KR102131840B1 - Estimation method and compensation method for rf chain imbalance in uca oam radio system - Google Patents

Abstract

In the UCA-based OAM system, an imbalance compensation method between RF chains includes estimating a maximum likelihood of a channel between a transmitter and a receiver in a UCA (Uniform Circular Array)-based Orbital Angular Momentum (OAM) system. Estimating a first change in gain or phase due to the RF chain of the transmitter and a second change in gain or phase due to the RF chain of the receiver based on a maximum likelihood, and the first to Fourier transform of the transmitter And performing inverse compensation for the change, and performing inverse compensation for the second change in the inverse Fourier transform of the receiver. The channel between the transmitter and the receiver is a first matrix having, as an element, the first change by each of the N RF chains of the transmitter, and a factor having the second change by each of the N RF chains of the receiver as an element. It is defined based on 2 matrices and ideal channels.

Description

ESTIMATION METHOD AND COMPENSATION METHOD FOR RF CHAIN IMBALANCE IN UCA OAM RADIO SYSTEM}

The technique described below relates to a technique for estimating and compensating for imbalance in RF chains of a transmitter and a receiver in a UCA OAM system.

OAM (Orbital Angular Momentum) is one of the momentum of all electromagnetic waves with Linear Momentum (LM) and Spin Angular Momentum (SAM). It has been discovered that an infinite number of OAM modes can be transmitted in a line-of-sight (LoS) environment without mutual interference. Research on OAM-related technologies is being conducted in the field of milimeter-wave and optical communication.

In a pure LoS environment, the UCA (Uniform Circular Array) OAM system pre-codes the transmitted signal from the transmitter and performs DFT post-processing at the receiving end when the transmitting UCA and the receiving UCA antenna are correctly aligned. The lower surface forms a parallel N AWGN channel without mutual interference. The advantage of the UCA OAM system arises because the UCA pair channel is expressed as a circulant matrix when the transmitting and receiving UCAs are correctly aligned.

S. M. Mohammadi, L. K. S. Daldorff, J. E. S.Bergman, R.L.Karlsson, B. Thide, K. Forozesh, T. D. Carozzi, and B. Isham, "Orbital angular momentum in radio-A system study," IEEE Trans. Antennas Propag., vol. 58, no. 2, pp. 565-572, Feb. 2010.

When gain or phase imbalance exists between N RF chains of a transmitter or N RF chains of a receiver, circulant characteristics between UCA antennas cannot be maintained Therefore, interference occurs between UCA OAM received signals. This leads to a decrease in the available capacity of the UCA OAM channel.

To solve this problem, it is necessary to perform equalization at the transmitter and receiver based on the real-time channel estimate. As a result, when gain or phase imbalance occurs between a plurality of RF chains of a transmitter or a receiver, the advantage of the UCA OAM system that the N parallel independent channels can be formed without an equalizer is greatly damaged.

The technique described below is intended to provide a technique for simultaneously estimating and compensating for gain/phase imbalance between transmitter RF chains and gain/phase imbalance between receiver RF chains.

The method for estimating the imbalance between RF chains in a UCA-based OAM system includes estimating a maximum likelihood of a channel between a transmitter and a receiver in a UCA (Uniform Circular Array)-based Orbital Angular Momentum (OAM) system, and the channel in the system. And estimating a first change in gain or phase due to the RF chain of the transmitter and a second change in gain or phase due to the RF chain of the receiver based on the maximum likelihood.

In the UCA-based OAM system, an imbalance compensation method between RF chains includes estimating a maximum likelihood of a channel between a transmitter and a receiver in a UCA (Uniform Circular Array)-based Orbital Angular Momentum (OAM) system. Estimating a first change in gain or phase due to the RF chain of the transmitter and a second change in gain or phase due to the RF chain of the receiver based on a maximum likelihood, and the first to Fourier transform of the transmitter And performing inverse compensation for the change, and performing inverse compensation for the second change in the inverse Fourier transform of the receiver. The channel between the transmitter and the receiver is a first matrix having, as an element, the first change by each of the N RF chains of the transmitter, and a factor having the second change by each of the N RF chains of the receiver as an element. It is defined based on 2 matrices and ideal channels.

