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Peijung Chung - One of the best experts on this subject based on the ideXlab platform.

  • robust transmit beamforming for multi user mimo systems using a Probabilistic Constraint approach
    International Conference on Signal Processing, 2012
    Co-Authors: Peijung Chung, Ming Chen
    Abstract:

    This paper considers the multi-user multiple-input and multiple-output (MU-MIMO) downlink system where each user is equipped with multiple receive antennas. As the design of transmit beamformers relies heavily on perfect channel state information, channel uncertainties may cause substantial performance degradation. Here we suggest a solution based on a Probabilistic Constraint approach. The suggested method maximizes the average signal power and keeps leakage power below an acceptable level, leading to an upper bound on signal to leakage noise ratio (SLNR). To solve the underlying problem efficiently, the Probabilistic Constraint is transformed to a deterministic, convex one through the application of the Markov inequality. Simulation results show that the Probabilistic Constraint approach provides excellent performance in terms of signal-to-interference and noise ratio (SINR) and bit error rate (BER) for large channel errors and various error distributions.

  • robust slnr downlink beamforming based on markov s inequality
    International Conference on Communications, 2012
    Co-Authors: Peijung Chung
    Abstract:

    This paper considers the multi-user multiple-input and multiple-output (MU-MIMO) downlink system where each user is equipped with multiple receive antennas. Due to the inevitable channel imperfection, the system performance may degrade significantly. A robust signal-to-leakage-and-noise ratio (SLNR)-based beamforming is developed to provide robustness against channel uncertainties, which maximizes the expectation of the signal power and maintains a low probability of the severe leakage. Two types of errors are taken into account, that is, the estimation Gaussian error in time division duplexing (TDD) system and the quantization error in frequency division duplexing (FDD) system. In order to solve the underlying problem efficiently, the Probabilistic Constraint is transformed into a convex one by using Markov's inequality, which places an upper bound of the robust scheme based on channel statis-tics. Furthermore, the proposed design is applicable to general error distributions, rather than restricted to Gaussian errors or quantization errors. Simulation results show that the proposed approach with Probabilistic Constraint can achieve high SLNR performance and prevent a pessimistic result by considering the leakage power proportionally.

  • a Probabilistic approach for robust leakage based mu mimo downlink beamforming with imperfect channel state information
    IEEE Transactions on Wireless Communications, 2012
    Co-Authors: Peijung Chung
    Abstract:

    Multi-user multiple-input and multiple-output (MU-MIMO) wireless systems have the potential to increase system capacity significantly by separating multiple users in the space domain through appropriate signal processing. These techniques require accurate channel state information at transmitter (CSIT) for their proper operations. With inevitable channel imperfections in practice, robustness has become an important issue in the development of beamforming techniques. In this work, we propose a robust leakage-based transmit beamforming design for multi-user MIMO systems by introducing a Probabilistic Constraint. In a multi-user system, the main challenge for transmit beamforming is to suppress the co-channel interference (CCI) from other users. Our approach optimizes the average signal-to-interference-plus-noise ratio (SINR) performance implicitly by maximizing the average signal power subject to Probabilistic leakage and noise power Constraint. Moreover, both the single-stream-per-user and multiple-stream-per-user cases are considered.In the latter case, a hybrid scheme is suggested by incorporating Alamouti code into the proposed design. Simulation results show that under proper control of the Probabilistic Constraint, both beamformers achieve good bit-error-rate (BER) performances, reliability of SINR levels as well as robustness against channel uncertainties.

  • a Probabilistic Constraint approach for robust transmit beamforming with imperfect channel information
    IEEE Transactions on Signal Processing, 2011
    Co-Authors: Peijung Chung, Jacek Gondzio
    Abstract:

    Transmit beamforming (or precoding) is a powerful technique for enhancing performance of wireless multiantenna communication systems. Standard transmit beamformers require perfect channel state information at the transmitter (CSIT) and are sensitive to errors in channel estimation. In practice, such errors are inevitable due to finite feedback resources, quantization errors and other physical Constraints. Hence, robustness has become a crucial issue recently. Among two popular robust designs, the stochastic approach exploits channel statistics and optimizes the average system performance while the maximin approach considers errors as deterministic and optimizes the worst case performance. The latter usually leads to a very conservative design against extreme (but rare) conditions which may occur at a very low probability. In this paper, we propose a more flexible approach that maximizes the average signal-to-noise ratio (SNR) and takes the extreme conditions into account using the probability with which they may occur. Simulation results show that the proposed beamformer offers higher robustness against channel estimation errors than several popular transmit beamformers.

