CN114189899B - 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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CN114189899B
CN114189899B CN202111503756.4A CN202111503756A CN114189899B CN 114189899 B CN114189899 B CN 114189899B CN 202111503756 A CN202111503756 A CN 202111503756A CN 114189899 B CN114189899 B CN 114189899B
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user equipment
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central node
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CN114189899A (en
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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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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W24/00—Supervisory, monitoring or testing arrangements
    • H04W24/06—Testing, supervising or monitoring using simulated traffic
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N20/00—Machine learning
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/086—Weighted combining using weights depending on external parameters, e.g. direction of arrival [DOA], predetermined weights or beamforming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H04L41/142—Network analysis or design using statistical or mathematical methods
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H04L41/145—Network analysis or design involving simulating, designing, planning or modelling of a network
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention discloses a user equipment selection method based on random aggregation beam forming, which adopts an air computing technology to improve communication efficiency when a federal learning aggregation model is adopted, and aggregation errors generated by the method have influence on 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 more and more researchers' attention as an emerging distributed learning mode. 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 a 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 beam forming 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 GDA0004080682770000021
Each user device k has its own local data set ≥>
Figure GDA0004080682770000022
And a global data set is combined from the local data sets>
Figure GDA0004080682770000023
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 selection number of the user equipment is low;
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 GDA0004080682770000031
A random number of samples N m Each cycle generates an auxiliary variable tmp, tmp max Is a variable that records the maximum tmp cycled through to the current round, and initializes tmp max =0; from 1 to N m Continuously circulating the following three steps B to D, namely totally executing N m Secondly;
step B, from complex Gaussian distribution
Figure GDA0004080682770000032
M is obtained by sampling at random once r Where I is an N × N dimensional identity matrix, and for m r Perform normalization m r ＝m r /||m r ||；
Step C, calculating equivalent channel power for each user equipment k
Figure GDA0004080682770000033
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 > tmp max Let tmp max = tmp, and then the subset of user equipments participating in the update to be selected in the round is determined as
Figure GDA0004080682770000034
And m = m r ；
E, after the circulation execution is finished, obtaining the required user equipment subset participating in the update
Figure GDA0004080682770000035
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 GDA0004080682770000036
Number of random samplings N m (ii) a And initializing a selectable maximum subset of user devices to an empty set, i.e. </er>
Figure GDA0004080682770000037
From 1 to N m Continuously circulating the four steps from step b to step e, namely circulating N m Secondly;
step b, from complex Gaussian distribution
Figure GDA0004080682770000038
In random sampling oneThen m is obtained r Where I is an N × N dimensional identity matrix, and for m r Normalization is carried out, i.e. m r ＝m r /||m r ||；
Step c, calculating for each user equipment k
Figure GDA0004080682770000039
Step d, determining the subset of the user equipment participating in the updating as
Figure GDA00040806827700000310
Figure GDA00040806827700000311
Step e, if
Figure GDA00040806827700000312
Then it is asserted>
Figure GDA00040806827700000313
Step f, obtaining the selectable maximum user equipment subset after the execution of the circulation process is finished
Figure GDA0004080682770000041
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 GDA00040806827700000416
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 GDA0004080682770000042
wherein the gradient is accumulated
Figure GDA0004080682770000043
Is expressed as->
Figure GDA0004080682770000044
And->
Figure GDA0004080682770000045
Figure GDA0004080682770000046
μ i Is the learning rate of step i; />
Figure GDA0004080682770000047
Is a mean loss function, wherein>
Figure GDA0004080682770000048
Is in a sample>
Figure GDA0004080682770000049
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 GDA00040806827700000410
further, the specific steps of step 2 are: in the nth round, the symbol matrix transmitted by the user equipment k is defined as
Figure GDA00040806827700000411
And normalized by the unit variance, i.e. < >>
Figure GDA00040806827700000412
Wherein I represents an identity matrix;
Figure GDA00040806827700000413
and g k Is abbreviated as s k ，w k And g k (ii) a Representing the selected set of user devices as ≧>
Figure GDA00040806827700000414
The ideal signal obtained by the central node is represented as:
Figure GDA00040806827700000415
s k after analog modulation, the transmission coefficient b k Performing precoding, b k Represents the transmission power of user equipment k, and its 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 GDA0004080682770000051
wherein h is k Is a channel vector from the user equipment k to the central node, subject to a complex Gaussian distribution of unity power, i.e.
