KR101625805B1 - maximum sum-rate based power efficient interference alignment in multi user mimo system - Google Patents

Abstract

Disclosed is a maximum sum-rate based power efficient interference alignment method in a multi-user MIMO system. The maximum sum-rate based power efficient interference alignment method in a multi-user MIMO system comprises a step of, for interference alignment on an interference channel, calculating a sum rate of working power of a transmitter as an objective function by taking into account the working power and then calculating pre-coding of the transmitter via the objective function.

Description

[0001] The present invention relates to a power-efficient interference sorting method based on capacity sum maximization in a multi-user multi-antenna system,

The following description relates to a method for constructing an interference sorting algorithm for efficient power usage in a network composed of multiple users based on multiple antennas.

In a multi-user network, interference occurs between users when using time, channel, and spatial radio resources at the same time. A common method for removing interference in such an interference channel is time division multiple access which divides time, frequency division multiple access which divides frequency, and the like. However, these methods allocate resources in terms of time and frequency only to a single user, resulting in a low band efficiency.

Therefore, to solve this problem, an interference alignment (IA) algorithm has been proposed. The interference alignment is a method of aligning a plurality of interference signals in a specific signal area at a receiver and demodulating only a desired message. To do this, the transmit signal of the transmitter must be adjusted so that each transmitter transmit signal is not included in the signal space region of the unwanted receiver but is included in the signal space region of the desired receiver. The interference alignment algorithm can be applied to both a single antenna system and a multi-antenna system, but when applied to a single antenna system, a symbol extension is required. In this case, since information about a significant period of channel is required, . Interference alignment is achieved by designing the transmit and receive vectors such that all interferences received from other users of the interfering channel are aligned in a limited space so that the KM / 2 degree of freedom (DoF) of the K M / Freedom has been proven to be achieved. The degree of freedom can be interpreted as the multiplexing gain as the extremum of the sum capacity and log (SNR) ratio at high SNR. The interference sorting algorithm has a closed-form method and an iterative method. The non-iterative method needs to know the channel information for all users and it is impossible to extend the existing interference sorting algorithm for cases other than K = 3 Do. The iterative algorithm can solve the problem that the transmission / reception vector for interference alignment is not obtained in a closed form, but requires all the channel information.

The iterative algorithms for interference alignment on interfering channels include a maximum signal-to-interference plus-noise ratio (max-SINR) algorithm, a maxium sum-rate algorithm, and alternating minimization. These algorithms can be called distributed algorithms in that the link connected to them knows the channel information, and the rest of them know only the statistics of the channel. This iterative algorithm alternately updates the transmit vector and the receive vector to maximize the objective function such as SINR, sum-rate, and so on. The purpose of existing algorithms is to maximize the transmission capacity and to design a transmitter, there is a need to study algorithms that consider not only transmission capacity but also performance in terms of power efficiency.

A method for constructing an interference sorting algorithm for efficient power usage in a network composed of multiple users based on multiple antennas is provided.

In order to perform interference alignment in a multi-user interference environment with multiple antennas, precoding is configured to satisfy some performance while minimizing the power used when the transmitter is running out of power. To do this, we design a new scheme considering the power using the capacity sum, which is an objective function used in the capacity sum maximization algorithm, and configure precoding by using it to reduce power consumption and maximize power efficiency.

A method of interfering alignment in a multi-user multi-antenna (MIMO) system implemented by a computer, comprising the steps of: calculating a sum- And calculating precoding of the transmitter through the objective function after the calculation.

(여기서, I_d는 간섭신호를 나타내고, S_k는 k번째 수신기에서 수신된 신호의 공분산 행렬을 나타내고, Q_k는 k번째 수신기에서의 간섭 더하기 잡음의 공분산 행렬을 나타낸다.)According to an aspect, the step may calculate the _{sum of} capacitances (R _sum ) through Equation (1). Equation (1)

(Where I _d denotes the interference signal, S _k denotes the covariance matrix of the signal received at the kth receiver, and Q _k denotes the covariance matrix of interference plus noise in the kth receiver).

