CN114189899A - User equipment selection method based on random aggregation beam forming - Google Patents

User equipment selection method based on random aggregation beam forming Download PDF

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CN114189899A
CN114189899A CN202111503756.4A CN202111503756A CN114189899A CN 114189899 A CN114189899 A CN 114189899A CN 202111503756 A CN202111503756 A CN 202111503756A CN 114189899 A CN114189899 A CN 114189899A
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刘升恒
黄永明
徐春梅
傅凝宁
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Southeast University
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Abstract

The invention discloses a user equipment selection method based on random aggregation beamforming, which adopts an air calculation technology to improve the communication efficiency when a federal learning aggregation model is adopted, and the generated aggregation error has influence on the final learning performance. The goal of the problem is to achieve both the goals of minimizing aggregation errors and maximizing the number of user equipments by selecting user equipments and designing an aggregate beamforming vector. Then, a user equipment selection method based on random aggregation beamforming is proposed. When the number of the user equipment is increased, compared with the original algorithm, the algorithm of the invention can obtain lower aggregation error and select more user equipment, thereby obtaining better learning performance.

Description

User equipment selection method based on random aggregation beam forming
Technical Field
The invention belongs to the field of wireless communication, and particularly relates to a user equipment selection method based on random aggregation beam forming.
Background
With the development of wireless communication and the breakthrough of artificial intelligence technology, the more and more intelligent services are undertaken by the edge of the wireless communication network. Usually, people will use traditional centralized training method to accomplish these tasks, but this method will bring high delay and privacy disclosure problems. In recent years, federal learning has attracted increasing researchers' attention as an emerging distributed learning approach. The learning mode does not need to transmit sensitive data when a global model is trained, so privacy disclosure is avoided, and transmission delay is reduced.
However, since the central node and the ue need to communicate frequently, and spectrum resources are very precious for an edge intelligent system, how to improve the communication efficiency becomes a bottleneck for the federal learning development. The traditional communication computation separation mechanism can only perform computation after decoding the signals, so that the efficiency is not high, and therefore, researchers introduce an emerging air computation technology into the framework of federal learning. The technology carries out analog modulation on signals, utilizes the waveform superposition principle, can complete calculation while transmitting, and has proved that under the same conditions, higher communication efficiency can be obtained than a digital modulation scheme based on a communication calculation separation mechanism.
However, due to the fading characteristics of the channel and the influence of noise, the over-the-air computation technique may also bring aggregation errors, and if the aggregation errors are too large, the model training may be negatively affected. On the other hand, selecting more user equipment to participate in model aggregation proves that the learning efficiency can be improved, and the model convergence is accelerated. Therefore, researchers have designed a joint optimization scheme of user equipment selection and aggregation beamforming vectors, which aims to reduce aggregation errors and select more user equipments at the same time, but this method is computationally complex and difficult to implement in practical applications. To solve the problem, a user equipment selection method based on random aggregation beamforming is provided, and the method has low complexity, can be realized in practical application and can ensure performance.
Disclosure of Invention
The invention aims to provide two user equipment selection methods based on random aggregation beamforming, which respectively aim at minimizing mean square error and maximizing the number of selected equipment users.
In order to solve the technical problems, the specific technical scheme of the invention is as follows:
a user equipment selection method based on random aggregation beamforming comprises the following steps:
step 1, constructing a federal learning system model;
step 1.1, in an edge intelligent system, K edge user devices equipped with an antenna and a central node equipped with N antennas, wherein N is less than K; the set of all user equipments is denoted as
Figure BDA0003403289860000021
Each user equipment k has its own local data set
Figure BDA0003403289860000022
The global data set is formed by combining the local data sets
Figure BDA0003403289860000023
The user devices together implement an intelligent application;
step 1.2, adopting a federal learning distributed learning framework;
step 2, training the distributed federal learning model constructed in the step 1, improving the communication efficiency by using an air computing technology, and determining an aggregation error generated by adopting the air computing technology;
step 3, constructing two optimization problems according to the aggregation error determined in the step 2, wherein one optimization problem is the problem of minimizing the mean square error under the condition that the selection number of the user equipment is fixed, and the other optimization problem is the problem of maximizing the number of the selectable user equipment under the condition that the mean square error is ensured to be at a low level;
step 4, aiming at the two optimization problems constructed in the step 3, respectively providing a minimum mean square error algorithm based on random aggregation beam forming and a maximum user equipment selection algorithm based on random aggregation beam forming for solving;
the minimum mean square error algorithm based on the random aggregation beamforming comprises the following steps:
step A, determining the number of user equipment to be selected
Figure BDA0003403289860000031
A random number of samples NmEach cycle generates an auxiliary variable tmp, tmpmaxIs a variable that records the maximum tmp cycled through to the current round, and initializes tmp max0; from 1 to NmContinuously circulating the following three steps B to D, namely executing N in totalmSecondly;
step B, from complex Gaussian distribution
Figure BDA0003403289860000032
M is obtained by sampling at random oncerWhere I is an N × N dimensional identity matrix, and for mrPerform normalization mr＝mr/‖mr‖；
Step C, calculating equivalent channel power for each user equipment k
Figure BDA0003403289860000033
Then, all equivalent channel powers are arranged in a descending order, and the S-th value is selected and recorded as tmp;
step D, if tmp > tmpmaxLet tmpmaxTmp, and the subset of user equipments participating in the update to be selected for the round is then determined as
Figure BDA0003403289860000034
And m is mr；
E, after the circulation execution is finished, obtaining the required user equipment subset participating in the update
Figure BDA00034032898600000313
And a beamforming vector m for the center node;
the maximized user equipment selection algorithm based on random aggregation beamforming comprises the following steps:
step a, firstly determining a threshold value for limiting MSE
Figure BDA0003403289860000035
Number of random samplings Nm(ii) a And initializing the selectable maximum subset of user equipments to an empty set, i.e.