Figure GDA0004080682770000052
The channels are subject to independent equal distribution; the vector n is additive white Gaussian noise, i.e. < >>
Figure GDA0004080682770000053
m H Represents the conjugate transpose of the beamforming vector, and therefore the aggregate error produced by the over-the-air computation technique is represented as:
Figure GDA0004080682770000054
order to
Figure GDA0004080682770000055
Wherein a is k Is the degree of deviation of the kth user equipment signal, the mean squared error is expressed as: />
Figure GDA0004080682770000056
The first item
Figure GDA0004080682770000057
Is an error caused by fading, the second term η m | | non-woven phosphor 2 σ 2 Is an error caused by noise;
according to equation (6), the following conditions are guaranteed to eliminate the fading related error:
Figure GDA0004080682770000058
finally, the mean square error is written as follows:
Figure GDA0004080682770000059
further, the optimization problem of minimizing the mean square error specifically includes:
making the number of user equipments selected per round fixed
Figure GDA0004080682770000061
Wherein->
Figure GDA0004080682770000062
Is the user device subset->
Figure GDA0004080682770000063
The number of the elements in the optimization problem is determined by the scaling factor eta and the transmission coefficient b k Subscriber device subset->
Figure GDA00040806827700000614
And a beamforming vector m; since these variables are independent of the noise n, the optimization goal need only be reduced to η | | | m | | survival 2 The whole optimization problem can be expressed as:
Figure GDA0004080682770000064
Figure GDA0004080682770000065
Figure GDA0004080682770000066
Figure GDA0004080682770000067
transmission coefficient b k The design is as follows:
Figure GDA0004080682770000068
the scale factor η is designed as:
Figure GDA0004080682770000069
where P is the maximum allowed transmit power of each ue, and equation (11) is replaced by equation (9 a), since m exists in the numerator and denominator, the optimization problem is equivalent to:
Figure GDA00040806827700000610
s.t.||m||＝1 (12b)
Figure GDA00040806827700000611
further, the optimization problem of maximizing the number of user equipments specifically includes: setting a MSE threshold as
Figure GDA00040806827700000612
The objective of the optimization problem is to maximize the number of ues under this constraint; we redefine a ≥ per user device>
Figure GDA00040806827700000613
Where m | =1, the final MSE is defined as
Figure GDA0004080682770000071
The transmission coefficient b is set to be the same as in the equations (10) and (11) k And the scale factor eta is taken as an optimal value, and the whole optimization problem is expressed as follows:
Figure GDA0004080682770000075
Figure GDA0004080682770000072
||m||＝1 (13c)。
the two user equipment selection methods based on the random aggregation beam forming have the following advantages:
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 diagram of a Federal 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) is an algorithm, DC algorithm and
Figure GDA0004080682770000073
comparing MSE results of the algorithm with a graph;
FIG. 4 (b) shows different random sampling times N according to the present invention m A schematic diagram of the influence on the MSE result of the algorithm of the invention;
FIG. 5 (a) shows the algorithm, DC algorithm and DC algorithm of the present invention for different total numbers of user equipments
Figure GDA0004080682770000074
A comparison schematic diagram when the total number of the user equipment selected by the algorithm is 50;
FIG. 5 (b) shows the algorithm, DC algorithm and DC algorithm of the present invention for different total numbers of user equipments
Figure GDA0004080682770000081
A comparison schematic diagram when the total number of the user equipment selected by the algorithm is 100;
FIG. 5 (c) shows the algorithm, DC algorithm and DC algorithm of the present invention for different total numbers of user equipments
Figure GDA0004080682770000082
Comparison of total number of user equipment selected by algorithm to 150A schematic diagram;
FIG. 6 (a) is a schematic diagram showing the effect of mean square error on MNIST10 data set on test accuracy;
FIG. 6 (b) is a schematic diagram showing the effect of mean square error on CIFAR10 data set on test accuracy;
fig. 7 (a) is a schematic diagram of the impact of user equipment count on 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 GDA0004080682770000083
Each user device k has its own local data set ≥>
Figure GDA0004080682770000084
And a global data set is combined from the local data sets>
Figure GDA0004080682770000085
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 w o So that the loss function->
Figure GDA0004080682770000086
Minimum, wherein +>
Figure GDA0004080682770000087
