Stuart C. Schwartz

Princeton University, Princeton, New Jersey, United States

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Publications (39)47.51 Total impact

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    ABSTRACT: The problem addressed is source localization from time differences of arrival (TDOA). This problem is also referred to as hyperbolic localization and it is non-convex in general. Traditional solutions proposed in the literature have generally poor robustness to errors in the TDOA estimates. More recent methods, which relax the non-convex problem to a convex optimization by applying a semi-definite relaxation (SDR) method, were found to be more robust to TDOA errors than the traditional methods. However, the SDR methods are not optimal in general. In this paper, three convex optimization methods with different computational costs are proposed to improve the hyperbolic localization accuracy. The first method takes an SDR approach to relax the hyperbolic localization to a convex optimization. The second method follows a linearized formulation of the problem and seeks for a biased estimate of improved accuracy. The first two methods perform comparably when the source is inside the convex hull of the sensors. When the source is located outside, the second approach performs better, at the cost of higher computation. A third method is proposed by exploiting the source sparsity. With this, the hyperbolic localization is formulated as an ℓ<sub>1</sub>-regularization problem, where the ℓ<sub>1</sub>-norm is used as source sparsity constraint. Computer simulations show that the ℓ<sub>1</sub>-regularization can offer further improved accuracy, but at the cost of additional computational effort.
    Full-text · Conference Paper · Mar 2011
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    ABSTRACT: The problem addressed is source localization via time-difference- of-arrival estimation in a multipath channel. Solving this localization problem typically implies cross-correlating the noisy signals received at pairs of sensors deployed within reception range of the source. Correlation-based localization is severely degraded by the presence of multipath. The proposed method exploits the sparsity of the multipath channel for estimation of the line-of-sight component. The time-delay estimation problem is formulated as an �∫ 1-regularization problem, where the �∫ 1-norm is used as a channel sparsity constraint. The proposed method requires knowledge of the pulse shape of the transmitted signal, but it is blind in the sense that information on the specific transmitted symbols is not required at the sensors. Simulation results show that the proposed method delivers higher accuracy and robustness to noise compared to conventional or even super-resolution MUSIC time-difference-of- arrival source localization methods.
    Full-text · Conference Paper · Jan 2011
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    ABSTRACT: The Ziv-Zakai bound (ZZB) is developed for the estimation error of a radiating source located in a plane, and observed by sensors widely distributed over the same plane. The source is non-cooperative in the sense that the transmitted waveform and its timing are unknown to the sensors. The sensors do have however, information on the power spectral density of the source. Moreover, sensors have ideal mutual time and phase synchronization. The source location is estimated by coherent processing exploiting the amplitude and phase information between pairs of sensors. An analytical expression is developed for the ZZB relating the estimation error to the carrier frequency, signal bandwidth, the number of sensors, and their location. Numerical examples demonstrate that the ZZB closely predicts the performance of the maximum likelihood estimate across the full range of signal to noise ratio (SNR) values. At low SNR, the ZZB bound demonstrates performance dominated by noise, at medium SNR, the performance is dictated by the presence of sidelobes in the localization metric, and at high SNR, it is shown that the ZZB converges to the Cramer-Rao bound.
    Preview · Conference Paper · Dec 2009
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    Farhad Meshkati · H. Vincent Poor · Stuart C. Schwartz · Radu V. Balan
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    ABSTRACT: A game-theoretic model is proposed to study the cross-layer problem of joint power and rate control with quality of service (QoS) constraints in multiple-access networks. In the proposed game, each user seeks to choose its transmit power and rate in a distributed manner in order to maximize its own utility while satisfying its QoS requirements. The user's QoS constraints are specified in terms of the average source rate and an upper bound on the average delay where the delay includes both transmission and queuing delays. The utility function considered here measures energy efficiency and is particularly suitable for wireless networks with energy constraints. The Nash equilibrium solution for the proposed non-cooperative game is derived and a closed-form expression for the utility achieved at equilibrium is obtained. It is shown that the QoS requirements of a user translate into a "size" for the user which is an indication of the amount of network resources consumed by the user. Using this competitive multiuser framework, the tradeoffs among throughput, delay, network capacity and energy efficiency are studied. In addition, analytical expressions are given for users' delay profiles and the delay performance of the users at Nash equilibrium is quantified.
