WO2019078547A1 - Method for estimating and compensating for imbalance between rf chains in uca-based oam system - Google Patents

Abstract

A method for compensating for imbalance between RF chains in a UCA-based OAM system includes: a step for estimating channel maximum likelihood between a transmitter and a receiver; a step for estimating a first change of a gain or phase by means of an RF chain of the transmitter and a second change of a gain or phase by means of an RF chain of the receiver on the basis of the channel maximum likelihood in the system; and a step for performing an inverse compensation for the first change on a Fourier transform of the transmitter and performing an inverse compensation for the second change on an inverse Fourier transform of the receiver. Channels between the transmitter and the receiver are defined on the basis of a first matrix which has, as elements, the first change by each of N RF chains of the transmitter, a second matrix which has, as elements, the second change by each of N RF chains of the receiver, and an ideal channel.

Description

Imbalance estimation and compensation method between RF chains in UCA-based OAM system

The UCA OAM system described below relates to techniques for estimating and compensating for imbalances in the RF chains of the transmitter and the receiver.

OAM (Orbital Angular Momentum) is one of the momentum of all electromagnetic waves together with LM (Linear Momentum) and SAM (Spin Angular Momentum). It has been found that in a LoS (line-of-sight) environment, theoretically an infinite number of OAM modes can be transmitted without mutual interference. OAM-related technologies are being studied in the fields of millimeter-wave and optical communication.

In a pure LoS environment, a UCA (Uniform Circular Array) OAM system precisely aligns a transmitting UCA and a receiving UCA antenna, precisely discrete Fourier transform (DFT) the transmission signal at the transmitter and applies an inverse DFT postprocessing at the receiving end To form parallel N AWGN channels without mutual interference. The advantage of the UCA OAM system is that the UCA pair channel is represented as a circulant matrix when the transmit and receive UCA are correctly aligned.

If the gain or phase imbalance exists between the N RF chains of the transmitter or between the N RF chains of the receiver, then the circulant characteristics between the UCA antennas may not be maintained Therefore, interference occurs between UCA OAM reception signals. This leads to a reduction in the usable capacity of the UCA OAM channel.

To solve this problem, equalization must be performed at the transmitter and receiver based on the real-time channel estimate. As a result, if 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 it can form N parallel independent channels without an equalizer is greatly impaired.

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

A method for estimating an imbalance between RF chains in a UCA-based OAM system includes estimating a channel maximum likelihood between a transmitter and a receiver in a UCA (Orbital Circular Array) based OAM (Orbital Angular Momentum) Estimating a first change in gain or phase by the RF chain of the transmitter based on the maximum likelihood and a second change in gain or phase by the RF chain of the receiver.

The method of compensating imbalance between RF chains in a UCA-based OAM system includes estimating a channel maximum likelihood between a transmitter and a receiver in a UCA (Orbital Circular Array) -based OAM (Orbital Angular Momentum) system, Estimating a first change in gain or phase by the RF chain of the transmitter based on the maximum likelihood and a second change in gain or phase by the RF chain of the receiver; Performing inverse compensation on the change, and performing inverse compensation on the second change in the inverse Fourier transform of the receiver. Wherein the channel between the transmitter and the receiver comprises a first matrix having the first change by each of the N RF chains of the transmitter as an element, a first matrix with the second change by each of the N RF chains of the receiver, 2 matrix and an ideal channel.

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

Figure 1 is an example of a UCA system model.

2 shows an example of a transmitter and a receiver structure of a UCA OAM system.

Figure 3 is an example of a UCA system that compensates for imbalances in RF chains.

Figure 4 shows the simulation results of the effectiveness of the proposed technique.

5 shows an example of achievable frequency efficiency of the proposed scheme.

The following description is intended to illustrate and describe specific embodiments in the drawings, since various changes may be made and the embodiments may have various embodiments. However, it should be understood that the following description does not limit the specific embodiments, but includes all changes, equivalents, and alternatives falling within the spirit and scope of the following description.

The terms first, second, A, B, etc., may be used to describe various components, but the components are not limited by the terms, but may be used to distinguish one component from another . For example, without departing from the scope of the following description, the first component may be referred to as a second component, and similarly, the second component may also be referred to as a first component. And / or < / RTI > includes any combination of a plurality of related listed items or any of a plurality of related listed items.

As used herein, the singular " include " should be understood to include a plurality of representations unless the context clearly dictates otherwise, and the terms " comprises & , Parts or combinations thereof, and does not preclude the presence or addition of one or more other features, integers, steps, components, components, or combinations thereof.

