CN115983390B - Edge intelligent reasoning method and system based on multi-antenna aerial calculation - Google Patents
Edge intelligent reasoning method and system based on multi-antenna aerial calculation Download PDFInfo
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Abstract
The invention relates to an edge intelligent reasoning method and system based on multi-antenna aerial calculation, which solves the problem that the calculation accuracy lacks theoretical support by using an index named as 'discrimination gain'; through jointly designing communication, calculation and perception models, the communication, calculation and perception models are organically fused, and the problem of high combination of data perception, feature calculation and communication in the process of intelligent reasoning of edges is solved; aggregating results of the plurality of perceptrons using an over-the-air computing technique to eliminate the effects of perception errors as much as possible, avoiding excessive perception errors from occurring in a single device; a multi-antenna (MIMO) air computing system is used for communication design, so that communication delay is further reduced, and communication efficiency is improved.
Description
Technical Field
The invention relates to an artificial intelligence technology of edge equipment, in particular to an intelligent edge reasoning method and system based on multi-antenna aerial calculation.
Background
With the popularity of edge devices (e.g., cell phones, notebook computers, etc.) and the development of artificial intelligence, end-of-life artificial intelligence applications are becoming more and more important at edge devices. This greatly facilitates the study of edge artificial intelligence, which reasoning is one of the most important parts of edge artificial intelligence. In general, artificial intelligence models require significant computational power and memory, which is often not available to edge devices. Edge intelligence reasoning deploys artificial intelligence models at edge devices and server-side in a specific manner, enabling users to run artificial intelligence applications using computing resource-constrained edge devices. Meanwhile, communication delay can be reduced to a certain extent through communication design between the user and the server, so that the user can obtain a calculation result required by the user within acceptable delay time. The intelligent reasoning of the edge generally has three schemes, namely server-side reasoning, device-side reasoning and server device joint reasoning. In server reasoning, a user uploads collected data to a server side, and then the server uses an artificial intelligent model to reason the data; the device-side reasoning requires the user to download the compressed artificial intelligent model to the local and to perform the reasoning locally; the server device joint reasoning is to deploy a part of models at the device end as a feature extractor, and the device sends the extracted features to the server to complete the rest reasoning.
In server reasoning, users need to upload original data to a server, which often causes a certain degree of privacy disclosure, and in addition, when the data uploaded by the users is too large, unacceptable communication delay is often caused in the transmission process. In the device side pushing, the user needs to download the compressed artificial intelligent model, but as the function required by the user increases, the number of the artificial intelligent models to be downloaded also increases, which causes no small burden on the memory of the edge device, and besides, the compressed artificial intelligent model also has a certain degree of reduction in the reasoning accuracy. Therefore, server device joint reasoning is receiving more and more attention. Since the feature is uploaded instead of the data itself, privacy disclosure can be avoided to some extent and communication delay can be reduced.
Existing server device joint reasoning approaches mostly focus on the balance between computational efficiency and communication latency. However, in artificial intelligence applications, the calculation accuracy is also an important index, and in most existing works, the calculation accuracy lacks a certain theoretical support, which makes it difficult to quantify the calculation accuracy into an index that can be directly calculated.
Disclosure of Invention
Aiming at the balance problem of calculation efficiency, communication efficiency and calculation accuracy in artificial intelligent model deployment, the edge intelligent reasoning method and system based on multi-antenna aerial calculation are provided, the reasoning accuracy is used as a guide, and the communication efficiency is ensured and the reasoning accuracy is maximized under the background of server equipment joint reasoning.