The technique described below compensates for imbalance in the RF chains of the transmitter and receiver using a channel estimation model. Therefore, the technique described below estimates and compensates for the imbalance of the RF chains in the UCA OAM system without a separate equalizer.

1 is an example of a UCA system model.
2 is an example of a transmitter and receiver structure of the UCA OAM system.
3 is an example of a UCA system that compensates for the imbalance of RF chains.
4 is a simulation result for the effectiveness of the proposed technique.
5 is an example of achievable frequency efficiency of the proposed technique.

The technique described below may be applied to various changes and may have various embodiments, and specific embodiments will be illustrated in the drawings and described in detail. However, this is not intended to limit the techniques described below to specific embodiments, and should be understood to include all changes, equivalents, or substitutes included in the spirit and scope of the techniques described below.

Terms such as first, second, A, B, etc. can be used to describe various components, but the components are not limited by the above terms, and only for distinguishing one component from other components Used only. For example, the first component may be referred to as a second component, and similarly, the second component may be referred to as a first component without departing from the scope of the technology described below. The term and/or includes a combination of a plurality of related described items or any one of a plurality of related described items.

In the terminology used herein, a singular expression should be understood to include a plurality of expressions unless clearly interpreted differently in the context, and terms such as “comprises” describe features, numbers, steps, operations, and components described. It is to be understood that it means that a part or a combination thereof is present, and does not exclude the presence or addition possibility of one or more other features or numbers, step operation components, parts or combinations thereof.

Prior to the detailed description of the drawings, it is intended to clarify that the division of components in this specification is only divided by the main functions of each component. That is, two or more components to be described below may be combined into one component, or one component may be divided into two or more for each subdivided function. In addition, each of the constituent parts to be described below may additionally perform some or all of the functions of other constituent parts in addition to the main functions of the constituent parts, and some of the main functions of the constituent parts are different. Needless to say, it may also be carried out in a dedicated manner.

In addition, in performing the method or the method of operation, each process constituting the method may occur differently from the specified order unless a specific order is explicitly stated in the context. That is, each process may occur in the same order as specified, may be performed substantially simultaneously, or may be performed in the reverse order.

In the UAC-based OAM system, the technique described below uniformly models a channel between a transmitter and a receiver, and compensates by estimating an imbalance between RF chains based on the channel model. Channel modeling and imbalance estimation or compensation processes can be explained through mathematical models and calculations.

는 하다마드(Hadamard) 연산을 의미하고,

는 행렬의 외적을 의미한다.In the following description, matrix operations are frequently used. Matrix operation symbols basically use symbols widely used in mathematics and engineering. For example, A ^T means the transpose matrix of matrix A, A ^H means the Hermitian matrix of matrix A,

Means the Hadamard operation,

Means the cross product of the matrix.

이고, 수신 UCA(20)는 반경이

이다. 송수신거리(T-R distance) D는 송신 UCA의 중심과 수신 UCA의 중심 사이의 거리이다. 송신측과 수신측의 UCA 안테나들의 안테나 소자들은 x-y 평면 상에 균일하게 원형으로 배치된다고 가정한다. 1 is an example of a UCA system model. The UCA system includes a transmitting UCA 10 and a receiving UCA 20. The transmitting UCA 10 has a radius

And the receiving UCA 20 has a radius

to be. The TR distance D is a distance between the center of the transmitting UCA and the center of the receiving UCA. It is assumed that the antenna elements of the UCA antennas of the transmitting side and the receiving side are arranged uniformly and circularly on the xy plane.

와

는 각각

와

로 표현된다.

는 송신 UCA(10)에서 기준(예컨대, 첫 번째) 안테나의 정면 방향인 안테나 기준 송신방향(boresight)과 사용자가 이루는 각도를 나타낸다.

는 수신 UCA(20)에서 기준(예컨대, 첫 번째) 안테나의 정면 방향인 안테나 기준 송신방향과 사용자가 이루는 각도를 나타낸다. 송신 UCA의 j번째 소자와 수신 UCA의 j번째 소자 사이의 거리

는

와 같이 표현된다. 여기서,

이다.

