KR101903293B1 - Method and apparatus of mimo detection - Google Patents

Abstract

Disclosed are a method and an apparatus for multiple-input multiple-output (MIMO) detection. According to an embodiment of the present invention, a method for MIMO detection comprises the steps of: acquiring a reception signal and a channel for MIMO detection; changing a MIMO detection problem into an alternating direction method of multipliers (ADMM) type using two variables by using the acquired reception signal and the channel, separating an objective function into a transmission signal and a variable, and updating the transmission signal to minimize the transmission signal by using an algorithm; updating the variable to minimize the variable by using an algorithm as the transmission signal is updated; updating a dual variable as the transmission signal and the variable are updated; and finally estimating a transmission signal by repeatedly minimizing the transmission signal until a predetermined stop condition is satisfied.

Description

METHOD AND APPARATUS OF MIMO DETECTION

The following embodiments relate to a method and apparatus for MIMO detection, and more particularly, to an ADMM-based MIMO detection method and apparatus having good performance with low complexity.

The demand for high data rates in wireless communication systems continues to grow. Accordingly, there is a growing interest in multiple-input multiple-output (MIMO) systems that can increase channel capacity without additional frequency bands or transmit power. MIMO systems are being applied to mobile communication systems such as IEEE 802.11n, LTE, and WiMAX. In addition to single-user and multi-user MIMO, a large capacity MIMO system using tens or hundreds of antennas has recently been proposed (Non-Patent Document 1).

Unlike the Single-Input Single-Output (SISO) system, the MIMO system transmits several symbols at the same time, so the receiving side receives symbols affected by random noise or interference. 2). Therefore, when designing a MIMO system, the receiving side needs a technique for detecting a distorted symbol, and various detection techniques have been studied.

The maximum likelihood (ML) detection method is well known for providing optimal bit error ratio (BER) performance. The ML detection method searches all the vectors that can be composed of constellation sets, maximizing the probability of the received signal vector for a given channel. The ML detection problem is NP-hard (Non-deterministic Polynomial-time hard) because it confirms the number of all cases (Non-Patent Document 3). The ML detection method has an exponential complexity depending on the number of transmit antennas and the magnitude of the modulation constellation. Therefore, other detection methods have been proposed that reduce the high cost of this complexity and slightly degrade the performance.

Zero forcing (ZF) detection method separates multiple streams from the received signal using the inverse of the MIMO channel matrix when the receiver knows the channel matrix. The ZF detection method has the advantage that the interference can be canceled while the computational complexity is very low. However, BER performance is very poor compared to ML detection method because it increases noise (Non-Patent Document 2).

Sphere Decoding (SD) detection method has been proposed to reduce the computational complexity of the ML detection method. Unlike the ML detection method of confirming the number of all cases, only the lattice points in the hypersphere having a radius of R from the received signal are searched (Non-Patent Document 4). The SD detection method has a polynomial complexity and often has an exponential complexity in the worst case (Non-Patent Document 5).

Semidefinite Relaxation (SDR) detection method is to use the ML approach based on the semidefinite program (Non-Patent Document 6). Most SDR detection methods use the Interior Point Method (IPM) and at worst have polynomial complexity. Most SDR detection methods only work with specific modulation constellations. SDR-RBR made by applying row-by-row technique to SDR is based on low complexity technique in every iteration and the execution time is considerably fast (Non-Patent Document 7).

Korean Patent No. 10-0790366 relates to a detection apparatus and a method thereof in a MIO system, and a reception signal of a receiving end while maintaining desired system performance in a communication system that simultaneously transmits and receives several symbols by using a multiple antenna (MIMO). It describes a technique that can reduce the amount of computation required to decode.

