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Robust MIMO Precoding for Cognitive Multiuser Relay Networks with Imperfect Channel State Information

Transactions of Tianjin University 2016年第6期22卷 590-595页

作者：俎云霄揭昕政 School of Electronic Engineering Beijing University of Posts and Telecommunications Beijing 100876 China

In this paper, a novel robust precoder with imperfect channel state information(CSI)is proposed for multi-input multi-output(MIMO)cognitive multiuser networks equipped with relays. In the proposed model, the secondary users(SUs)are allowed to share the spectrum with the primary users(PUs)when the interference temperature(IT)is below a specific threshold. The transmitting strategy of relays is amplify-and-forward(AF), and the CSI error is characterized in terms of spherical uncertainty region. A minmax problem for the transmit power of the relays is considered when the mean square error(MSE)of SUs and the IT of PU meet their corresponding thresholds, and it is transformed into a semi-definite programming(SDP)problem to search for the solution. Numerical simulations demonstrate the effectiveness of the proposed precoder.

关键词： cognitive radio multi-input multi-output imperfect channel state information semi-definite programming robust precoding

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Atomic-Norm for Joint Data Recovery and Narrow-Band Interference Mitigation in OFDM Systems 27

Atomic-Norm for Joint Data Recovery and Narrow-Band Interfer...

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27th IEEE Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC)

作者： Al-Tous, Hanan Barhumi, Imad Al-Dhahir, Naofal UAE Univ Coll Engn Al Ain U Arab Emirates Univ Texas Dallas Erik Jonsson Sch Engn & Comp Sci Richardson TX 75083 USA

ISBN: (纸本)9781509032549

In this paper, a novel approach is proposed to jointly recover the transmitted signal and mitigate narrow-band interference (NBI) in OFDM systems using a compressive sensing (CS) framework. NBI degrades the performance of OFDM systems which motivates the need for mitigation techniques to reduce its effect. The main idea behind our approach is to represent the transmitted data and the NBI signal as sparse atoms and then to solve a joint compressive sensing (JCS) problem. The recovery problem is formulated as a weighted optimization problem of two atomic norms and then solved using convex programming. The solution aims to recover the transmitted signal and NBI jointly. The off-grid problem of NBI signal is avoided using the atomic norm. The bit error rate (BER) performance of our proposed JCS recovery approach outperforms the BER performance of the conventional CS-based approach as demonstrated by simulation results.

关键词： OFDM NBI atomic norm compressive sensing semi-definite programming

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Convex Relaxation of Optimal Power Flow in Distribution Feeders with Embedded Solar Power 3

Convex Relaxation of Optimal Power Flow in Distribution Feed...

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3rd International Conference on Power and Energy Systems Engineering, (CPESE)

作者： Hermann, Alexander Wu, Qiuwei Huang, Shaojun Nielsen, Arne Hejde Tech Univ Denmark Ctr Elect Power & Energy Bldg 325 DK-2800 Lyngby Denmark

There is an increasing interest in using Distributed Energy Resources (DER) directly coupled to end user distribution feeders. This poses an array of challenges because most of today's distribution feeders are designed for unidirectional power flow. Therefore when installing DERs such as solar panels with uncontrolled inverters, the upper limit of installable capacity is quickly reached in many of today's distribution feeders. This problem can often be mitigated by optimally controlling the voltage angles of inverters. However, the optimal power flow problem in its standard form is a large scale non-convex optimization problem, and thus can't be solved precisely and also is computationally heavy and intractable for large systems. This paper examines the use of a convex relaxation using semi-definite programming to optimally control solar power inverters in a distribution grid in order to minimize the global line losses of the feeder. The mathematical model is presented in details. Further, case studies are completed with simulations involving a 15-bus radial distribution system. These simulations are run for 24 hour periods, with actual solar data and demand data. (C) 2016 The Authors. Published by Elsevier Ltd.

关键词： semi-definite programming Optimal Power Flow Convex Relaxation 15 bus test feeder

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Interpolant Synthesis for Quadratic Polynomial Inequalities and Combination with EUF 8th

Interpolant Synthesis for Quadratic Polynomial Inequalities ...

