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48
Grasp Analysis as Linear Matrix Inequality Problems
"... Three important problems in the study of grasping and manipulation by multifingered robotic hands are: (a) Given a grasp characterized by a set of contact points and the associated contact models, determine if the grasp has force closure; (b) If the grasp does not have force closure, determine if th ..."
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Cited by 33 (2 self)
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Three important problems in the study of grasping and manipulation by multifingered robotic hands are: (a) Given a grasp characterized by a set of contact points and the associated contact models, determine if the grasp has force closure; (b) If the grasp does not have force closure, determine if the ngers are able to apply a specified resultant wrench on the object; and (c) Compute "optimal" contact forces if the answer to problem (b) is affirmative. In this paper, based on an early result by Buss, Hashimoto and Moore, which transforms the nonlinear friction cone constraints into positive definiteness of certain symmetric matrices, we further cast the friction cone constraints into linear matrix inequalities (LMIs) and formulate all three of the problems stated above as a set of convex optimization problems involving LMIs. The latter problems have been extensively studied in optimization and control community and highly efficient algorithms with polynomial time complexity are now available for their solutions. We perform simulation studies to show the simplicity and efficiency of the LMI formulation to the three problems.
GPCAD: A Tool for CMOS OpAmp Synthesis
 IN PROCEEDINGS OF THE IEEE/ACM INTERNATIONAL CONFERENCE ON COMPUTER AIDED DESIGN
, 1998
"... We present a method for optimizing and automating component and transistor sizing for CMOS operational amplifiers. We observe that a wide variety of performance measures can be formulated as posynomial functions of the design variables. As a result, amplifier design problems can be formulated as a g ..."
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Cited by 29 (10 self)
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We present a method for optimizing and automating component and transistor sizing for CMOS operational amplifiers. We observe that a wide variety of performance measures can be formulated as posynomial functions of the design variables. As a result, amplifier design problems can be formulated as a geometric program, a special type of convex optimization problem for which very efficient global optimization methods have recently been developed. The synthesis method is therefore fast, and determines the globally optimal design; in particular the final solution is completely independent of the starting point (which can even be infeasible), and infeasible specifications are unambiguously detected. After briefly
A Robust Optimization Solution to the Data Hiding Problem using Distributed Source Coding Principles
 in Proc. of SPIE Vol. 3974: Image and Video Communications and Processing 2000
, 2000
"... Inspired by a recently proposed constructive framework for the distributed source coding problem, 1 we propose a powerful constructive approach to the watermarking problem, emphasizing the dual roles of "source codes" and "channel codes." In our framework, we explore various source and channel codes ..."
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Cited by 27 (1 self)
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Inspired by a recently proposed constructive framework for the distributed source coding problem, 1 we propose a powerful constructive approach to the watermarking problem, emphasizing the dual roles of "source codes" and "channel codes." In our framework, we explore various source and channel codes to achieve watermarks that are robust to attackers in terms of maximizing the distortion between the corrupted codedsource signal and the original signal while holding the distortion between the codedsource signal and the original signal constant. We solve the resulting combinatorial optimization problem using an original technique based on robust optimization and convex programming. Keywords: Data Hiding, Digital Watermarking, Multimedia, Convex Optimization, Robustness 1. INTRODUCTION Digital watermarking (data hiding) is an emerging research area that has received a considerable amount of attention in recent years. The basic idea behind digital watermarking is to embed information...
Optimum linear joint transmitreceive processing for MIMO channels with QoS constraints
 IEEE Transactions on Signal Processing
, 2004
"... Abstract—This paper considers vector communications through multipleinput multipleoutput (MIMO) channels with a set of quality of service (QoS) requirements for the simultaneously established substreams. Linear transmitreceive processing (also termed linear precoder at the transmitter and linear ..."
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Cited by 23 (3 self)
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Abstract—This paper considers vector communications through multipleinput multipleoutput (MIMO) channels with a set of quality of service (QoS) requirements for the simultaneously established substreams. Linear transmitreceive processing (also termed linear precoder at the transmitter and linear equalizer at the receiver) is designed to satisfy the QoS constraints with minimum transmitted power (the exact conditions under which the problem becomes unfeasible are given). Although the original problem is a complicated nonconvex problem with matrixvalued variables, with the aid of majorization theory, we reformulate it as a simple convex optimization problem with scalar variables. We then propose a practical and efficient multilevel waterfilling algorithm to optimally solve the problem for the general case of different QoS requirements. The optimal transmitreceive processing is shown to diagonalize the channel matrix only after a very specific prerotation of the data symbols. For situations in which the resulting transmit power is too large, we give the precise way to relax the QoS constraints in order to reduce the required power based on a perturbation analysis. We also propose a robust design under channel estimation errors that has an important interest for practical systems. Numerical results from simulations are given to support the mathematical development of the problem. Index Terms—Array signal processing, beamforming, joint transmitreceive equalization, linear precoding, MIMO channels, spacetime filtering, waterfilling. I.
Optimal Power Control in Interference Limited Fading Wireless Channels with Outage Probability Specifications
, 2000
"... We propose a new method of power control for interference limited wireless networks with Rayleigh fading of both the desired and interference signals. Our method explictly takes into account the statistical variation of both the received signal and interference power, and optimally allocates powe ..."