  • robust leakage based transmit beamforming with Probabilistic Constraint for downlink multi user mimo system
    2009 IEEE SP 15th Workshop on Statistical Signal Processing, 2009
    Co-Authors: Peijung Chung
    Abstract:

    Multi-user multiple-input and multiple-output (MU-MIMO) wireless systems have the potential to provide a substantial gain by using transmit beamforming to allow multi-user communication in the same frequency and time slots. The main challenge for transmit beamforming design is to suppress the co-channel interference (CCI) from other users. In order to completely cancel the CCI at each user, perfect channel state information (CSI) is required at base station, which is generally not available in practice. To overcome the performance degradation caused by the imperfections, the most common approach is the worst-case method, which leads to conservative result as the extreme (but rare) conditions may occur at a very low probability. In this work, we propose a Probabilistic-constrained beamforming based on signal-to-leakage ratio (SLR) criterion under consideration of inaccurate channel information. The simulation results show that the proposed beamformer achieves the lowest bit error rate (BER) and leaks the least transmit power from the desired user to all other users among the state-of-art transmit beamformers.

Miguel A Lejeune - One of the best experts on this subject based on the ideXlab platform.

  • multi objective Probabilistically constrained programs with variable risk models for multi portfolio financial optimization
    European Journal of Operational Research, 2016
    Co-Authors: Miguel A Lejeune, Siqian Shen
    Abstract:

    Abstract We consider a class of multi-objective Probabilistically constrained programs (MOPCP) with a joint Probabilistic Constraint and a variable risk level. We consider two cases with only a random right-hand side vector or a multi-row random technology matrix, and propose a Boolean modeling framework to derive new mixed-integer linear programs (MILP) that are either equivalent reformulations or inner approximations of MOPCP, respectively. Via testing randomly generated MOPCP instances, we demonstrate modeling insights pertaining to the most suitable MILP, to the trade-offs between conflicting objectives of cost/revenue and reliability, and to the parameter scalarization determining relative importance of each objective. We then focus on several MOPCP variants of a multi-portfolio financial optimization problem to implement a downside risk measure, which can be used in a centralized or decentralized investment context. We study the impact of modeling parameters on the portfolios, show, via a cross-validation study, robustness of MOPCP, and perform a comparative analysis of the optimal investment decisions.

  • stochastic network design for disaster preparedness
    Iie Transactions, 2015
    Co-Authors: Xing Hong, Miguel A Lejeune, Nilay Noyan
    Abstract:

    This article introduces a risk-averse stochastic modeling approach for a pre-disaster relief network design problem under uncertain demand and transportation capacities. The sizes and locations of the response facilities and the inventory levels of relief supplies at each facility are determined while guaranteeing a certain level of network reliability. A Probabilistic Constraint on the existence of a feasible flow is introduced to ensure that the demand for relief supplies across the network is satisfied with a specified high probability. Responsiveness is also accounted for by defining multiple regions in the network and introducing local Probabilistic Constraints on satisfying demand within each region. These local Constraints ensure that each region is self-sufficient in terms of providing for its own needs with a large probability. In particular, the Gale–Hoffman inequalities are used to represent the conditions on the existence of a feasible network flow. The solution method rests on two pillars. A ...

  • threshold boolean form for joint Probabilistic Constraints with random technology matrix
    Mathematical Programming, 2014
    Co-Authors: Alexander Kogan, Miguel A Lejeune
    Abstract:

    We develop a new modeling and solution method for stochastic programming problems that include a joint Probabilistic Constraint in which the multirow random technology matrix is discretely distributed. We binarize the probability distribution of the random variables in such a way that we can extract a threshold partially defined Boolean function (pdBf) representing the Probabilistic Constraint. We then construct a tight threshold Boolean minorant for the pdBf. Any separating structure of the tight threshold Boolean minorant defines sufficient conditions for the satisfaction of the Probabilistic Constraint and takes the form of a system of linear Constraints. We use the separating structure to derive three new deterministic formulations for the studied stochastic problem, and we derive a set of strengthening valid inequalities. A crucial feature of the new integer formulations is that the number of integer variables does not depend on the number of scenarios used to represent uncertainty. The computational study, based on instances of the stochastic capital rationing problem, shows that the mixed-integer linear programming formulations are orders of magnitude faster to solve than the mixed-integer nonlinear programming formulation. The method integrating the valid inequalities in a branch-and-bound algorithm has the best performance.