The technical scheme of the invention is as follows: an edge intelligent reasoning method based on multi-antenna air calculation specifically comprises the following steps:
1) Training an artificial intelligence model: at the cloud server end, an artificial intelligent model is deployed, a standard data set is collected, and the dimension of each data is set to be N; firstly, training a principal component analysis model, extracting features, setting the dimension after extraction as M, and enabling M=2N t, wherein Nt The number of transmit antennas for each sensor; after principal component analysis, training an artificial intelligent model by using the extracted features, and deploying the trained principal component analysis model to each sensor;
2) Sensing and data processing: for the same target, each sensor k obtains sensing data x through sensing k Sending the sensor data into a principal component analysis model for feature extraction to obtain feature data of each sensor;
3) Communication: each sensor k transmits the characteristics to a cloud server through a wireless channel, and the cloud server obtains data of each sensor, wherein the data comprise a channel matrix, a precoding matrix and channel noise, and the received data are used for artificial intelligent calculation;
4) Multi-antenna aerial computation: the whole system uses an air computing technology to aggregate the characteristics of all perceptrons in a cloud server, sends the characteristics into an artificial intelligent model for classification after training, uses a discrimination gain as an index to conduct parameter adjustment of target guidance, and adjusts a target to maximize classification accuracy;
wherein the discrimination gain between any two classes is defined as the symmetrical KL divergence between the two classes, and the parameters are a beam forming matrix A and a precoding matrix B of a kth sensor k Solving two parameter matrixes;
5) Reasoning: and the cloud server uses the parameters obtained by the aerial calculation to aggregate global features to perform artificial intelligent reasoning.
Further, the specific implementation method of the step 1) is as follows: standard dataset, set the dataset as x, and assume it obeys a gaussian mixture distributionWherein L represents the number of classifications, m l Mean value of standard data of the first class is represented, E represents covariance matrix; firstly, training a principal component analysis model, and extracting features to enable feature vectors to be +.>Then-> wherein />V is a matrix of dimension NxM whose columns are defined by the matrix +.>Is an orthogonal matrix, N is the dimension of the original perceived data, M is the dimension of the reduced-dimension data, and m=2n t ，N t Is the number of sensor transmit antennas; after principal component analysis, the extracted features, i.e. +.>Training an artificial intelligence inference model while deploying a principal component analysis model onto each sensor.
Further, the specific implementation method of the step 2) is as follows: having a configuration N r Cloud server with root receiving antenna, and K cloud servers with N t A sensor of the root transmitting antenna, all sensors observing a target at the same time; for any sensor k, the original data obtained by sensing is x k After sensing, each sensor uses principal component analysis for feature extraction. Since the targets observed by the respective perceptrons are the same for each x k ＝x+d k Wherein x represents standard data, d k Representing a perceived error of the kth sensor;
is provided with a main componentCharacteristic data after analysis isIt is subjected to a gaussian mixture distribution, i.eWherein L represents the number of classifications, μ l ＝[μ l，1 ，μ l，2 ，...，μ l，M ] T Representing the mean value of the class i data,as covariance matrix, for perceptual error, let d be assumed due to orthogonality of matrix V k ～N(0，D k), wherein />Representing the covariance matrix of the error.
Further, the step 3) the cloud server receives the signal as follows:
wherein ,for the channel matrix of the kth sensor, < >>Precoding matrix for kth sensor, and +.>Is Gaussian white noise, s k For transmitting the sign and satisfy
wherein ,representing feature vector +.>Is the i-th element of (c).
And further, the step 4) of multi-antenna space calculation is to weight the extracted characteristics of each sensor under the constraint of the transmitting energy, perform discrimination gain calculation, solve a precoding matrix and a beam forming matrix, and obtain weight distribution under the maximum discrimination gain.
Further, the discrimination gain in the step 4) is defined as follows:
wherein ,xm Symmetrical KL divergence G between categories l and l' for the x mth element l，l′ (x m ) Expressed as:
the numerator of the symmetrical KL divergence is the distance between the categories l and l', and the denominator is the variance of the dimension m;
after the server receives the signal, the server performs beamforming after receiving the signal to obtain
Wherein A is a beamforming matrix; b (B) k Needs to meet energy constraints, i.e wherein Pk Representing the transmit power limit of the kth sensor; will->Is unfolded intoVector get->Maximizing the discrimination gain, assigning weights to each dimension, and the final problem is expressed as:
further, the precoding matrix and the beam forming matrix are paired, the problem is solved by the precoding matrix and is a non-convex problem, the objective function is in the form of a proportional sum and is also non-convex, the problem is simplified by using Zero-forming precoding, and then auxiliary variables are introduced to enable the objective function of the problem to be changed into a convex function; the problem was then converted to a difference of convex (d.c.) form using semi-normal relaxation and shrinkage; finally, solving the problem by using a continuous convex approximation method to obtain a suboptimal solution.