According to another aspect, the step comprises: a first step of constructing a decoding matrix U _k of the kth receiver that minimizes leakage interference for the precoding matrix V _l of the _lth transmitter; A second step of calculating a differential of a capacity sum with respect to a decoding matrix U _k of the _kth receiver; A third step of calculating a solution of the interference alignment for the kth receiver by applying a shortest geodesic solution to the differential of the capacity sum with respect to the decoding matrix Uk of the _kth receiver; a fourth step of constructing a precoding matrix V _k of the k-th transmitter that minimizes leakage interference for the decoding matrix Ul of the _lth receiver; A fifth step of calculating a differential of a capacity sum with respect to a precoding matrix V _k of the k-th transmitter; And a sixth step of calculating a solution of the interference alignment for the k-th transmitter by applying a shortest starter solution to the differential of the capacity sum for the precoding matrix V _k of the k-th transmitter.

According to another aspect, the step repeats the first through sixth steps until the solution of the interference alignment for the kth receiver and the solution of the interference alignment for the kth transmitter converge.

According to another aspect, the precoding matrix V _l of the l-th transmitter and the precoding matrix V _k of the k-th transmitter are expressed by a precoding vector according to the transmission power with the number of antennas and the number of columns.

According to another aspect, in the third step, the decoding matrix U _k of the kth receiver is updated using a singular value decomposition (SVD) of a tangent vector for a Grassmann manifold, The precoding matrix V _k of the k-th transmitter is updated using the SVD of the tangent vector for Grassman manifold.

According to embodiments of the present invention, when a mobile device using interference alignment needs to operate in a power minimization mode due to power shortage, it is possible to reconfigure the objective function in consideration of power usage, Capacity sum maximization interference sorting algorithm can be applied, and power consumption can be reduced and power efficiency can be maximized.

1 is a diagram illustrating a network comprised of multiple antenna systems participating in interference alignment in accordance with an embodiment of the present invention.
2 is a diagram illustrating an implementation of a capacity sum maximization algorithm considering transmission power according to an embodiment of the present invention.
3 is a graph illustrating normalized power consumption versus SNR of a capacity sum maximization algorithm considering transmission power according to an exemplary embodiment of the present invention.
FIG. 4 is a graph illustrating normalized power consumption versus the number of repetitions of a capacity sum maximization algorithm considering transmission power according to an exemplary embodiment of the present invention.
FIG. 5 is a graph illustrating an average capacity-to-SNR ratio of a capacity-sum maximization algorithm considering transmission power according to an exemplary embodiment of the present invention.
FIG. 6 is a graph illustrating power efficiency as a sum of average SNR per used power of a capacity sum maximization algorithm considering transmission power according to an exemplary embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

The present invention relates to an interference sorting algorithm which is a method of newly constructing a capacity sum derivative used in a capacity sum maximization algorithm to design precoding considering power consumption. For this purpose, the objective function related to the capacity sum is newly constructed in consideration of the power consumption of the transmitter, and by operating the precoding of the transmitter through the objective function, the power saving mode can be operated in which the power efficiency can be maximized.

In the present invention, a series of methods for calculating the decoding of a receiver using an existing method is repeatedly performed after the capacity sum considering power-efficient precoding is configured as an objective function, the precoding of the transmitter is calculated using the objective function, And the interference is aligned.

The power efficient capacity sum maximization interference sorting algorithm in the multi-user interference environment with multiple antennas proposed in the present invention comprises a capacity sum considering the power used as an objective function, differentiating the capacity sum, and calculating a tangent vector of Grassmann manifold And a shortest geodesic solution for a Grassman manifold using a compact SVD of tangent vectors. The method of constructing the capacity sum considering the use power as the objective function can be used as an optimal function for the use power considering the power used by the transmitter for the existing capacity sum. At this time, the tangent vector is a method of deriving the directionality of the precoding matrix according to the objective function, and the short-term baseline solution is a method used to derive the precoding matrix for the objective function.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

1 is a diagram illustrating a network comprised of multiple antenna systems 100 participating in an interference alignment in accordance with an embodiment of the present invention.

