KR20210000645A - Method and apparatus of massive mimo detection based on deep neural network - Google Patents

Abstract

The present invention provides a method and an apparatus of large MIMO signal detection using a deep neural network which has high detection performance at low complexity. According to various embodiments of the present invention, the method and the apparatus of large MIMO signal detection using a deep neural network can be configured to estimate a transmission signal based on a reception signal and a channel for the reception signal, derive a MIMO detection problem based on the reception signal, the channel, and the transmission signal, detect augmented Lagrange of the MIMO detection problem, apply an R-A-ADMM algorithm to augmented Lagrange, apply a proximal term to optimize the transmission signal to derive R-A-ADMM, and apply an integrable nonlinear function to the R-A-ADMM to optimize the transmission signal to implement an R-A-ADMM network having learning parameters.

Description

A method and apparatus for detecting large-capacity MIMO signals using a deep neural network {METHOD AND APPARATUS OF MASSIVE MIMO DETECTION BASED ON DEEP NEURAL NETWORK}

Various embodiments relate to a method and apparatus for detecting a large-capacity MIMO signal using a deep neural network.

As the 4th industrial revolution has recently become an issue, technologies such as Internet of Things (IoT), autonomous driving, and artificial intelligence have developed, and the demand for high transmission rates in wireless communication systems continues to increase. Although many methods are being studied to increase the transmission rate, since the bandwidth is limited, there is a limitation due to a trade-off relationship to simultaneously improve the transmission rate and performance. Accordingly, interest in a multiple-input multiple-output (MIMO) system capable of increasing channel capacity without additional bandwidth and transmission power is increasing.

Unlike the Single Input Single Output (SISO) system, the MIMO system simultaneously transmits several symbols at the transmitting side, so the receiving side receives the symbols affected by random noise or interference. Therefore, when designing a MIMO system, a signal detector for a transmission signal is required on the receiving side. However, in a large-capacity MIMO system, the complexity of the system increases exponentially as a plurality of antennas are used, and it is difficult to implement in reality. Therefore, algorithms such as zero forcing (ZF), semi-definite relaxation-row by row (SDR-RBR), and sphere decoding (SD) have been studied to perform signal detection with low complexity.

Another issue of the 4th industrial revolution is machine learning. With the development of hardware equipment and deep neural networks (DNNs), interest in machine learning has increased, and is widely used to solve problems in the field of engineering. As a result, success stories for machine learning are exploding in most engineering fields. In the communication field, machine learning is also applied in various fields, and has shown good results in channel estimation and blind detection, and a method with high detection accuracy by applying a recurrent neural network (RNN) to the MIMO detection problem is also proposed.

G. Franca, D. P. Robinson, and R. Vidal, "A dynamical systems perspective on nonsmooth constrained optimization," arXiv:1808.04048, 2019. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, "Distributed optimization and statistical learning via the alternating direction method of multipliers," Foundations and Trends in Machine Learning, 2010. T. Goldstein, B. O'Donoghue, S. Setzer, R. Baraniuk, "Fast Alternating Direction Optimization Methods," SIAM Im. Sci., 2014. https://kgatsis.github.io/learning_for_control_workshop_CDC2018/assets/slides/Vidal_CDC18.pdf

Various embodiments propose a new MIMO detection method and apparatus having high detection performance at low complexity by applying a deep neural network to an optimization algorithm.

A method of detecting a large-capacity MIMO signal using a deep neural network according to various embodiments relates to a method in which a receiver detects a transmission signal of a transmitter from a received signal in a MIMO system, based on a received signal and a channel for the received signal, Estimating a transmission signal, deriving a MIMO detection problem based on the received signal, channel, and transmission signal, detecting an enhanced Lagrange of the MIMO detection problem, and applying a RA-ADMM algorithm to the enhanced Lagrange And an operation of optimizing the transmission signal by applying a proximal term, and thus deriving an RA-ADMM.

An apparatus for detecting a large-capacity MIMO signal using a deep neural network according to various embodiments relates to an apparatus for detecting a transmission signal of a transmitter from a received signal in a receiver of a MIMO system, and includes a plurality of receiving antennas to which a received signal is input, and the And a detector configured to detect a transmission signal from a received signal, the detector estimating a transmission signal based on a received signal and a channel for the received signal, and based on the received signal, the channel and the transmission signal, Derive a MIMO detection problem, detect the enhanced Lagrange of the MIMO detection problem, apply a RA-ADMM algorithm to the enhanced Lagrange, and apply a proximal term to optimize the transmission signal, thereby optimizing the RA-ADMM. It can be configured to derive.