는 i와 j의 차(즉, i-j)에만 의존하는 변수이므로

도 i와 j의 차에 의해서만 결정된다.The angle in the xy plane of the i-th antenna element of the transmitting UCA and the i-th antenna element of the receiving UCA

Wow

Each

Wow

It is expressed as

Denotes an antenna reference transmission direction (boresight), which is a front direction of the reference (eg, first) antenna in the transmission UCA 10, and an angle formed by the user.

Denotes an angle formed by a user and an antenna reference transmission direction that is a front direction of a reference (eg, first) antenna in the receiving UCA 20. Distance between the jth element of the sending UCA and the jth element of the receiving UCA

The

It is expressed as here,

to be.

Is a variable that depends only on the difference between i and j (that is, ij)

It is determined only by the difference between i and j.

In a pure LoS environment where only a direct path exists between the transmitting and receiving UCAs, the channel between the j-th element of the receiving UCA 20 and the i-th element of the transmitting UCA 10 is represented by Equation 1 below. It is expressed as

It is assumed that all antenna elements are omni-directional antenna elements having the same radiation pattern value β regardless of the element indexes i and j. The UCA pair channel response to a narrowband signal having an arbitrary wavelength is determined by the distance between these antenna elements. That is, the channel response between the antenna elements results in being determined only by the difference between the antenna element indexes i and j. Therefore, assuming that both the transmitting UCA 10 and the receiving UCA 20 have N antenna elements, the channel matrix H becomes a circulant matrix.

2 is an example of the structure of the transmitter 100 and the receiver 200 of the UCA OAM system. 2 does not show all the configurations in the transmitter 100 and the receiver 200, only the configuration necessary for the description. The transmitter 100 includes an OAM modulator 110 that Fourier transforms the input signals {s ₁ , s ₂ ,..., s _N }. The OAM modulator 110 performs DFT on the input signal. Q is a DFT matrix for N points. The transmitter 100 transmits the modulated input signals {x ₁ , x ₂ ,..., x _N } through N antenna elements. The receiver 200 includes an OAM demodulator 210 that inverse Fourier transforms the signals {y ₁ , y ₂ ,..., y _N } received through N antenna elements. The OAM demodulator 210 performs an inverse DFT on the input signal. Q ^H means an inverse DFT matrix for N points. Then, the receiver 200 decodes the inverse DFT-converted signal {r ₁ , r ₂ ,..., r _N }.

과

는 각각 송신기(100)와 수신기(200)의

개 RF 체인들에 의한 이득 내지 위상의 변화를 나타낸다. RF 체인에 의한 이득 내지 위상 변화 정도(변화값)는 하드웨어 구조, 통신환경 등에 따라 달라질 수 있다. 설명의 편의를 위해 RF 체인에 의한 이득 내지 위상 변화 정도를 이하 이득/위상 변화값이라고 명명한다.

,

라고 정의한다. 또,

이고

라고 정의한다. 이 경우 수신신호

는 아래 수학식 2와 같이 표현될 수 있다.In Figure 2

and

Of the transmitter 100 and the receiver 200, respectively

It shows the change in gain or phase by the dog RF chains. The gain or phase change degree (change value) by the RF chain may vary depending on hardware structure, communication environment, and the like. For convenience of explanation, the degree of gain or phase change by the RF chain is hereinafter referred to as gain/phase change value.

,

Is defined as In addition,

ego

Is defined as In this case, the received signal

Can be expressed as Equation 2 below.

이고,

는 송신기의 RF 체인들의 입력 신호 벡터이고,

은 수신기의 RF 체인들의 출력단에 나타나는 N 차원의 복소 가우시안 잡음 벡터이다. 수학식 2로부터 수신 신호 대 잡음비(SNR, signal-to-noise ratio)는

로 표현되고(여기서,

임), 채널

의 달성가능주파수효율(ASE, achievable spectral efficiency)는

로 표현된다.here,

ego,

Is the input signal vector of the transmitter's RF chains,

Is an N-dimensional complex Gaussian noise vector appearing at the output of the receiver's RF chains. From Equation 2, the received signal-to-noise ratio (SNR) is

Is expressed as (here,

Im), channel

The achievable spectral efficiency (ASE) is

It is expressed as

이고

인 이상적인 송신기와 수신기 쌍(pair)의 경우, UCA OAM 변조기(110)와 복조기(120)는 다음과 같이

개의 병렬 채널을 형성한다. 이 경우,

이고, 따라서

가 되어

도 또한 순환 행렬이 된다.

ego

For an ideal transmitter and receiver pair, the UCA OAM modulator 110 and demodulator 120 are as follows:

Form two parallel channels. in this case,

And therefore

Become

Also becomes a circular matrix.