Korean Patent Registration No. 10-0790366

S., Computational complexity of multiuser detection. Algorithmica, vol. 4, no. 1-4, pp. 303-312, 1989. M. O. Damen, H. El Gamal, and G. Caire, "On maximum-likelihood detection and the search for the closest lattice point," IEEE Transactions on Information Theory, vol. 49, no. 10, pp. 2389-2402, Oct. 2003. B. Hassibi and H. Vikalo, "On the sphere-decoding algorithm I. expected complexity," IEEE Trans. Signal Process., vol. 53, no. 8, pp. 2806-2818, Aug. 2005. P. H. Tan and L. K. Rasmussen, "The application of semidefinite programming for detection in CDMA," IEEE J. Sel. Areas Commun., vol. 19, no. 8, pp. 1442-1449, Aug. 2001. H.-T. Wai, W.-K. Ma, and A.M.-C. So, "Cheap semidefinite relaxation MIMO detection using row-by-row block coordinate descent," in Proc. 2011 IEEE ICASSP, pp.3256-3259, May 2011. P. W. Wolniansky, G. J. Foschini, G. D. Golden, and R. A. Valenzuela, "V-BLAST: An architecture for realizing very high data rates over the rich-scattering wireless channel," in Proc. URSI ISSSE, Pisa, Italy, pp. 295-300, Sep. 1998. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, "Distributed optimization and statistical learning via the alternating direction method of multipliers," Foundations and Trends in Machine Learning, vol. 3, no. 1, pp. 1-122, 2010. J. Hoydis, ST Brink, and M. Debbah, "Massive MIMO: how many antennas do we need ?," in Proc. Allerton Conf. Commun. Control Comput., Pp. 545-550, Monticello, USA, Sep. 2011. S. Yang and L. Hanzo, "Fifty years of MIMO detection: The road to large-scale MIMOs," IEEE Commun. Surveys Tuts., Vol. 17, no. 4, pp. 1941-1988, 4th Quart. 2015.

S., Computational complexity of multiuser detection. Algorithmica, vol. 4, no. 1-4, pp. 303-312, 1989. MO Damen, H. El Gamal, and G. Caire, "On maximum-likelihood detection and the search for the closest lattice point," IEEE Transactions on Information Theory, vol. 49, no. 10, pp. 2389-2402, Oct. 2003. B. Hassibi and H. Vikalo, "On the sphere-decoding algorithm I. expected complexity," IEEE Trans. Signal Process., Vol. 53, no. 8, pp. 2806-2818, Aug. 2005. PH Tan and LK Rasmussen, "The application of semidefinite programming for detection in CDMA," IEEE J. Sel. Areas Commun., Vol. 19, no. 8, pp. 1442-1449, Aug. 2001. H.-T. Wai, W.-K. Ma, and AM-C. So, "Cheap semidefinite relaxation MIMO detection using row-by-row block coordinate descent," in Proc. 2011 IEEE ICASSP, pp.3256-3259, May 2011. PW Wolniansky, GJ Foschini, GD Golden, and RA Valenzuela, "V-BLAST: An architecture for realizing very high data rates over the rich-scattering wireless channel," in Proc. URSI ISSSE, Pisa, Italy, pp. 295-300, Sep. 1998. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, "Distributed optimization and statistical learning via the alternating direction method of multipliers," Foundations and Trends in Machine Learning, vol. 3, no. 1, pp. 1-122, 2010.

Embodiments describe a method and apparatus for MIMO detection, and more specifically, provide an ADMM-based MIMO detection technique with good performance with low complexity.

Embodiments transform the MIMO detection problem into an ADMM format using two variables using an instruction function, create an augmented Lagrange of this problem, combine linear and quadratic terms, and transform it into a useful format using scale dual variables. The present invention provides a method and apparatus for MIMO detection that exhibits good performance with low complexity by repeating until convergence minimization of variables is converged.

According to an embodiment, a method for detecting a MIMO may include: obtaining a received signal and a channel for detecting a multiple-input multiple-output (MIMO); Using the received signal and the channel, the MIMO detection problem is changed into an alternate direction method of multipliers (ADMM) using two variables, an objective function is divided into a transmission signal and a variable, and then the algorithm is transmitted using an algorithm. Updating to minimize the; Updating to minimize the variable using an algorithm as the transmission signal is updated; Updating a dual variable as the transmission signal and the variable are updated; And repeatedly minimizing until the predetermined stop condition is satisfied to finally estimate the transmission signal.

When the number of antennas increases, the computational complexity increases, but as the algorithm converges a smaller number of times, it has a lower complexity. On the receiving side, the transmission signal can be restored using the matrix of the received signal and the channel.