Figure BDA0003403289860000036
From 1 to NmContinuously circulating the four steps from step b to step e, namely circulating NmSecondly;
step b, from complex Gaussian distribution
Figure BDA0003403289860000037
M is obtained by sampling at random oncerWhere I is an N × N dimensional identity matrix, and for mrNormalization is carried out, i.e. mr＝mr/‖mr‖；
Step c, calculating for each user equipment k
Figure BDA0003403289860000038
Step d, determining the subset of the user equipment participating in the updating as
Figure BDA0003403289860000039
Figure BDA00034032898600000310
Step e, if
Figure BDA00034032898600000311
Then order
Figure BDA00034032898600000312
m＝mr；
Step f, obtaining the selectable maximum user equipment subset after the execution of the circulation process is finished
Figure BDA0003403289860000041
And an optimal beamforming vector m for the center node.
Further, the step 1.2 of adopting a federal learning distributed learning framework includes the following steps:
step 1.2.1, selecting a subset among all user equipments
Figure BDA00034032898600000416
To participate in the training of the round;
step 1.2.2, the selected user equipment updates the local model parameters for E times according to the local data set of the user equipment, and then uploads the parameters to the central node;
and step 1.2.3, the central node updates the global model according to the received parameters.
Further, in step 1.2.2, the specific update formula of the local model parameters of the kth ue in the nth round is:
Figure BDA0003403289860000042
wherein the gradient is accumulated
Figure BDA0003403289860000043
Is shown as
Figure BDA0003403289860000044
While
Figure BDA0003403289860000045
Figure BDA0003403289860000046
μiIs the learning rate of step i;
Figure BDA0003403289860000047
is an average loss function, wherein
Figure BDA0003403289860000048
Is in the sample
Figure BDA0003403289860000049
The loss value on the jth data of (1);
let each user equipment have a local data set of the same size, then in the nth pass the global model parameters of the central node can be obtained by:
Figure BDA00034032898600000410
further, the specific steps of step 2 are: in the nth round, the symbol matrix transmitted by user equipment k is defined as
Figure BDA00034032898600000411
And normalized by unit variance, i.e.
Figure BDA00034032898600000412
Wherein I represents an identity matrix;
Figure BDA00034032898600000413
and gkIs abbreviated as sk，wkAnd gk(ii) a Representing the selected set of user devices as
Figure BDA00034032898600000414
The ideal signal obtained by the central node is represented as:
Figure BDA00034032898600000415
skafter analog modulation, the transmission coefficient bkPerforming precoding, bkAmplitude of (2)Represents the transmission power of the user equipment k, whose phase can be used to help the central node to align the received signal; these signals are then superimposed in the air and multiplied by the beamforming vector of the central node; finally, amplifying by a scale factor eta; due to fading and noise in the wireless channel, the signal y actually received by the central node is represented as:
Figure BDA0003403289860000051
wherein h iskIs a channel vector from the user equipment k to the central node, subject to a complex Gaussian distribution of unity power, i.e.
Figure BDA0003403289860000052
The channels are subject to independent equal distribution; the vector n being additive white Gaussian noise, i.e.