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8th International Joint Conference on Automated Reasoning (IJCAR)

作者： Gan, Ting Dai, Liyun Xia, Bican Zhan, Naijun Kapur, Deepak Chen, Mingshuai Peking Univ LMAM Beijing Peoples R China Peking Univ Sch Math Sci Beijing Peoples R China Chinese Acad Sci State Key Lab Comp Sci Inst Software Beijing Peoples R China Univ New Mexico Dept Comp Sci Albuquerque NM 87131 USA Wuhan Univ State Key Lab Software Engn Wuhan Hubei Peoples R China

ISBN: (纸本)9783319402291

An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that quadratic polynomial inequalities can be linearized if they are concave. A generalization of Motzkin's transposition theorem is proved, which is used to generate an interpolant between two mutually contradictory conjunctions of polynomial inequalities, using semi-definite programming in time complexity O(n(3) + nm), where n is the number of variables and m is the number of inequalities (This complexity analysis assumes that despite the numerical nature of approximate SDP algorithms, they are able to generate correct answers in a fixed number of calls.). Using the framework proposed in [22] for combining interpolants for a combination of quantifier-free theories which have their own interpolation algorithms, a combination algorithm is given for the combined theory of concave quadratic polynomial inequalities and the equality theory over uninterpreted functions (EUF).

关键词： Program verification Interpolant Concave quadratic polynomial Motzkin's theorem SOS semi-definite programming

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CAMPARY: Cuda Multiple Precision Arithmetic Library and Applications

CAMPARY: Cuda Multiple Precision Arithmetic Library and Appl...

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5th International Congress on Mathematical Software (ICMS)

作者： Joldes, Mioara Muller, Jean-Michel Popescu, Valentina Tucker, Warwick LAAS CNRS 7 Ave Colonel Roche F-31077 Toulouse France ENS Lyon LIP Lab 46 Allee Italie F-69364 Lyon 07 France Uppsala Univ Dept Math Box 480 S-75106 Uppsala Sweden

ISBN: (纸本)9783319424323;9783319424316

Many scientific computing applications demand massive numerical computations on parallel architectures such as Graphics Processing Units (GPUs). Usually, either floating-point single or double precision arithmetic is used. Higher precision is generally not available in hardware, and software extended precision libraries are much slower and rarely supported on GPUs. We develop CAMPARY: a multipleprecision arithmetic library, using the CUDA programming language for the NVidia GPU platform. In our approach, the precision is extended by representing real numbers as the unevaluated sum of several standard machine precision floating-point numbers. We make use of error-free transforms algorithms, which are based only on native precision operations, but keep track of all rounding errors that occur when performing a sequence of additions and multiplications. This offers the simplicity of using hardware highly optimized floating-point operations, while also allowing for rigorously proven rounding error bounds. This also allows for easy implementation of an interval arithmetic. Currently, all basic multiple-precision arithmetic operations are supported. Our target applications are in chaotic dynamical systems or automatic control.

关键词： Floating-point arithmetic Multiple precision library GPGPU computing Error-free transform Floating-point expansions Dynamical systems Henon map semi-definite programming

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ON CONVEXITY AND IDENTIFIABILITY IN 1-D FOURIER PHASE RETRIEVAL 41

ON CONVEXITY AND IDENTIFIABILITY IN 1-D FOURIER PHASE RETRIE...

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41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Huang, Kejun Eldar, Yonina C. Sidiropoulos, Nicholas D. Univ Minnesota Minneapolis MN 55455 USA Technion Israel Inst Technol IL-32000 Haifa Israel

ISBN: (纸本)9781479999880

This paper considers phase retrieval from the magnitude of 1-D over-sampled Fourier measurements. We first revisit the well-known lack of identifiability in this case, and point out that there always exists a solution that is minimum phase, even though the desired signal is not. Next, we explain how the least-squares formulation of this problem can be optimally solved via PhaseLift followed by spectral factorization, and this solution is always minimum phase. A simple approach is then proposed to circumvent non-identifiability: adding an impulse to an arbitrary complex signal (offset to the Fourier transform) before taking the quadratic measurements, so that a minimum phase signal is constructed and thus can be uniquely estimated. Simulations with synthetic data show the effectiveness of the proposed method.