Updating the dual variable as the transmission signal and the variable are updated, forming an augmented Lagrange of the MIMO detection problem and combining linear and quadratic terms, using the scale dual variable to convert the ADMM format into a useful format. And alternating, repeating alternately until the convergence of the two variables, the transmission signal and the minimization, is converged.

The updating of the transmission signal to minimize may include: fixing the variable and the scale dual variable, minimizing augmented lagranging with respect to the transmission signal, and updating to minimize the variable, updating the transmission signal and the scale. Fixing the dual variable, minimizing the projection function for the variable, and updating the dual variable as the transmission signal and the variable are updated, a penalty that is positive for the dual variable corresponding to the case where the transmission signal and the variable are the same. A scale dual variable multiplied by the inverse of the parameter is updated, and the convergence of the solution of the ADMM format can be strongly dependent on the value of the penalty parameter.

According to another embodiment, an apparatus for detecting a MIMO may include: an acquirer configured to acquire a received signal and a channel for detecting a multiple-input multiple-output (MIMO); Using the received signal and the channel, the MIMO detection problem is changed into an alternate direction method of multipliers (ADMM) using two variables, an objective function is divided into a transmission signal and a variable, and then the algorithm is transmitted using an algorithm. A minimizing unit for updating to minimize the variable, and updating the minimizing variable by using an algorithm as the transmission signal is updated; A dual variable unit for updating a dual variable as the transmission signal and the variable are updated; And a determination unit configured to repeatedly minimize the predetermined stop condition to finally estimate the transmission signal.

The dual variable unit forms an augmented Lagrange of the MIMO detection problem and combines linear and quadratic terms to transform the ADMM format into a useful format using scale dual variables, the two variables being the transmission signal and the variable. You can alternately repeat for minimizing until.

The minimizing unit fixes the variable and the scale dual variable and minimizes the enhancement Lagrange for the transmission signal, fixes the transmission signal and the scale dual variable and minimizes the projective function for the variable. Update a scale binary variable multiplied by an inverse of a positive penalty parameter corresponding to a dual variable corresponding to the case where the transmission signal is equal to the variable, and the convergence of the solution of the ADMM type is strongly dependent on the value of the penalty parameter; Can be.

According to embodiments, the MIMO detection problem is transformed into an ADMM format using two variables using an instruction function, creating an augmented Lagrange of this problem, combining linear and quadratic terms, and transforming it into a useful format using scale dual variables. By repeating until convergence minimization of two variables is converged, it is possible to provide a method and apparatus for MIMO detection with good performance with low complexity.

According to the embodiments, the computational complexity increases as the number of antennas increases.However, a method for detecting MIMO that has good performance with low complexity because the execution time does not increase even though the number of antennas increases due to convergence of algorithms in a smaller number of times. And an apparatus.

1 is a flowchart illustrating an ADMM-based MIMO detection algorithm according to an embodiment.
2 is a graph illustrating BER according to SNR in a 10x10 MIMO system having 10 transmission / reception antennas according to an embodiment.
3 is a graph illustrating BER according to SNR in a 40x40 system having 40 transmit / receive antennas according to an embodiment.
4 is a graph illustrating BER according to SNR in a 70x70 system having 70 transmit / receive antennas according to an embodiment.
5 is a graph illustrating BER according to the number of transmit / receive antennas when SNR = 10dB according to an embodiment.
6 is a graph illustrating execution time according to the number of transmit / receive antennas when SNR = 10dB according to an embodiment.
7 is a graph illustrating execution time according to the number of transmit / receive antennas when SNR = 20dB according to an embodiment.
8 is a graph illustrating NMSE according to the number of iterations of an ADMM algorithm when the number of transmit / receive antennas is 80 according to an embodiment.

Hereinafter, exemplary embodiments will be described with reference to the accompanying drawings. However, the described embodiments may be modified in many different forms, and the scope of the present invention is not limited to the embodiments described below. In addition, various embodiments are provided to more fully describe the present invention to those skilled in the art. Shape and size of the elements in the drawings may be exaggerated for more clear description.

Multiple-Input Multiple-Output (MIMO) systems can increase channel capacity without using additional frequency bands or transmit power. Since the transmitting side transmits a plurality of symbols at the same time and the effects of random noise and interference are large, the receiving side requires MIMO detection technique. As described above, MIMO detection methods include ML, ZF, SD, and SDR-RBR. Among them, the ML detection method provides the best performance, but the computational complexity increases exponentially as the number of transmit antennas increases, making it difficult to use in a large-capacity MIMO system.