Before describing the drawings in detail, it is to be clarified that the division of constituent parts in this specification is merely a division by main functions of each constituent part. That is, two or more constituent parts to be described below may be combined into one constituent part, or one constituent part may be divided into two or more functions according to functions that are more subdivided. In addition, each of the constituent units described below may additionally perform some or all of the functions of other constituent units in addition to the main functions of the constituent units themselves, and that some of the main functions, And may be carried out in a dedicated manner.

Also, in performing a method or an operation method, each of the processes constituting the method may take place differently from the stated order unless clearly specified in the context. That is, each process may occur in the same order as described, may be performed substantially concurrently, or may be performed in the opposite order.

In the UAC-based OAM system described below, the channel between the transmitter and the receiver is constantly modeled, and the imbalance between the RF chains is estimated and compensated based on the channel model. The channel modeling and the imbalance estimation or compensation process can be described through mathematical models and calculations.

는 하다마드(Hadamard) 연산을 의미하고,

는 행렬의 외적을 의미한다. Matrix operations are often used in the following description. Matrix operators use symbols that are widely used in mathematical and engineering fields by default. For example, A ^T denotes a transpose matrix of matrix A, A ^H denotes a Hermitian matrix of matrix A,

Means a Hadamard operation,

Denotes the outer 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.Figure 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. TR distance D is the distance between the center of the transmitting UCA and the center of the receiving UCA. It is assumed that the antenna elements of the transmitting and receiving UCA antennas are uniformly arranged in a circle 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.Represents 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

Respectively

Wow

Lt; / RTI >

(Boresight), which is the front direction of the reference (e.g., first) antenna at the transmitting UCA 10, and the angle the user makes.

Represents the angle that the user makes with the antenna reference transmission direction, which is the front direction of the reference (e.g., first) antenna, at the receiving UCA 20. [ The distance between the jth element of the transmitting UCA and the jth element of the receiving UCA

The

. here,

to be.

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

Is determined solely by the difference between i and j.

The channel between the jth element of the receiving UCA 20 and the i th element of the transmitting UCA 10 in a pure LoS environment in which there is only a direct path between the transmitting and receiving UCA is given by: .

[Equation 1]

를 갖는 전방성 안테나 소자 (omni-directional antenna elements)라고 가정한다. 임의의 파장을 갖는 협대역 신호에 대한 UCA 페어 채널 응답은 이 안테나 소자들 사이의 거리에 의해서 결정된다. 즉 안테나 소자들 사이의 채널 응답은 안테나 소자 인덱스 i와 j의 차이에 의해서만 결정되는 결과를 가져온다. 따라서, 송신 UCA(10)와 수신 UCA(20)가 모두 N개의 안테나 소자를 가지고 있다고 가정할 때, 채널 행렬 H는 순환 행렬(circulant matrix)이 된다.If all antenna elements have the same radiation pattern value regardless of the element indices i, j

≪ / RTI > are assumed to be omni-directional antenna elements. The UCA fair channel response for a narrowband signal with arbitrary wavelength is determined by the distance between these antenna elements. That is, the channel response between the antenna elements is determined only by the difference between the antenna element indices 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 shows 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, and shows only the configuration necessary for the explanation. The transmitter 100 includes an OAM modulator 110 for Fourier transforming the input signals {s ₁ , s ₂ , ..., s _N }. The OAM modulator 110 performs a DFT on the input signal. Q denotes a DFT matrix for N points. Transmitter 100 transmits the modulated input signal _{{x 1, x 2, ...} , x N} from the N antenna elements. The receiver 200 includes an OAM demodulator 210 for performing an inverse Fourier transform on signals {y ₁ , y ₂ , ..., y _N } received via N antenna elements. OAM demodulator 210 performs an inverse DFT on the input signal. Q ^H denotes an inverse DFT matrix for N points. The receiver 200 then decodes the inverse DFT transformed signal {r ₁ , r ₂ , ..., r _N }.

과

는 각각 송신기(100)와 수신기(200)의 N개 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.2,

and

Represents a change in gain or phase by N RF chains of the transmitter 100 and the receiver 200, respectively. The degree of gain or phase change (change value) by the RF chain may vary depending on the hardware structure, communication environment, and the like. For convenience of explanation, the degree of gain or phase change by the RF chain is referred to as a gain / phase change value.

,

. In addition,

ego

. In this case,

Can be expressed by Equation (2) below.

&Quot; (2) "

이고,

는 송신기의 RF chain들의 입력 신호 벡터이고,

은 수신기의 RF chain들의 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

표현된다.here,

ego,

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

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

Lt; / RTI >

, Channel

Achievable spectral efficiency (ASE) of

Is expressed.

