• ETRI Journal
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• 제41권5호
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• pp.619-625
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• 2019

In this paper, we propose an array pattern synthesis scheme using semidefinite programming (SDP) under array excitation power constraints. When an array pattern synthesis problem is formulated as an SDP problem, it is known that an additional rank-one constraint is generated inevitably and relaxed via semidefinite relaxation. If the solution to the relaxed SDP problem is not of rank one, then conventional SDP-based array pattern synthesis approaches fail to obtain optimal solutions because the additional rank-one constraint is not handled appropriately. To overcome this drawback, we adopted a bisection technique combined with a penalty function method. Numerical applications are presented to demonstrate the validity of the proposed scheme.

• 한국통신학회논문지
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• 제33권11C호
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• pp.932-939
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• 2008

공간 다중화 방식의 MIMO(Multiple-Input Multiple-Output) 시스템에서 MLD(Maximum-Likelihood Detector)는 최적의 성능을 보이지만, 그 복잡성이 상당히 큰 단점이 있다. 이를 보완하기 위해 여러 가지 기법들이 제안되었으며, Lattice-reduction(LR) 검출기 또한 MIMO 시스템의 성능을 개선하기 위해 제안되었다. 본 논문에서는 확장된 잡음분산 행렬을 이용해 rounding operation 과정에서 발생하는 양자화 오류를 이용해 송신 신호 벡터에 근접한 candidate symbol set을 찾고, 여기서 Semidefinite Relaxation을 이용해 최대 우도 symbol을 검출한다. 그러나 그 복잡도는 MLD의 복잡도 보다 현저히 작고, LR 검출기의 복잡도에 근접한다.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2005년도 한국컴퓨터종합학술대회 논문집 Vol.32 No.1 (A)
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• pp.892-894
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• 2005

Graph partitioning provides an important tool for data clustering, but is an NP-hard combinatorial optimization problem. Spectral clustering where the clustering is performed by the eigen-decomposition of an affinity matrix [1,2]. This is a popular way of solving the graph partitioning problem. On the other hand, semidefinite relaxation, is an alternative way of relaxing combinatorial optimization. issuing to a convex optimization[4]. In this paper we present a semidefinite programming (SDP) approach to graph equi-partitioning for clustering and then we use eigen-decomposition to obtain an optimal partition set. Therefore, the method is referred to as semidefinite spectral clustering (SSC). Numerical experiments with several artificial and real data sets, demonstrate the useful behavior of our SSC. compared to existing spectral clustering methods.

• 대한수학회보
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• 제42권4호
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• pp.837-849
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• 2005

In this paper, we obtain a successive quadratic programming algorithm for solving the semidefinite programming (SDP) relaxation of the binary quadratic programming. Combining with a randomized method of Goemans and Williamson, it provides an efficient approximation for the binary quadratic programming. Furthermore, its convergence result is given. At last, We report some numerical examples to compare our method with the interior-point method on Maxcut problem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.137-147
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• 2001

Nonconvex Quadratic Optimization Problems (QOP) are solved approximately by SDP (semidefinite programming) relaxation and SOCP (second order cone programmming) relaxation. Nonconvex QOPs with special structures can be solved exactly by SDP and SOCP. We propose a method to formulate general nonconvex QOPs into the special form of the QOP, which can provide a way to find more accurate solutions. Numerical results are shown to illustrate advantages of the proposed method.

• ETRI Journal
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• 제38권5호
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• pp.934-940
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• 2016

In this paper, secure multicasting with the help of cooperative decode-and-forward relays is considered for the case in which a source securely sends a common message to multiple destinations in the presence of a single eavesdropper. We show that the secrecy rate maximization problem in the secure multicasting scenario under an overall power constraint can be solved using semidefinite programing with semidefinite relaxation and a bisection technique. Further, a suboptimal approach using zero-forcing beamforming and linear programming based power allocation is also proposed. Numerical results illustrate the secrecy rates achieved by the proposed schemes under secure multicasting scenarios.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2004년도 가을 학술발표논문집 Vol.31 No.2 (1)
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• pp.697-699
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• 2004

Despite many successful spectral clustering algorithm (based on the spectral decomposition of Laplacian(1) or stochastic matrix(2) ) there are several unsolved problems. Most spectral clustering Problems are based on the normalized of algorithm(3) . are close to the classical graph paritioning problem which is NP-hard problem. To get good solution in polynomial time. it needs to establish its convex form by using relaxation. In this paper, we apply a novel optimization technique. semidefinite programming(SDP). to the unsupervised clustering Problem. and present a new multiple Partitioning method. Experimental results confirm that the Proposed method improves the clustering performance. especially in the Problem of being mixed with non-compact clusters compared to the previous multiple spectral clustering methods.

• Journal of Communications and Networks
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• 제16권1호
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• pp.45-55
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• 2014

The paper investigates the problem of designing the multiple-antenna relay in a two-way relay network by taking into account the imperfect channel state information (CSI). The objective is to design the multiple-antenna relay based upon the CSI estimates, where the estimation errors are included to attain the robust design under the worst-case philosophy. In particular, the worst-case transmit power at the multiple-antenna relay is minimized while guaranteeing the worst-case quality of service requirements that the received signal-to-noise ratio (SNR) at both sources are above a prescribed threshold value. Since the worst-case received SNR expression is too complex for subsequent derivation and processing, its lower bound is explored instead by minimizing the numerator and maximizing the denominator of the worst-case SNR. The aforementioned problem is mathematically formulated and shown to be nonconvex. This motivates the pursuit of semidefinite relaxation coupled with a randomization technique to obtain computationally efficient high-quality approximate solutions. This paper has shown that the original optimization problem can be reformulated and then relaxed to a convex problem that can be solved by utilizing suitable randomization loop. Numerical results compare the proposed multiple-antenna relay with the existing nonrobust method, and therefore validate its robustness against the channel uncertainty. Finally, the feasibility of the proposed design and the associated influencing factors are discussed by means of extensive Monte Carlo simulations.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권6호
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• pp.2204-2224
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• 2021

This paper studies secure wireless transmission from a multi-antenna transmitter to a single-antenna intended receiver overheard by multiple eavesdroppers with considering the imperfect channel state information (CSI) of wiretap channel. To enhance security of communication link, the artificial noise (AN) is generated at transmitter. We first design the robust joint optimal beamforming of secret signal and AN to minimize transmit power with constraints of security quality of service (QoS), i.e., minimum allowable signal-to-interference-and-noise ratio (SINR) at receiver and maximum tolerable SINR at eavesdroppers. The formulated design problem is shown to be nonconvex and we transfer it into linear matrix inequalities (LMIs). The semidefinite relaxation (SDR) technique is used and the approximated method is proved to solve the original problem exactly. To verify the robustness and tightness of proposed beamforming, we also provide a method to calculate the worst-case SINR at eavesdroppers for a designed transmit scheme using semidefinite programming (SDP). Additionally, the secrecy rate maximization is explored for fixed total transmit power. To tackle the nonconvexity of original formulation, we develop an iterative approach employing sequential parametric convex approximation (SPCA). The simulation results illustrate that the proposed robust transmit schemes can effectively improve the transmit performance.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제10권1호
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• pp.187-199
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• 2016

In this paper, we consider secure communications in multi-hop relaying systems, where multiple decode-and-forward (DF) relays are located at each individual hop and perform cooperative beamforming to improve physical layer security. In order to determine the cooperative relay beamformer at each hop, we propose an iterative beamformer update scheme using semidefinite relaxation and bisection techniques. Numerical results are presented to verify the secrecy rate performance of the proposed scheme.