According to various embodiments, a new MIMO detection technique having high performance at low complexity is proposed. Since the device according to various embodiments is implemented based on an optimization algorithm, it may have a much smaller amount of learning parameters than the existing artificial intelligence detector. Therefore, learning is possible in less time. In addition, by designing to process a large amount of data at once, it can have a faster processing time than existing algorithms.

와

함수를 보여주는 그래프이다.
도 6은 BPSK와 변하는 30×60 MIMO채널에서 SNR에 따른 비트 오류율을 보여주는 그래프이다.
도 7은 4QAM와 변하는 20×30 MIMO채널에서 SNR에 따른 심볼 오류율을 보여주는 그래프이다.
도 8은 16QAM과 변하는 15×25 MIMO채널에서 SNR에 따른 심볼 오류율을 보여주는 그래프이다.
도 9는 배치의 크기에 따른 알고리즘 실행시간을 보여주는 그래프이다.
도 10은 레이어 개수에 따른 심볼 오류율을 보여주는 그래프이다.1 is a diagram illustrating a detector of a receiver according to various embodiments.
FIG. 2 is a diagram illustrating a proximal gradient portion of FIG. 1.
3 is a diagram illustrating a relaxation part of FIG. 1.
FIG. 4 is a diagram illustrating an acceleration portion of FIG. 1.
Figure 5 is in the 4-PAM

Wow

This is a graph showing the function.
6 is a graph showing a bit error rate according to SNR in a 30×60 MIMO channel that changes with BPSK.
7 is a graph showing a symbol error rate according to SNR in a 4QAM and a variable 20×30 MIMO channel.
8 is a graph showing a symbol error rate according to SNR in a 16QAM and a varying 15×25 MIMO channel.
9 is a graph showing algorithm execution time according to the size of the batch.
10 is a graph showing a symbol error rate according to the number of layers.

Hereinafter, various embodiments of the present document will be described with reference to the accompanying drawings.

Hereinafter, a method and apparatus for detecting a large-capacity MIMO signal using a deep neural network according to various embodiments are proposed. According to various embodiments, in a MIMO system, a method and apparatus are proposed for a receiver to detect a transmission signal of a transmitter from a received signal. Various embodiments propose a new MIMO detection scheme with high performance at low complexity. Since the device according to various embodiments is implemented based on an optimization algorithm, it may have a much smaller amount of learning parameters than the existing artificial intelligence detector. Therefore, learning is possible in less time. In addition, by designing to process a large amount of data at once, it can have a faster processing time than existing algorithms.

In the MIMO system, the received signal can be represented by the following [Equation 1].

개와 수신 안테나

개를 사용한다면,

는 수신 신호 벡터를 나타내고,

는 MIMO 채널 행렬을 나타내고,

는 송신 신호 벡터를 나타내고,

은 가산성 백색 가우시안 잡음(Additive White Gaussian Noise, AWGN)을 나타낼 수 있다.

는 성상도에서 표현되는 점들의 집합을 나타내며,

는 복소수 집합을 나타낼 수 있다. Here, the transmitting antenna

Dog and receiving antenna

If you use a dog,

Represents the received signal vector,

Denotes the MIMO channel matrix,

Denotes the transmission signal vector,

May represent additive white Gaussian noise (AWGN).

Represents the set of points expressed in the constellation diagram,

Can represent a set of complex numbers.

는 수신기에서 알고 있으며 원소들은 가우시안 분포로 이루어져 있을 수 있다.

는

크기의 채널 행렬로

번째 행,

번째 열의 원소는

번째 수신 안테나에서

번째 송신 안테나 사이의 채널 이득을 나타낼 수 있다. 수신기의 MIMO 신호 검출기는 잡음이 섞인 수신 신호 벡터

와 채널 행렬

를 사용하여 송신 신호 벡터

를 복원할 수 있다.Channel matrix in MIMO system

Is known by the receiver, and the elements may consist of a Gaussian distribution.

Is

As a channel matrix of size

Second row,

The element in the first column is

At the second receiving antenna

It can represent the channel gain between the th transmit antennas. The receiver's MIMO signal detector is a noisy vector of the received signal

And channel matrix

Transmit signal vectors using

Can be restored.

In order to avoid the complex variable in [Equation 1], the following [Equation 2] can be applied. At this time, [Equation 1] can be expressed as [Equation 3] below.