In the following embodiment, it is possible to provide an MIMM detection method based on alternating direction method of multipliers (ADMM) which has good performance with low complexity. Simulation results show that when the signal to noise ratio (SNR) is 10dB, the number of transmit / receive antennas is better than the SDR-RBR detection method in BER and execution time from 50 antennas, and the larger the number of antennas, the better the performance gap. You can see more happening.

1 is a flowchart illustrating an ADMM-based MIMO detection algorithm according to an embodiment.

FIG. 1 shows an algorithm which repeatedly operates until a stop condition is satisfied to finally estimate the transmission signal s. Referring to FIG. 1, in the method for detecting a MIMO according to an embodiment, obtaining a received signal and a channel for detecting a multiple-input multiple-output (MIMO) operation 110, using the obtained received signal and the channel Converting the MIMO detection problem into an alternating direction method of multipliers (ADMM) using two variables, separating the objective function into a transmission signal and a variable, and then updating to minimize the transmission signal using an algorithm (120); Updating 130 to minimize the variable using an algorithm as the transmission signal is updated; updating 140 as the transmission signal and the variable are updated; and satisfying a preset stop condition. And repeatedly estimating the transmission signal to finally minimize the transmission signal.

Here, when the number of antennas increases, the computational complexity increases, but as the algorithm converges a smaller number of times, it has a lower complexity, and the receiving side can restore the transmission signal using the matrix of the received signal and the channel.

Meanwhile, the method for detecting MIMO according to an embodiment may be described in more detail by using an apparatus for detecting MIMO according to an embodiment as an example. An apparatus for detecting a MIMO according to an embodiment may include an acquisition unit, a minimizer, a dual variable unit, and a determination unit. Here, the apparatus for detecting MIMO according to an embodiment may be one system or a plurality of systems, and may also consist of one algorithm or a plurality of algorithms.

In operation 110, the acquirer may acquire a received signal and a channel for MIMO detection.

In step 120, the minimizing unit converts the MIMO detection problem into an ADMM format using two variables using the obtained received signal and channel, separates the objective function into a transmission signal and a variable, and then minimizes the transmission signal using an algorithm. To be updated. Here, the minimization unit may fix the variable and the scale dual variable and minimize the augmented Lagrange for the transmission signal, which will be described in more detail using Equation 11 below.

In operation 130, the minimizing unit may update to minimize the variable using an algorithm as the transmission signal is updated. Here, the transmission signal and the scale dual variable can be fixed and the projective function for the variable can be minimized, which will be described in more detail using Equation 12 below.

In operation 140, the dual variable unit may update the dual variable as the transmission signal and the variable are updated. More specifically, the dual variable portion forms an augmented Lagrange of the MIMO detection problem and combines linear and quadratic terms to transform the ADMM format into a useful format using scale dual variables, minimizing the two variables, the transmitted signal and the variable. Can be repeated alternately until convergence.

Here, the dual variable unit may update the scale dual variable multiplied by the inverse of the positive parameter to the dual variable corresponding to the case where the transmission signal and the variable are the same, which is described in more detail using Equation 13 below. Let's explain. At this time, the convergence of the solution of the ADMM format may be strongly dependent on the value of the penalty parameter.

In operation 150, the determiner may repeatedly minimize the transmission signal until the predetermined stop condition is satisfied to finally estimate the transmission signal.

According to the embodiments, the computational complexity increases as the number of antennas increases.However, a method for detecting MIMO that has good performance with low complexity because the execution time does not increase even though the number of antennas increases due to convergence of algorithms in a smaller number of times. And an apparatus.

Hereinafter, an ADMM-based MIMO detection algorithm according to an embodiment will be described in more detail.

The MIMO system model can be expressed as the following equation.