The intelligent edge reasoning system based on multi-antenna aerial computation comprises perceptrons in all edge devices and a cloud server, wherein the cloud server divides a trained principal component analysis model into all edge devices, the perceptrons in all edge devices detect the same target and then send the principal component analysis model to perform feature extraction, feature data of all the perceptrons are transmitted to the cloud server through wireless channels, the cloud server receives data through multiple antennas in the air, an air computing technology is used for combining data perception, feature computation and communication computation, the influence of perception errors is eliminated, and global features are deduced.
The invention has the beneficial effects that: the invention relates to an edge intelligent reasoning method and system based on multi-antenna aerial calculation, which solves the problem that the calculation accuracy lacks theoretical support by using an index named as 'discrimination gain'; through jointly designing communication, calculation and perception models, the communication, calculation and perception models are organically fused, and the problem of high combination of data perception, feature calculation and communication in the process of intelligent reasoning of edges is solved; aggregating results of the plurality of perceptrons using an over-the-air computing technique to eliminate the effects of perception errors as much as possible, avoiding excessive perception errors from occurring in a single device; a multi-antenna (MIMO) air computing system is used for communication design, so that communication delay is further reduced, and communication efficiency is improved.
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Fig. 1 is a schematic diagram of an edge intelligent reasoning system based on multi-antenna air computing according to an embodiment of the present invention;
FIG. 2 is an aerial computing model provided in an embodiment of the present invention;
FIG. 3 is a graph of the relationship between the index of the discrimination gain and the inference accuracy used in the present invention;
FIG. 4a is a graph of performance versus graph of the proposed method, conventional air computing system, and stochastic method of the present invention on using a multi-layer perceived robot gesture recognition dataset;
FIG. 4b is a graph II illustrating the performance of the proposed method, conventional air computing system and stochastic method on using a multi-layer perceived robot gesture recognition dataset;
FIG. 4c is a graph of performance versus graph of the proposed method, conventional air computing system, and stochastic method of the present invention on a human gesture recognition dataset using a support vector machine;
FIG. 4d is a graph II illustrating the performance of the proposed method, conventional air computing system and stochastic method on human gesture recognition datasets using support vector machines.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples. The present embodiment is implemented on the premise of the technical scheme of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following examples.
As shown in fig. 1, the architecture diagram of the edge intelligent reasoning system adopts the discrimination gain as an index, combines the air computing technology, aggregates the perception data of a plurality of perceptrons, and uses a multi-antenna (MIMO) air computing system to provide an edge intelligent reasoning system with high communication efficiency based on multi-antenna air computing, which specifically comprises the following steps:
step 1, training an artificial intelligent model: in the cloudAnd a server side is provided with an artificial intelligent model, such as a support vector machine, a neural network and the like. At the same time, a standard dataset is collected. Let the dimension of each data be N. A principal component analysis (principle component analysis, PCA) model is first trained and feature extraction is performed. Let the dimension after extraction be M, let m=2n in general t, wherein Nt The number of transmit antennas for each sensor. After PCA, the artificial intelligence model is trained using the extracted features, while the trained PCA model is deployed to each sensor.
Step 2, sensing and data processing: for the same target, each sensor k obtains sensing data x through sensing k And sending the data into a PCA model for feature extraction to obtain feature data of each sensor.
Step 3, communication: each sensor k transmits the characteristics to a cloud server through a wireless channel, and the cloud server obtains data of each sensor, including a channel matrix, a precoding matrix and channel noise, and the received data is used for artificial intelligent calculation, namely reasoning.
