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Adaptive efficient sparse estimator achieving oracle properties

IET SIGNAL PROCESSING 2013年第4期7卷 259-268页

作者： Rezaii, Tohid Yousefi Tinati, Mohammad Ali Beheshti, Soosan Univ Tabriz Fac Elect & Comp Engn Tabriz *** Iran Ryerson Univ Dept Elect & Comp Engn Toronto ON M5B 2K3 Canada

Compressed Sensing is the new trend in the signal processing context which aims to sample a compressible signal with a rate less than the Nyquist lower bound sampling rate. The main challenge arises due to the non-convex optimisation problem to be solved in the reconstruction stage. This paper introduces a suitable objective function in order to simultaneously recover the true support of the underlying sparse signal while achieving an acceptable estimation error. Inspired by the well-known Lasso objective function, we have developed an objective function based on a new penalty denoted by the Linearised Exponentially Decaying (LED) penalty. The comprehensive analysis of the LED based objective function shows that the new approach satisfies the oracle properties, as opposed to the conventional Lasso objective function. Furthermore, we have developed a Sequential Adaptive Coordinate-wise (SAC) solution for the proposed objective function. The simulation results for the proposed LED-SAC reconstruction algorithm are given and compared with other state of the art methods. It is shown that LED-SAC approaches the least mean squared error criterion. Moreover, compared to the other methods, LED-SAC has much more adaptation rate in terms of tracking the variations in the support of the underlying sparse signal.

关键词： adaptive signal processing concave programming least mean squares methods signal reconstruction adaptive efficient sparse estimator oracle properties compressed sensing signal processing signal processing context nonconvex optimisation problem Nyquist lower bound sampling rate objective function sparse signal Lasso objective function linearised exponentially decaying-based objective function LED- based objective function sequential adaptive coordinate-wise solution LED-SAC reconstruction algorithm least mean squared error criterion adaptive signal processing concave programming least mean squares methods signal reconstruction adaptive efficient sparse estimator oracle properties compressed sensing signal processing signal processing context nonconvex optimisation problem Nyquist lower bound sampling rate objective function sparse signal Lasso objective function linearised exponentially decaying-based objective function LED- based objective function sequential adaptive coordinate-wise solution LED-SAC reconstruction algorithm least mean squared error criterion

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Power allocation over time-varying multi-user multi-relay amplify-and-forward networks

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IET COMMUNICATIONS 2016年第18期10卷 2636-2648页

作者： Baidas, Mohammed W. Alsusa, Emad Hamdi, Khairi A. Kuwait Univ Dept Elect Engn Coll Engn & Petr Kuwait Kuwait Univ Manchester Sch Elect & Elect Engn Manchester Lancs England

In this study, power allocation over time-varying multi-user multi-relay amplify-and-forward networks is studied. Specifically, stochastic network sum-rate, max-min rate power allocation and total power minimisation problems are formulated. However, solving such stochastic problems relies on perfect global instantaneous channel state information (CSI), and thus entails complex computations and excessive communication overheads. To circumvent these issues, second-order statistics of the CSI (i.e. partial CSI) are utilised to transform the stochastic formulations into deterministic optimisation problems in terms of ergodic capacity while satisfying quality-of-service constraints via target outage probability. The obtained optimal deterministic problems are non-convex and thus are computationally prohibitive. However, at high enough signal-to-noise ratio, such problems can be transformed into asymptotically convex ones, and thus solved efficiently. Simulation results illustrate that the proposed approximate deterministic power allocation reformulations closely agree with their optimal exact deterministic and dynamic counterparts.

关键词： time-varying channels amplify and forward communication relay networks (telecommunication) multiuser channels minimisation higher order statistics stochastic programming quality of service concave programming probability time-varying multiuser multirelay amplify-and-forward networks stochastic network sum-rate max-min rate power allocation total power minimisation problems stochastic problems perfect global instantaneous channel state information CSI communication overheads second-order statistics deterministic optimisation problems ergodic capacity quality-of-service constraints target outage probability signal-to-noise ratio approximate deterministic power allocation reformulations

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ONLINE AND OFF-LINE VERTEX ENUMERATION BY ADJACENCY LISTS

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OPERATIONS RESEARCH LETTERS 1991年第7期10卷 403-409页

作者： CHEN, PC HANSEN, P JAUMARD, B GERAD MONTREAL H3C 3A7QUEBECCANADA ECOLE POLYTECH MONTREAL H3C 3A7QUEBECCANADA

We propose a new algorithm to solve the on-line vertex enumeration problem for polytopes, doing all computations in n-space, where n is the dimension of the polytope. This algorithm exploits adjacency lists between vertices and uses no simplex tableaux. It can handle the cases of empty or degenerate polyhedra. A theoretical and numerical comparison with existing approaches for off-line vertex enumeration is presented.