[Equation 1]

는 수신 신호 벡터,

는 MIMO 채널 행렬,

는 송신된 신호 벡터,

는 추가적인 가우시안 랜덤 잡음 벡터를 나타낸다. S는 성상도에서 표현되는 점들의 집합이다. 본 실시예에서는 QPSK(Quadrature Phase Shift Keying) 변조 방식을 다루며, 이 때의

이다. 그리고 C는 복소수 집합을 의미한다. MIMO 채널 행렬 H는 수신 측에서 알고 있으며 H의 원소들은 가우시안 분포를 이룬다.At this time, the transmitting antenna N _t Dog and Receive Antenna N _r If you use a dog,

Receive signal vector,

Mimo channel matrix,

Is the transmitted signal vector,

Denotes an additional Gaussian random noise vector. S is the set of points represented in the constellation. This embodiment deals with Quadrature Phase Shift Keying (QPSK) modulation.

to be. And C stands for complex set. The MIMO channel matrix H is known at the receiver and the elements of H form a Gaussian distribution.

A standard example of a linear memoryless channel is the V-BLAST (Vertical Bell Laboratories Layered Space-Time) system of flat fading channels (Non-Patent Document 8). Since the output in the current time interval and the input in the previous time interval are independent of each other, Equation 1 can be expressed as the following equation.

[Equation 2]

Where h _{j and i} are N _t I th transmit antenna and N _{r of 10} transmit antennas Corresponds to an impulse response between the j th receive antennas among the 10 receive antennas. On the receiving side, the detector may recover the transmitted signal vector s using the received signal vector y and the MIMO channel matrix H.

The MIMO detection problem of the system model of Equation 1 can be expressed as the following equation.

[Equation 3]

If the problem is expressed in ADMM format, it can be expressed as follows.

[Equation 4]

는 S의 지시(indicator) 함수이다. 즉,

을 만족하면

이고

을 만족하면

이다. 수학식 4는 제약 조건이 있는 컨벡스 최적화 방식으로 해결될 수 있다. 목적 함수는 s와 z로 분리할 수 있다. 수학식 4의 증강 라그랑주(Lagrange)는 다음 식과 같이 나타낼 수 있다. here,

Is the indicator function of S. In other words,

If you satisfy

ego

If you satisfy

to be. Equation 4 can be solved with a convex optimization method with constraints. The objective function can be separated into s and z. Augmented Lagrange of the equation (4) can be expressed by the following equation.

[Equation 5]

는 페널티(penalty) 파라미터이다. Where v is a dual variable corresponding to s = z,

Is a penalty parameter.

ADMM can alternately minimize s and z. In the k- th iteration can be carried out in the same step as the following formula (Non-Patent Document 9).

[Equation 6]

[Equation 7]

[Equation 8]

와 2차항

을 결합시키고, 스케일(scaled) 쌍대 변수를 사용하여 ADMM 형식을 더 유용하게 바꿀 수 있다(비특허문헌 9). q = s - z로 정의하면, 두 항을 결합하여 다음 식과 같이 나타낼 수 있다. Linear term in Equation 5 showing the augmented Lagrange

And secondary term

Can be combined and scaled dual variables can be used to change the ADMM format more usefully (Non-Patent Document 9). If q = s-z, two terms can be combined and expressed as follows.

[Equation 9]

는 스케일 쌍대 변수이다. here,

Is a scale dual variable.

Therefore, Equation 5 of augmented Lagrangian can be expressed in a combined form as follows.

[Equation 10]

Here, Equations 6, 7, and 8, which are the steps in the k- th iteration, may be expressed as in the following equations.

[Equation 11]

[Equation 12]

[Equation 13]

는 S에서 가장 가까운 성상도 점으로의 사영(projection)하는 것을 의미한다.

이기 때문에

는 가역 행렬이 될 수 있다. 첫째로, z와 u를 고정시키고 s에 대해서 증강 라그랑주를 최소화할 수 있다(수학식 11). 둘째로, s와 u를 고정시키고 z에 대한 사영 함수를 최소화할 수 있다(수학식 12). 마지막으로, 쌍대 변수 u를 갱신할 수 있다(수학식 13).here,

Means projection to the nearest constellation point in S.

Because

Can be an invertible matrix. First, we can fix z and u and minimize the enhancement Lagrange for s (Equation 11). Second, we can fix s and u and minimize the projection function for z (Equation 12). Finally, the dual variable u can be updated (Equation 13).

