Stuart C. Schwartz

Princeton University, Princeton, New Jersey, United States

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Publications (22)4.93 Total impact

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    IEEE Transactions on Wireless Communications 01/2008; 7:1208-1216. · 2.42 Impact Factor
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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.
    06/2007;
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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.
    05/2007;
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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 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.
    05/2006;
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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.
    02/2006;
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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.
    Proceedings of the 2006 IEEE International Conference on Multimedia and Expo, ICME 2006, July 9-12 2006, Toronto, Ontario, Canada; 01/2006
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    ABSTRACT: A unified approach to energy-efficient power control, applicable to a large family of receivers including the matched filter, the decorrelator, the (linear) minimum-mean-square-error detector (MMSE), and the individually and jointly optimal multiuser detectors, has recently been proposed for code-division-multiple-access (CDMA) networks. This unified power control (UPC) algorithm 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 large systems. Based on this principle and by computing the multiuser efficiency, the UPC algorithm updates the users' transmit powers in an iterative way to achieve the desired target SIR. In this paper, the convergence of the UPC algorithm is proved for the matched filter, the decorrelator, and the MMSE detector. In addition, the performance of the algorithm in finite-size systems is studied and compared with that of existing power control schemes. The UPC algorithm is particularly suitable for systems with randomly generated long spreading sequences (i.e., sequences whose period is longer than one symbol duration).
    11/2005;
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    ABSTRACT: In this work, the cross-layer design problem of joint multiuser detection and power control is studied using a game-theoretic approach. The uplink of a direct-sequence code division multiple access (DS-CDMA) data network is considered and a non-cooperative 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 SIR-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 non-cooperative 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.
    08/2005;
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    ABSTRACT: Energy efficiency, low latency, high estimation accuracy, and fast convergence are important goals in distributed incremental estimation algorithms for sensor networks. One approach that adds flexibility in achieving these goals is clustering. In this paper, the framework of distributed incremental estimation is extended by allowing clustering amongst the nodes. Among the observations made is that a scaling law exists where the estimation accuracy increases proportionally with the number of clusters. The distributed parameter estimation problem is posed as a convex optimization problem involving a social cost function and data from the sensor nodes. An in-cluster algorithm is then derived using the incremental subgradient method. Sensors in each cluster successively update a cluster parameter estimate based on local data, which is then passed on to a fusion center for further processing. We prove convergence results for the distributed in-cluster algorithm, and provide simulations that demonstrate the benefits clustering for least squares and robust estimation in sensor networks.
    07/2005;
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    Farhad Meshkati, H. Vincent Poor, Stuart C. Schwartz
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    ABSTRACT: A game-theoretic approach for studying power control in multiple-access networks with transmission delay constraints is proposed. A non-cooperative power control game is considered in which each user seeks to choose a transmit power that maximizes its own utility while satisfying the user's 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 minimum mean square error multiuser detectors. The effects of delay constraints on the users' utilities (in bits/Joule) and network capacity (i.e., the maximum number of users that can be supported) are quantified. Comment: To apprear in the proceedings of the 2005 IEEE International Symposium on Information Theory, Adelaide, Australia, September 4-9, 2005
    06/2005;
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    Juhua Zhu, Stuart C. Schwartz, Bede Liu
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    ABSTRACT: Accurate foreground segmentation is a difficult task due to such factors as illumination variation, occlusion, background movements, and noise. In this paper we present a novel adaptive transform domain approach for foreground segmentation in video sequences. A set of DCT-based features is employed to exploit the spatial and temporal correlation in the video sequences. We maintain an adaptive background model and make a decision based on the distance between the features of the current frame and that of the background model. Additional higher level processing is employed to deal with the variation of the environment and to improve the accuracy of segmentation. The approach is shown to be insensitive to illumination change and to noise. It also overcomes many common difficulties of segmentation such as foreground aperture, and moved background objects. The algorithm can perform in real-time.