Figure BDA0003403289860000053
mHRepresents the conjugate transpose of the beamforming vector, and therefore the aggregate error produced by the over-the-air computation technique is represented as:
Figure BDA0003403289860000054
order to
Figure BDA0003403289860000055
Wherein a iskIs the degree of deviation of the kth ue signal, the mean squared error is expressed as:
Figure BDA0003403289860000056
the first item of
Figure BDA0003403289860000057
Is an error caused by fading, the second term | m |2σ2Is an error caused by noise;
according to equation (6), the following conditions are ensured for eliminating fading related errors:
Figure BDA0003403289860000058
finally, the mean square error is written as follows:
Figure BDA0003403289860000059
further, the optimization problem of minimizing the mean square error specifically includes:
making the number of user equipments selected per round fixed
Figure BDA0003403289860000061
Wherein
Figure BDA0003403289860000062
Is a subset of user equipment
Figure BDA0003403289860000063
The number of the elements in the optimization problem is determined by the scaling factor eta and the transmission coefficient bkSubset of user equipments
Figure BDA00034032898600000615
And a beamforming vector m; since these variables are independent of the noise n, the optimization goal need only be reduced to η | m |)2The whole optimization problem can be expressed as:
Figure BDA0003403289860000064
Figure BDA0003403289860000065
Figure BDA0003403289860000066
Figure BDA0003403289860000067
transmission coefficient bkThe design is as follows:
Figure BDA0003403289860000068
the scale factor η is designed as:
Figure BDA0003403289860000069
where P is the maximum allowed transmit power of each ue, and equation (11) is replaced by equation (9a), since m exists in the numerator and denominator, the optimization problem is equivalent to:
Figure BDA00034032898600000610
s.t.‖m‖＝1 (12)
Figure BDA00034032898600000611
further, the optimization problem of maximizing the number of user equipments specifically includes: setting a MSE threshold as
Figure BDA00034032898600000612
The objective of the optimization problem is to maximize the number of ues under this constraint; we redefine one for each user equipment
Figure BDA00034032898600000613
Wherein m | 1, the final MSE is defined as
Figure BDA00034032898600000614
The transmission coefficient b is expressed as in the equations (10) and (11)kAnd the scale factor eta is taken as an optimal value, and the whole optimization problem is expressed as follows:
Figure BDA0003403289860000071
Figure BDA0003403289860000072
‖m‖＝1 (13c)。
the two user equipment selection methods based on the random aggregation beam forming have the following advantages that:
1. the MSE minimizing algorithm based on the random aggregation beamforming adopts a random sampling mode to replace iterative computation to approach an optimal solution, so that the complexity of the algorithm is greatly reduced, the method can be realized in an actual application scene, and the performance is also ensured.
2. The algorithm for maximizing the number of the user equipment based on the random aggregation beamforming can select the equipment participating in updating as much as possible under the condition of ensuring that the MSE does not exceed a certain threshold value, so that the diversity of the equipment is increased, and the prediction capability of the model is improved.
Drawings
FIG. 1 is a schematic representation of a federated learning system model of the present invention;
FIG. 2 is a schematic diagram of pseudo code of the mean square error minimization algorithm based on random aggregation beamforming according to the present invention;
FIG. 3 is a pseudo code diagram of a UE number maximization algorithm based on random aggregation beamforming according to the present invention;
FIG. 4(a) shows an algorithm, a DC algorithm and l of the present invention1+ MSE result comparison of SDR algorithm;
FIG. 4(b) shows different random sampling times N according to the present inventionmA schematic diagram of the influence on the MSE result of the algorithm of the invention;
FIG. 5(a) shows the algorithm, DC algorithm and l of the present invention for different total numbers of user equipments1A comparison schematic diagram when the total number of the user equipment selected by the + SDR algorithm is 50;
FIG. 5(b) shows the algorithm, DC algorithm and l of the present invention for different total numbers of user equipments1A comparison schematic diagram when the total number of the user equipment selected by the + SDR algorithm is 100;
FIG. 5(c) shows the algorithm, DC algorithm and l of the present invention for different total numbers of user equipments1A comparison schematic diagram when the total number of the user equipment selected by the + SDR algorithm is 150;
FIG. 6(a) is a graph showing the effect of mean square error on MNIST10 data set on test accuracy;
FIG. 6(b) is a graph showing the effect of mean square error on CIFAR10 data set on test accuracy;
fig. 7(a) is a schematic diagram of the effect of user equipment count on the MNIST10 data set on test accuracy;
fig. 7(b) is a diagram illustrating the effect of the number of user equipments on the accuracy of the test on the CIFAR10 data set.
Detailed Description
For better understanding of the purpose, structure and function of the present invention, a method for selecting a ue based on random aggregation beamforming according to the present invention is described in further detail below with reference to the accompanying drawings.