의 값에 강하게 종속될 수 있다(비특허문헌 9). 적합한

의 값을 선택하면, ADMM 검파 방법은 몇 십 번 정도의 반복만으로 매우 정확한 해에 수렴할 수 있다. 하지만,

의 값을 부적합하게 선택하면, 수렴을 위해 큰 횟수의 반복을 필요로 할 수 있다.The convergence of the solution of ADMM is a penalty parameter

It may be strongly dependent on the value of (Non Patent Literature 9). suitable

If you choose, the ADMM detection method can converge to a very accurate solution with only a few dozen iterations. However,

Inappropriate selection of may require a large number of iterations to converge.

The k- th primitive residual and the dual residual can be expressed as follows.

[Equation 14]

The iterative procedure can be completed by stopping criterion using raw residuals and dual residuals.

[Equation 15]

와

는 실행 가능성 허용치(feasibility tolerance)이며, 다음 식과 같이 정의될 수 있다. here,

Wow

Is the feasibility tolerance, and can be defined as

[Equation 16]

와

는 각각 절대(absolute) 허용치와 상대(relative) 허용치이다(비특허문헌 9). 이와 같이, 정지 조건을 만족할 때까지 반복적으로 동작하여 최종적으로 송신 신호 s를 추정할 수 있다.
here,

Wow

Are absolute tolerance and relative tolerance, respectively (Non-Patent Document 9). In this way, it is possible to repeatedly operate until the stop condition is satisfied to finally estimate the transmission signal s.

In the following, BER performance and complexity performance of the conventional detection methods ZF, SD, and SDR-RBR described above in the MIMO system and the ADMM detection method according to an embodiment are compared. Herein, a method for detecting an ADMM-based MIMO according to an embodiment described above will be simply referred to as an 'ADMM detection method'.

In this case, QPSK modulation is used and the number of transmit antennas and the number of receive antennas are the same. It is assumed that the receiving side knows a MIMO channel matrix having a complex Gaussian distribution of independent identity distributions (i.i.d.) with a mean of 0 and unit variance. The simulation runs MATLAB R2016a on a computer with an i7-6700 quad-core 3.40GHz CPU and 8GB of RAM.

2 is a graph illustrating BER performance according to SNR when the number of transmit / receive antennas is 10 according to an embodiment.

As shown in FIG. 2, as a result of verifying BER according to SNR in a 10x10 MIMO system having 10 transmit / receive antennas according to an embodiment, the best BER performance is SD detection method, and then SDR-RBR. The lowest BER was in the order of ADMM, and the ZF detection method showed higher BER than the other three methods.

3 is a graph illustrating BER according to SNR in a 40x40 system having 40 transmit / receive antennas according to an embodiment.

As shown in FIG. 3, the BER performance according to SNR when the number of transmit / receive antennas is 40 each can be checked. In this case, the SD detection method does not operate when the number of antennas is high. Therefore excluded from the experiment.

BER performance is good in order of SDR-RBR, ADMM, ZF. However, when the SNR is 12dB, the ADMM detection method has lower BER than the SDR-RBR detection method.

4 is a graph illustrating BER according to SNR in a 70x70 system having 70 transmit / receive antennas according to an embodiment.

As shown in FIG. 4, the BER performance according to SNR when the number of transmit / receive antennas is 70 each can be checked. The BER performance of SNR from 0dB to 6dB is the same as before, SDR-RBR, ADMM, You can see the good thing with the ZF order.

When the number of antennas is 40, the performance order is reversed when the SNR is 12dB, but when the number of 70 antennas is 9dB, the ADMM detection method has lower BER than the SDR-RBR detection method.

5 is a graph illustrating BER according to the number of transmit / receive antennas when SNR = 10dB according to an embodiment.

As shown in FIG. 5, when the SNR is 10 dB, BER performance according to the number of transmit / receive antennas may be checked. When the number of antennas is 40 or less, BER performance is good in the order of SDR-RBR, ADMM, and ZF. When the number of antennas is 50 or more, the BER performance is changed in the order of ADMM, SDR-RBR, and ZF.

In the ZF detection method, the BER increases as the number of antennas increases. In addition, the SDR-RBR detection method reduces the BER up to 40 but increases the BER if more. In the ADMM detection method according to an embodiment, as the number of antennas increases, the BER continues to decrease.

6 is a graph illustrating execution time according to the number of transmit / receive antennas when SNR = 10dB according to an embodiment.