이고

인 이상적인 송신기와 수신기 쌍(pair)의 경우, UCA OAM 변조기(110)와 복조기(120)는 다음과 같이 N 개의 병렬 채널을 형성한다. 이 경우,

이고, 따라서

가 되어

도 또한 순환 행렬이 된다.

ego

In the case of an ideal transmitter and receiver pair, the UCA OAM modulator 110 and the demodulator 120 form N parallel channels as follows. in this case,

And therefore

Become

Also becomes a circulation matrix.

&Quot; (3) "

는 수학식 3과 같이 N-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.A circulating matrix

Is an N-point DFT matrix < RTI ID = 0.0 >

Wow

A complex diagonal matrix

As shown in Fig. Therefore, when Equation (3) is used in Equation (2), the following Equation (4) can be obtained.

&Quot; (4) "

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 채널간 간섭 제거없이 N개의 평행 독립 채널들을 구성할 수 있게 된다.

(4), < / RTI >

. Therefore, the output signal of the inverse DFT of the receiver 200 is

. here,

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

또는

인 경우에

로 표현되는

행렬이 더 이상 순환 행렬이 되지 않기 때문이다. In the case of actual implemented systems, 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.

or

in case of

Expressed as

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

Hereinafter, a technique for compensating 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. i번 째 시간/주파수 자원을 통해 n번 째 송신기 RF 체인으로 송신되는 파일럿 심볼을

로, m번 째 수신기 RF 체인을 통해 수신되는 신호를

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

And transmit pilot symbols using N different time / frequency resources to estimate the time / frequency resources. The pilot symbols transmitted to the n th transmitter RF chain through the i th time / frequency resource

, The signal received through the mth receiver RF chain

. In this case, the signal received through the i-th time / frequency is expressed by Equation (5) below.

&Quot; (5) "

,

이고,

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

와

로 정의하고,

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

,

ego,

Is an N-dimensional complex Gaussian noise. The signal transmitted through the L time / frequency resources and the received signal are respectively

Wow

Respectively,

, The received signal can be expressed by Equation (6) below.

&Quot; (6) "

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 is given by Equation (7) below. Substituting Equation (6) into Equation (7) yields Equation (8).

&Quot; (7) "

&Quot; (8) "

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

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

&Quot; (9) "

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.

Under the conditions of

Is satisfied. At this time

, In other words

Are complex Gaussian random variables with equally distributed zero-mean. Further, assuming a PSK pilot,

Because of,

Can be expressed as Equation (10) below.

&Quot; (10) "

RF chain imbalance estimation

에 대한 ML 추정은 아래 수학식 11과 같이 표현된다.

Is expressed by Equation (11) below. &Quot; (11) "

&Quot; (11) "

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. N _a is the zero-mean complex Gaussian variance,

If known,

Wow

Can be estimated as follows. On the other hand, the distance D between the transmitter and the receiver UCA and (

,

) And (

) Is given, the ideal channel

. The both sides of the equation (11) are vectorized as shown in the equation (12).

&Quot; (12) "

,

로 정의하면, 다시 아래의 수학식 13과 같이 정리할 수 있다.

,

, It can be rearranged as shown in Equation (13) below.

&Quot; (13) "

와

이기 때문에

임을 적용한 것이다. 세 번째 등호 내용은

는

와

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

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

Wow

Because

. The third equal sign

The

Wow

Hadamard product of Hadamard. The fourth equal sign

.

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.Home 1.

ego,

Phase must be zero (i.e.,

)). The reason for this assumption is that the RF imbalance model of equation (13)

Wow

≪ / RTI >

Wow

Instead of

Wow

The same value will be obtained.

Wow

It is not specifically limited.

가 제로 평균 복소 가우시안이므로,

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

와

의 함수로 표현된다.

Is a zero-mean complex Gaussian,

The

And the covariance matrix is

A complex Gaussian random vector. therefore

The conditional probability density function for < RTI ID = 0.0 >

Wow

.

&Quot; (14) "

는

에 대한 우도 함수이므로,

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

The

Lt; RTI ID = 0.0 >

Is given by Equation (15) below.

&Quot; (15) "

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

, The following equation (16) is obtained.

&Quot; (16) "

Equation (16) can be written as Equation (17) below.

&Quot; (17) "

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 content of the second inequality

.

Represents the hadamard inverse. this is

To minimize

Is equivalent to finding the solution of equation (15). therefore,

Lt; / RTI >

Can be rewritten as Equation 18 below.