는 수학식 3과 같이

-point DFT 행렬

와

복소 대각 행렬(complex diagonal matrix)

의 함수로 분해할 수 있다. 따라서 수학식 3을 수학식 2에 사용하면 아래의 수학식 4를 얻을 수 있다.Circular matrix

Equation 3

-point DFT matrix

Wow

Complex diagonal matrix

Can be decomposed as a function of Therefore, when Equation 3 is used in Equation 2, Equation 4 below can be obtained.

로 놓으면, 수학식 4는

와 같이 정리된다. 따라서, 수신기(200)의 역 DFT의 출력신호는

이 된다. 여기서,

이다. 결과적으로, 송신기(100)에서 DFT 프리코더를 사용하고 수신기(200)에서 역 DFT 처리를 사용함으로써 채널정보 피드백과 채널간간섭제거없이 N개의 평행 독립 채널들을 구성할 수 있게 된다.

Equation 4 is

It is arranged as follows. Therefore, the output signal of the inverse DFT of the receiver 200 is

It becomes. here,

to be. As a result, by using the DFT precoder in the transmitter 100 and the inverse DFT processing in the receiver 200, it is possible to configure N parallel independent channels without channel information feedback and channel interference cancellation.

또는

인 경우에

로 표현되는

행렬이 더 이상 순환 행렬이 되지 않기 때문이다.In the case of an actual implemented system, it is difficult to preserve the advantages of the UCA OAM system because the gain/phase parameters of the RF chains generally do not have the same value. this is

or

in case of

Expressed as

This is because the matrix is no longer a circular matrix.

Hereinafter, a technique for compensating for gain/phase imbalance between the RF chains of the receiver and the transmitter will be described.

Channel estimation

를 추정하기 위하여 N개의 다른 시간/주파수 자원을 사용하여 파일럿 심볼(pilot symbol)들을 송신한다. i번째 시간/주파수 자원을 통해 n번째 송신기 RF 체인으로 송신되는 파일럿 심볼을

로, m번?? 수신기 RF 체인을 통해 수신되는 신호를

로 정의하자. 이 경우, i번째 시간/주파수를 통해 수신된 신호는 아래의 수학식 5와 같이 표현된다.

In order to estimate E, pilot symbols are transmitted using N different time/frequency resources. pilot symbols transmitted through the i-th time/frequency resource to the n-th transmitter RF chain.

Low, m times?? The signal received through the receiver RF chain

Let's define In this case, the signal received through the i-th time/frequency is expressed as Equation 5 below.

,

이고,

는 N차원 복소 가우시안 잡음이다. L개의 시간/주파수 자원을 통해 송신된 신호와 수신된 신호를 각각

와

로 정의하면 수신 신호는 아래의 수학식 6과 같이 나타낼 수 있다.here,

,

ego,

Is the N-dimensional complex Gaussian noise. Signals transmitted and received through L time/frequency resources, respectively

Wow

When defined as, the received signal can be expressed as Equation 6 below.

에 대한 최대 우도 추정(maximum-likelihood estimate)은 아래의 수학식 7과 같고, 수학식 6을 수학식 7에 대입하면 아래의 수학식 8과 같다.From this

The maximum-likelihood estimate for is equal to Equation 7 below, and when Equation 6 is substituted for Equation 7, Equation 8 below.

이다. 수학식 8로부터 MSE는 아래의 수학식 9와 같이 표현된다.here,

to be. From Equation 8, the MSE is expressed as Equation 9 below.

의 조건에서 MSE는

이 만족될 때 최소화된다. 이 때

, 즉

의 요소들은 동일하게 분산된 제로 평균(zero-mean)을 갖는 복소 가우시안 확률 변수(complex Gaussian random variable)가 된다. 또한, PSK 파일럿을 가정하면,

이므로,

이 만족될 때 아래의 수학식 10과 같이 표현할 수 있다.