    Full-text · Article · Dec 2009 · IEEE Transactions on Communications
  • Farhad Meshkati · H. Vincent Poor · Stuart C. Schwartz
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    ABSTRACT: A game-theoretic approach for studying energy efficiency-delay tradeoffs in multiple-access networks is proposed. Focusing on the uplink of a code-division multiple-access (CDMA) network, a noncooperative game is considered in which each user seeks to choose a transmit power that maximizes its own utility while satisfying its (transmission) delay requirements. The utility function measures the number of reliable bits transmitted per joule of energy and the user's delay constraint is modeled as an upper bound on the delay outage probability. The Nash equilibrium for the proposed game is derived, and its existence and uniqueness are proved. Using a large-system analysis, explicit expressions for the utilities achieved at equilibrium are obtained for the matched filter, decorrelating and (linear) minimum-mean-square-error (MMSE) multiuser detectors. The effects of delay quality-of-service (QoS) constraints on the users' utilities (in bits per joule) and network capacity (i.e., the maximum number of users that can be supported) are quantified. Using the proposed framework, the tradeoffs between energy efficiency and delay are quantified in a competitive multiuser setting.
    No preview · Article · Aug 2009 · IEEE Transactions on Information Theory
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    Farhad Meshkati · Dongning Guo · H. Vincent Poor · Stuart C. Schwartz

    Full-text · Article · Jan 2008 · IEEE Transactions on Wireless Communications
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    ABSTRACT: A game-theoretic framework is used to study the effect of constellation size on the energy efficiency of wireless networks for M-QAM modulation. A non-cooperative game is proposed in which each user seeks to choose its transmit power (and possibly transmit symbol rate) as well as the constellation size in order to maximize its own utility while satisfying its delay quality-of-service (QoS) constraint. The utility function used here measures the number of reliable bits transmitted per joule of energy consumed, and is particularly suitable for energy-constrained networks. The best-response strategies and Nash equilibrium solution for the proposed game are derived. It is shown that in order to maximize its utility (in bits per joule), a user must choose the lowest constellation size that can accommodate the user's delay constraint. This strategy is different from one that would maximize spectral efficiency. Using this framework, the tradeoffs among energy efficiency, delay, throughput and constellation size are also studied and quantified. In addition, the effect of trellis-coded modulation on energy efficiency is discussed.
    Full-text · Article · Sep 2007 · IEEE Journal on Selected Areas in Communications
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    Farhad Meshkati · H. Vincent Poor · Stuart C. Schwartz
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    ABSTRACT: An overview of game-theoretic approaches to energy-efficient resource allocation in wireless networks is presented. Focusing on multiple-access networks, it is demonstrated that game theory can be used as an effective tool to study resource allocation in wireless networks with quality-of-service (QoS) constraints. A family of non-cooperative (distributed) games is presented in which each user seeks to choose a strategy that maximizes its own utility while satisfying its QoS requirements. The utility function considered here measures the number of reliable bits that are transmitted per joule of energy consumed and, hence, is particulary suitable for energy-constrained networks. The actions available to each user in trying to maximize its own utility are at least the choice of the transmit power and, depending on the situation, the user may also be able to choose its transmission rate, modulation, packet size, multiuser receiver, multi-antenna processing algorithm, or carrier allocation strategy. The best-response strategy and Nash equilibrium for each game is presented. Using this game-theoretic framework, the effects of power control, rate control, modulation, temporal and spatial signal processing, carrier allocation strategy and delay QoS constraints on energy efficiency and network capacity are quantified.