Step 4, multi-antenna aerial calculation: the whole system uses an air computing technology to aggregate the characteristics of all perceptrons in a cloud server, sends the characteristics into an artificial intelligent model for classification after training, uses a discrimination gain as an index to adjust target guiding parameters, and adjusts the target to maximize classification accuracy. The discrimination gain between any two classes is defined as the symmetrical divergence between the two classes, and the parameters are the beamforming matrix A and the precoding matrix B of the kth perceptron k And solving the two parameter matrixes.
Step 5, reasoning: and the cloud server uses the parameters obtained by the aerial calculation to aggregate global features to perform artificial intelligent reasoning.
The implementation steps are as follows:
step one, training an artificial intelligent model: at the server side, an artificial intelligent model, such as a support vector machine, a neural network and the like, is deployed. At the same time, a standard (group-wire) dataset is collected, which is assumed to be x, and is assumed to follow a Gaussian mixture distributionWherein L represents the number of classifications, m l Represents the mean of the standard data of class i, E represents the covariance matrix. First, a PCA model is trained and feature extraction is performed. Let feature vectors after feature extraction beThen-> wherein />V is a matrix of dimension N M and its columns are defined by the matrixIs an orthogonal matrix, where N is the dimension of the original perceived data, M is the dimension of the reduced-dimension data, and typically let m=2n t ，N t Is the number of transmit antennas of the sensor. After PCA, the extracted features are used, i.e. +.>An artificial intelligence inference model is trained while a PCA model is deployed to each sensor.
Step two, sensing and data processing: the invention has a total of N r Server with root receiving antenna, and K number of server with N t A sensor (e.g., camera, radar sensor, etc.) of the root transmit antenna. All sensors observe one target at a time. For any sensor k, the original data obtained by sensing is x k . After sensing, each sensor uses PCA for feature extraction. Since the targets observed by the respective perceptrons are the same for each x k It can be considered that x k ＝x+d k Wherein x represents standard data and d k Representing the perceived error of the kth sensor. And we need to classify the data at the server sideAnd (5) calculating.
Let PCA post-characteristic data beIt also follows a gaussian mixture distribution, i.eWherein L represents the number of classifications, μ l ＝[μ l，1 ，μ l，2 ，...，μ l，M ] T Representing the mean value of the class i data,as a covariance matrix, it is a reasonable assumption to be a diagonal matrix due to the orthogonality of matrix V in PCA. For perceptual error, assume d k ～N(0，D k), wherein />Representing the covariance matrix of the error.
Step three, communication: after the feature extraction, each sensor is uploaded to a cloud server for subsequent processing. The cloud server side can receive the signal as
wherein ,for the channel matrix of the kth sensor, < >>Precoding matrix for kth sensor, and +.>Is Gaussian white noise, s k For transmitting the sign and satisfy
wherein ,representing feature vector +.>Is the i-th element of (c).
Step four, aerial calculation: as shown in fig. 2, after the server receives the signal, the server performs beamforming after receiving the signal to obtain
Where a is the beamforming matrix. Note that B k Needs to meet energy constraints, i.e wherein Pk Representing the transmit power limit of the kth sensor.
For signalsThere is-> wherein />For vector->Is the i-th element of (c). Expand it into vector +.>And classifying it using a trained machine learning model.
In order to maximize the classification accuracy, the invention uses a target-oriented parameter design method, i.e. uses the discrimination gain as an index to pair parameters A and B k Designing, and defining the discrimination gain as follows:
for any arbitraryThe discrimination gain between any two classes is defined as the symmetric Kullback-Leibler (KL) divergence between the two classes, expressed as follows:
wherein ,xm Is x m element, G l，l′ (x m ) Can be expressed as:
it can be seen that the numerator of the symmetric KL divergence is the distance between categories l and l', and the denominator is the variance of dimension m. When the symmetry KL divergence is larger, the farther the distance between the two classes is, the smaller the variance is, which means that the distance between the two classes becomes larger and the divergence within the class becomes smaller. Smaller dispersion within the class indicates more accurate classification.