When [Equation 3] is expressed again as a MIMO detection problem, it can be expressed as [Equation 4] below.

는 성좌도 집합

에 대한 지시(indicator) 함수일 수 있다. 즉,

을 만족하면

이고,

을 만족하면

일 수 있다.

는

와

중 어느 곳에 더 중요성을 두는 지 정하는 변수일 수 있다. 즉,

가 작을수록,

에 대한 중요성이 증가하고,

가 클수록,

에 대한 중요성이 증가할 수 있다. here,

The constellation is also set

It may be an indicator function for. In other words,

If you are satisfied with

ego,

If you are satisfied with

Can be

Is

Wow

It may be a variable that determines which of these places is more important. In other words,

The smaller is,

Of increasing importance,

The greater is,

Can increase in importance.

The augmented Lagrangian multiplier method for [Equation 4] may be expressed as [Equation 5] below.

는 패널티 변수로서,

와 같이 중요성을 나타내는 지표일 수 있다. 즉,

가 클수록, (

)을 더 만족하도록 결과가 도출되며,

가 작을수록,

에 초점을 맞춰서 최적화가 수행될 수 있다.

는 라그랑주 승수(Lagrange multiplier 또는 dual variable)를 나타낼 수 있다.here,

Is the penalty variable,

It can be an indicator of importance, such as. In other words,

The greater is, (

) To more satisfying the results,

The smaller is,

Focusing on the optimization can be performed.

Can represent a Lagrange multiplier or dual variable.

When the R-A-ADMM (Relaxed Accelerated Alternating Direction Method of Multipliers) algorithm is applied to the MIMO detection problem such as [Equation 5], it can be expressed as [Equation 6].

및

가 만족될 수 있다.

인 경우 A-ADMM이며,

인 경우 ADMM 알고리즘에 해당한다. here,

And

Can be satisfied.

Is A-ADMM,

If it is, it corresponds to the ADMM algorithm.

에 대하여 최적화하는 문제는 행렬의 역행렬을 구하는 문제와 관련되어 복잡할 수 있다. 따라서, 다양한 실시예들에서는 프록시멀 항(proximal term)을 사용하여 압축 센싱(Compressive Sensing, CS) 문제를 해결한 것과 유사하게,

에 대하여 최적화하는 문제를 해결하고자 한다. 이를 위해, 하기 [수학식 7]과 같이

가 정의될 수 있다. 이 때

는 매끄러운 함수(smooth function)로, 하기 [수학식 8]과 같은 조건을 만족할 수 있다. In [Equation 6] above

The problem of optimizing for can be complicated in relation to the problem of obtaining the inverse matrix of the matrix. Therefore, in various embodiments, similar to the solution of the Compressive Sensing (CS) problem using a proximal term,

We try to solve the problem of optimizing for. To this end, as shown in [Equation 7]

Can be defined. At this time

Is a smooth function, and may satisfy conditions such as the following [Equation 8].

에 대하여 최적화하는 문제는, 하기 [수학식 9]와 같이 표현될 수 있다. Based on this,

The problem of optimizing for can be expressed as [Equation 9] below.

(

고유 값 중 가장 큰 값)가 만족되어야 한다.here,

(

The largest of the unique values) must be satisfied.

By applying the proximal term, the (inexact) R-A-ADMM solving the problem expressed as in [Equation 9] may be expressed as [Equation 10] below.

를 도입하여, 상기 [수학식 10]을 간단히 하면, 하기 [수학식 11]과 같이 표현될 수 있다. here,

By introducing [Equation 10], it can be expressed as [Equation 11] below.

를 최적화하는 과정에서,

는 미분 가능하지 않게 때문에 학습 모델로 구현할 수 없다. 따라서, 다양한 실시예들에서는,

를 비 선형 함수

로 제안한다.

는 쌍곡 탄젠트(hyperbolic tangent)로 구성되어 있으며,

에 따라서 성상도

로 매핑하는 정도를 다르게 설정할 수 있다.

는 하기 [수학식 12]와 같이 표현될 수 있다.

In the process of optimizing,

Cannot be implemented as a learning model because it is not differentiateable. Thus, in various embodiments,

Nonlinear function

As suggested.

Is composed of hyperbolic tangent,

Depending on the constellation

The degree of mapping to can be set differently.

Can be expressed as the following [Equation 12].

