Browsing by Subject "Minimax"
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Item Open Access Joint mixability of some integer matrices(Elsevier B.V., 2016) Bellini, F.; Karaşan, O. E.; Pınar, M. Ç.We study the problem of permuting each column of a given matrix to achieve minimum maximal row sum or maximum minimal row sum, a problem of interest in probability theory and quantitative finance where quantiles of a random variable expressed as the sum of several random variables with unknown dependence structure are estimated. If the minimum maximal row sum is equal to the maximum minimal row sum the matrix has been termed jointly mixable (see e.g. Haus (2015), Wang and Wang (2015), Wang et al. (2013)). We show that the lack of joint mixability (the joint mixability gap) is not significant, i.e., the gap between the minimum maximal row sum and the maximum minimal row sum is either zero or one for a class of integer matrices including binary and complete consecutive integers matrices. For integer matrices where all entries are drawn from a given set of discrete values, we show that the gap can be as large as the difference between the maximal and minimal elements of the discrete set. The aforementioned result also leads to a polynomial-time approximation algorithm for matrices with restricted domain. Computing the gap for a {0,1,2}-matrix is proved to be equivalent to finding column permutations minimizing the difference between the maximum and minimum row sums. A polynomial procedure for computing the optimum difference by solving the maximum flow problem on an appropriate graph is given. © 2016 Elsevier B.V. All rights reserved.Item Open Access The latest arrival hub location problem(Institute for Operations Research and the Management Sciences (INFORM), 2001) Kara, B. Y.; Tansel, B. Ç.The traditionally studied hub location problems in the literature pay attention to flight times but not to transient times spent at hubs for unloading, loading, and sorting operations. The transient times may constitute a significant portion of the total delivery time for cargo delivery systems. We focus on the minimization of the arrival time of the last arrived item in cargo delivery systems and develop a model that correctly computes the arrival times by taking into account both the flight times and the transient times. Nonlinear and linear integer formulations are given and computational results are provided. The effects of delays on the system performance are analyzed.Item Open Access Noise enhanced detection in the restricted Bayesian framework(IEEE, 2010) Bayram, Suat; Gezici, Sinan; Poor H.V.Effects of additive independent noise are investigated for sub-optimal detectors according to the restricted Bayes criterion. The statistics of optimal additive noise are characterized. Also, sufficient conditions for improvability or nonimprovability of detection via additive noise are obtained. A detection example is presented to study the theoretical results. ©2010 IEEE.Item Open Access Noise-enhanced M-ary hypothesis-testing in the minimax framework(IEEE, 2009-09) Bayram, Suat; Gezici, SinanIn this study, the effects of adding independent noise to observations of a suboptimal detector are studied for M-ary hypothesis-testing problems according to the minimax criterion. It is shown that the optimal additional noise can be represented by a randomization of at most M signal values under certain conditions. In addition, a convex relaxation approach is proposed to obtain an accurate approximation to the noise probability distribution in polynomial time. Furthermore, sufficient conditions are presented to determine when additional noise can or cannot improve the performance of a given detector. Finally, a numerical example is presented. © 2009 IEEE.Item Open Access Optimal detector randomization for multiuser communications systems(IEEE, 2013) Tutay, M. E.; Gezici, Sinan; Arıkan, OrhanOptimal detector randomization is studied for the downlink of a multiuser communications system, in which users can perform time-sharing among multiple detectors. A formulation is provided to obtain optimal signal amplitudes, detectors, and detector randomization factors. It is shown that the solution of this joint optimization problem can be calculated in two steps, resulting in significant reduction in computational complexity. It is proved that the optimal solution is achieved via randomization among at most min{K, Nd} detector sets, where K is the number of users and Nd is the number of detectors at each receiver. Lower and upper bounds are derived on the performance of optimal detector randomization, and it is proved that the optimal detector randomization approach can reduce the worst-case average probability of error of the optimal approach that employs a single detector for each user by up to K times. Various sufficient conditions are obtained for the improvability and nonimprovability via detector randomization. In the special case of equal crosscorrelations and noise powers, a simple solution is developed for the optimal detector randomization problem, and necessary and sufficient conditions are presented for the uniqueness of that solution. Numerical examples are provided to illustrate the improvements achieved via detector randomization.Item Open Access Optimal joint modulation classification and symbol decoding(IEEE, 2019-05) Kazıklı, Ertan; Dulek, Berkan; Gezici, SinanIn this paper, modulation classification and symbol decoding problems are jointly considered and optimal strategies are proposed under various settings. In the considered framework, there exist a number of candidate modulation formats and the aim is to decode a sequence of received signals with an unknown modulation scheme. To that aim, two different formulations are proposed. In the first formulation, the prior probabilities of the modulation schemes are