And the total discrimination gain may be defined as follows:
it can be seen that the larger the discrimination gain, the longer the distance between any two classes is, the smaller the inter-class dispersion, which can help to improve the accuracy of the classifier to some extent. As shown in fig. 3, the relationship between the discrimination gain index and the inference accuracy used in the present invention increases continuously as the discrimination gain increases, so as to meet the requirements of the present invention.
Under the constraint of emission energy, weighting the extracted characteristics of each perceptron, carrying out discrimination gain calculation, solving a precoding matrix and a beam forming matrix, and obtaining weight distribution under the maximum discrimination gain.
To maximize the discrimination gain, the appropriate weights are given to each dimension, and the final problem can be expressed as:
the problem is not convex because the precoding matrix and the beamforming matrix are paired, and in addition, the objective function is in the form of a proportional sum, which is also not convex. To solve this problem, the present invention first simplifies the problem using Zero-Forcing (ZF) precoding, and then introduces auxiliary variables so that the problem objective function becomes a convex function. The problem was then converted to a difference of convex (d.c.) form using semi-normal relaxation (semidefinite relaxation, SDR) and decompression. Finally, the problem can be solved using a continuous convex approximation (Successive Convex Approximation, SCA), resulting in a suboptimal solution.
To facilitate analysis of this problem, zero-Forcing (ZF) precoding is used for problem reduction. The ZF precoding design is as follows:
AH k B k ＝C k ，1≤k≤K
wherein ,is a diagonal array and c k，i 0 represents the importance of the ith feature of the perceptron k, i.e. the weight. From which B can be pushed out k ＝(AH k ) -1 C k Then the energy constraint is converted into
Bringing ZF precoding into the received signal to obtainFor->Is->Has the following components wherein sk，i An ith element, a, representing a transmission vector of a kth sensor i Representing vector A n Is the i-th element of (c). Expansion into vectors gives +.>Is represented by the expression:
from the above, the relation can be foundIs a distribution of:
wherein ：
wherein Ai Represents line i of A, and subscriptsAnd->Representing the real and imaginary parts, respectively. Similarly, there are
According to the above equation, the problem can be optimized to translate into:
wherein
The problem is then simplified using a semi-positive relaxation method (semidefinite relaxation, SDR).
It can be seen that
Order theIt is a symmetric matrix.
The problem can then be translated into
Based on SDR reduction, low rank constraints may be discarded. If the solution of the problem is found asAnd->The beamforming matrix a may be recovered using the following formula:
wherein ,and->Is->And->Maximum characteristic value ∈>And->Is its corresponding feature vector. In summary, problem P2 can be converted into
To further solve the problem, one of the summation terms in the P3 objective function is expanded, i.e
Is available in the form of
Introducing an auxiliary variable { alpha } l，l′，i }, such that
Problem P3 can be converted into
It can be demonstrated that problem P4 is equivalent to the following problem:
/>
without loss of generality, for any of l, l',2i (2 i-1 is also a classSimilarly), provided withFor one of the optimal solutions of problem P5, the Lagrangian function pair of problem P5 +.>Should be equal to 0, i.e
wherein ,λl，l′，2i And 0 is Lagrangian multiplier constrained as follows:
due toIf lambda is l，l′，2i When 0, the partial derivative is not equal to 0, contradicts the equation, and λ is l，l′，2i > 0. Because of the complementary relaxation theorem, the inequality constraint can only take an equal sign, so P5 is equivalent to P4.
Note that problem P5 is simply a non-convex problem, whose non-convex nature comes mainly from the first constraint and the last two constraints.
For the first constraint, scaling it, there is
So it can be converted into
Root numbers are taken from two sides of the inequality to obtain
Then by means of mean inequalityObtaining the product
The constraint is a convex constraint in that the first term on the left is a convex function and the right can be represented by the convex function tr (A -1 ) The linear transformation is converted by the linear transformation, and the convexity of the function is maintained by the linear transformation, so that the left side of the inequality is a convex function, and the whole constraint is a convex set.