    Full-text · Article · Jun 2007
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    Farhad Meshkati · Dongning Guo · H. Vincent Poor · Stuart C. Schwartz
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    ABSTRACT: A unified approach to energy-efficient power control is proposed for code-division multiple access (CDMA) networks. The approach is applicable to a large family of multiuser receivers including the matched filter, the decorrelator, the linear minimum mean-square error (MMSE) receiver, and the (nonlinear) optimal detectors. It exploits the linear relationship that has been shown to exist between the transmit power and the output signal-to-interference-plus-noise ratio (SIR) in the large-system limit. It is shown that, for this family of receivers, when users seek to selfishly maximize their own energy efficiency, the Nash equilibrium is SIR-balanced. In addition, a unified power control (UPC) algorithm for reaching the Nash equilibrium is proposed. The algorithm adjusts the user's transmit powers by iteratively computing the large-system multiuser efficiency, which is independent of instantaneous spreading sequences. The convergence of the algorithm is proved for the matched filter, the decorrelator, and the MMSE receiver, and is demonstrated by means of simulation for an optimal detector. Moreover, the performance of the algorithm in finite-size systems is studied and compared with that of a conventional power control scheme, in which user powers depend on the instantaneous spreading sequences.
    Full-text · Article · May 2007
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    ABSTRACT: A game-theoretic framework is used to study the effect of constellation size on the energy efficiency of wireless networks for M-QAM modulation. A non-cooperative game is proposed in which each user seeks to choose its transmit power (and possibly transmit symbol rate) as well as the constellation size in order to maximize its own utility while satisfying its delay quality-of-service (QoS) constraint. The utility function used here measures the number of reliable bits transmitted per joule of energy consumed, and is particularly suitable for energy-constrained networks. The best-response strategies and Nash equilibrium solution for the proposed game are derived. It is shown that in order to maximize its utility (in bits per joule), a user must choose the lowest constellation size that can accommodate the user's delay constraint. Using this framework, the tradeoffs among energy efficiency, delay, throughput and constellation size are also studied and quantified. The effect of trellis-coded modulation on energy efficiency is also discussed
    No preview · Conference Paper · Feb 2007
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    ABSTRACT: The authors develop a centralized information fusion architecture from basic principles of information theory and Bayesian statistics. It is well known that any clustering, quantizing, or thresholding of data causes loss of information unless a sufficient statistic is computed in the processing. For the case of wideband active ranging systems, the coherent output of an optimum beamformer and a matched filter is a sufficient statistic that can be transmitted to the fusion center. For unknown target velocity, range, and bearing, the wideband space-time matched filter output can be interpreted as a multidimensional wavelet transform or a delay-scale-bearing map. In this paper, a Bayesian, joint estimation-detection approach is used for computation of sufficient statistics and multisensor information fusion. An approach borrowed from sequential Bayesian processing is used to compute prior densities for joint Bayesian estimation-detection. In this approach, a posteriori densities become priors after a coordinate transformation that transforms the outputs of each sensor to a common reference frame for all sensors. Reproducing prior densities are used to simplify Bayesian computation
    No preview · Article · Nov 2006 · IEEE Transactions on Signal Processing
  • Andrei D. Radulescu · Robert A. Calderbank · Stuart C. Schwartz
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    ABSTRACT: This paper presents a novel way to construct unitary space-time block codes suitable for differential modulation. The new codes rely on quaternionic algebra to achieve finite constellation. Among these, a particular code with a codebook of size 48 is studied and shown to be differentially decodable by means of two symbol-by-symbol decoders (each symbol having 2 bits) and one larger decoder for a size 16 constellation. Simulations in a realistic WiMAX environment show the proposed code to outperform an optimized size 48 diagonal MPSK code by 1 dB. Ways to counter reduced performance in highly mobile environments are also suggested
    No preview · Conference Paper · Oct 2006
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    Farhad Meshkati · Mung Chiang · H. Vincent Poor · Stuart C. Schwartz