개의 송신 안테나(101)와

개의 수신 안테나(104)를 갖는다고 할 때, 얻을 수 있는 자유도는

다. 본 발명에서 모든 사용자는

개의 동일한 안테나와

의 동일한 자유도를 갖는 것을 가정한다. 이러한 대칭적 다중안테나 간섭 채널은

로 표현될 수 있다. 이러한 시스템 모델에서 송신기(102)와 수신기(103) 중 송신기 k는 수신기 k와 원하는 신호를 주고 받게 되고, 따라서 송신기 k는 원하지 않는 모든 수신기들에 대해 동일채널 간섭을 발생시키게 된다. 본 발명에서 고려하는 다중안테나 간섭채널모델은 협대역 블록페이딩이고, 여기서 채널은 하나의 심볼전송구간 동안 정적인 것으로 간주한다.Figure 1 shows an interference channel network for three or more K users (transmitter-receiver pairs) having multiple antennas. Each transmitter 102 and receiver 103

The transmission antennas 101 and

Lt; RTI ID = 0.0 > 104, < / RTI >

All. In the present invention, all users

With the same antenna

Of the same degree of freedom. This symmetric multi-antenna interference channel

. ≪ / RTI > In this system model, the transmitter k of the transmitter 102 and the receiver 103 is exchanged with the receiver k for the desired signal, so that transmitter k causes co-channel interference for all undesired receivers. The multi-antenna interference channel model considered in the present invention is narrowband block fading, where the channel is considered static for one symbol transmission period.

)는 수학식 1과 같다.Thus, the signal received at receiver k

) ≪ / RTI >

[Equation 1]

는 안테나 개수 N과 자유도 d를 행과 열의 개수로 하는 송신기 k의 프리코딩 벡터를 나타낸다. 이러한 프리코딩 벡터는

의 유니터리 행렬이고 d의 열은 선형독립이며 P_k는 송신기 k의 송신전력을 나타낸다. 그리고,

는 N×N 크기의 l번째 송신기에서 k번째 수신기로 가는 독립항등분포를 갖는 복소페이딩 계수로 이뤄진 다중안테나 채널행렬을 나타낸다. 또한, H_kk는 송신기 k에서 수신기 k로 가는 다중안테나 채널행렬을, x_k는 송신기 k의 송신신호를, v_k는 송신기 k의 프리코딩 행렬을 나타낸다.

는 공분산행렬이

가 되는 수신기 k에서의 0평균 독립항등분포를 갖는 복소가우시안 잡음벡터를 나타낸다. 송신하는 심볼 x_l는 독립항등분포를 가지고 채널 H_kl는 full rank이며 상호독립임을 가정한다. 이러한 신호 모델은 모든 K개의 송신기 동기화되고 주파수 오프셋은 없는 것으로 가정한다. 그러면, 수신기 k에서 디코딩을 통해 수신되는 신호는 수학식 2와 같다.here,

Represents the precoding vector of the transmitter k having the number N of antennas and the degree of freedom d as the number of rows and columns. This precoding vector

The column of d is linearly independent and P _k is the transmit power of transmitter k. And,

Denotes a multi-antenna channel matrix formed of a complex fading coefficient having an independent-likelihood distribution from the Nth N-th transmitter to the kth receiver. H _kk denotes a multi-antenna channel matrix from a transmitter k to a receiver k, x _k denotes a transmission signal of the transmitter k, and v _k denotes a precoding matrix of the transmitter k.

Is the covariance matrix

And a zero-mean independent term distribution at receiver k, which is a complex Gaussian noise vector. It is assumed that the transmitted symbol x _l has independent distribution and the channel H _kl is full rank and mutually independent. This signal model assumes that all K transmitters are synchronized and that there is no frequency offset. Then, the signal received through decoding at the receiver k is expressed by Equation (2).

&Quot; (2) "

는 디코딩을 통해 추정한 k의 송신신호,

는 N행 d열의 선형독립열을 갖는 디코딩 행렬이고 직교성을 갖도록

의 유니터리 행렬로 설계될 수 있다.here,

A transmission signal of k estimated through decoding,

Is a decoding matrix with linearly independent columns of N rows and d columns and is orthogonally

Lt; / RTI >

Considering these precoding, decoding, and signal models, the instantaneous capacity sum of the system is given by Equation (3).