Thus, problem P5 can be converted into
/>
The last two constraints of the problem P5.1 can be expressed as:
note that these two constraints are of the form difference of convex (d.c.). Because both the left and right sides of the inequality sign are convex functions. For the left, it is the sum of the quadratic function and the trace of the matrix, obviously a convex function. And for the right it can be formed by a convex functionObtained by linear transformation, which retains convexity, so the right side is also a convex function. The problem P5.1 is thus a d.c. problem, which can be solved using a continuous convex approximation (Successive Convex Approximation, SCA).
Firstly, performing convex relaxation on the last two constraints, and performing first-order expansion on the right side of the inequality to obtain
/>
Wherein the superscript (t) represents the value of the variable in the t-th iteration of SCA. Thus, problem P5.1 can be converted into the following convex problem:
/>
in summary, after the server receives the signal, the precoding matrix and the beamforming matrix are solved by using the following steps:
1. random generationRandomly choose +.>
2. Let t=0.
3. And (3) circulation:
4、t＝t+1；
5. usingObtaining a problem P6;
6. solving the problemsP6, obtaining the optimal solution
7. If the algorithm converges
8. Jumping out of the circulation;
9. usingRecovering A.
10. Returning to the optimal solution
And fifthly, the cloud server aggregates global features according to the parameters obtained in the previous step, and performs artificial intelligent reasoning by using the features.
The intelligent edge reasoning system based on multi-antenna aerial computation comprises perceptrons in all edge devices and a cloud server, wherein the cloud server divides a trained principal component analysis model into all edge devices, the perceptrons in all edge devices detect the same target and then send the principal component analysis model to perform feature extraction, feature data of all the perceptrons are transmitted to the cloud server through wireless channels, the cloud server receives data through multiple antennas in the air, an air computing technology is used for combining data perception, feature computation and communication computation, the influence of perception errors is eliminated, and global features are deduced.
Fig. 4 a-4 d are graphs comparing the performance of the proposed method of the present invention with conventional air computing systems and stochastic methods on a human gesture recognition dataset. The number of the transmission antennas and the transmission power are respectively used as the abscissa, the reasoning accuracy is used as the ordinate, and two artificial intelligent models of the multi-layer perceptron and the support vector machine are used as the artificial intelligent models deployed at the server side. The traditional air computing system uses the mean square error as an index to carry out air computing parameter design, and the random method uses the air computing parameter by randomly taking the air computing parameter under the condition that the energy constraint is satisfied. Compared with a comparison method, the method provided by the invention has higher final reasoning accuracy.
The above examples illustrate only a few embodiments of the invention, which are described in detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
Claims (3)
1. The intelligent edge reasoning method based on multi-antenna air calculation is characterized by comprising the following steps:
1) Training an artificial intelligence model: at the cloud server end, an artificial intelligent model is deployed, a standard data set is collected, and the dimension of each data is set to be N; firstly, training a principal component analysis model, extracting features, setting the dimension after extraction as M, and enabling M=2N t, wherein Nt The number of transmit antennas for each sensor; after principal component analysis, training an artificial intelligent model by using the extracted features, and deploying the trained principal component analysis model to each sensor;
2) Sensing and data processing: for the same target, each sensor k obtains sensing data x through sensing k Sending the sensor data into a principal component analysis model for feature extraction to obtain feature data of each sensor;
3) Communication: each sensor k transmits the characteristics to a cloud server through a wireless channel, and the cloud server obtains data of each sensor, wherein the data comprise a channel matrix, a precoding matrix and channel noise, and the received data are used for artificial intelligent calculation;
4) Multi-antenna aerial computation: the whole system uses an air computing technology to aggregate the characteristics of all perceptrons in a cloud server, sends the characteristics into an artificial intelligent model for classification after training, uses a discrimination gain as an index to conduct parameter adjustment of target guidance, and adjusts a target to maximize classification accuracy;