는 쌍곡 탄젠트를 평행 이동시키는 역할을 할 수 있다. 예를 들어, 4진 진폭 변조에서,

일 때,

일 수 있다. 이 때

는, 도 5에 도시된 바와 같이

에 따라 다르게 표현될 수 있다. here,

May serve to translate the hyperbolic tangent. For example, in quaternary amplitude modulation,

when,

Can be At this time

Is, as shown in Figure 5

It can be expressed differently according to the.

When solving an optimization problem with an algorithm such as ADMM, performance is sensitive to the parameter values that appear in the algorithm. Determining a value with optimal performance may be more important than solving a problem with an algorithm, and it is difficult to find an exact value. Accordingly, in various embodiments, the R-A-ADMM network expressed as shown in Equation 13 below may be implemented by using the parameter of the algorithm as a learnable parameter.

In this case, [Equation 13] may be an equation for one layer in the R-A-ADMM network. The learnable parameters can learn different values for each layer. The learnable parameters and loss functions may be expressed as shown in [Equation 14] and [Equation 15], respectively.

는 고정된 상수로 100을 사용할 수 있다. 학습 가능한 파라미터의 초기 값은 R-A-ADMM의 조건을 만족하는 값일 수 있다. here,

Can use 100 as a fixed constant. The initial value of the learnable parameter may be a value that satisfies the condition of RA-ADMM.

Various embodiments propose a new MIMO detection scheme with high performance at low complexity. Since the MIMO detection apparatus according to various embodiments is implemented based on an optimization algorithm, it may have a much smaller amount of learning parameters than the conventional artificial intelligence detector. Therefore, learning is possible in less time. In addition, by designing to process a large amount of data at once, it can have a faster processing time than existing algorithms.

1 is a diagram illustrating a detector 100 of a receiver according to various embodiments. FIG. 2 is a diagram illustrating the proximal gradient module 110 of FIG. 1. 3 is a diagram illustrating the relaxation module 120 of FIG. 1. FIG. 4 is a diagram illustrating the acceleration module 130 of FIG. 1.

,

,

,

,

,

에 대해 학습 파라미터들

와

를 사용하여 연산을 수행함으로써, 해들

,

을 구할 수 있다. 릴렉세이션 모듈(120)은 도 3에 도시된 바와 같이 구성되고, 입력 변수들

,

,

에 대해 학습 파라미터들

와

를 사용하여 연산을 수행함으로써, 해들

,

을 구할 수 있다. 가속화 모듈(130)은 도 4에 도시된 바와 같이 구성되고, 입력 변수들

,

,

,

에 대해 학습 파라미터

를 사용하여 연산을 수행함으로써, 해들

,

을 구할 수 있다. Referring to FIG. 1, the detector 100 of a receiver according to various embodiments may detect a transmission signal output from a transmission signal from a reception signal input through a plurality of reception antennas. To this end, the detector 100 may be configured to implement an RA-ADMM network as expressed in [Equation 13]. The detector 100 may include a proximal gradient module 110, a relaxation module 120 and an acceleration module 130. The proximal gradient module 110 is configured as shown in FIG. 2, and input variables

,

,

,

,

,

Learning parameters for

Wow

By performing the operation using

,

Can be obtained. The relaxation module 120 is configured as shown in FIG. 3, and input variables

,

,

Learning parameters for

Wow

By performing the operation using

,

Can be obtained. The acceleration module 130 is configured as shown in FIG. 4, and input variables

,

,

,

For learning parameters

By performing the operation using

,

Can be obtained.

An apparatus for detecting a transmission signal of a transmitter from a reception signal in a receiver of a MIMO system according to various embodiments includes a plurality of reception antennas to which a reception signal is input, and a detector configured to detect a transmission signal from the reception signal. ) Can be included.

According to various embodiments, the detector 100 estimates a transmission signal based on a received signal and a channel for the received signal, and derives a MIMO detection problem based on the received signal, channel, and transmission signal. And, it can be configured to detect the enhanced Lagrange of the MIMO detection problem, apply a RA-ADMM algorithm to the enhanced Lagrange, and apply a proximal term to optimize the transmission signal, thereby deriving RA-ADMM. have.

According to various embodiments, the detector 100 is configured to optimize the transmission signal by applying a differentiable nonlinear function to the RA-ADMM, thereby implementing a RA-ADMM network having a learning parameter. I can.