Is a parameter of the model, wherein>
Figure GDA0004080682770000088
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 GDA00040806827700000915
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 GDA0004080682770000091
wherein the gradient is accumulated
Figure GDA0004080682770000092
Can be expressed as->
Figure GDA0004080682770000093
And->
Figure GDA0004080682770000094
Figure GDA0004080682770000095
μ i Is the learning rate of the ith step. />
Figure GDA0004080682770000096
Is a mean loss function, wherein &>
Figure GDA0004080682770000097
Is in the sample->
Figure GDA0004080682770000098
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 GDA0004080682770000099
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 GDA00040806827700000910
And assumes normalization with unit variance, i.e. < >>
Figure GDA00040806827700000911
Where I is the identity matrix. For convenience of presentation, be>
Figure GDA00040806827700000912
And g k The d-th element of (a) can be abbreviated as s k ，w k And g k . Representing a selected set of user devices as ÷ based>
Figure GDA00040806827700000913
The desired signal for the central node can be expressed as:
Figure GDA00040806827700000914
due to the use of over-the-air computing techniques, s k After analog modulation, the transmission coefficient b k To carry out pre-preparationCode, b k Represents 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 GDA0004080682770000101
wherein h is k Is 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 GDA0004080682770000102
This also assumes that the channels follow independent co-distributions. The vector n being additive white Gaussian noise, i.e.
Figure GDA0004080682770000103
m H Is a conjugate transpose of the beamforming vector. Thus, the aggregate error produced by the over-the-air computation technique can be expressed as:
Figure GDA0004080682770000104
order to
Figure GDA0004080682770000105
The Mean Square Error (MSE) may be expressed as:
Figure GDA0004080682770000106
wherein a is k Is the degree of deviation from the kth user equipment signal,
Figure GDA0004080682770000107
is to the | | e | | non-conducting phosphor 2 The mathematical expectation is obtained.First item
Figure GDA0004080682770000108
Is an error caused by fading, the second term is η | | | m | | caly 2 σ 2 Is 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 GDA0004080682770000109
finally, the MSE can be written as follows:
Figure GDA00040806827700001010
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 GDA0004080682770000111
Wherein->
Figure GDA0004080682770000112
Is the user device subset->
Figure GDA0004080682770000113
Number of elements in (1). The decision variables of the optimization problem then include the scaling factor η, the transmission coefficient b k Subscriber device subset->
Figure GDA0004080682770000114
And a beamforming vector m. Since these variables are independent of noise n, the optimization goal need only be reduced to η | | | m | | computation 2 . The whole optimization problem can be expressed as:
Figure GDA0004080682770000115
Figure GDA0004080682770000116
Figure GDA0004080682770000117
/>
Figure GDA0004080682770000118
according to the existing literature, the transmission coefficient b k Can be directly designed as follows:
Figure GDA0004080682770000119
then, the scale factor η can be designed as:
Figure GDA00040806827700001110
where P is the maximum allowed transmit power of each ue, and equation (11) is replaced by equation (9 a), since m exists in the numerator and denominator, the optimization problem is equivalent to:
Figure GDA00040806827700001111
s.t.||m||＝1 (12b)
Figure GDA00040806827700001112
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 GDA0004080682770000121
The goal of the problem is to maximize the number of user equipments under this constraint. We redefine a @ per user device>
Figure GDA0004080682770000122
Where m | =1, MSE k Representing the mean square error of the kth user equipment, the final MSE being defined as ≥>
Figure GDA0004080682770000123
Transmission coefficient b is measured as above k And the scale factor η takes an optimum value. The whole optimization problem can be expressed as:
Figure GDA0004080682770000124
Figure GDA0004080682770000125
||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 GDA0004080682770000126
Transmission coefficient b k A 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 literature, we refer to the transmission coefficient b k And the scaling factor eta is designed to an optimal value, and then the beamforming vector m and the user device selection scheme->
Figure GDA0004080682770000127
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 GDA0004080682770000128
A random number of samples N m And initializing two auxiliary variables, tmp max And =0. From 1 to N m Continuously circulating the following three steps (2) to (4), namely executing N in total m Next, the process is carried out.