wherein the discrimination gain between any two classes is defined as between the two classesThe parameters are the beam forming matrix A and the precoding matrix B of the kth sensor k Solving two parameter matrixes;
5) Reasoning: the cloud server uses the parameters obtained by the aerial calculation to aggregate global features and performs artificial intelligent reasoning;
the specific implementation method of the step 1) comprises the following steps: standard dataset, set the dataset as x, and assume it obeys a gaussian mixture distributionWherein L represents the number of classifications, m l Mean value of standard data of the first class is represented, E represents covariance matrix; firstly, training a principal component analysis model, and extracting features to enable feature vectors to be +.>Then wherein />V is a matrix of dimension NxM whose columns are defined by the matrix +.>Is an orthogonal matrix, N is the dimension of the original perceived data, M is the dimension of the reduced-dimension data, and m=2n t ，N t Is the number of sensor transmit antennas; after principal component analysis, the extracted features, i.e. +.>Training an artificial intelligent reasoning model, and deploying a principal component analysis model to each sensor;
the specific implementation method of the step 2) comprises the following steps: having a configuration N r Root jointCloud server with receiving antenna and K cloud servers with N t A sensor of the root transmitting antenna, all sensors observing a target at the same time; for any sensor k, the original data obtained by sensing is x k After sensing, each sensor uses principal component analysis to extract characteristics; since the targets observed by the respective perceptrons are the same for each x k ＝x+d k Wherein x represents standard data, d k Representing a perceived error of the kth sensor;
let the feature data after principal component analysis beIt is subjected to a gaussian mixture distribution, i.eWherein L represents the number of classifications, μ l ＝[μ l，1 ，μ l，2 ...，μ l，M ] T Representing the mean value of the class i data,as covariance matrix, for perceptual error, let d be assumed due to orthogonality of matrix V k ～N(0，D k), wherein />A covariance matrix representing the error; the step 3) is that the cloud server receives the signal:
wherein ,for the channel matrix of the kth sensor, < >>Precoding matrix for kth sensor, and +.>Is Gaussian white noise, s k For transmitting the sign and satisfy
wherein ,representing feature vector +.>Is the i-th element of (a);
the step 4) of multi-antenna space calculation is to weight the extracted characteristics of each perceptron under the constraint of transmitting energy, perform discrimination gain calculation, solve a precoding matrix and a beam forming matrix, and obtain weight distribution under the maximum discrimination gain;
wherein the discrimination gain is defined as follows:
wherein ,xm Symmetrical KL divergence G between categories l and l' for the x mth element l，l′ (x m ) Expressed as:
the numerator of the symmetrical KL divergence is the distance between the categories l and l', and the denominator is the variance of the dimension m;
after the server receives the signal, the server performs beamforming after receiving the signal to obtain
Wherein A is a beamforming matrix; b (B) k Needs to meet energy constraints, i.e wherein Pk Representing the transmit power limit of the kth sensor; will->Expansion into vectors yields->Maximizing the discrimination gain, assigning weights to each dimension, and the final problem is expressed as:
2. the edge intelligent reasoning method based on multi-antenna air calculation according to claim 1, wherein the precoding matrix and the beam forming matrix are paired, the solution problem is a non-convex problem, the objective function is in the form of a proportional sum and is also non-convex, the problem is simplified by first using Zero-forming precoding, and then auxiliary variables are introduced to enable the objective function of the problem to be changed into a convex function; the problem was then converted to a difference of convex (d.c.) form using semi-normal relaxation and shrinkage; finally, solving the problem by using a continuous convex approximation method to obtain a suboptimal solution.
3. The intelligent edge reasoning system based on multi-antenna aerial computation is characterized by comprising perceptrons and cloud servers in all edge devices, wherein the intelligent edge reasoning method based on multi-antenna aerial computation is used for training and constructing the system, the cloud servers divide a trained principal component analysis model into all edge devices, the perceptrons in all edge devices detect the same target and send the principal component analysis model to perform feature extraction, feature data of all the perceptrons are transmitted to the cloud servers through wireless channels, the cloud servers receive data through multiple antennas in the air, the air computation technology is used for combining data perception, feature computation and communication computation, the influence of perception errors is eliminated, and global features are deduced.
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