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    ABSTRACT: A game-theoretic model for studying power control in multicarrier code-division multiple-access systems is proposed. Power control is modeled as a noncooperative game in which each user decides how much power to transmit over each carrier to maximize its own utility. The utility function considered here measures the number of reliable bits transmitted over all the carriers per joule of energy consumed and is particularly suitable for networks where energy efficiency is important. The multidimensional nature of users' strategies and the nonquasi-concavity of the utility function make the multicarrier problem much more challenging than the single-carrier or throughput-based-utility case. It is shown that, for all linear receivers including the matched filter, the decorrelator, and the minimum-mean-square-error detector, a user's utility is maximized when the user transmits only on its "best" carrier. This is the carrier that requires the least amount of power to achieve a particular target signal-to-interference-plus-noise ratio at the output of the receiver. The existence and uniqueness of Nash equilibrium for the proposed power control game are studied. In particular, conditions are given that must be satisfied by the channel gains for a Nash equilibrium to exist, and the distribution of the users among the carriers at equilibrium is characterized. In addition, an iterative and distributed algorithm for reaching the equilibrium (when it exists) is presented. It is shown that the proposed approach results in significant improvements in the total utility achieved at equilibrium compared with a single-carrier system and also to a multicarrier system in which each user maximizes its utility over each carrier independently
    Full-text · Article · Jul 2006 · IEEE Journal on Selected Areas in Communications
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    Farhad Meshkati · H. Vincent Poor · Stuart C. Schwartz · Radu V. Balan
    [Show abstract] [Hide abstract]
    ABSTRACT: A game-theoretic model is proposed to study the cross-layer problem of joint power and rate control with quality of service (QoS) constraints in multiple-access networks. In the proposed game, each user seeks to choose its transmit power and rate in a distributed manner in order to maximize its own utility and at the same time satisfy its QoS requirements. The user's QoS constraints are specified in terms of the average source rate and average delay. The utility function considered here measures energy efficiency and the delay includes both transmission and queueing delays. The Nash equilibrium solution for the proposed non-cooperative game is derived and a closed-form expression for the utility achieved at equilibrium is obtained. It is shown that the QoS requirements of a user translate into a "size" for the user which is an indication of the amount of network resources consumed by the user. Using this framework, the tradeoffs among throughput, delay, network capacity and energy efficiency are also studied.
    Full-text · Article · May 2006
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    ABSTRACT: This paper examines the uplink user capacity in a two-tier code division multiple access (CDMA) system with hotspot microcells when user terminal power is limited and the wireless channel is finitely-dispersive. A finitely-dispersive channel causes variable fading of the signal power at the output of the RAKE receiver. First, a two-cell system composed. of one macrocell and one embedded microcell is studied and analytical methods are developed to estimate the user capacity as a function of a dimensionless parameter that depends on the transmit power constraint and cell radius. Next, novel analytical methods are developed to study the effect of variable fading, both with and without transmit power constraints. Finally, the analytical methods are extended to estimate uplink user capacity for multicell CDMA systems, composed of multiple macrocells and multiple embedded microcells. In all cases, the analysis-based estimates are compared with and confirmed by simulation results.
    Full-text · Article · Mar 2006 · IEEE Transactions on Wireless Communications
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    Farhad Meshkati · H. Vincent Poor · Stuart C. Schwartz · Radu V. Balan
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    ABSTRACT: The energy-delay tradeoffs in wireless networks are studied using a game-theoretic framework. A multi-class multiple-access network is considered in which users choose their transmit powers, and possibly transmission rates, in a distributed manner to maximize their own utilities while satisfying their delay quality-of-service (QoS) requirements. The utility function considered here measures the number of reliable bits transmitted per Joule of energy consumed and is particularly useful for energy-constrained networks. The Nash equilibrium solution for the proposed non-cooperative game is presented and closed-form expressions for the users' utilities at equilibrium are obtained. Based on this, the losses in energy efficiency and network capacity due to presence of delay-sensitive users are quantified. The analysis is extended to the scenario where the QoS requirements include both the average source rate and a bound on the average total delay (including queuing delay). It is shown that the incoming traffic rate and the delay constraint of a user translate into a "size" for the user, which is an indication of the amount of resources consumed by the user. Using this framework, the tradeoffs among throughput, delay, network capacity and energy efficiency are also quantified.