  • threshold boolean form for joint Probabilistic Constraints with random technology matrix
    2013
    Co-Authors: Alexander Kogan, Miguel A Lejeune
    Abstract:

    We develop a new modeling and exact solution method for stochastic programming problems that include a joint Probabilistic Constraint in which the multirow random technology matrix is discretely distributed. We binarize the probability distribution of the random variables in such a way that we can extract a threshold partially defined Boolean function (pdBf) representing the Probabilistic Constraint. We then construct a tight threshold Boolean minorant for the pdBf. Any separating structure of the tight threshold Boolean minorant defines sufficient conditions for the satisfaction of the Probabilistic Constraint and takes the form of a system of linear Constraints. We use the separating structure to derive three new deterministic formulations equivalent to the studied stochastic problem. We derive a set of strengthening valid inequalities for the reformulated problems. A crucial feature of the new integer formulations is that the number of integer variables does not depend on the number of scenarios used to represent uncertainty. The computational study, based on instances of the stochastic capital rationing problem, shows that the MIP reformulations are orders of magnitude faster to solve than the MINLP formulation. The method integrating the derived valid inequalities in a branch-and-bound algorithm has the best performance.

  • an exact solution approach for portfolio optimization problems under stochastic and integer Constraints
    Operations Research, 2009
    Co-Authors: Pierre Bonami, Miguel A Lejeune
    Abstract:

    In this paper, we study extensions of the classical Markowitz mean-variance portfolio optimization model. First, we consider that the expected asset returns are stochastic by introducing a Probabilistic Constraint, which imposes that the expected return of the constructed portfolio must exceed a prescribed return threshold with a high confidence level. We study the deterministic equivalents of these models. In particular, we define under which types of probability distributions the deterministic equivalents are second-order cone programs and give closed-form formulations. Second, we account for real-world trading Constraints (such as the need to diversify the investments in a number of industrial sectors, the nonprofitability of holding small positions, and the Constraint of buying stocks by lots) modeled with integer variables. To solve the resulting problems, we propose an exact solution approach in which the uncertainty in the estimate of the expected returns and the integer trading restrictions are simultaneously considered. The proposed algorithmic approach rests on a nonlinear branch-and-bound algorithm that features two new branching rules. The first one is a static rule, called idiosyncratic risk branching, while the second one is dynamic and is called portfolio risk branching. The two branching rules are implemented and tested using the open-source Bonmin framework. The comparison of the computational results obtained with state-of-the-art MINLP solvers ( MINLP_BB and CPLEX ) and with our approach shows the effectiveness of the latter, which permits to solve to optimality problems with up to 200 assets in a reasonable amount of time. The practicality of the approach is illustrated through its use for the construction of four fund-of-funds now available on the major trading markets.

Jacek Gondzio - One of the best experts on this subject based on the ideXlab platform.

  • a Probabilistic Constraint approach for robust transmit beamforming with imperfect channel information
    IEEE Transactions on Signal Processing, 2011
    Co-Authors: Peijung Chung, Jacek Gondzio
    Abstract:

    Transmit beamforming (or precoding) is a powerful technique for enhancing performance of wireless multiantenna communication systems. Standard transmit beamformers require perfect channel state information at the transmitter (CSIT) and are sensitive to errors in channel estimation. In practice, such errors are inevitable due to finite feedback resources, quantization errors and other physical Constraints. Hence, robustness has become a crucial issue recently. Among two popular robust designs, the stochastic approach exploits channel statistics and optimizes the average system performance while the maximin approach considers errors as deterministic and optimizes the worst case performance. The latter usually leads to a very conservative design against extreme (but rare) conditions which may occur at a very low probability. In this paper, we propose a more flexible approach that maximizes the average signal-to-noise ratio (SNR) and takes the extreme conditions into account using the probability with which they may occur. Simulation results show that the proposed beamformer offers higher robustness against channel estimation errors than several popular transmit beamformers.

  • a Probabilistic Constraint approach for robust transmit beamforming with imperfect channel information
    European Signal Processing Conference, 2009
    Co-Authors: Peijung Chung, Jacek Gondzio
    Abstract:

    Transmit beamforming is a powerful technique for enhancing performance of wireless communication systems. Most existing transmit beamforming techniques require perfect channel state information at the transmitter (CSIT), which is typically not available in practice. In such situations, the design should take errors in CSIT into account to avoid performance degradation. Among two popular robust designs, the stochastic approach exploits channel statistics and optimizes the average system performance. The maximin approach considers errors as deterministic and optimizes the worst-case performance. The latter usually leads to conservative results as the extreme (but rare) conditions may occur at a very low probability. In this work, we propose a more flexible approach that maximizes the average signal-to-noise ratio (SNR) and takes the extreme conditions into account proportionally. Simulation results show that the proposed beamformer offers higher robustness against channel estimation errors than several popular transmit beamformers.