&Quot; (3) "

는 수신기 k에서 수신된 신호의 공분산행렬을 나타내고,

는 수신기 k에서의 간섭 더하기 잡음의 공분산 행렬을 나타낸다. here,

Denotes the covariance matrix of the received signal at receiver k,

Represents the covariance matrix of interference plus noise at receiver k.

2 is a diagram illustrating an implementation of a capacity sum maximization algorithm 200 considering transmission power according to an embodiment of the present invention.

In the present invention, the capacity sum maximization algorithm 200 configures the capacity sum as Equation (4) so as to operate in the power minimization mode by reducing the transmitter power when the transmitter power is insufficient.

&Quot; (4) "

와

는 수학식 5와 수학식 6으로 구성된다.here,

Wow

Is composed of Equations (5) and (6).

&Quot; (5) "

&Quot; (6) "

는 상수 파라미터이고 적절한 성능을 위해 실험적으로 구성하였다.here,

Is a constant parameter and is experimentally constructed for proper performance.

에 대해 미분한 용량합의 미분

은 수학식 7과 같이 표현될 수 있다.The capacity sum of Equation (4)

Lt; RTI ID = 0.0 >

Can be expressed by Equation (7).

&Quot; (7) "

에 대한 용량합의 미분은 이와 유사하게 얻어질 수 있다. 용량합의 미분을 한 뒤 간섭정렬의 해를 빠르게 찾을 수 있도록 그라스만(Grassmann) 다양체(manifold)에 대한 탄젠트 벡터를 사용하며 이러한 탄젠트 벡터는 수학식 8로 표현될 수 있다.

Can be obtained in a similar manner. The tangent vector for the Grassmann manifold is used to quickly find the solution of the interference alignment after differentiating the capacity sum, and such a tangent vector can be expressed by equation (8).

&Quot; (8) "

은 수학식 7로 나타낸 용량합의 미분을 나타내고,

은 탄젠트벡터를 나타낸다. 그리고, V_k는 송신기 k의 프리코딩벡터,

는 V_k의 허미션을 나타낸다.The solution to the minimization of the cross interference using this tangent vector can be found by the shortest geodesic solution for the Grassman manifold expressed in Equation (9). here,

Represents the differential of the capacity sum expressed by the equation (7)

Represents a tangent vector. V _k is a precoding vector of the transmitter k,

Represents the hermetian of V _k .

&Quot; (9) "

는

의 compact 특이값 분해(SVD: singular value decomposition)을 나타낸다. 그리고,

는 수학식 9에 의해

로 갱신되며, t는 알고리즘 갱신을 위한 증분량(step size)을 나타낸다.here

The

(Singular value decomposition) of SVD. And,

Is expressed by Equation (9)

, And t represents the step size for updating the algorithm.

The capacity sum maximization algorithm considering the transmission power is shown in FIG. 2, and a series of iterative processes for interference alignment are shown in Table 1. [

로 알고리즘 시작
2. 간섭정렬을 위한 반복 과정의 시작
3. l번째 송신기의 프리코딩 행렬 V_l에 대해 누설간섭을 최소화 하는 k번째 수신기의 디코딩 행렬

을 구성

여기서,

는 d개의 최소고유값을 나타낸다.
4. 수학식 7과 같이 k번째 수신기의 디코딩 행렬

에 대한 용량합의 미분을 계산
5. k번째 수신기의 디코딩 행렬

를 그라스만 다양체에 대한 탄젠트 벡터의 compact SVD를 사용하여

로 갱신
(k번째 수신기에 대한 간섭정렬의 해를 구함)
6. l번째 수신기의 디코딩 행렬

에 대해 누설간섭을 최소화 하는 k번째 송신기의 프리코딩 행렬

를 구성

7. 수학식 7을 사용하여 k번째 송신기의 프리코딩 행렬

에 대한 용량합의 미분을 계산
8. 수학식 9를 사용하여 k번째 송신기의 프리코딩 행렬

를 그라스만 다양체에 대한 탄젠트 벡터의 compact SVD를 사용하여 갱신
(k번째 송신기에 대한 간섭정렬의 해를 구함)
9. k번째 수신기와 송신기 간의 간섭정렬의 해가 수렴할 때까지 상기한 3. 과정 내지 8. 과정을 반복 수행함1. Initialization: The precoding matrix of any kth transmitter