(2) From complex Gaussian distribution
Figure GDA0004080682770000131
M is obtained by sampling at random once r Where I is an N identity matrix. And to m r Perform normalization m r ＝m r /||m r ||。
(3) For each user equipment k, calculating equivalent channel power
Figure GDA0004080682770000132
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 > tmp max Let tmp max = tmp, and then the subset of user equipments participating in the update to be selected in the round can be determined as
Figure GDA0004080682770000133
And m = m r 。
(5) After the loop execution is completed, the required user equipment subset participating in the update can be obtained
Figure GDA0004080682770000134
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 GDA0004080682770000135
A random number of samples N m . And initializing the selectable maximum subset of user devices to an empty set, i.e. < >>
Figure GDA0004080682770000136
From 1 to N m Continuously cycling through the four steps (2) to (5), namely, cycling N m Next, the process is carried out.
(2) From complex Gaussian distribution
Figure GDA00040806827700001312
M is obtained by sampling at random once r Where I is an N identity matrix. And to m r Normalization is carried out, i.e. m r ＝m r /||m r ||。
(3) For each user equipment k, calculating
Figure GDA0004080682770000137
(4) It may then be determined that a subset of the user devices participating in the update are
Figure GDA0004080682770000138
Figure GDA0004080682770000139
(5) If it is not
Figure GDA00040806827700001310
Then it is asserted>
Figure GDA00040806827700001311
(6) After the loop process is completed, the selectable maximum user equipment subset can be obtained
Figure GDA0004080682770000141
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 0dB. In order to prove the effectiveness of the method, several most advanced algorithms are selected for comparison. For the problem of minimizing MSE, a comparison algorithm is an iterative user equipment selection scheme, and the method is to optimize a beam forming vector by using a convex difference function method, select a user equipment subset by the size of equivalent channel power, and continuously iterate until convergence; the second algorithm for comparison is called random ue selection, which also uses the convex difference function to optimize the beamforming vector, but the subset of ues is randomly selectedIn (1). 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
Figure GDA0004080682770000142
Algorithm using l 1 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 the number of ues participating in updating per round S =10 and the number of random sampling times N of the beamforming vector under the experimental condition m =1, the total number of user equipments in the system tests two cases of K =1000 and K =10000, and the number of antennas of the central node is gradually increased from 2 to 12. The results of the test 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 changed N m Gradually 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 is m The 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 GDA0004080682770000151
Is limited to [ -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. Is differentThe experimental results of the algorithm 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 that of the algorithm
Figure GDA0004080682770000152
The algorithm selects more user equipments. And with N m And the performance of the algorithm is improved continuously due to the increase of K, and although the performance of the algorithm is comparable to that of the DC algorithm when K =50, the performance of the algorithm is obviously better than that of the DC algorithm when K = 150.