&Quot; (18) "

와

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

Wow

The joint estimator for (2) is derived as follows. First, the following equation (19) is defined.

&Quot; (19) "

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

&Quot; (20) "

를 적용하면 아래의 수학식 21과 같다. In Equation 20,

The following equation (21) is obtained.

&Quot; (21) "

을 풀면, 아래의 수학식 22를 얻을 수 있다.

The following equation (22) can be obtained.

&Quot; (22) "

자리에 대입하면, 아래의 수학식 23과 같다. Next, equation (22) is substituted into equation

The following equation (23) is obtained.

&Quot; (23) "

&Quot; (24) "

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. According to Equation 24,

On the hyperplane satisfying the condition, the solution of equation (24)

The eigenvectors corresponding to the largest eigenvalues among the eigenvectors of eigenvectors of eigenvectors. This eigenvector

By definition,

also

The eigenvectors are not unique because they are the eigenvectors corresponding to the largest eigenvalues of eigenvectors. Among these eigenvectors,

The eigenvector satisfying the condition is expressed by Equation 25 below.

&Quot; (25) "

은

의 첫 번째 요소를 나타낸다. here,

silver

Represents the first element of.

를 얻는다. Finally, by substituting the equation (25) into the equation (22), the following equation

.

&Quot; (26) "

와

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

으로 정의하고

으로 정의하자. OAM 시스템은

와

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. (25) and (26), the diagonal elements A and B described above, respectively,

Wow

Respectively. The OAM system thereby estimates the imbalance between the RF chains.

And

. The OAM system

Wow

(25) and (26) to correct the converted value in the modulator 310 of the transmitter 300 inversely and to correct the converted value in the demodulator 410 of the receiver 400 inversely.

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.Figure 3 is an example of a UCA system that compensates for imbalances in RF chains. Fig. 3 is basically the same as the configuration of Fig. 3 does not show all the configurations in the transmitter 300 and the receiver 400, and shows only the configuration required for RF chain unbalance estimation and correction. The transmitter 300 includes an OAM modulator 310 for Fourier transforming the input signal {s ₁ , s ₂ , ..., s _N }. The OAM modulator 310 performs a DFT on the input signal. Q denotes a DFT matrix for N points. The OAM modulator 310

Is used as a DFT matrix. This is for correcting the gain / phase change value by the RF chain of the transmitter. Transmitter 300 transmits the modulated input signal _{{x 1, x 2, ...} , x N} from the N antenna elements.

는 N개 포인트에 대한 역 DFT 행렬을 의미한다. OAM 복조기(410)는

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 performing an inverse Fourier transform on signals {y ₁ , y ₂ , ..., y _N } received via N antenna elements. OAM demodulator 410 performs an inverse DFT on the input signal.

Denotes an inverse DFT matrix for N points. The OAM demodulator 410

Is used as an inverse DFT matrix. This is for correcting the gain / phase change value by the RF chain of the receiver. The receiver 400 then decodes the inverse DFT transformed signal {r ₁ , r ₂ , ..., r _N }.

와

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)와 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. The UAC-based OAM system

Wow

And outputs to the OAM modulator 310 and the OAM demodulator 410, respectively,

and

Is applied. In a UAC-based OAM system,

Wow

Lt; / RTI >

and

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

To its own OAM modulator 310, and the receiver 400 estimates the gain / phase change value by the RF chain

May be applied to their OAM demodulator 410. < RTI ID = 0.0 >

,

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

,

cm (ie,

GHz).

Wow

Has a zero mean complex Gaussian distribution with a unit variance. A DFT sequence is used for the pilot sequence for channel estimation. All performance measures were obtained through a 10 ⁵ iterative 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. Figure 4 shows the simulation results of the effectiveness of the proposed technique. Figure 4

,

, And

Gt; (NMSE) < / RTI >

NMSE for

Lt; / RTI >

Wow

NMSE for each

Wow

. NMSE is the SNR and the length of the pilot symbol (

) To observe the dependence

The simulation results are shown in Fig. The simulation result, as expected from equation (10)

The NMSE for the pilot sequence decreases by 1/10 every time the SNR increases by 10 dB, and the length of the pilot sequence

And inversely proportional to. Also, as the SNR increases

Is affected by the smaller NMSE for

Wow

It is observed that the NMSE also decreases monotonically.