In terms of MSE

When it is satisfied, it is minimized. At this time

, In other words

The elements of are complex Gaussian random variables with equally distributed zero-mean. Also, assuming a PSK pilot,

Because of,

When this is satisfied, it can be expressed as Equation 10 below.

RF chain imbalance estimation

에 대한 ML 추정은 아래 수학식 11과 같이 표현된다.

The ML estimate for is expressed by Equation 11 below.

는 제로 평균 복소 가우시안 분산이며,

가 알려진 경우,

와

의 대각 요소들은 다음과 같이 추정할 수 있다. 한편 송신기와 수신기 UCA 사이의 거리 D와 (

,

) 및 (

)가 주어지면, 이상적인 채널에 대한

를 알 수 있다. 수학식 11의 양변을 벡터화하면 수학식 12와 같다.

Is the zero mean complex Gaussian variance,

If is known,

Wow

The diagonal elements of can be estimated as follows. Meanwhile, the distance D between the transmitter and the receiver UCA and (

,

) And (

), for the ideal channel

Can be seen. When both sides of Equation (11) are vectorized, Equation (12) is obtained.

,

로 정의하면, 다시 아래의 수학식 13과 같이 정리할 수 있다.

,

If defined as, it can be summarized as in Equation 13 below.

와

이기 때문에

임을 적용한 것이다. 세번째 등호 내용은

는

와

의 하다마드 곱셈(hadamard product)로 표현한 것이다. 네번째 등호 내용은

를 적용한 것이다.The second equality in equation (13) is

Wow

Because it is

Is applied. The third equal sign

The

Wow

It is expressed by the Hadamard product of. The fourth equal sign

Is applied.

이고,

의 phase가 zero가 되어야 한다(즉,

)고 가정한다. 이 가정을 하는 이유는 수학식 13의 RF 불균형 모델이

와

의 곱으로 되어 있어서

와

대신에

와

를 사용해도 마찬가지로 동일한 값을 갖게 되어

와

특이적으로 한정하지 못하기 때문이다.Assumption 1.

ego,

Phase must be zero (ie,

). The reason for this assumption is that the RF imbalance model in Equation 13

Wow

Multiplied by

Wow

Instead of

Wow

Even if you use, it will have the same value

Wow

Because it is not specifically limited.

가 제로 평균 복소 가우시안이므로, 수학식 13의

는

을 평균으로 갖고 공분산 행렬(covariance matrix)이

인 복소 가우시안 랜덤 벡터가 된다. 따라서

에 대한 조건부 확률밀도함수는 아래 수학식 14와 같이 알려지지 않은 파라미터 a와 b의 함수로 표현된다.

Is zero mean complex Gaussian, so

The

With the mean and the covariance matrix

It becomes a phosphorus complex Gaussian random vector. therefore

The conditional probability density function for is expressed as a function of unknown parameters a and b as shown in Equation 14 below.

는

에 대한 우도 함수이므로,

에 대한 ML 추정은 아래의 수학식 15와 같다.Equation 14

The

Since it is likelihood function for

The ML estimation for is as shown in Equation 15 below.

로 정의하면, 아래의 수학식 16과 같다.The objective function of Equation (15)

If defined as, Equation 16 below.

Equation 16 can be written again as Equation 17 below.

을 적용한 것이다.

는 하다마드 역 연산(hadamard inverse)을 나타낸다. 이것은

를 최소화하는

를 찾는 것이 수학식 15의 해를 찾는 것과 동치임을 나타낸다. 따라서,

로 정의하면,

에 대한 추정 문제는 아래의 수학식 18과 같이 다시 쓸 수 있다.Here, the second inequality

Is applied.

Denotes the Hadamard inverse. this is

To minimize

Indicates that finding is equivalent to finding the solution of equation (15). therefore,

If defined as

The estimation problem for can be rewritten as in Equation 18 below.

와

에 대한 joint estimator는 다음과 같이 유도된다. 먼저, 아래의 수학식 19와 같이 정의한다.From Equation 18

Wow

The joint estimator for is derived as follows. First, it is defined as Equation 19 below.

Then, Equation 19 can be rewritten as Equation 20 below.