    01/2005; 2:685-688.
  • IEEE Transactions on Communications. 01/2005; 53:1885-1894.
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    Stuart C. Schwartz, Kobayashi Hisashi, Ma Xiaoqiang
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    ABSTRACT: Estimating a channel that is subject to frequency-selective Rayleigh fading is a challenging problem in an orthogonal frequency division multiplexing (OFDM) system. We propose three EM-based algorithms to efficiently estimate the channel impulse response (CIR) or channel frequency response of such a system operating on a channel with multipath fading and additive white Gaussian noise (AWGN). These algorithms are capable of improving the channel estimate by making use of a modest number of pilot tones or using the channel estimate of the previous frame to obtain the initial estimate for the iterative procedure. Simulation results show that the bit error rate (BER) as well as the mean square error (MSE) of the channel can be significantly reduced by these algorithms. We present simulation results to compare these algorithms on the basis of their performance and rate of convergence. We also derive Cramer-Rao-like lower bounds for the unbiased channel estimate, which can be achieved via these EM-based algorithms. It is shown that the convergence rate of two of the algorithms is independent of the length of the multipath spread. One of them also converges most rapidly and has the smallest overall computational burden.
    EURASIP Journal on Advances in Signal Processing. 01/2004;
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    ABSTRACT: This paper studies the number of voice users (user capacity) supported on the uplink of a single-macrocell/single-microcell CDMA system. A \hotspot" microcell is embedded within a larger macrocell and operates over the same bandwidth as the larger cell. Analytic methods are presented for computing user capacity which account for propagation loss, multiple-access interference, power-control and random locations of user terminals, as well as two distinct methods by which users select base stations (tiers). Along with the exact user capacity, a technique for making accurate approximations is also presented. Simulation results verify both the exact and approximate analytical methods. This simulation is also employed to study the capacity gains of a third, more optimal, tier-selection scheme. These results point to diierences in capacity performance based on the tier-selection method as well as on the traac density within the hotspot region.
    IEEE Transactions on Wireless Communications. 01/2003; 2:364-374.
  • Juhua Zhu, Stuart C. Schwartz, Bede Liu
    Signal and Image Processing (SIP 2003), Proceedings of the IASTED International Conference, August 13-15, 2003, Honolulu, HI, USA; 01/2003
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    Tim Dyson, Stuart C. Schwartz
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    ABSTRACT: Nonlinear diffusions defined by stochastic differential equations (s.d.e.) which admit exact recursive filtering solutions for the associated (unnormalized) conditional density (UCD) are presented. The diffusions are characterized by conditions on the s.d.e. drift and diffusion coefficient pair which admit a C¿ transformation to an equivalent diffusion having linear dynamics.
    Decision and Control, 1984. The 23rd IEEE Conference on; 01/1985
  • Stuart C. Schwartz, Kenneth S. Vastola
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    ABSTRACT: A general receiver is developed for the optimum detection of stochastic signals in narrowband non-Gaussian noise. Exploiting the Middleton Class A noise model, we obtain a generalization of the estimator-correlator structure: the likelihood ratio processor involves a series of estimator-correlators which then get exponentiated, weighted and summed. It appears that for most situations of interest the series involves just a few terms; as indicated by preliminary examples, three or four terms generally suffice to closely approximate the optimum receiver.
    Decision and Control, 1983. The 22nd IEEE Conference on; 01/1984
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    Peter J. Denning, Stuart C. Schwartz
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    ABSTRACT: A program's working set W (t, T) at time t is the set of distinct pages among the T most recently referenced pages. Relations between the average working-set size, the missing-page rate, and the interreference-interval distribution may be derived both from time-average definitions and from ensemble-average (statistical) definitions. An efficient algorithm for estimating these quantities is given. The relation to LRU (least recently used) paging is characterized. The independent-reference model, in which page references are statistically independent, is used to assess the effects of interpage dependencies on working-set size observations. Under general assumptions, working-set size is shown to be normally distributed.
    Communications of the ACM 01/1972; 15:191-198. · 2.51 Impact Factor
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    Peter J. Denning, Stuart C. Schwartz
    01/1971
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    ABSTRACT: In this paper, a unified approach to power control is proposed for a large family of receivers which includes the matched filter, decorrelator, and minimum mean square error detectors as well as the individually and jointly optimal multiuser detectors. The proposed algorithm exploits the linear relationship that has been shown to exist between the transmit power and the out-put signal to noise plus interference ratio in large sys-tems. Simulation is used to show the convergence of the proposed power control scheme and demonstrate its per-formance in finite-size systems.