The invention specifically comprises the following steps:
step 1, model construction
Step 1.1, the system model is as shown in fig. 1, in an edge intelligent system, there are K edge user equipments equipped with one antenna and a center node equipped with N antennas, where N is much smaller than K. The set of all user equipments is denoted as
Figure BDA0003403289860000081
Each user equipment k has its own local data set
Figure BDA0003403289860000082
The global data set is composed of the local data setsAre combined to form
Figure BDA0003403289860000083
These user devices together implement an intelligent application. In general, the goal of a machine learning task is to find a set of model parameters woMake the loss function
Figure BDA0003403289860000084
At a minimum, wherein
Figure BDA0003403289860000085
Is a parameter of the model, wherein
Figure BDA0003403289860000086
Is a D-dimensional real vector space.
Step 1.2, adopting a distributed learning framework of federal learning
Each round of federal learning can be divided into three phases: 1) selecting a subset of all user equipments
Figure BDA0003403289860000087
To participate in the training of the round; 2) the selected user equipment updates local model parameters for E times according to the local data set of the user equipment, and then uploads the parameters to the central node; 3) the central node updates the global model based on the received parameters.
The specific update formula of the local model parameters of the kth ue in the nth round is as follows:
Figure BDA0003403289860000091
wherein the gradient is accumulated
Figure BDA0003403289860000092
Can be expressed as
Figure BDA0003403289860000093
While
Figure BDA0003403289860000094
μiIs the learning rate of the ith step.
Figure BDA0003403289860000095
Is an average loss function, wherein
Figure BDA0003403289860000096
Is in the sample
Figure BDA0003403289860000097
The loss value on the jth data of (1). Assuming that each user equipment has a local data set of the same size, then in the nth pass, the global model parameters of the central node can be obtained by:
Figure BDA0003403289860000098
and 2, training the distributed federal learning model constructed in the step 1, improving the communication efficiency by using an air computing technology, and determining an aggregation error generated by adopting the air computing technology.
In the nth round, the symbol matrix transmitted by user equipment k may be defined as
Figure BDA0003403289860000099
And assuming normalization with unit variance, i.e.
Figure BDA00034032898600000910
Where I is the identity matrix. For the sake of convenience of presentation,
Figure BDA00034032898600000911
and gkThe d-th element of (a) can be abbreviated as sk，wkAnd gk. Representing the selected set of user devices as
Figure BDA00034032898600000912
The desired signal for the central node can be expressed as:
Figure BDA00034032898600000913
due to the use of over-the-air computing techniques, skAfter analog modulation, the transmission coefficient bkPerforming precoding, bkRepresents the transmission power of the user equipment k, whose phase can be used to help the central node align the received signal; these signals are then superimposed in the air and multiplied by the beamforming vector of the central node; finally, the amplification is carried out through a scaling factor eta. Due to fading and noise in the wireless channel, the signal y actually received by the central node can be expressed as:
Figure BDA0003403289860000101
wherein h iskIs a channel vector from the user equipment k to the central node, assumed to be a complex gaussian distribution with unity power, i.e.
Figure BDA0003403289860000102
This also assumes that the channels follow independent co-distributions. The vector n being additive white Gaussian noise, i.e.
Figure BDA0003403289860000103
mHIs a conjugate transpose of the beamforming vector. Thus, the aggregate error produced by the over-the-air computation technique can be expressed as:
Figure BDA0003403289860000104
order to
Figure BDA0003403289860000105
The Mean Square Error (MSE) may be expressed as:
Figure BDA0003403289860000106
wherein a iskIs the degree of deviation from the kth user equipment signal,
Figure BDA0003403289860000107
is pair | e |2The mathematical expectation is obtained. First item
Figure BDA0003403289860000108
Is an error caused by fading, the second term | m |2σ2Is an error caused by noise.
To reduce MSE, we can eliminate errors due to fading while minimizing errors due to noise. Thus, although the resulting MSE is not optimal, if the error due to fading is dominant and the central node is equipped with multiple antennas, the resulting MSE is very close to the minimum. According to equation (6), the following conditions must be ensured for eliminating fading related errors:
Figure BDA0003403289860000109
finally, the MSE can be written as follows:
Figure BDA00034032898600001010
and 3, constructing two optimization problems according to the aggregation error determined in the step 2, wherein one optimization problem is the problem of minimizing the mean square error under the condition that the selection number of the user equipment is fixed, and the other optimization problem is the problem of maximizing the number of the selectable user equipment under the condition that the mean square error is ensured to be at a low level.