를 적용하면 아래의 수학식 21과 같다.Equation 20

When is applied, it is as shown in Equation 21 below.

을 풀면 아래의 수학식 22를 얻을 수 있다.

Solving can give Equation 22 below.

Subsequently, when Equation 22 is substituted for the a position in Equation 19, Equation 23 is as follows.

조건을 만족하는 초평면(hyperplane) 상에서 수학식 24의 해는

의 고유벡터(eigenvector)들 중에서 가장 큰 고유값(eigenvalue)에 해당하는 고유 벡터가 된다. 이 고유 벡터를

라고 정의하면,

도 또한

의 가장 큰 고유값에 해당하는 고유 벡터이므로 이러한 고유 벡터는 특정(unique)되지 않게 된다. 이러한 고유 벡터들 중에서 가정 1의

조건을 만족시키는 고유 벡터는 아래의 수학식 25와 같다.Equation 1 according to Equation 24

The solution of equation (24) on the hyperplane that satisfies the condition

It is the eigenvector corresponding to the largest eigenvalue among the eigenvectors of. This eigenvector

If you define

also

Since the eigenvector corresponding to the largest eigenvalue of, these eigenvectors are not unique. Of these eigenvectors, assumption 1

The eigenvector that satisfies the condition is expressed by Equation 25 below.

은

의 첫 번째 요소를 나타낸다.here,

silver

Represents the first element of

를 얻는다.Lastly, by substituting equation (25) into equation (22), as shown in equation (26) below

Get

와

를 추정하였다. OAM 시스템은 이를 통해 RF 체인들 사이의 불균형을 추정한다.

으로 정의하고

으로 정의하자. OAM 시스템은

과

를 수학식 25와 수학식 26으로부터 구하고, 송신기(300)의 변조기(310)에 변환값을 역으로 보정하도록 하고, 수신기(400)의 복조기(410)에도 변환값을 역으로 보정하도록 한다.Diagonal elements of A and B described above through Equations 25 and 26, respectively.

Wow

Was estimated. The OAM system estimates the imbalance between the RF chains.

Defined as

Let's define OAM system

and

Is calculated from Equation 25 and Equation 26, and the modulator 310 of the transmitter 300 is inversely corrected, and the demodulator 410 of the receiver 400 is also inversely corrected.

를 DFT 행렬로 사용한다. 이는 송신기의 RF 체인에 의한 이득/위상 변화값을 보정하기 위한 것이다. 송신기(300)는 변조한 입력 신호 {x₁, x₂,..., x_N}를 N개의 안테나 소자를 통해 송신한다. 3 is an example of a UCA system that compensates for the imbalance of RF chains. 3 is basically the same as that of FIG. 2. FIG. 3 does not show all configurations in the transmitter 300 and the receiver 400, but only the configuration necessary for RF chain imbalance estimation and correction. The transmitter 300 includes an OAM modulator 310 that Fourier transforms the input signals {s ₁ , s ₂ ,..., s _N }. The OAM modulator 310 performs DFT on the input signal. Q is a DFT matrix for N points. OAM modulator 310 is

Is used as a DFT matrix. This is to correct the gain/phase change value by the RF chain of the transmitter. The transmitter 300 transmits the modulated input signals {x ₁ , x ₂ ,..., x _N } through N antenna elements.

를 역DFT 행렬로 사용한다. 이는 수신기의 RF 체인에 의한 이득/위상 변화값을 보정하기 위한 것이다. 이후 수신기(400)는 역 DFT 변환된 신호 {r₁, r₂,..., r_N}를 복호한다.The receiver 400 includes an OAM demodulator (410) for inverse Fourier transforming signals {y ₁ , y ₂ ,..., y _N } received through N antenna elements. The OAM demodulator 410 performs an inverse DFT on the input signal. Q ^H means an inverse DFT matrix for N points. OAM demodulator 410

Is used as an inverse DFT matrix. This is to correct the gain/phase change value by the RF chain of the receiver. Then, the receiver 400 decodes the inverse DFT-converted signal {r ₁ , r ₂ ,..., r _N }.