4. Learning performance
We also tested how much the increasing the number of ues can have an impact on the final machine learning task, and 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 same distribution. The MNIST10 data set for which we used a multi-layer perceptron neural network contains ten-digit black and white handwritten digital pictures from 0 to 9 digits. CIFAR10 contains color pictures of class 10 objects and is therefore more difficult to train than MNIST10, so we use the ResNet18 neural network for this data set. To conveniently represent the impact of aggregation error on learning performance, we model the impact of aggregation error as a model retransmission probability p, expressed as p =1-exp (-aMSE/σ) 2 ) Wherein a is set to 1.
The total number of the user equipments in the experiment is set to K =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 schemes 2 0.3221,0.3410 and 1.3531, respectively. As shown in fig. 6, the present algorithm and iterative ue selection scheme have comparable training results, while the random ue selection scheme is slightly lower than the first two, whereby a reduced MSE/σ can be found 2 The classification capability of the model can be improved to a certain extent.
Then we set the MSE threshold to MSE/σ 2 = 2dB. In this case, the present algorithm (N) m Case of = 1000), DC algorithm and
Figure GDA0004080682770000161
the algorithm yields maximum numbers of ues of 30, 17 and 3, respectively. FIG. 7 illustrates 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 devices than the DC algorithm and ^ and/or ^ based on the user device>
Figure GDA0004080682770000162
The algorithm performs much 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 FDA0004080682760000011
Each user device k has its own local data set ≥>
Figure FDA0004080682760000012
And a global data set is combined from the local data sets>
Figure FDA0004080682760000013
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 FDA0004080682760000014
A random number of samples N m Each cycle generates an auxiliary variable tmp, tmp max Is a variable that records the maximum tmp cycled through to the current round, and initializes tmp max =0; from 1 to N m Continuously circulating the following three steps B to D, namely totally executing N m Secondly; wherein +>
Figure FDA0004080682760000015
Representing the number of elements in S;
step B, from complex Gaussian distribution
Figure FDA0004080682760000016
Obtaining m by sampling at random r Where I is an N × N dimensional identity matrix, and for m r Perform normalization m r ＝m r /||m r ||；m r Slave complex gaussian distribution->
Figure FDA0004080682760000017
The physical meaning of the result obtained by sampling once at random is a beam forming vector generated at random;
step C, calculating equivalent channel power for each user equipment k
Figure FDA0004080682760000021
Then, all equivalent channel powers are arranged in a descending order, and the S-th value is selected and recorded as tmp; h is k Is the channel vector between the kth user and the central node;
step D, if tmp>tmp max Let tmp max = tmp, then the subset of user equipments participating in the update to be selected for the round is determined as
Figure FDA0004080682760000022
And m = m r ；
Step E, obtaining the required user equipment subset participating in updating after the circulation execution is finished
Figure FDA00040806827600000212
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 FDA0004080682760000023
Number of random samplings N m (ii) a And initializing a selectable maximum subset of user devices to an empty set, i.e. </er>
Figure FDA0004080682760000024
From 1 to N m Continuously circulating the four steps from step b to step e, namely circulating N m Secondly;
step b, from complex Gaussian distribution
Figure FDA0004080682760000025
M is obtained by sampling at random once r Where I is an N × N dimensional identity matrix, and for m r Normalization is carried out, i.e. m r ＝m r /||m r ||；/>
Step c, calculating for each user equipment k
Figure FDA0004080682760000026
P is the upper limit value of the signal transmission power of each user equipment;
step d, determining the subset of the user equipment participating in the updating as
Figure FDA0004080682760000027
Figure FDA0004080682760000028
Step e, if
Figure FDA0004080682760000029
Then it is asserted>
Figure FDA00040806827600000210
m＝m r ；
Step f, obtaining the selectable maximum user equipment subset after the execution of the circulation process is finished
Figure FDA00040806827600000211
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 of all user equipments
Figure FDA00040806827600000316
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 2, 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 FDA0004080682760000031
in which the gradient is accumulated
Figure FDA0004080682760000032
Is expressed as->
Figure FDA0004080682760000033
And/or>
Figure FDA0004080682760000034
Figure FDA0004080682760000035
μ i Is the learning rate of step i; />
Figure FDA0004080682760000036
Is a function of the average loss of the signal,wherein +>
Figure FDA0004080682760000037
Is in the sample->
Figure FDA0004080682760000038
The loss value on the jth data of (1); />
Figure FDA0004080682760000039
Representing the local model parameters of the kth user equipment in the nth round, wherein the nth round is nE because the local user equipment updates the model parameters for E times in each round; w is a (n-1)E Global model parameters representing the (n-1) th round; />
Figure FDA00040806827600000310
Representing the model parameters updated by the (i + 1) th local user equipment in the nth round; />
Figure FDA00040806827600000311
Representing the model parameters updated by the ith local user equipment in the nth round;
let each user equipment have a local data set of the same size, then in the nth round, the global model parameters of the central node can be obtained by:
Figure FDA00040806827600000312
wherein w nE Representing the global model parameters for the nth pass.