assumed to be known and a formulation is proposed under the Bayesian framework. This formulation takes a constrained approach in which the objective function is related to symbol decoding performance whereas the constraint is related to modulation classification performance. The second formulation, on the other hand, addresses the case in which the prior probabilities of the modulation schemes are unknown, and provides a method under the minimax framework. In this case, a constrained approach is employed as well; however, the introduced performance metrics differ from those in the first formulation due to the absence of the prior probabilities of the modulation schemes. Finally, the performance of the proposed methods is illustrated through simulations. It is demonstrated that the proposed techniques improve the introduced symbol detection performance metrics via relaxing the constraint(s) on the modulation classification performance compared with the conventional techniques in a variety of system configurations.Item Open Access Optimal randomization of signal constellations on downlink of a multiuser DS-CDMA system(IEEE, 2013-10) Tutay, M. E.; Gezici, Sinan; Arıkan, OrhanIn this study, the jointly optimal power control with signal constellation randomization is proposed for the downlink of a multiuser communications system. Unlike a conventional system in which a fixed signal constellation is employed for all the bits of a user (for given channel conditions and noise power), power control with signal constellation randomization involves randomization/time- sharing among different signal constellations for each user. A formulation is obtained for the problem of optimal power control with signal constellation randomization, and it is shown that the optimal solution can be represented by a randomization among (K+1) or fewer distinct signal constellations for each user, where K denotes the number of users. In addition to the original nonconvex formulation, an approximate solution based on convex relaxation is derived. Then, detailed performance analysis is presented when the receivers employ symmetric signaling and sign detectors. Specifically, the maximum asymptotical improvement ratio is shown to be equal to the number of users, and the conditions under which the maximum and minimum asymptotical improvement ratios are achieved are derived. Numerical examples are presented to investigate the theoretical results, and to illustrate performance improvements achieved via the proposed approach. © 2002-2012 IEEE.Item Open Access Robust estimation in flat fading channels under bounded channel uncertainties(Elsevier, 2013-09) Donmez, M. A.; Inan, H. A.; Kozat, S. S.We investigate channel equalization problem for time-varying flat fading channels under bounded channel uncertainties. We analyze three robust methods to estimate an unknown signal transmitted through a time-varying flat fading channel. These methods are based on minimizing certain meansquare error criteria that incorporate the channel uncertainties into their problem formulations instead of directly using the inaccurate channel information that is available. We present closed-form solutions to the channel equalization problems for each method and for both zero mean and nonzero mean signals. We illustrate the performances of the equalization methods through simulations.Item Open Access Robust least squares methods under bounded data uncertainties(Academic Press, 2015) Vanli, N. D.; Donmez, M. A.; Kozat, S. S.We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems, where the estimator has imperfect data matrix and output vector information. We define the performance of an estimator relative to the performance of the optimal least squares (LS) estimator tuned to the underlying unknown data matrix and output vector, which is defined as the regret of the estimator. We then introduce an efficient robust LS estimation approach that minimizes this regret for the worst possible data matrix and output vector, where we refrain from any structural assumptions on the data. We demonstrate that minimizing this worst-case regret can be cast as a semi-definite programming (SDP) problem. We then consider the regularized and structured LS problems and present novel robust estimation methods by demonstrating that these problems can also be cast as SDP problems. We illustrate the merits of the proposed algorithms with respect to the well-known alternatives in the literature through our simulations.Item Open Access Signal and detector randomization for multiuser and multichannel communication systems(Bilkent University, 2013) Tutay, Mehmet EminRandomization can be considered as a possible approach to enhance error performance of communication systems subject to average power constraints. In the first part of this dissertation, we consider downlink of a multiuser communications system subject to an average power constraint, where randomization is employed at the transmitter and receiver sides by modeling signal levels as random variables (stochastic signals) and employing different sets of detectors via time-sharing (detector randomization), respectively. In the second part, we consider single-user systems, where we assume that there exist multiple channels between the transmitter and receiver with arbitrary noise distributions over each of them and only one of the channels can be employed for transmission at any given time. In this case, randomization is performed by choosing the channel in use according to some probability mass function and employing stochastic signaling at the transmitter. First, the jointly optimal power control with signal constellation randomization is proposed for the downlink of a multiuser communications system. Unlike a conventional system in which a fixed signal constellation is employed for all the bits of a user (for given channel conditions