과

를 추정하고, OAM 변조기(310)과 OAM 복조기(410)에 각각

과

를 적용한다. UAC 기반 OAM 시스템에서 특정한 제어 장치가

와

를 연산하고,

과

를 각각 OAM 변조기(310)과 OAM 복조기(410)에 전달할 수 있다. 제어 장치는 RF 체인에 의한 이득/위상 변화값을 추정하고 보정하는 알고리즘이 임베디드된 장치일 수 있다. 또는 송신기(300)가 RF 체인에 의한 이득/위상 변화값을 추정하여

를 자신의 OAM 변조기(310)에 적용하고, 수신기(400)가 RF 체인에 의한 이득/위상 변화값을 추정하여

를 자신의 OAM 복조기(410)에 적용할 수도 있다.UAC based OAM system

and

Is estimated, respectively, to the OAM modulator 310 and the OAM demodulator 410

and

Apply. In UAC based OAM system, a specific control device

Wow

Calculate

and

To the OAM modulator 310 and the OAM demodulator 410, respectively. The control device may be a device in which an algorithm for estimating and correcting a gain/phase change value by the RF chain is embedded. Alternatively, the transmitter 300 estimates the gain/phase change value by the RF chain

Is applied to its OAM modulator 310, and the receiver 400 estimates the gain/phase change value by the RF chain.

May be applied to one's OAM demodulator 410.

,

cm(i.e.,

GHz)이다.

와

는 단위 분산(unit variance)를 갖는 제로 평균 복소 가우신안 분포를 갖도록 하였다. 채널추정을 위한 파일럿 시퀀스에는 DFT 시퀀스를 사용하였다. 모든 성능 측정치들은

의 반복 시뮬레이션 실행을 통해 얻었다.Simulation was performed to verify the effectiveness of the proposed technique. The UCA antenna parameters applied to the simulation are N = 8,

,

cm(ie,

GHz).

Wow

Has a zero-average complex Gaussian distribution with unit variance. A DFT sequence was used for the pilot sequence for channel estimation. All performance measurements

It was obtained through repeated simulation run.

,

, 그리고

에 대한 정규화된 MSE(NMSE)를 나타낸 것이다.

에 대한 NMSE는

으로 정의되고,

와

에 대한 NMSE는 각각

와

로 정의된다. NMSE가 SNR과 파일럿 심볼의 길이(

)에 의존성을 관찰하기 위해

의 3가지 경우에 대해 시뮬레이션을 하였다. 시뮬레이션 결과는, 수학식 10에서 예상한 대로,

에 대한 NMSE는 SNR이 10 dB 증가할 때마다 1/10배로 감소하며, 파일럿 시퀀스의 길이

에 대해 반비례하여 감소함을 보여주었다. 또한, SNR이 증가함에 따라

에 대한 NMSE가 작아짐에 영향을 받아

와

에 대한 NMSE도 단조적으로 감소하는 것이 관찰된다.4 is a simulation result for the effectiveness of the proposed technique. Figure 4

,

, And

Normalized MSE for (NMSE).

NMSE for

Is defined as,

Wow

NMSE for each

Wow

Is defined as NMSE is the length of the SNR and the pilot symbol (

) To observe dependencies

Three cases were simulated. The simulation results, as expected in Equation 10,

The NMSE for is reduced by 1/10 each time the SNR increases by 10 dB, the length of the pilot sequence

It showed a decrease in inverse proportion to. Also, as SNR increases

Affected by the smaller NMSE for

Wow

It is observed that the NMSE for monotonically also decreases.

5 is an example of achievable frequency efficiency of the proposed technique. Figure 5 shows the achievable frequency efficiency according to the transmission and reception distance of the UCA OAM system in the condition of SNR = 20 dB. Fig. 5 shows that the ASE has a maximum transmission and reception distance at a Rayleigh distance of 19.23 m, monotonically decreases at a distance of 28 m or more, and compensates using the proposed RF chain imbalance estimate 41.5 when not compensated at Rayleigh distance Compensation of bps/Hz to 51.5 bps/Hz through compensation shows the achievable frequency efficiency close to zero imbalance.

In addition, the method for estimating or compensating for the imbalance between RF chains in the terrestrial UCA-based OAM system as described above may be implemented as a program (or application) including executable algorithms that can be executed on a computer. The program may be stored and provided in a non-transitory computer readable medium.