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Cited by 16 (2 self)
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We propose a new method of power control for interference limited wireless networks with Rayleigh fading of both the desired and interference signals. Our method explictly takes into account the statistical variation of both the received signal and interference power, and optimally allocates power subject to constraints on the probability of fading induced outage for each transmitter/receiver pair. We establish several results for this type of problem. For the case
Design of robust global power and ground networks
 In ISPD
, 2001
"... We consider the problem of determining optimal wire widths for a power or ground network, subject to limits on wire widths, voltage drops, total wire area, current density, and power dissipation. To account for the variation of the current demand, we model it as a random vector with known statistics ..."
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Cited by 16 (4 self)
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We consider the problem of determining optimal wire widths for a power or ground network, subject to limits on wire widths, voltage drops, total wire area, current density, and power dissipation. To account for the variation of the current demand, we model it as a random vector with known statistics, possibly including correlation between subsystem currents. Other researchers have shown that when the variation in the current is not taken into account, the optimal network topology is a tree. A tree topology is, however, almost never used in practice, because it is not robust with respect to variations in the block currents. We show that when the current variation is taken into account, the optimal network is usually not a tree. We formulate a heuristic method based on minimizing a linear combination of total average power and total wire area. We show that this results in designs that obey the reliability constraints, occupy small area, and most importantly are robust against variations in block currents. The problem can be formulated as a nonlinear convexoptimization problem that can be globally solved very efficiently.
Semidefinite relaxation for detection of 16QAM signaling in mimo channels
 IEEE Signal Processing Letters
, 2005
"... Abstract—We develop a computationally efficient approximation of the maximum likelihood (ML) detector for 16 quadrature amplitude modulation (16QAM) in multipleinput multipleoutput (MIMO) systems. The detector is based on a convex relaxation of the ML problem. The resulting optimization is a semi ..."
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Cited by 16 (0 self)
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Abstract—We develop a computationally efficient approximation of the maximum likelihood (ML) detector for 16 quadrature amplitude modulation (16QAM) in multipleinput multipleoutput (MIMO) systems. The detector is based on a convex relaxation of the ML problem. The resulting optimization is a semidefinite program that can be solved in polynomial time with respect to the number of inputs in the system. Simulation results in a random MIMO system show that the proposed algorithm outperforms the conventional decorrelator detector by about 2.5 dB at high signaltonoise ratios. Index Terms—Maximum likelihood detection, MIMO systems, semidefinite relaxation. I.
Outage capacities and optimal power allocation for fading multipleaccess channels
 IEEE Trans. Inform. Theory
, 2005
"... Abstract—We derive the outage capacity region of anuser fading multipleaccess channel (MAC) under the assumption that both the transmitters and the receiver have perfect channel side information (CSI). The outage capacity region is implicitly obtained by deriving the outage probability region for ..."
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Cited by 16 (5 self)
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Abstract—We derive the outage capacity region of anuser fading multipleaccess channel (MAC) under the assumption that both the transmitters and the receiver have perfect channel side information (CSI). The outage capacity region is implicitly obtained by deriving the outage probability region for a given rate vector. Given a required rate and average power constraint for each user, we find a successive decoding strategy and a power allocation policy that achieves points on the boundary of the outage probability region. We discuss the scenario where an outage must be declared simultaneously for all users (common outage) and when outages can be declared individually (individual outage) for each user. Index Terms—Capacity region, fading channels, multipleaccess channels (MACs), optimal power allocation, outage probability. I.
FDMACapacity of Gaussian MultipleAccess Channels with ISI
 IEEE Trans. Commun
, 2000
"... This paper proposes a numerical method for characterizing the rate region achievable with frequencydivision multiple access (FDMA) for a Gaussian multipleaccess channel with intersymbol interference. The frequency spectrum is divided into discrete frequency bins and the discrete binassignment pro ..."
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Cited by 16 (3 self)
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This paper proposes a numerical method for characterizing the rate region achievable with frequencydivision multiple access (FDMA) for a Gaussian multipleaccess channel with intersymbol interference. The frequency spectrum is divided into discrete frequency bins and the discrete binassignment problem is shown to have a convex relaxation, making it tractable to numerical optimization algorithms. A practical lowcomplexity algorithm for the twouser case is also proposed. The algorithm is based on the observation that the optimal frequency partition has a twoband structure when the two channels are identical or when the signaltonoise ratio is high. Simulation result shows that the algorithm performs well in other cases as well. The FDMAcapacity algorithm is used to devise the optimal frequencydivision duplex plan for veryhighspeed digital subscriber lines.
FIR Filter Design via Semidefinite Programming and Spectral Factorization
, 1996
"... We present a new semidefinite programming approach to FIR lter design with arbitrary upper and lower bounds on the frequency response magnitude. It is shown that the constraints can be expressed as linear matrix inequalities (LMIs), and hence they can be easily handled by recent interiorpoint metho ..."
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Cited by 15 (6 self)
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We present a new semidefinite programming approach to FIR lter design with arbitrary upper and lower bounds on the frequency response magnitude. It is shown that the constraints can be expressed as linear matrix inequalities (LMIs), and hence they can be easily handled by recent interiorpoint methods. Using this LMI formulation, we can cast several interesting filter design problems as convex or quasiconvex optimization problems, e.g., minimizing the length of the FIR filter and computing the Chebychev approximation of a desired power spectrum or a desired frequency response magnitude on a logarithmic scale.