As shown in FIG. 6, when the SNR is 10 dB, execution time according to the number of transmit / receive antennas may be checked. While the ZF detection method has poor BER performance, the execution time is short, indicating that the complexity is very low. In the ZF detection method and the SDR-RBR detection method, the execution time increases as the number of antennas increases.

On the other hand, in the ADMM detection method according to an embodiment, as the number of antennas increases, the execution time increases very finely. When SNR is 10 dB in FIG. 5, when the number of antennas is 50 or more, the ADMM detection method has higher BER performance than the SDR-RBR detection method. In FIG. 6, when the execution time is also higher based on 50 antennas, the ADMM detection method is performed. It can be seen that the method takes less than the SDR-RBR detection method.

Therefore, when the SNR is 10dB, the ADMM detection method is superior in both BER and complexity performance compared to the SDR-RBR detection method from the number of antennas of 50, and the gap continues as the number of antennas increases.

7 is a graph illustrating execution time according to the number of transmit / receive antennas when SNR = 20dB according to an embodiment.

As shown in FIG. 7, when the SNR is 20 dB, an execution time according to the number of transmit / receive antennas may be checked. Looking at the difference from FIG. 6 when the SNR is 10 dB, the execution time of the other detection method is almost the same, while the execution time of the SDR-RBR is increased by about 1.58 times when the SNR is 20 dB than the 10 dB. have.

In addition, in terms of execution time, the performance reversal of the ADMM detection method and the SDR-RBR detection method occurs from 50 antennas at 10 dB, whereas the performance reversal is performed from 40 antennas at 10 dB.

8 is a graph illustrating NMSE according to the number of iterations of an ADMM algorithm when the number of transmit / receive antennas is 80 according to an embodiment.

As shown in FIG. 8, the NMSE according to the number of repetitions of the ADMM algorithm when the number of transmit / receive antennas is 80 can be checked. If the SNR is 10dB, it can be confirmed that convergence is performed 10 times. If the SNR is 20dB, it can be seen that convergence is performed only with four iterations. In other words, the higher the SNR, the less the number of algorithm iterations required to converge.

As described above, even if the number of antennas is increased in FIG. 6 and FIG. 7, the execution time of the ADMM detection method is slightly increased. This is because, as the number of antennas increases, the computational complexity increases, but the algorithm converges with a smaller number of times.

As described above, according to embodiments, a MIMO detection method using ADMM may be provided. First, the MIMO detection problem can be transformed into an ADMM format using two variables using an indication function. We can create augmented Lagrange of the problem, combine linear and quadratic terms and transform them into useful formats using scale dual variables. The iteration can then be repeated until convergence minimization of the two variables is converged.

The simulation results show the BER performance and runtime performance of the conventional ZF, SD, and SDR-RBR detection methods and the ADMM detection method (ADMM detection method) in the MIMO system using QPSK modulation. Compared. When the SNR is 10dB, when the number of antennas is more than 50, it is confirmed that the ADMM detection method is ahead of the SDR-RBR detection method in BER performance and runtime performance. In addition, as the number of antennas increases, the performance difference between the two detection methods continues to increase.

This means that as the number of antennas increases, the number of repetitions required for convergence of the ADMM algorithm decreases, so that the execution time of the ADMM detection method increases only slightly even if the number of antennas increases.

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 devices and components described in the embodiments include, for example, processors, controllers, arithmetic logic units (ALUs), digital signal processors, microcomputers, field programmable arrays (FPAs), It may be implemented using one or more general purpose or special purpose computers, such as a programmable logic unit (PLU), 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 the execution of the software. For convenience of explanation, one processing device may be described as being used, but one of ordinary skill in the art will appreciate that the processing device includes a plurality of processing elements and / or a plurality of types of processing elements. It can be seen that it may include. For example, the processing device may include a plurality of processors or one processor and one controller. In addition, other processing configurations are possible, such as parallel processors.

The software may include a computer program, code, instructions, or a combination of one or more of the above, and configure the processing device to operate as desired, or process it independently or collectively. You can command the device. Software and / or data may be any type of machine, component, physical device, virtual equipment, computer storage medium or device in order to be interpreted by or to provide instructions or data to the processing device. It can be embodied in. The software may be distributed over networked computer systems so that they may be stored or executed in a distributed manner. Software and data may be stored on one or more computer readable recording media.