and noise power), power control with signal constellation randomization involves randomization/time-sharing among different signal constellations for each user. A formulation is obtained for the problem of optimal power control with signal constellation randomization, and it is shown that the optimal solution can be represented by a randomization of (K + 1) or fewer distinct signal constellations for each user, where K denotes the number of users. In addition to the original nonconvex formulation, an approximate solution based on convex relaxation is derived. Then, detailed performance analysis is presented when the receivers employ symmetric signaling and sign detectors. Specifically, the maximum asymptotical improvement ratio is shown to be equal to the number of users, and the conditions under which the maximum and minimum asymptotical improvement ratios are achieved are derived. In the literature, it is known that employing different detectors with corresponding deterministic signals via time-sharing may enhance error performance of communications systems subject to average power constraints. Motivated by this result, as a second approach, we study optimal detector randomization for the downlink of a multiuser communications system. A formulation is provided to obtain optimal signal amplitudes, detectors, and detector randomization factors. It is shown that the solution of this joint optimization problem can be calculated in two steps, resulting in significant reduction in computational complexity. It is proved that the optimal solution is achieved via randomization among at most min{K, Nd} detector sets, where K is the number of users and Nd is the number of detectors at each receiver. Lower and upper bounds are derived on the performance of optimal detector randomization, and it is proved that the optimal detector randomization approach can reduce the worst-case average probability of error of the optimal approach that employs a single detector for each user by up to K times. Various sufficient conditions are obtained for the improvability and nonimprovability via detector randomization. In the special case of equal crosscorrelations and noise powers, a simple solution is developed for the optimal detector randomization problem, and necessary and sufficient conditions are presented for the uniqueness of that solution. Next, a single-user M−ary communication system is considered in which the transmitter and the receiver are connected via multiple additive (possibly nonGaussian) noise channels, any one of which can be utilized for a given symbol transmission. Contrary to deterministic signaling (i.e., employing a fixed constellation), a stochastic signaling approach is adopted by treating the signal values transmitted for each information symbol over each channel as random variables. In particular, the joint optimization of the channel switching (i.e., time-sharing among different channels) strategy, stochastic signals, and decision rules at the receiver is performed in order to minimize the average probability of error under an average transmit power constraint. It is proved that the solution to this problem involves either one of the following: (i) deterministic signaling over a single channel, (ii) randomizing (time-sharing) between two different signal constellations over a single channel, or (iii) switching (time-sharing) between two channels with deterministic signaling over each channel. For all cases, the optimal strategies are shown to employ corresponding maximum a posteriori probability (MAP) decision rules at the receiver.Item Open Access Stochastic signal design on the downlink of a multiuser communications system(IEEE, 2012-06) Tutay, Mehmet Emin; Gezici, Sinan; Arıkan, OrhanStochastic signal design is studied for the downlink of a multiuser communications system. First, a formulation is proposed for the joint design of optimal stochastic signals. Then, an approximate formulation, which can get arbitrarily close to the optimal solution, is obtained based on convex relaxation. In addition, when the receivers employ symmetric signaling and sign detectors, it is shown that the maximum asymptotical improvement ratio is equal to the number of users, and the conditions under which that maximum asymptotical improvement ratio is achieved are presented. Numerical examples are provided to explain the theoretical results. © 2012 IEEE.Item Open Access Stochastic signaling in the presence of channel state information uncertainty(Elsevier, 2013) Goken, C.; Gezici, Sinan; Arıkan, OrhanIn this paper, stochastic signaling is studied for power-constrained scalar valued binary communications systems in the presence of uncertainties in channel state information (CSI). First, stochastic signaling based on the available imperfect channel coefficient at the transmitter is analyzed, and it is shown that optimal signals can be represented by a randomization between at most two distinct signal levels for each symbol. Then, performance of stochastic signaling and conventional deterministic signaling is compared for this scenario, and sufficient conditions are derived for improvability and nonimprovability of deterministic signaling via stochastic signaling in the presence of CSI uncertainty. Furthermore, under CSI uncertainty, two different stochastic signaling strategies, namely, robust stochastic signaling and stochastic signaling with averaging, are proposed. For the robust stochastic signaling problem, sufficient conditions are derived for reducing the problem to a simpler form. It is shown that the optimal signal for each symbol can be expressed as a randomization between at most two distinct signal values for stochastic signaling with averaging, as well as for robust stochastic signaling under certain conditions. Finally, two numerical examples are presented to explore the theoretical results.