The non-transitory readable medium means a medium that stores data semi-permanently and that can be read by a device, rather than a medium that stores data for a short time, such as registers, caches, and memory. Specifically, the various applications or programs described above may be stored and provided in a non-transitory readable medium such as a CD, DVD, hard disk, Blu-ray disk, USB, memory card, ROM, and the like.

The drawings attached to the present embodiment and the present specification merely show a part of the technical spirit included in the above-described technology, and are easily understood by those skilled in the art within the scope of the technical spirit included in the above-described technical specification and drawings. It will be apparent that all of the examples and specific examples that can be inferred are included in the scope of the above-described technology.

Claims (11)

Estimating a channel maximum likelihood between a transmitter and a receiver in a UCA (Uniform Circular Array)-based Orbital Angular Momentum (OAM) system; And
Estimating a first change in gain or phase due to the RF chain of the transmitter and a second change in gain or phase due to the RF chain of the receiver based on the maximum likelihood of the channel in the system,
The channel between the transmitter and the receiver is a first matrix having, as an element, the first change by each of the N RF chains of the transmitter, and a factor having the second change by each of the N RF chains of the receiver as an element. A method for estimating imbalance between RF chains in a UCA-based OAM system defined based on 2 matrices and ideal channels. According to claim 1,
The maximum likelihood of the channel is determined based on the first matrix, the second matrix, the ideal channel, and a complex Gaussian random variable having a zero mean. According to claim 1,
The maximum likelihood of the channel

Is expressed as,

Is the maximum likelihood of the channel,

And a is the first matrix,

And b is the second matrix,

Ideal channel,

Is a method for estimating imbalance between RF chains in a UCA-based OAM system, which is a complex Gaussian random variable with zero mean. According to claim 1,
The ideal channel is a distance between the transmitter and the receiver, the antenna radius of the transmitter and the receiver, and the asymmetry between the RF chain in the UCA-based OAM system determined by the azimuth of the transmitter and the receiver. According to claim 1,
In the second matrix

And b is an imbalance estimation method between RF chains in a UCA-based OAM system that is a diagonal element of the second matrix. According to claim 1,
The first change and the second change are respectively

It is determined by the diagonal element a of the first matrix and the diagonal element b of the second matrix minimizing,

Is the maximum likelihood of the channel,

Hadamard operation,

Is an ideal channel UCA-based OAM system. Estimating a channel maximum likelihood between a transmitter and a receiver in a UCA (Uniform Circular Array)-based Orbital Angular Momentum (OAM) system;
Estimating a first change in gain or phase due to the RF chain of the transmitter and a second change in gain or phase due to the RF chain of the receiver based on the maximum likelihood of the channel in the system; And
And performing inverse compensation for the first change in the Fourier transform of the transmitter, and performing inverse compensation for the second change in the inverse Fourier transform of the receiver.
The channel between the transmitter and the receiver is a first matrix having, as an element, the first change by each of the N RF chains of the transmitter, and a factor having the second change by each of the N RF chains of the receiver as an element. 2 An imbalance compensation method between RF chains in a UCA-based OAM system defined based on a matrix and an ideal channel. The method of claim 7,
The maximum likelihood of the channel

Is expressed as,

Is the maximum likelihood of the channel,

And a is the first matrix,

And b is the second matrix,

Ideal channel,

Is an imbalance compensation method between RF chains in a UCA-based OAM system, which is a complex Gaussian random variable having a zero mean. The method of claim 7,
The first change and the second change are respectively

It is determined by the diagonal element a of the first matrix and the diagonal element b of the second matrix minimizing,

Is the maximum likelihood of the channel,

Hadamard operation,

Is an ideal channel UCA-based OAM system, an imbalance compensation method between RF chains. The method of claim 7,
Inverse compensation for the first change is performed using the inverse matrix of the estimated diagonal elements for the first matrix, and inverse compensation for the second change is performed using the inverse matrix of the estimated diagonal elements for the second matrix. In the UCA-based OAM system to perform the imbalance compensation method between the RF chain. A computer-readable, non-transitory readable medium recording a program for executing an imbalance compensation method between RF chains in a UCA-based OAM system according to any one of claims 7 to 10 in a computer.

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