The method according to the embodiment may be embodied in the form of program instructions that can be executed by various computer means and recorded in a computer readable medium. The computer readable medium may include program instructions, data files, data structures, etc. alone or in combination. The program instructions recorded on the media may be those specially designed and constructed for the purposes of the embodiments, or they may be of the kind well-known and available to those having skill in the computer software arts. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tape, optical media such as CD-ROMs, DVDs, and magnetic disks, 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 not only machine code generated by a compiler, but also high-level language code that can be executed by a computer using an interpreter or the like.

Although the embodiments have been described by the limited embodiments and the drawings as described above, various modifications and variations are possible to those skilled in the art from the above description. For example, the described techniques may be performed in a different order than the described method, and / or components of the described systems, structures, devices, circuits, etc. may be combined or combined in a different form than the described method, or other components. Or even if replaced or substituted by equivalents, an appropriate result can be achieved.

Therefore, other implementations, other embodiments, and equivalents to the claims are within the scope of the claims that follow.

Claims (7)

Obtaining a received signal and a channel for multiple-input multiple-output (MIMO) detection;
Using the received signal and the channel, the MIMO detection problem is transformed into an alternating direction method of multipliers (ADMM) format using two variables, the objective function is separated into a transmission signal and a variable, and then the Updating a scale dual variable to minimize the transmitted signal as fixed and minimizing augmented Lagrange for the transmitted signal;
Fixing the transmission signal and the scale dual variable and minimizing the projection function for the variable to update the algorithm to minimize the variable as the transmission signal is updated;
Updating a dual variable as the transmission signal and the variable are updated; And
Estimating a transmission signal finally by repeatedly minimizing until a predetermined stop condition is satisfied
Including,
Updating the dual variable as the transmission signal and the variable is updated,
Update a scale binary variable multiplied by an inverse of a positive penalty parameter corresponding to a dual variable corresponding to the case where the transmission signal and the variable are equal, the convergence of the solution of the ADMM format is strongly dependent on the value of the penalty parameter,
When the number of antennas increases, the computational complexity increases but has a low complexity as the algorithm converges in a smaller number of times, and the receiving side restores the transmission signal using the matrix of the received signal and the channel.
Method for detecting MIMO, characterized in that. delete The method of claim 1,
Updating the dual variable as the transmission signal and the variable is updated,
Form an augmented Lagrange of the MIMO detection problem and combine linear and quadratic terms to transform the ADMM format into a useful format using scale duality variables, converging minimization for the two variables, the transmitted signal and the variable Repeating alternately until
Method for detecting MIMO, characterized in that. delete An acquisition unit for acquiring a received signal and a channel for multiple-input multiple-output (MIMO) detection;
Using the received signal and the channel, the MIMO detection problem is transformed into an alternating direction method of multipliers (ADMM) format using two variables, the objective function is separated into a transmission signal and a variable, and then the Update to minimize the transmission signal by fixing a scale dual variable and minimizing augmented Lagrange for the transmission signal, fixing the transmission signal and the scale dual variable and minimizing the projection function for the variable A minimizing unit for updating to minimize the variable using an algorithm as is updated;
A dual variable unit for updating a dual variable as the transmission signal and the variable are updated; And
Determination unit that is operated to repeatedly minimize until the predetermined stop condition is satisfied to finally estimate the transmission signal
Including,
The dual variable portion,
Update a scale binary variable multiplied by an inverse of a positive penalty parameter corresponding to a dual variable corresponding to the case where the transmission signal and the variable are equal, the convergence of the solution of the ADMM format is strongly dependent on the value of the penalty parameter,
When the number of antennas increases, the computational complexity increases but has a low complexity as the algorithm converges in a smaller number of times, and the receiving side restores the transmission signal using the matrix of the received signal and the channel.
Apparatus for detecting MIMO, characterized in that. The method of claim 5,
The dual variable portion,
Form an augmented Lagrange of the MIMO detection problem and combine linear and quadratic terms to transform the ADMM format into a useful format using scale duality variables, converging minimization for the two variables, the transmitted signal and the variable Repeating alternately until
Apparatus for detecting MIMO, characterized in that. delete

Images