Start the algorithm with
2. Start an iterative process for interference alignment
3. The decoding matrix of the kth receiver that minimizes the leakage interference for the precoding matrix V _l of the _lth transmitter

Constitute

here,

Represents the d minimum eigenvalues.
4. The decoding matrix of the k < th > receiver as shown in Equation (7)

Calculate the derivative of the capacity sum for
5. The decoding matrix of the kth receiver

Using the compact SVD of the tangent vector for the Grassman manifold

Update to
(Obtain the solution of the interference alignment for the kth receiver)
6. The decoding matrix of the lth receiver

Lt; RTI ID = 0.0 > k < / RTI > transmitter that minimizes leakage interference

Constitute

7. Using Equation (7), the precoding matrix < RTI ID = 0.0 >

Calculate the derivative of the capacity sum for
8. Using Equation (9), the precoding matrix < RTI ID = 0.0 >

Using the compact SVD of the tangent vector for Grassman manifold
(Obtain the solution of the interference alignment for the kth transmitter)
9. Repeat steps 3 to 8 until the solution of the interference alignment between the k-th receiver and the transmitter converges.

)을 사용하는 것을 가정하였다. 그리고, 사용된 상수

는 실험적인 값으로서 0.1을 사용하였다.3, 4, 5, and 6 illustrate the results of computer simulation of the present invention. In the system environment, the number of antennas N = 2 and the number of users K = 3 are assumed, and the power used in each transmitter is normalized power(

) Is assumed to be used. And, the constant used

0.1 was used as an experimental value.

FIG. 3 is a graph 300 showing the amount of normalized power used for the SNR according to an exemplary embodiment of the present invention. In the graph 300, a comparison is made between an existing capacity sum maximization algorithm 310 and a power optimization capacity sum maximization algorithm 320 FIG.

The conventional algorithm uses 95% power between 20dB and 50dB, but the algorithm according to the present invention uses only 50% power.

FIG. 4 is a graph 400 showing the amount of normalized power used for the number of iterations of an algorithm according to an embodiment of the present invention. In the SNR 5dB, an existing capacity sum maximization algorithm 410 and a power optimization capacity sum maximization algorithm 420 ). ≪ / RTI >

The method according to the present invention uses approximately 60% of the power, thereby confirming that the algorithm according to the present invention uses less power.

5 is a graph 500 showing the average capacity sum of the SNR according to an exemplary embodiment of the present invention, and is a graph comparing the existing capacity sum maximization algorithm 510 and the power optimization capacity sum maximization algorithm 520 to be.

It can be seen that instead of using less power, the method according to the present invention averages a capacity sum loss of 4.45 bps / Hz.

FIG. 6 is a graph 600 showing the power efficiency as an average capacity ratio per used power of the SNR according to an embodiment of the present invention. The conventional capacity sum maximization algorithm 610 and the power optimization capacity sum maximization algorithm 620 ). ≪ / RTI >

Up to 10dB, the power efficiency of the existing algorithm is rather good, but at 15dB or more, the performance of the method according to the present invention starts to improve. It can be seen that the method according to the present invention is improved by 34 power efficiency numerically by 50dB .

As described above, according to embodiments of the present invention, in order to perform interference alignment in a multi-user interference environment having multiple antennas, precoding is performed to satisfy a certain performance while minimizing power used when a transmitter lacks power. . To do this, we design a new scheme considering the power using the capacity sum, which is an objective function used in the capacity sum maximization algorithm, and configure precoding by using it to reduce power consumption and maximize power efficiency.

The apparatus described above may be implemented as a hardware component, a software component, and / or a combination of hardware components and software components. For example, the apparatus and components described in the embodiments may be implemented as a processor, a controller, an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable gate array (FPGA), a programmable logic unit, a microprocessor, or any other device capable of executing and responding to instructions. The processing device may execute an operating system (OS) and one or more software applications running on the operating system. The processing device may also access, store, manipulate, process, and generate data in response to execution of the software. For ease of understanding, the processing apparatus may be described as being used singly, but those skilled in the art will recognize that the processing apparatus may have a plurality of processing elements and / As shown in FIG. For example, the processing unit may comprise a plurality of processors or one processor and one controller. Other processing configurations are also possible, such as a parallel processor.