The minimization of the mean square error optimization problem specifically includes the following: to ensure the learning performance of the model, it is necessary to reduce the value of MSE as much as possible, assuming that the number of ues selected per round is fixed
Figure BDA0003403289860000111
Wherein
Figure BDA0003403289860000112
Is a subset of user equipment
Figure BDA0003403289860000113
Number of elements in (1). The decision variables of the optimization problem then include the scaling factor η, the transmission coefficient bkSubset of user equipments
Figure BDA00034032898600001112
And a beamforming vector m. Since these variables are independent of the noise n, the optimization goal need only be reduced to η | m |)2. The whole optimization problem can be expressed as:
Figure BDA0003403289860000114
Figure BDA0003403289860000115
Figure BDA0003403289860000116
Figure BDA0003403289860000117
according to the existing literature, the transmission coefficient bkCan be directly designed as follows:
Figure BDA0003403289860000118
then, the scale factor η can be designed as:
Figure BDA0003403289860000119
where P is the maximum allowed transmit power of each ue, and equation (11) is replaced by equation (9a), since m exists in the numerator and denominator, the optimization problem is equivalent to:
Figure BDA00034032898600001110
s.t.‖m‖＝1 (12)
Figure BDA00034032898600001111
the optimization problem of maximizing the number of user equipments specifically includes the following: in a real-world situation, if the value of MSE is small, the aggregate error due to the over-the-air computation can be used as a regularization tool to prevent overfitting of the model. In case it is guaranteed that the value of MSE is maintained at a low level, as many user equipments as possible may be selected, which may improve the learning efficiency. Therefore, we set a threshold for MSE to be noted
Figure BDA0003403289860000121
The goal of the problem is to maximize the number of user equipments under this constraint. We redefine one for each user equipment
Figure BDA0003403289860000122
Wherein m | 1, MSEkRepresents the mean square error of the kth user equipment, and the final MSE is defined as
Figure BDA0003403289860000123
Transmission coefficient b is measured as abovekAnd the scale factor η takes an optimum value. The entire optimization problem can then be expressed as:
Figure BDA0003403289860000124
Figure BDA0003403289860000125
‖m‖＝1 (13c)
step 4, aiming at the two optimization problems constructed in the step 3, respectively providing a minimum mean square error algorithm based on random aggregation beam forming and a maximum user equipment selection algorithm based on random aggregation beam forming for solving;
random aggregation beamforming scheme:
the final learning performance of the Federal learning model established by the invention depends on the relevant hyper-parameters of machine learning, such as data quantity, data distribution, equipment computing capacity and the like, and relevant parameters under communication transmission, such as the number of user equipment participating in updating
Figure BDA0003403289860000126
Transmission coefficient bkA beamforming vector m for the center node, a scaling factor η, etc. The user equipments considered in this patent assume the same data volume, data distribution and computational power, but only differences in communication transmission related parameters exist. According to the prior art, we will refer to the transmission coefficient bkAnd the scale factor eta is designed to be an optimal value, and then the beam forming vector m of the central node and the user equipment selection scheme are carried out
Figure BDA0003403289860000128
And (5) performing joint optimization.
For the problem of minimizing Mean Square Error (MSE), the algorithm for minimizing MSE based on random aggregation beamforming specifically includes the following steps, and the pseudo code of the algorithm is shown in fig. 2:
(1) determining number of user equipments per round selection
Figure BDA0003403289860000127
A random number of samples NmAnd initializing two auxiliary variables, tmp max0. From 1 to NmConstantly circulate below(2) To (4) three steps, i.e. a total of NmNext, the process is carried out.
(2) From complex Gaussian distribution
Figure BDA0003403289860000131
M is obtained by sampling at random oncerWhere I is an N identity matrix. And to mrPerform normalization mr＝mr/‖mr‖。
(3) For each user equipment k, calculating equivalent channel power
Figure BDA0003403289860000132
Then all the equivalent channel powers are sorted in descending order, and the S-th value is selected and recorded as tmp.
(4) If tmp > tmpmaxLet tmpmaxTmp, the subset of user equipment participating in the update to be selected for the round may then be determined as
Figure BDA0003403289860000133
And m is mr。
(5) After the loop execution is completed, the required user equipment subset participating in the update can be obtained
Figure BDA00034032898600001313
And a beamforming vector m for the center node.
For the problem of maximizing the number of user equipments, the algorithm for maximizing the number of user equipments based on random aggregation beamforming specifically includes the following steps, and the pseudo code of the algorithm is shown in fig. 3:
(1) first, a threshold value limiting MSE is determined
Figure BDA0003403289860000134
A random number of samples Nm. And initializing the selectable maximum subset of user equipments to an empty set, i.e.