In the MIMO system according to various embodiments, a method for a receiver to detect a transmission signal of a transmitter from a received signal includes an operation of estimating a transmission signal based on a received signal and a channel for the received signal, the received signal, and a channel. And an operation of deriving a MIMO detection problem based on a transmission signal, an operation of detecting an enhanced Lagrange of the MIMO detection problem, an operation of applying an RA-ADMM algorithm to the enhanced Lagrange, and applying a proximal term, and the transmission. It may involve optimizing the signal, thereby deriving the RA-ADMM.

According to various embodiments, the method further includes an operation of optimizing the transmission signal by applying a differentiable nonlinear function to the RA-ADMM, thereby implementing a RA-ADMM network having a learning parameter. I can.

6, 7, 8, 9, and 10 are diagrams for explaining the performance of a receiver according to various embodiments.

6 is a graph showing BER performance according to SNR when 30 transmit antennas and 60 receive antennas are used in a variable channel and a BPSK digital modulation technique is used. Referring to FIG. 6, the overall performance may be excellent in the order of SD, R-A-ADMM network, DetNet, R-A-ADMM, and ZF. The initial performance of R-A-ADMM without learning is not better than DetNet, but the performance at 13dB may be similar to that of DetNet learning less data. The performance of the R-A-ADMM network for learning is always better than that of DetNet, and as the SNR increases, the performance of DetNet can show a larger difference.

7 is a graph showing SER performance according to SNR when 20 transmit antennas and 30 receive antennas are used in a variable channel and a 4QAM digital modulation technique is used. Referring to FIG. 7, the overall performance may be excellent in the order of SD, R-A-ADMM network, DetNet, R-A-ADMM, and ZF. As the SNR increases, the difference between the performance of the R-A-ADMM network and the performance of DetNet can be greater. When the SNR is 13 dB, the difference between the performance of the RA-ADMM network and the fully learned DetNet is about 0.2 dB, and the difference between the performance of the RA-ADMM network and the learned DetNet at the same time may be about 0.8 dB. .

8 is a graph showing SER performance according to SNR when 15 transmit antennas and 25 receive antennas are used in a variable channel and a 16QAM digital modulation technique is used. Referring to FIG. 8, the overall performance may be excellent in the order of SD, R-A-ADMM network, R-A-ADMM, DetNet, and ZF. The initial performance of R-A-ADMM without learning is similar to that of DetNet, and the performance at 10 dB can be superior to that of DetNet. The performance of the R-A-ADMM network for learning is always better than that of DetNet, and if the SNR is higher than 10 dB, it can be better than that of DetNet by 1 dB or more.

9 is a graph showing execution time according to the size of a batch. SD processes one piece of data and complex operations can be performed. Therefore, it is difficult for SD to batch-process multiple data in batch units. Accordingly, as shown in FIG. 9, SD may represent an execution time for one piece of data. In the case of ZF, DetNet and R-A-ADMM, batch processing is possible because they consist of simple operations. At this time, the R-A-ADMM and R-A-ADMM networks perform the same operation, so the execution time may be the same. Accordingly, as shown in FIG. 9, the execution time of the algorithm capable of batch processing may be proportionally reduced according to the size of the batch. If the batch size is 100 or more, the R-A-ADMM can have an execution time 100 times or more faster than SD.

10 is a graph of a signal error rate according to the number of layers in an R-A-ADMM network. Referring to FIG. 10, solutions may converge as they pass through a layer of an R-A-ADMM network. For situations in which various MIMO channels and digital modulation techniques are applied, solutions can converge in fewer than 20 layers in R-A-ADMM networks. In the MIMO signal detection, 30 layers above are used for stability, but if the solution is solved using fewer layers, the execution speed of the algorithm can be faster.

According to various embodiments, a new MIMO detection technique having high performance at low complexity is proposed. Since the device according to various embodiments is implemented based on an optimization algorithm, it may have a much smaller amount of learning parameters than the existing artificial intelligence detector. Therefore, learning is possible in less time. In addition, by designing to process a large amount of data at once, it can have a faster processing time than existing algorithms.

Electronic devices according to various embodiments disclosed in this document may be devices of various types. The electronic device may include, for example, a portable communication device (eg, a smart phone), a computer device, a portable multimedia device, a portable medical device, a camera, a wearable device, or a home appliance. The electronic device according to various embodiments of the present document is not limited to the above-described devices.