关键词： VERTEX ENUMERATION CUTTING-PLANE GLOBAL OPTIMIZATION concave programming

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Resource optimisation for downlink non-orthogonal multiple access systems: a joint channel bandwidth and power allocations approach

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IET COMMUNICATIONS 2018年第19期12卷 2429-2437页

作者： Wu, Yuan Mao, Haowei Ni, Kejie Feng, Xu Qian, Liping Huang, Liang Shi, Zhiguo Zhejiang Univ Technol Coll Informat Engn Hangzhou Zhejiang Peoples R China Xidian Univ State Key Lab Integrated Serv Networks Xian 710071 Shaanxi Peoples R China Zhejiang Univ Dept Informat & Elect Engn Hangzhou Zhejiang Peoples R China

The emerging non-orthogonal multiple access (NOMA) has been considered as a promising scheme to reach the goals of 5G cellular systems. By enabling a group of mobile users (MUs) to share a same frequency channel and adopting the successive interference cancellation to mitigate the co-channel interference, NOMA can improve the spectrum efficiency compared with the orthogonal multiple access (OMA). This study proposes a joint optimisation scheme of the channel bandwidth and the transmit-power allocations for the NOMA downlink transmission, which aims at minimising the overall resource consumption cost including both the spectrum consumption and the power consumption, while satisfying the MUs' traffic requirements. In spite of the non-convexity nature of the joint optimisation problem, this study characterises the connection between the channel bandwidth and the associated transmit powers for the MUs. Based on this connection, this study transforms the joint optimisation problem into an equivalent bandwidth optimisation problem, and further proposes an efficient algorithm to compute the optimal bandwidth allocation (which enables us to derive the corresponding transmit powers for the MUs). Extensive numerical results are provided to validate the proposed algorithm and the advantage of the proposed joint channel bandwidth and power allocations for the NOMA transmission.

关键词： cellular radio 5G mobile communication interference suppression radio spectrum management telecommunication traffic bandwidth allocation multi-access systems resource allocation wireless channels cochannel interference concave programming resource optimisation downlink nonorthogonal multiple access systems joint channel bandwidth ultra-high throughput massive connectivity 5G cellular systems frequency channel successive interference cancellation spectrum efficiency limited spectrum resources crowded spectrum resources NOMA transmission joint optimisation scheme transmit-power allocations NOMA-enabled downlink transmission resource consumption cost spectrum consumption cost power consumption cost joint optimisation problem equivalent bandwidth optimisation problem optimal bandwidth allocation NOMA-enabled transmission conventional OMA-based transmission power allocation approach co-channel interference mitigation nonorthogonal multiple access mobile users MU traffic requirements nonconvex optimization

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Block-sparse compressed sensing with partially known signal support via non-convex minimisation

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IET SIGNAL PROCESSING 2016年第7期10卷 717-723页

作者： He, Shiying Wang, Yao Wang, Jianjun Xu, Zongben Xi An Jiao Tong Univ Sch Math & Stat Xian Peoples R China Chinese Acad Sci Shenyang Inst Automat State Key Lab Robot Shenyang Peoples R China Southwest Univ Sch Math & Stat Chongqing Peoples R China

The mixed l(2)/l(p) (0 < p 1) norm minimisation method with partially known support for recovering block-sparse signals is studied. The authors mainly extend this work on block-sparse compressed sensing by incorporating some known part of the block support information as a priori and establish sufficient restricted p-isometry property (p-RIP) conditions for exact and robust recovery. The authors' theoretical results show it is possible to recover the block-sparse signals via l(2)/l(p) minimisation from reduced number of measurements by applying the partially known support. The authors also derive a lower bound on necessary random Gaussian measurements for the p-RIP conditions to hold with high possibility. Finally, a series of numerical experiments are carried out to illustrate that fewer measurements with smaller p are needed to reconstruct the signal.