Figure BDA0003403289860000135
From 1 to NmContinuously circulating the four steps (2) to (5),i.e. a common cycle NmNext, the process is carried out.
(2) From complex Gaussian distribution
Figure BDA0003403289860000136
M is obtained by sampling at random oncerWhere I is an N identity matrix. And to mrNormalization is carried out, i.e. mr＝mr/‖mr‖。
(3) For each user equipment k, calculating
Figure BDA0003403289860000137
(4) It may then be determined that a subset of the user devices participating in the update are
Figure BDA0003403289860000138
Figure BDA0003403289860000139
(5) If it is not
Figure BDA00034032898600001310
Then order
Figure BDA00034032898600001311
m＝mr。
(6) After the loop process is executed, the selectable maximum user equipment subset can be obtained
Figure BDA00034032898600001312
And an optimal beamforming vector m for the center node.
To verify the performance advantage of the algorithm, an example flow of the invention is given below.
1. Experimental parameter settings
According to the research of practical situation, we set the maximum transmission power P allowed by each ue to 0 dB. In order to prove the effectiveness of the method, several most advanced algorithms are selected for comparison. For the problem of minimizing MSE, a ratioThe algorithm is an iterative user equipment selection scheme, the method optimizes a beam forming vector by using a convex difference function method, selects a user equipment subset by using the equivalent channel power, and continuously iterates until convergence; the second comparative algorithm is called random ue selection, which also uses the disparity function to optimize the beamforming vector, but the subset of ues is randomly selected. For the problem of maximizing the number of the user equipment selections, a comparative algorithm is a DC algorithm, sparsity is introduced by using a convex difference representation, and then an optimal beam forming vector is obtained; the second algorithm for comparison is l1+ SDR algorithm, use of such algorithm
Figure BDA0003403289860000141
The norm introduces sparsity and then a beam forming vector is obtained by using an SDR method.
2. The effect of the algorithm of the present invention in reducing mean square error
To fully illustrate the effectiveness of the algorithm of the present invention, we stipulate that under the experimental condition, the number of user equipments participating in updating per round S is 10, and the random sampling times N of the beamforming vector is providedm1, the total number of the user equipment in the system tests two cases of K1000 and K10000, and the number of the antennas of the central node is gradually increased from 2 to 12. The results of the tests are shown in fig. 4(a), and it can be seen that the present algorithm is significantly superior to the random ue selection scheme. In addition, although the MSE obtained by the algorithm is slightly higher than the iterative ue selection scheme, the computational complexity of the algorithm is significantly less than that of the iterative method, and the gap between them is smaller as the K value increases.
After that we change NmGradually increased from 1 to 100, and the test results are shown in fig. 4 (b). It can be seen from the figure that the larger the sampling times of the beamforming vector is, the smaller the value of MSE obtained by the algorithm is, and when N ismThe algorithm can even exceed the iterative user equipment selection scheme when the number N of the antennas of the central node is large.
3. The algorithm of the present invention increases the number of user equipments
In this experimental environment, we will
Figure BDA0003403289860000151
Is limited to a value of [ -6, +6]Between dB, the number of antennas at the central node is 4. We consider three experimental scenarios in which the total number of user equipments K is 50, 100 and 150, respectively. The experimental results of different algorithms under the three scenes are shown in fig. 5, and it can be seen that under the same conditions, the algorithm can be obviously better than l1The + SDR algorithm selects more user equipments. And with NmAnd the performance of the algorithm is continuously improved due to the increase of K, and although the performance of the algorithm is comparable to that of the DC algorithm when K is 50, the performance of the algorithm is obviously better than that of the DC algorithm when K is 150.
4. Learning performance
We also tested how much the increasing number of ues can have an impact on the final machine learning task, in this experiment we selected two most classical machine learning datasets, MNIST10 and CIFAR10, respectively, and assumed that the datasets on each ue are not subject to independent and identical distributions. The MNIST10 data set contains ten-digit black and white handwritten digital pictures from 0 to 9, and for this data set we use a multi-layer perceptron neural network. CIFAR10 contains color pictures of class 10 objects and is therefore more difficult to train than MNIST10, so for this dataset we have adopted the ResNet18 neural network. To conveniently express the influence of aggregation errors on learning performance, we model the influence of aggregation errors as a model retransmission probability p, which is expressed as p-1-exp (-aMSE/σ)2) Wherein a is set to 1.
In the experiment, the total number of the user equipments is set to K as 100, 10 user equipments are selected to participate in the update in each round, and the number of the antennas of the central node is 4. MSE/sigma derived from the present algorithm, iterative and random UE selection schemes20.3221, 0.3410, and 1.3531, respectively. As shown in FIG. 6, the present algorithm and iterative user equipment selection scheme have comparable training results, while the random user equipment selection scheme is slightly lower than the first two, thereby resulting in a more or less robust algorithmReduced MSE/sigma may be found2The classification capability of the model can be improved to a certain extent.