Various embodiments of the present document and terms used therein are not intended to limit the technology described in this document to a specific embodiment, and should be understood to include various modifications, equivalents, and/or substitutes of the corresponding embodiment. In connection with the description of the drawings, similar reference numerals may be used for similar elements. Singular expressions may include plural expressions unless the context clearly indicates otherwise. In this document, expressions such as "A or B", "at least one of A and/or B", "A, B or C" or "at least one of A, B and/or C" are all of the items listed together. It can include possible combinations. Expressions such as "first", "second", "first" or "second" can modify the corresponding elements regardless of their order or importance, and are only used to distinguish one element from another. The components are not limited. When it is mentioned that a certain (eg, first) component is “(functionally or communicatively) connected” or “connected” to another (eg, second) component, the certain component is It may be directly connected to the component, or may be connected through another component (eg, a third component).

The term "module" used in this document includes a unit composed of hardware, software, or firmware, and may be used interchangeably with terms such as, for example, logic, logic blocks, parts, or circuits. A module may be an integrally configured component or a minimum unit or a part of one or more functions. For example, the module may be configured as an application-specific integrated circuit (ASIC).

Various embodiments of the present document may be implemented as software including one or more instructions stored in a storage medium readable by a machine. For example, the processor of the device may invoke and execute at least one of the one or more instructions stored from the storage medium. This enables the device to be operated to perform at least one function according to the at least one command invoked. The one or more instructions may include code generated by a compiler or code that can be executed by an interpreter. A storage medium that can be read by a device may be provided in the form of a non-transitory storage medium. Here,'non-transient' only means that the storage medium is a tangible device and does not contain a signal (e.g., electromagnetic wave), and this term refers to the case where data is semi-permanently stored in the storage medium. It does not distinguish between temporary storage cases.

According to various embodiments, each component (eg, a module or program) of the described components may include a singular number or a plurality of entities. According to various embodiments, one or more components or operations among the above-described corresponding components may be omitted, or one or more other components or operations may be added. Alternatively or additionally, a plurality of components (eg, a module or a program) may be integrated into one component. In this case, the integrated component may perform one or more functions of each component of the plurality of components in the same or similar to that performed by the corresponding component among the plurality of components prior to integration. According to various embodiments, operations performed by a module, program, or other component may be sequentially, parallel, repeatedly, or heuristically executed, or one or more of the operations may be executed in a different order, or omitted. , Or one or more other actions may be added.

Claims (7)

In a MIMO system, a method for a receiver to detect a transmission signal of a transmitter from a received signal,
Estimating a transmission signal based on a received signal and a channel for the received signal;
Deriving a MIMO detection problem based on the received signal, channel, and transmission signal;
Detecting the enhanced Lagrange of the MIMO detection problem;
Applying a Relaxed Accelerated Alternating Direction Method of Multipliers (RA-ADMM) algorithm to the augmented Lagrange;
Applying a proximal term to optimize the transmission signal, thereby deriving an RA-ADMM; And
And applying a differentiable nonlinear function to the RA-ADMM to optimize the transmission signal, thereby implementing an RA-ADMM network having a learning parameter,
The nonlinear function is composed of a hyperbolic tangent as shown in the following equation.

,

Here, above

Denotes a set of constellations, above

Serves to translate the hyperbolic tangent, and the nonlinear function is

It is expressed differently according to.
The method of claim 1,
The received signal, channel, and transmission signal have a relationship as shown in the following equation,

Here, above

Represents the received signal, and

Represents the channel, and the

Represents the transmission signal, and

Represents additive white Gaussian noise.
The operation of deriving the MIMO detection problem,
A method of deriving the MIMO detection problem as shown in the following equation.

,

Here, above

Is the constellation also set

Represents an indicator function for, and

Is reminded

And remind

It represents a variable that determines which of these places is more important.
The method of claim 2, wherein the enhanced Lagrange detection operation,
A method of detecting the enhanced Lagrange as shown in the following equation.

Here, above

Denotes an index indicating the importance of terms in the equation, and

Stands for Lagrange multiplier or dual variable.
The method of claim 3, wherein the operation of applying the RA-ADMM algorithm,
A method of applying the RA-ADMM algorithm to the augmented Lagrange as shown in the following equation.

The method of claim 4,
The proximal term is defined as the following equations,

,

The RA-ADMM derivation operation,
By applying the proximal term, the transmission signal is optimized as shown in the following equation,

A method of deriving the RA-ADMM as shown in the following equation.

Here, above

Represents.
The method of claim 5,
The RA-ADMM network implementation operation,
A method of implementing the RA-ADMM network as shown below by applying the non-linear function.

The method of claim 6,
The learning parameter learns a different value for each layer, and is configured as shown in the following equation.

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