    Full-text · Article · Feb 2006
  • Farhad Meshkati · Mung Chiang · H. Vincent Poor · Stuart C. Schwartz
    [Show abstract] [Hide abstract]
    ABSTRACT: A game-theoretic model for studying power control in multicarrier code-division multiple-access systems is proposed. Power control is modeled as a noncooperative game in which each user decides how much power to transmit over each carrier to maximize its own utility. The utility function considered here measures the number of reliable bits transmitted over all the carriers per joule of energy consumed and is particularly suitable for networks where energy efficiency is important. The multidi- mensional nature of users' strategies and the nonquasi-concavity of the utility function make the multicarrier problem much more challenging than the single-carrier or throughput-based-utility case. It is shown that, for all linear receivers including the matched filter, the decorrelator, and the minimum-mean-square-error detector, a user's utility is maximized when the user transmits only on its "best" carrier. This is the carrier that requires the least amount of power to achieve a particular target signal-to-in- terference-plus-noise ratio at the output of the receiver. The existence and uniqueness of Nash equilibrium for the proposed power control game are studied. In particular, conditions are given that must be satisfied by the channel gains for a Nash equilibrium to exist, and the distribution of the users among the carriers at equilibrium is characterized. In addition, an iterative and distributed algorithm for reaching the equilibrium (when it exists) is presented. It is shown that the proposed approach results in significant improvements in the total utility achieved at equilibrium compared with a single-carrier system and also to a multicarrier system in which each user maximizes its utility over each carrier independently.
    No preview · Article · Jan 2006
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    Lan Dong · Imad Zoghlami · Stuart C. Schwartz
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    ABSTRACT: In this paper, a novel robust tracking algorithm in compressed video is proposed. Within the framework of video compression standards, we consider how to accurately estimate motion of an object by utilizing motion vectors available in compressed video together with derived confidence measures. These confidence measures are based on DCT coefficients, spatial continuity of motion and texture measure of the object. We perform tracking directly on the compressed data and also consider tracking of an object with image scale change. In order to achieve robust tracking, we develop a system which enables us to detect object appearance change such as illumination change and occlusion by exploring the confidence measures derived above. Preliminary results indicate that our tracking algorithm works well with a variety of video sequences.
    Preview · Conference Paper · Jan 2006
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    Sung-Hyun Son · Sanjeev R Kulkarni · Stuart C Schwartz
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    ABSTRACT: A wireless sensor network with a fusion center is consid-ered to study the effects of dependent observations on the parameter estimation problem. The sensor observations are corrupted by Gaussian noise with geometric spatial correla-tion. From an energy point of view, sending all the local data to the fusion center is the most costly, but leads to optimum performance results since all the dependencies are taken into account. From an estimation accuracy point of view, send-ing only parameter estimates is the least accurate, but is the most parsimonious in terms of communication costs. Hence, this tradeoff between the energy efficiency and the estima-tion accuracy is explored by comparing the performance of maximum likelihood estimator (MLE) and the sample aver-age estimator (SAE) under various topologies and commu-nication protocols. We start by reviewing the results from the one-dimensional case and continue by extending those results to various two-dimensional topologies. Surprisingly, we discover a class of regular polygon topologies where the MLE under spatial correlation reduces to the SAE.
    Preview · Article · Jan 2006
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    ABSTRACT: In this paper, the cross-layer design problem of joint multiuser detection and power control is studied, using a game-theoretic approach that focuses on energy efficiency. The uplink of a direct-sequence code-division multiple-access data network is considered, and a noncooperative game is proposed in which users in the network are allowed to choose their uplink receivers as well as their transmit powers to maximize their own utilities. The utility function measures the number of reliable bits transmitted by the user per joule of energy consumed. Focusing on linear receivers, the Nash equilibrium for the proposed game is derived. It is shown that the equilibrium is one where the powers are signal-to-interference-plus-noise ratio-balanced with the minimum mean-square error (MMSE) detector as the receiver. In addition, this framework is used to study power-control games for the matched filter, the decorrelator, and the MMSE detector; and the receivers' performance is compared in terms of the utilities achieved at equilibrium (in bits/joule). The optimal cooperative solution is also discussed and compared with the noncooperative approach. Extensions of the results to the case of multiple receive antennas are also presented. In addition, an admission-control scheme based on maximizing the total utility in the network is proposed.
    Full-text · Article · Dec 2005 · IEEE Transactions on Communications