Then we set the MSE threshold as MSE/σ2-2 dB. In this case, the present algorithm (N)m1000 case), DC algorithm and l1The maximum number of user equipments obtained by the + SDR algorithm is 30, 17 and 3, respectively. FIG. 7 shows the training effect of the three methods on MNIST10 and CIFAR10, which performs slightly better than the DC algorithm because the algorithm can select slightly more user equipments than the DC algorithm, and l1The + SDR algorithm performs far less than the first two.
It is to be understood that the present invention has been described with reference to certain embodiments, and that various changes in the features and embodiments, or equivalent substitutions may be made therein by those skilled in the art without departing from the spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims (6)

1. A method for selecting user equipment based on Random Aggregation Beamforming (RABF), comprising the steps of:
step 1, constructing a federal learning system model;
step 1.1, in an edge intelligent system, K edge user devices equipped with an antenna and a central node equipped with N antennas, wherein N is less than K; the set of all user equipments is denoted as
Figure FDA0003403289850000011
Each user equipment k has its own local data set
Figure FDA0003403289850000012
The global data set is composed of these local data setsAre combined to form
Figure FDA0003403289850000013
The user devices together implement an intelligent application;
step 1.2, adopting a federal learning distributed learning framework;
step 2, training the distributed federal learning model constructed in the step 1, improving the communication efficiency by using an air computing technology, and determining an aggregation error generated by adopting the air computing technology;
step 3, constructing two optimization problems according to the aggregation error determined in the step 2, wherein one optimization problem is the problem of minimizing the mean square error under the condition that the selection number of the user equipment is fixed, and the other optimization problem is the problem of maximizing the number of the selectable user equipment under the condition that the mean square error is ensured to be at a low level;
step 4, aiming at the two optimization problems constructed in the step 3, respectively providing a minimum mean square error algorithm based on random aggregation beam forming and a maximum user equipment selection algorithm based on random aggregation beam forming for solving;
the minimum mean square error algorithm based on the random aggregation beamforming comprises the following steps:
step A, determining the number of user equipment to be selected
Figure FDA0003403289850000014
A random number of samples NmEach cycle generates an auxiliary variable tmp, tmpmaxIs a variable that records the maximum tmp cycled through to the current round, and initializes tmpmax0; from 1 to NmContinuously circulating the following three steps B to D, namely executing N in totalmSecondly;
step B, from complex Gaussian distribution
Figure FDA0003403289850000015
M is obtained by sampling at random oncerWhere I is an N × N dimensional identity matrix, and for mrPerform normalization mr＝mr/||mr||；
Step C, calculating equivalent channel power for each user equipment k
Figure FDA0003403289850000021
Then, all equivalent channel powers are arranged in a descending order, and the S-th value is selected and recorded as tmp;
step D, if tmp > tmpmaxLet tmpmaxTmp, and the subset of user equipments participating in the update to be selected for the round is then determined as
Figure FDA0003403289850000022
And m is mr；
E, after the circulation execution is finished, obtaining the required user equipment subset participating in the update
Figure FDA00034032898500000213
And a beamforming vector m for the center node;
the maximized user equipment selection algorithm based on random aggregation beamforming comprises the following steps:
step a, firstly determining a threshold value for limiting MSE
Figure FDA0003403289850000023
Number of random samplings Nm(ii) a And initializing the selectable maximum subset of user equipments to an empty set, i.e.
Figure FDA0003403289850000024
From 1 to NmContinuously circulating the four steps from step b to step e, namely circulating NmSecondly;
step b, from complex Gaussian distribution
Figure FDA0003403289850000025
M is obtained by sampling at random oncerWhere I is an N × N dimensional identity matrix, and for mrNormalization is carried out, i.e. mr＝mr/||mr||；
Step c, calculating for each user equipment k
Figure FDA0003403289850000026
Step d, determining the subset of the user equipment participating in the updating as
Figure FDA0003403289850000027
Figure FDA0003403289850000028
Step e, if
Figure FDA0003403289850000029
Then order
Figure FDA00034032898500000210
m＝mr；
Step f, obtaining the selectable maximum user equipment subset after the execution of the circulation process is finished
Figure FDA00034032898500000211
And an optimal beamforming vector m for the center node.