关键词： compressed sensing concave programming minimisation signal reconstruction block-sparse compressed sensing signal support non-convex minimisation mixed l(2)/l(p)(0 < p <= 1) norm minimisation method block-sparse signals p-isometry property random Gaussian measurements p-RIP conditions signal reconstruction

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Joint user scheduling and channel allocation for cellular networks with full duplex base stations

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IET COMMUNICATIONS 2016年第5期10卷 479-486页

作者： Yu, Guanding Wen, Dingzhu Qu, Fengzhong Zhejiang Univ Dept Informat Sci & Elect Engn Hangzhou 310027 Zhejiang Peoples R China Zhejiang Univ Dept Ocean Sci & Engn Hangzhou 310027 Zhejiang Peoples R China

Full-duplex communication (FDC) can potentially double the network capacity by allowing a device to transmit and receive simultaneously on the same frequency band. In this study, a novel resource allocation and user scheduling algorithm is proposed to maximise the network throughput for a cellular network with full-duplex (FD) base stations (BSs). The authors consider that FDC is utilised at the BS with imperfect self-interference (SI) cancellation while user devices only work in the traditional half-duplex (HD) way. In addition, to potentially cancel co-channel interference caused by other users, the opportunistic interference cancellation (OIC) technique is applied at user side. Since FDC does not always perform better than HD due to residual SI (RSI), a joint mode selection, user scheduling, and channel allocation problem is formulated to maximise the system throughput. The optimisation problem is non-convex and NP-hard, thereby a suboptimal heuristic algorithm with low computational complexity is proposed. Numerical results demonstrate that user diversity gain, FD gain, and OIC gain can be achieved by the proposed algorithm, respectively. The performance of FDC depends on the intensity of RSI and the distribution of user devices.

关键词： cellular radio interference suppression cochannel interference resource allocation channel allocation telecommunication scheduling computational complexity concave programming heuristic programming joint user scheduling-channel allocation algorithm cellular networks full duplex base stations FDC full-duplex communication network capacity resource allocation FD BSs imperfect self-interference cancellation half-duplex base stations SI cancellation cochannel interference cancellation opportunistic interference cancellation technique OIC technique RSI residual SI joint mode selection system throughput nonconvex optimisation problem NP-hard problem suboptimal heuristic algorithm computational complexity RSI intensity

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Joint active and passive beamforming optimization for multigroup multicast system aided by intelligent reflecting surface

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IET COMMUNICATIONS 2021年第4期15卷 642-652页

作者： Wang, Junzhi Liao, Xiangbai Liu, Yingzhuang Huazhong Univ Sci & Technol Sch Elect Informat & Commun Wuhan Peoples R China Jiaxing Univ Coll Math Phys & Informat Engn South Yuexiu Rd Jiaxing Zhejiang Peoples R China

An intelligent-reflecting-surface aided multigroup multicast communication system is investigated in this paper. We develop energy-efficient designs for both the precoding matrix at the base station and passive reflecting beamforming at intelligent-reflecting-surface, subject to the minimum signal-to-interference-plus-noise ratio constraint of each user and the unit-modulus constraint imposed by passive intelligent-reflecting-surface. This leads to a complex non-convex problem for which to tackle we propose two novel algorithms based on alternating optimization techniques. Specifically, one algorithm employs semi-definite relaxation to obtain the suboptimal reflection coefficient vector and suboptimal precoding vector for each group. In order to reduce the computational complexity, the second algorithm transforms this non-convex problem into two second-order cone programming problems. Numerical results show that intelligent-reflecting-surface can significantly reduce the power consumption of the base station.

关键词： multicast communication convex programming Optimisation techniques Signal processing and detection intelligent-reflecting-surface aided multigroup multicast communication system Codes precoding optimisation nonconvex problem passive reflecting concave programming multigroup multicast system intelligent reflecting surface minimum signal-to-interference-plus-noise ratio constraint array signal processing computational complexity Radio links and equipment passive beamforming optimization suboptimal reflection coefficient vector MIMO communication

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Radio resource allocation for heterogeneous traffic in GFDM-NOMA heterogeneous cellular networks

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IET COMMUNICATIONS 2016年第12期10卷 1444-1455页

作者： Mokdad, Ali Azmi, Paeiz Mokari, Nader Tarbiat Modares Univ Dept Elect & Comp Engn Tehran Iran

In this study, the authors consider the downlink radio resource allocation for heterogeneous traffic in generalised frequency division multiplexing (GFDM)-non-orthogonal multiple access (NOMA) based heterogeneous cellular networks. In this scheme, multiple number of users can be allocated on each subcarrier. Two types of traffic are considered, elastic and streaming. The problem of maximising the weighted sum-rate of elastic users is addressed subject to streaming users minimum rate in addition to subcarrier and transmit power constraints. This problem is a non-convex NP-hard optimisation problem. To solve this problem, the authors divide it into two subproblems, subcarrier allocation and power allocation then an iterative algorithm is proposed. Subcarrier allocation is updated by solving an integer linear program, where a successive convex approximation approach is adopted to transform the power allocation subproblem to a sequence of convex subproblems, using one of the three methods, successive convex approximation for low ComplExity, arithmetic-geometric mean approximation (AGMA) and difference of two concave functions to find the power allocation optimal solutions. Numerical experiments show that the proposed algorithms can improve the system performance. Furthermore, they show that AGMA can achieve a sum-rate near to the global optimal solution, at the expense of more computational time.

