z ═ mu_k+σ_kε、z＝μ_k+λ_kε, ε represents the random variables that follow a normal distribution N (0, 1) with a mean of 0 and a variance of 1, or a Laplace distribution L (0, 1) with a location parameter of 0 and a scale parameter of 1;

output vector Y of decoder of conditional variational self-encoder model_dExpressed as:

Y_d＝[Y_d1，Y_d2，…，Y_dn]^T (4)

in formula (4): y is_dnAn output vector representing the n-th training sample of the decoder and having an expression of Y_dn＝y_n，y_nThe nth training sample restored by the decoder;

during training, the training samples generated by the decoder do not contain channel amplitude information, and the channel amplitude of the training sample with the minimum Euclidean distance from a new sample generated by the decoder to all the training samples in a CVAE training sample set is used as the channel amplitude of the new sample by calculating the Euclidean distance between the new sample and the CVAE training samples;

minimizing a loss function L of a conditional variational self-encoder model based on Laplace distribution and a conditional variational self-encoder model based on normal distribution, thereby completing training;

obtaining a prediction set obtained when a neural network model is trained by using an original training sample set, wherein the original training sample set is an imperfect training sample set, traversing each prediction sample in the prediction set, calculating the proximity p of each prediction sample and other prediction samples, counting the number of all other prediction samples of which the proximity p to the current prediction sample is not more than a threshold thr, and further obtaining the number of similar samples of each prediction sample;

defining the sparsity Ω (i) of the user in the ray sample space as shown by the following equation:

in the formula (5), M (i)_ρ≤thrTo predict the number of similar samples, Max, possessed by sample i_j∈[1，N](M(j)_p≤thr) The number of similar samples in the prediction set is the largest;

calculating the number and sparsity of similar samples of each prediction sample, dividing the prediction samples into M sparsity intervals based on sparsity, dividing a prediction set into M prediction subsets according to the sparsity intervals, simultaneously obtaining a channel amplitude absolute value interval range corresponding to each sparsity interval, defining the channel amplitude absolute value interval range as a large interval, and obtaining K different large intervals, wherein each large interval at least comprises 1 or more than 1 sub-interval in the step 1;

reconstructing each prediction sample in the M prediction subsets by respectively adopting a Laplace distribution-based conditional variational self-encoder model and a normal distribution-based conditional variational self-encoder model which are used for completing training to obtain 2M reconstruction sample sets;

comparing the same prediction subset with channel amplitude error values between two reconstruction sample sets obtained through a condition variational self-encoder model based on Laplace distribution and a condition variational self-encoder model based on normal distribution respectively, selecting the condition variational self-encoder model based on Laplace distribution and corresponding to the reconstruction sample set with small channel amplitude error values and the condition variational self-encoder model based on normal distribution as a condition variational self-encoder model of a large interval where a sparsity interval corresponding to the current prediction subset is located, and completing construction of the enhanced condition variational self-encoder;

step 3, obtaining a neural network training sample set to be completed, designating subintervals, and obtaining designated class label directions based on class labels corresponding to the designated subintervalsQuantity l_cThe enhanced conditional variational self-encoder selects the most suitable conditional variational self-encoder model based on the Laplace distribution in the large region corresponding to the appointed subinterval and randomly samples in the conditional variational self-encoder model based on the normal distribution to obtain L hidden variables z, wherein L is the number of new samples of the appointed subinterval to be generated and is a label vector L of the appointed class_cThe training samples are input into the decoder of the trained enhancement condition variation self-encoder together, and the generation of the training samples of the appointed channel amplitude interval can be realized.

2. The method as claimed in claim 1, wherein in step 2, the posterior distribution q (z | x |) in the Laplace distribution-based conditional variational autocoder model is posterior distribution q (z | x |)_k) Is a position parameter of mu_kWith a scale parameter of λ_kL (z; mu) of the Laplace distribution_k，λ_k) Prior distribution p (z) is a laplacian distribution L (z; 0, λ), the loss function L is:

in the formula: l (x)_kY) is the lower bound of the variation of the conditional variation autoencoder model based on the Laplace distribution, y is the training sample restored by the decoder, y_iThe value of the i-th quantization interval, x, of the training sample restored by the decoder_iIs the value of the ith quantization interval of the training sample corresponding to y, J is the dimension of the implicit variable z, D is the number of quantization intervals, μ_jAnd λ_jThe j-th dimension components of the position parameter and the scale parameter of the hidden variable z learned by the encoder are respectively.

3. The method of claim 1, wherein in step 2, the proximity p is calculated as follows:

in the formula (6), T₁And T₂Are both two different prediction samples in the prediction set, t_1iAnd t_2iAre respectively T₁And T₂For the mean value of ray delays of the ith quantization interval of (1), for the predicted sample T₁For all the conditional prediction samples that meet the formula (6) are similar samples.

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