  • robust transmit beamforming based on Probabilistic Constraint
    European Signal Processing Conference, 2008
    Co-Authors: Peijung Chung, Jacek Gondzio, B Mulgrew
    Abstract:

    Transmit beamforming is a powerful technique for enhancing performance of wireless communication systems. Most existing transmit beamforming techniques require perfect channel state information at the transmitter (CSIT), which is typically not available in practice. In such situations, the design should take into account errors in the channel estimates, so that the beamformers are less sensitive to these errors. Two robust approaches are widely used. The stochastic approach optimizes the average performance of the system and assumes that the statistics, such as mean and covariance, of the errors are known. The maximin approach assumes that the errors belong to a worst-case uncertainty region and optimizes the worst-case system performance. This type of design usually leads to conservative results as the worst-case conditions may occur at a very low probability. In this paper, we propose a more flexible approach that optimizes the average beamforming performance and takes the extreme (but rare) conditions into account proportionally. Simulation results show that the proposed beamformer offers higher robustness against errors in CSIT than serval state-of-the-art beamformers.

Chong Jin Ong - One of the best experts on this subject based on the ideXlab platform.

  • Constraint admissible sets for systems with soft Constraints and their application in model predictive control
    International Journal of Robust and Nonlinear Control, 2012
    Co-Authors: Chen Wang, Chong Jin Ong
    Abstract:

    SUMMARY Constraint-admissible sets have been widely used in the study of control systems with hard Constraints. This paper proposes a generalization of the maximal Constraint-admissible set for constrained linear discrete-time systems to the case where soft or Probabilistic Constraints are present. Defined in the most obvious way, the maximal Probabilistic Constraint-admissible set is not invariant. An inner approximation of it is proposed which is invariant and has other nice properties. The application of this approximate set in a model predictive control framework with Probabilistic Constraints is discussed, including the feasibility and stability of the resulting closed-loop system. The effectiveness of the proposed approach is illustrated via numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.

  • linear systems with chance Constraints Constraint admissible set and applications in predictive control
    Conference on Decision and Control, 2009
    Co-Authors: Chen Wang, Chong Jin Ong, Melvyn Sim
    Abstract:

    Maximal Constraint-admissible sets have been widely used in the study of linear systems with hard Constraints. This paper proposes a generalization of the maximal Constraint-admissible set to the case where chance or Probabilistic Constraints are present in a linear system. Properties of the Probabilistic Constraint-admissible set are discussed and it is shown that the maximal chance Constraint-admissible set is not time invariant. An inner approximation to the maximal set is then proposed to ensure its invariance property. This approximate set is then applied in the design of a model predictive controller for a linear system with additive disturbances and chance Constraints. Feasibility and stability of the resultant closed-loop system are discussed.

George L Nemhauser - One of the best experts on this subject based on the ideXlab platform.

  • an integer programming approach for linear programs with Probabilistic Constraints
    Mathematical Programming, 2009
    Co-Authors: James Luedtke, Shabbir Ahmed, George L Nemhauser
    Abstract:

    Linear programs with joint Probabilistic Constraints (PCLP) are difficult to solve because the feasible region is not convex. We consider a special case of PCLP in which only the right-hand side is random and this random vector has a finite distribution. We give a mixed-integer programming formulation for this special case and study the relaxation corresponding to a single row of the Probabilistic Constraint. We obtain two strengthened formulations. As a byproduct of this analysis, we obtain new results for the previously studied mixing set, subject to an additional knapsack inequality. We present computational results which indicate that by using our strengthened formulations, instances that are considerably larger than have been considered before can be solved to optimality.

  • an integer programming approach for linear programs with Probabilistic Constraints
    Integer Programming and Combinatorial Optimization, 2007
    Co-Authors: James Luedtke, Shabbir Ahmed, George L Nemhauser
    Abstract:

    Linear programs with joint Probabilistic Constraints (PCLP) are known to be highly intractable due to the non-convexity of the feasible region. We consider a special case of PCLP in which only the right-hand side is random and this random vector has a finite distribution. We present a mixed integer programming formulation and study the relaxation corresponding to a single row of the Probabilistic Constraint, yielding two strengthened formulations. As a byproduct of this analysis, we obtain new results for the previously studied mixing set, subject to an additional knapsack inequality. We present computational results that indicate that by using our strengthened formulations, large scale instances can be solved to optimality.