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 FDA00040806827600000313
And normalized by the unit variance, i.e. < >>
Figure FDA00040806827600000314
Wherein I represents an identity matrix; />
Figure FDA00040806827600000315
And g k Is abbreviated as s k ，w k And g k (ii) a Representing a selected set of user devices as ÷ based>
Figure FDA0004080682760000041
The ideal signal obtained by the central node is represented as:
Figure FDA0004080682760000042
s k after analog modulation, the transmission coefficient b k Performing precoding, b k Represents 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 FDA0004080682760000043
wherein h is k Is a channel vector from the user equipment k to the central node, subject to a complex Gaussian distribution of unity power, i.e.
Figure FDA0004080682760000044
The channels are subject to independent equal distribution; the vector n is additive white Gaussian noise, i.e. < >>
Figure FDA0004080682760000045
m H Represents the conjugate transpose of the beamforming vector, and therefore the aggregate error produced by the over-the-air computation technique is represented as:
Figure FDA0004080682760000046
order to
Figure FDA0004080682760000047
Wherein a is k Is the degree of deviation of the kth ue signal, the mean squared error is expressed as:
Figure FDA0004080682760000048
the first item of
Figure FDA0004080682760000049
Is an error caused by fading, the second term η m | | non-woven phosphor 2 σ 2 Is an error caused by noise;
according to equation (6), the following conditions are ensured for eliminating fading related errors:
Figure FDA00040806827600000410
finally, the mean square error is written as follows:
Figure FDA0004080682760000051
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 FDA00040806827600000510
Wherein->
Figure FDA00040806827600000511
Is the user device subset->
Figure FDA00040806827600000512
The number of the elements in the optimization problem is determined by the scaling factor eta and the transmission coefficient b k Subscriber device subset->
Figure FDA00040806827600000513
And a beamforming vector m; since these variables are independent of the noise n, the optimization goal need only be reduced to η | | | m | | survival 2 The whole optimization problem can be expressed as:
Figure FDA0004080682760000052
Figure FDA0004080682760000053
Figure FDA0004080682760000054
Figure FDA0004080682760000055
transmission coefficient b k The design is as follows:
Figure FDA0004080682760000056
/>
the scale factor η is designed as:
Figure FDA0004080682760000057
where P is the maximum allowed transmit power of each ue, and equation (11) is replaced by equation (9 a), since m exists in the numerator and denominator, the optimization problem is equivalent to:
Figure FDA0004080682760000058
s.t.||m||＝1 (12b)
Figure FDA0004080682760000059
6. the method of claim 5, wherein the optimization problem of maximizing the number of ues specifically comprises: setting a MSE threshold as
Figure FDA0004080682760000061
The objective of the optimization problem is to maximize the number of ues under this constraint; we redefine one for each user equipment
Figure FDA0004080682760000062
Where m | =1, the final MSE is defined as | |>
Figure FDA0004080682760000063
The transmission coefficient b is expressed as in the equations (10) and (11) k And the scale factor eta is taken as an optimal value, and the whole optimization problem is expressed as follows:
Figure FDA0004080682760000064
Figure FDA0004080682760000065
||m||＝1 (13c)。
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