关键词： phase retrieval over-sampled Fourier measurements minimum phase auto-correlation estimation semi-definite programming

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A Robust Adaptive Beamformer Based on Worst-Case semi-definite programming

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2010年第11期58卷 5914-5919页

作者： Yu, Zhu Liang Gu, Zhenghui Zhou, Jianjiang Li, Yuanqing Ser, Wee Er, Meng Hwa S China Univ Technol Coll Automat Sci & Engn Guangzhou 510640 Guangdong Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Informat Sci & Technol Nanjing 210016 Peoples R China Nanyang Technol Univ Sch EEE Singapore 639798 Singapore

In this correspondence, a novel robust adaptive beamformer is proposed based on the worst-case semi-definite programming (SDP). A recent paper has reported that a beamformer robust against large steering direction error can be constructed by using linear constraints on magnitude response in SDP formulation. In practice, however, array system also suffers from many other array imperfections other than steering direction error. In order to make the adaptive beamformer robust against all kinds of array imperfections, the worst-case optimization technique is proposed to reformulate the beamformer by minimizing the array output power with respect to the worst-case array imperfections. The resultant beamformer has the mathematical form of a regularized SDP problem and possesses superior robustness against arbitrary array imperfections. Although the formulation of robust beamformer uses weighting matrix, with the help of spectral factorization approach, the weighting vector can be obtained so that the beamformer can be used for both signal power and waveform estimation. Simple implementation, flexible performance control, as well as significant signal-to-interference-plus-noise ratio (SINR) enhancement, support the practicability of the proposed method.

关键词： Adaptive array constraints on magnitude response robust adaptive beamforming semi-definite programming spectral factorization worst-case optimization

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Tight wavelet frames via semi-definite programming

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JOURNAL OF APPROXIMATION THEORY 2010年第8期162卷 1429-1449页

作者： Charina, Maria Stoeckler, Joachim Tech Univ Dortmund Fak Math D-44221 Dortmund Germany

In this paper we state the "oblique extension principle" as a problem of semi-definite programming. Using this optimization technique we show that the existence of a tight frame is equivalent to the existence of a certain matrix from a cone of positive semi-definite matrices, whose entries satisfy linear constraints. We also discuss how to use the optimization techniques to reduce the number of frame generators in univariate and multivariate cases. We apply our results for constructing light frames for several subdivision schemes. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Wavelet frames Oblique extension principle Subdivision semi-definite programming

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On a New SDP-SOCP Method for Acoustic Source Localization Problem

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ACM TRANSACTIONS ON SENSOR NETWORKS 2016年第4期12卷 36-36页

作者： Gao, Mingjie Yiu, Ka-Fai Cedric Nordholm, Sven Ye, Yinyu South China Normal Univ Sch Math Sci Guangzhou Guangdong Peoples R China Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China Curtin Univ Dept Elect & Comp Engn Perth WA Australia Stanford Univ Dept Management Sci & Engn Stanford CA 94305 USA Stanford Univ Elect Engn Stanford CA 94305 USA

Acoustic source localization has many important applications. Convex relaxation provides a viable approach of obtaining good estimates very efficiently. There are two popular convex relaxation methods using either semi-definite programming (SDP) or second-order cone programming (SOCP). However, the performances of the methods have not been studied properly in the literature and there is no comparison in terms of accuracy and performance. The aims of this article are twofold. First of all, we study and compare several convex relaxation methods. We demonstrate, by numerical examples, that most of the convex relaxation methods cannot localize the source exactly, even in the performance limit when the time difference of arrival (TDOA) information is exact. In addressing this problem, we propose a novel mixed SDP-SOCP relaxation model and study the characteristics of the optimal solutions and its localizable region. Furthermore, an error correction scheme for the proposed SDP-SOCP model is developed so that exact localization can be achieved in the performance limit. Experimental data have been collected in a room with two different array configurations to demonstrate our proposed approach.

关键词： Design Algorithms Performance Beamforming localization convex relaxation semi-definite programming second-order cone programming

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On solving a class of linear semi-infinite programming by SDP method

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OPTIMIZATION 2015年第3期64卷 603-616页

作者： Xu, Yi Sun, Wenyu Qi, Liqun Nanjing Normal Univ Sch Math Sci Jiangsu Key Lab NSLSCS Nanjing Jiangsu Peoples R China Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China

In this paper, we present a new method to solve linear semi-infinite programming. This method bases on the fact that the nonnegative polynomial on could be turned into a positive semi-definite system, so we can use the nonnegative polynomials to approximate the semi-infinite constraint. Furthermore, we set up an approximate programming for the primal linear semi-infinite programming, and obtain an error bound between two programming problems. Numerical results show that our method is efficient.

关键词： 90C22 90C34 semi-infinite programming SOS method semi-definite programming nonnegative polynomial error bound

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