2. The method of claim 1, wherein the step 1.2 of employing a federated learning distributed learning framework comprises the steps of:
step 1.2.1, selecting a subset among all user equipments
Figure FDA00034032898500000212
To participate in the training of the round;
step 1.2.2, the selected user equipment updates the local model parameters for E times according to the local data set of the user equipment, and then uploads the parameters to the central node;
and step 1.2.3, the central node updates the global model according to the received parameters.
3. The method of claim 1, wherein the specific update formula of the local model parameters of the kth ue in step 1.2.2 in the nth round is as follows:
Figure FDA0003403289850000031
wherein the gradient is accumulated
Figure FDA0003403289850000032
Is shown as
Figure FDA0003403289850000033
While
Figure FDA0003403289850000034
Figure FDA0003403289850000035
μiIs the learning rate of step i;
Figure FDA0003403289850000036
is an average loss function, wherein
Figure FDA0003403289850000037
Is in the sample
Figure FDA0003403289850000038
The loss value on the jth data of (1);
let each user equipment have a local data set of the same size, then in the nth pass the global model parameters of the central node can be obtained by:
Figure FDA0003403289850000039
4. the method of claim 3, wherein the step 2 comprises the following steps: in the nth round, the symbol matrix transmitted by user equipment k is defined as
Figure FDA00034032898500000310
And normalized by unit variance, i.e.
Figure FDA00034032898500000311
Wherein I represents an identity matrix;
Figure FDA00034032898500000312
and the d-th element of gk is abbreviated as sk，wkAnd gk(ii) a Representing the selected set of user devices as
Figure FDA00034032898500000313
The ideal signal obtained by the central node is represented as:
Figure FDA00034032898500000314
skafter analog modulation, the transmission coefficient bkPerforming precoding, bkRepresents the transmission power of the user equipment k, whose phase can be used to help the central node align the received signal; these signals are then superimposed in the air and multiplied by the beamforming vector of the central node; finally, amplifying by a scale factor eta; due to fading and noise in the wireless channel, the signal y actually received by the central node is represented as:
Figure FDA0003403289850000041
wherein h iskIs a channel vector from the user equipment k to the central node, subject to a complex Gaussian distribution of unity power, i.e.
Figure FDA0003403289850000042
The channels are subject to independent equal distribution; the vector n being additive white Gaussian noise, i.e.
Figure FDA0003403289850000043
mHRepresents the conjugate transpose of the beamforming vector, and therefore the aggregate error produced by the over-the-air computation technique is represented as:
Figure FDA0003403289850000044
order to
Figure FDA0003403289850000045
Wherein a iskIs the degree of deviation of the kth ue signal, the mean squared error is expressed as:
Figure FDA0003403289850000046
the first item of
Figure FDA0003403289850000047
Is an error caused by fading, the second term η m | | non-woven phosphor2σ2Is an error caused by noise;
according to equation (6), the following conditions are ensured for eliminating fading related errors:
Figure FDA0003403289850000048
finally, the mean square error is written as follows:
Figure FDA0003403289850000049
5. the method of claim 4, wherein the optimization problem of minimizing mean square error specifically comprises:
making the number of user equipments selected per round fixed
Figure FDA00034032898500000410
Wherein
Figure FDA00034032898500000411
Is a subset of user equipment
Figure FDA00034032898500000412
The number of the elements in the optimization problem is determined by the scaling factor eta and the transmission coefficient bkSubset of user equipments
Figure FDA0003403289850000051
And a beamforming vector m; since these variables are independent of the noise n, the optimization goal need only be reduced to η | | | m | | survival2The whole optimization problem can be expressed as:
Figure FDA0003403289850000052
Figure FDA0003403289850000053
Figure FDA0003403289850000054
Figure FDA0003403289850000055
transmission coefficient bkThe design is as follows:
Figure FDA0003403289850000056
the scale factor η is designed as:
Figure FDA0003403289850000057
where P is the maximum allowed transmit power of each ue, and equation (11) is replaced by equation (9a), since m exists in the numerator and denominator, the optimization problem is equivalent to:
Figure FDA0003403289850000058
s.t.||m||＝1 (12b)
Figure FDA0003403289850000059
6. the method of claim 5, wherein the optimization problem of maximizing the number of ues specifically comprises: setting a MSE threshold as
Figure FDA00034032898500000510
The objective of the optimization problem is to maximize the number of ues under this constraint; we redefine one for each user equipment
Figure FDA00034032898500000511
Where m 1, the final MSE is defined as
Figure FDA00034032898500000512
The transmission coefficient b is expressed as in the equations (10) and (11)kAnd the scale factor eta is taken as an optimal value, and the whole optimization problem is expressed as follows:
Figure FDA0003403289850000061
Figure FDA0003403289850000062
||m||＝1 (13c)。
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