The software may include a computer program, code, instructions, or a combination of one or more of the foregoing, and may be configured to configure the processing device to operate as desired or to process it collectively or collectively Device can be commanded. The software and / or data may be in the form of any type of machine, component, physical device, virtual equipment, computer storage media, or device , Or may be permanently or temporarily embodied in a transmitted signal wave. The software may be distributed over a networked computer system and stored or executed in a distributed manner. The software and data may be stored on one or more computer readable recording media.

The method according to an embodiment may be implemented in the form of a program command that can be executed through various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, and the like, alone or in combination. The program instructions to be recorded on the medium may be those specially designed and configured for the embodiments or may be available to those skilled in the art of computer software. Examples of computer-readable media include magnetic media such as hard disks, floppy disks and magnetic tape; optical media such as CD-ROMs and DVDs; magnetic media such as floppy disks; Magneto-optical media, and hardware devices specifically configured to store and execute program instructions such as ROM, RAM, flash memory, and the like. Examples of program instructions include machine language code such as those produced by a compiler, as well as high-level language code that can be executed by a computer using an interpreter or the like. The hardware devices described above may be configured to operate as one or more software modules to perform the operations of the embodiments, and vice versa.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. For example, it is to be understood that the techniques described may be performed in a different order than the described methods, and / or that components of the described systems, structures, devices, circuits, Lt; / RTI > or equivalents, even if it is replaced or replaced.

Therefore, other implementations, other embodiments, and equivalents to the claims are also within the scope of the following claims.

Claims (6)

A method of interference alignment in a computer implemented multiuser multi antenna (MIMO) system,
Calculating a sum-rate for the used power in consideration of the power used by the transmitter for the interference alignment on the interference channel as an objective function, and calculating precoding of the transmitter through the objective function
Lt; / RTI >
Wherein the step
And reconstructing an objective function related to the sum of the capacities considering the power used by the transmitter to operate in a power minimization mode in the transmitter using the interference alignment,
constructing a decoding matrix U _k of the kth receiver that minimizes leakage interference for the precoding matrix V _l of the _lth transmitter;
A second step of calculating a differential of a capacity sum with respect to a decoding matrix U _k of the _kth receiver;
A third step of calculating a solution of the interference alignment for the kth receiver by applying a shortest geodesic solution to the differential of the capacity sum with respect to the decoding matrix Uk of the _kth receiver;
a fourth step of constructing a precoding matrix V _k of the k-th transmitter that minimizes leakage interference for the decoding matrix Ul of the _lth receiver;
A fifth step of calculating a differential of a capacity sum with respect to a precoding matrix V _k of the k-th transmitter; And
A sixth step of calculating a solution of the interference alignment for the k-th transmitter by applying a short-term guide solution to the differential of the capacity sum with respect to the precoding matrix V _k of the k-th transmitter,
Lt; / RTI >
In the third step,
The decoding matrix U _k of the k-th receiver is updated using singular value decomposition (SVD) of a tangent vector for Grassmann manifold,
In the sixth step,
The precoding matrix V _k of the k-th transmitter is updated using the SVD of the tangent vector for the grub only manifold,
Wherein the step
Repeating the first through sixth steps until the solution of the interference alignment for the kth receiver and the solution of the interference alignment for the kth transmitter converge
≪ / RTI > The method according to claim 1,
Wherein the step
The calculation of the capacity sum (R _sum ) through Equation (1)
≪ / RTI >
Equation (1)

(Where I _d denotes the interference signal, S _k denotes the covariance matrix of the signal received at the kth receiver, and Q _k denotes the covariance matrix of interference plus noise in the kth receiver). delete delete The method according to claim 1,
The precoding matrix V _l of the ₁ < th > transmitter and the precoding matrix V _k of the k < th > transmitter are expressed by a precoding vector according to the transmission power of the number of antennas and the number of degrees of freedom
≪ / RTI > delete

Images