关键词： resource allocation telecommunication traffic cellular radio frequency division multiplexing concave programming convex programming computational complexity iterative methods approximation theory geometry integer programming linear programming downlink radio resource allocation heterogeneous traffic GFDM-NOMA heterogeneous cellular networks generalised frequency division multiplexing nonorthogonal multiple access elastic type streaming type weighted elastic user sum-rate maximisation subcarrier power constraint transmit power constraint nonconvex NP-hard optimisation problem subcarrier allocation power allocation iterative algorithm integer linear program successive convex approximation approach arithmetic-geometric mean approximation AGMA concave functions computational time

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Recover feasible solutions for SOCP relaxation of optimal power flow problems in mesh networks

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IET GENERATION TRANSMISSION & DISTRIBUTION 2019年第7期13卷 1078-1087页

作者： Tian, Zhuang Wu, Wenchuan Tsinghua Univ Dept Elect Engn State Key Lab Power Syst Beijing Peoples R China

The AC optimal power flow (OPF) problem is essential for the schedule and operation of power systems. Convex relaxation methods have been studied and used extensively to obtain an optimal solution to the OPF problem. When the exactness of convex relaxations is not guaranteed, it is important to recover a feasible solution for the convex relaxation methods. This paper presents an alternative convex optimisation (ACP) approach that can efficiently recover a feasible solution from the result of second-order cone programming (SOCP) relaxed OPF in mesh networks. The OPF problem is first formulated as a difference-of-convex programming (DCP) problem, then efficiently solved by a penalty convex concave procedure (CCP). By using the solution of a tightened SOCP OPF as an initial point, the proposed algorithm is able to find a global or near-global optimal solution to the AC OPF problem. Numerical tests show that the proposed method outperforms those semi-definite programming (SDP) and quadratically constrained quadratic programming (QCQP)-based algorithms.

关键词： convex programming concave programming load flow scheduling near-global optimal solution AC OPF problem recover feasible solutions mesh networks AC optimal power flow problem power systems convex relaxation methods alternative convex optimisation approach second-order cone programming difference-of-convex programming problem penalty convex concave procedure tightened SOCP OPF global solution ACP approach SOCP relaxed OPF numerical tests semidefinite programming quadratically constrained quadratic programming-based algorithms

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Locally convexified rigid tube MPC

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IET CONTROL THEORY AND APPLICATIONS 2023年第4期17卷 446-462页

作者： Sun, Haidi Zhang, Sixing Dai, Li Rakovic, Sasa, V Beijing Inst Technol Sch Automat Beijing Peoples R China

This paper proposes a locally convexified rigid tube model predictive control for obstacle avoidance for linear, discrete-time, systems subject to additive, bounded disturbances and state and control constraints. The inherently nonconvex obstacle avoidance constraints are locally convexified and converted into closed polyhedral constraints by deploying recent notions of safe sets and tubes. The proposed method leverages these recent notions of safe sets and tubes to reformulate the original nonconvex optimization problem for obstacle avoidance within the context of disturbances into a computationally highly efficient, strictly convex quadratic programming problem. In order to analyze the separation between a predicted state set and each obstacle avoidance constraint set, we employ the Euclidean distance between these two sets and the radius of the Chebyshev ball of their intersection. In the strict separation case, the separating hyperplanes are constructed by utilizing the separation theorem for convex sets, while in the weak separation case, the construction of separating hyperplanes is achieved through the use of the separation theorem and the properties of convex cones. The proposed method provides guarantees of strong system theoretic properties such as robust recursive feasibility, robust positive invariance and robust stability of the controlled uncertain system. A simulation example is also provided to numerically verify the effectiveness of the proposed method.

关键词： Optimisation techniques strict separation case original nonconvex optimization problem uncertain systems convex programming Mobile robots Linear control systems control constraints quadratic programming predicted state set systems subject strictly convex quadratic programming problem closed polyhedral constraints weak separation case Discrete control systems convex sets separation theorem obstacle avoidance constraint predictive control strong system theoretic properties separating hyperplanes safe sets locally convexified rigid tube model predictive control controlled uncertain system robust control inherently nonconvex obstacle avoidance constraints collision avoidance Stability in control theory Optimal control Spatial variables control concave programming bounded disturbances

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