5 shows an example of achievable frequency efficiency of the proposed scheme. 5 shows the achievable frequency efficiency according to the transmission / reception distance of the UCA OAM system under the condition of SNR = 20 dB. 5 shows that ASE has a maximum value at a Rayleigh distance of 19.23 m, monotonically decreases at a distance of 28 m or more, and compensates by using the proposed RF chain unbalance estimate, bps / Hz to 51.5 bps / Hz through compensation to show achievable frequency efficiency close to zero imbalance.

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

A non-transitory readable medium is a medium that stores data for a short period of time, such as a register, cache, memory, etc., but semi-permanently stores data and is readable by the apparatus. In particular, the various applications or programs described above may be stored on non-volatile readable media such as CD, DVD, hard disk, Blu-ray disk, USB, memory card, ROM,

The present embodiment and drawings attached hereto are only a part of the technical idea included in the above-described technology, and it is easy for a person skilled in the art to easily understand the technical idea included in the description of the above- It will be appreciated that variations that may be deduced and specific embodiments are included within the scope of the foregoing description.

Claims (15)

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

Lt; / RTI >

Is the channel maximum likelihood, A = diag {a} a is the first matrix, B = diag {b} and b is the second matrix, H is an ideal channel, N _A is _a complex number having a zero (zero) average An Imbalance Estimation Method between RF Chains in UCA - based OAM Systems with Gaussian Random Variables. The method according to claim 1, Wherein the ideal channel is determined by a distance between the transmitter and the receiver, an antenna radius of the transmitter and the receiver, and an azimuth of the transmitter and the receiver. The method according to claim 1, In the second matrix

, And b is a diagonal element of the second matrix, UCA-based OAM system. The method according to claim 1, Wherein the first change and the second change are respectively

A " of the first matrix and a diagonal element " b " of the second matrix,

The channel maximum likelihood,

Is the Hadamard operation, and H is the ideal channel. The method according to claim 1, The first change and the second change

A target eigenvector having a largest eigenvalue of the eigenvectors of the target eigenvectors and a first element of the target eigenvectors,

,

Is the channel maximum likelihood, a is the first matrix,

Hadamard operation,

A method of estimating an imbalance between RF chains in a UCA - based OAM system that is an inverse Hadamard operation. 8. The method of claim 7, The estimated second change

, And the estimated first change is

Lt; / RTI >

Is the target eigenvector,

Is a first element of the target eigenvector. Estimating channel maximum likelihood between a transmitter and a receiver in a UCA (Orbital Circular Array) based OAM (Orbital Angular Momentum) system; Estimating a first change in gain or phase by the RF chain of the transmitter based on the channel maximum likelihood in the system and a second change in gain or phase by the RF chain of the receiver; And Performing inverse compensation on the first change in the Fourier transform of the transmitter and performing inverse compensation on the second change in the inverse Fourier transform of the receiver, Wherein the channel between the transmitter and the receiver comprises a first matrix having the first change by each of the N RF chains of the transmitter as an element, a first matrix with the second change by each of the N RF chains of the receiver, A method of imbalance compensation between RF chains in a UCA - based OAM system defined by two matrices and ideal channels. 10. The method of claim 9, The channel maximum likelihood

Lt; / RTI >

Is the channel maximum likelihood, A = diag {a} a is the first matrix, B = diag {b} and b is the second matrix, H is an ideal channel, N _A is _a complex number having a zero (zero) average Unbalance compensation method between RF chains in UCA - based OAM system with Gaussian random variable. 10. The method of claim 9, Wherein the first change and the second change are respectively

A " of the first matrix and a diagonal element " b " of the second matrix,

The channel maximum likelihood,

Is an Hadamard operation, and H is an ideal channel. 10. The method of claim 9, Performing inverse compensation on the first change using the inverse of the estimated diagonal element for the first matrix and performing inverse compensation on the inverse of the second transformation using the inverse matrix of the estimated diagonal elements for the second matrix, A method of imbalance compensation between RF chains in a UCA - based OAM system that performs. 10. The method of claim 9, The first change and the second change

A target eigenvector having a largest eigenvalue of the eigenvectors of the target eigenvectors and a first element of the target eigenvectors,

,

Is the channel maximum likelihood, a is the first matrix,

Hadamard operation,

Unbalance Compensation Method between RF Chains in UCA - based OAM System with Inverse Hadamard Operation. 14. The method of claim 13, The estimated second change

, And the estimated first change is

Lt; / RTI >

Is the target eigenvector,

Is an imbalance compensation method between RF chains in a UCA-based OAM system that is the first element of the target eigenvector. A computer-readable recording medium having recorded thereon a program for executing an imbalance compensation method between RF chains in a UCA-based OAM system according to any one of claims 9 to 14.

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