Moment Generating Function

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H. Jafarkhani - One of the best experts on this subject based on the ideXlab platform.

  • Performance evaluation of super-orthogonal space-time trellis codes using a Moment Generating Function-based approach
    GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489), 2003
    Co-Authors: M.k. Simon, H. Jafarkhani
    Abstract:

    We extend the method based on the Moment Generating Function (MGF), previously applied to analyzing the performance of orthogonal space-time block and trellis codes, to super-orthogonal codes that combine set-partitioning with a super set of orthogonal space-time block codes in such a way as to provide full diversity with increased rate and improved coding gain. It is shown that the maximum-likelihood (ML) metric and expressions for the pairwise error probability (PEP), previously developed for the Alamouti code combined with multidimensional trellis-coded modulation (TCM), can be readily extended to the super-orthogonal case.

  • Performance evaluation of super-orthogonal space-time trellis codes using a Moment Generating Function-based approach
    IEEE Transactions on Signal Processing, 2003
    Co-Authors: M.k. Simon, H. Jafarkhani
    Abstract:

    A new class of space-time codes called super-orthogonal trellis codes was introduced that combine set-partitioning with a super set of orthogonal space-time block codes in such a way as to provide full diversity with increased rate and improved coding gain over previous space-time trellis code (STTC) constructions. Here, we extend the Moment Generating Function-based method, which was previously applied to analyzing the performance of space-time block orthogonal and trellis codes, to the above-mentioned super-orthogonal codes. It is shown that the maximum-likelihood metric and expressions for the pairwise error probability previously developed for the Alamouti (1998) space-time block code combined with multidimensional trellis-coded modulation can be readily extended to the super-orthogonal case. As such, the evaluation of the pairwise error probability for the latter can be performed in a similar manner to that previously described with the specific results depending on the particular trellis code design.

M.k. Simon - One of the best experts on this subject based on the ideXlab platform.

  • Performance evaluation of super-orthogonal space-time trellis codes using a Moment Generating Function-based approach
    GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489), 2003
    Co-Authors: M.k. Simon, H. Jafarkhani
    Abstract:

    We extend the method based on the Moment Generating Function (MGF), previously applied to analyzing the performance of orthogonal space-time block and trellis codes, to super-orthogonal codes that combine set-partitioning with a super set of orthogonal space-time block codes in such a way as to provide full diversity with increased rate and improved coding gain. It is shown that the maximum-likelihood (ML) metric and expressions for the pairwise error probability (PEP), previously developed for the Alamouti code combined with multidimensional trellis-coded modulation (TCM), can be readily extended to the super-orthogonal case.

  • Performance evaluation of super-orthogonal space-time trellis codes using a Moment Generating Function-based approach
    IEEE Transactions on Signal Processing, 2003
    Co-Authors: M.k. Simon, H. Jafarkhani
    Abstract:

    A new class of space-time codes called super-orthogonal trellis codes was introduced that combine set-partitioning with a super set of orthogonal space-time block codes in such a way as to provide full diversity with increased rate and improved coding gain over previous space-time trellis code (STTC) constructions. Here, we extend the Moment Generating Function-based method, which was previously applied to analyzing the performance of space-time block orthogonal and trellis codes, to the above-mentioned super-orthogonal codes. It is shown that the maximum-likelihood metric and expressions for the pairwise error probability previously developed for the Alamouti (1998) space-time block code combined with multidimensional trellis-coded modulation can be readily extended to the super-orthogonal case. As such, the evaluation of the pairwise error probability for the latter can be performed in a similar manner to that previously described with the specific results depending on the particular trellis code design.

F. Dicesare - One of the best experts on this subject based on the ideXlab platform.

  • Integration of Petri nets and Moment Generating Function approaches for system performance evaluation
    Journal of Systems Integration, 1993
    Co-Authors: M. Zhou, F. Dicesare
    Abstract:

    This article integrates arbitrary stochastic Petri nets (ASPN) and Moment Generating Function approaches for performance evaluation of discrete event dynamic systems (DEDS). These systems include computer-integrated manufacturing systems, resource-shared distributed systems, and communication networks. ASPN can describe various DEDS in which the time duration for activities may be a random variable of arbitrary distributions. In ASPN models, transitions with firing delays of general distributions are used to model these activities. Using our proposed performance analysis methodology, we first represent a system as an ASPN model, then generate its reachability graph and convert it into a state machine Petri net, derive the transfer Functions of interesting performance measures through stepwise reductions, and finally obtain the analysis results. This method makes it possible to obtain analytical solutions of important performance indices. We use a robotic assembly system to illustrate the method. We obtain several important performance measures of a closed-form. Finally, we discuss the limitations of this approach and future research.

  • A Moment Generating Function based approach for evaluating extended stochastic Petri Nets
    IEEE Transactions on Automatic Control, 1993
    Co-Authors: F. Dicesare, M.c. Zhou
    Abstract:

    A Moment-Generating-Function (MGF)-based approach for performance analysis of extended stochastic Petri nets (ESPNs) is presented. The method integrates Petri nets, MGF and stochastic network concepts, and Mason's rule into a tool for evaluating various discrete-event dynamic systems. The ESPNs are modeled, given the specification of a system. Then, the state machine PN is derived, the transfer Functions based on the MGFs of the related transitions are found, the network is reduced to a single transition with its transfer Function for each performance measure, and system performance is calculated. Firing delays of transitions in ESPNs can be either deterministic or stochastic with an extended distribution. Three fundamental structures that can be reduced into a single transition are discussed. The machine-repairman model with a buffer is given as an example to illustrate the method for evaluating performance parameters.

  • Moment Generating Function approach to performance analysis of extended stochastic Petri nets
    Proceedings. 1991 IEEE International Conference on Robotics and Automation, 1991
    Co-Authors: F. Dicesare, M. Zhou
    Abstract:

    A Moment Generating Function approach for performance analysis of extended stochastic Petri nets (ESPN) is proposed. In ESPN, firing delays of transitions can be either deterministic or stochastic with an extended distribution. Transfer Functions for transitions are first defined based on Moment Generating Functions of all transitions and then used to evaluate system performance. Three fundamental structures that can be reduced into a single transition are discussed. Two examples are given to illustrate the proposed approach for system performance evaluation. The advantages and limitations of such an approach are discussed, and future research directions are indicated.

  • ICRA - Moment Generating Function approach to performance analysis of extended stochastic Petri nets
    Proceedings. 1991 IEEE International Conference on Robotics and Automation, 1991
    Co-Authors: F. Dicesare, M. Zhou
    Abstract:

    A Moment Generating Function approach for performance analysis of extended stochastic Petri nets (ESPN) is proposed. In ESPN, firing delays of transitions can be either deterministic or stochastic with an extended distribution. Transfer Functions for transitions are first defined based on Moment Generating Functions of all transitions and then used to evaluate system performance. Three fundamental structures that can be reduced into a single transition are discussed. Two examples are given to illustrate the proposed approach for system performance evaluation. The advantages and limitations of such an approach are discussed, and future research directions are indicated. >

  • Matrix Moment Generating Function based approach for evaluating extended stochastic Petri nets
    Conference Proceedings 1991 IEEE International Conference on Systems Man and Cybernetics, 1991
    Co-Authors: Zhihuai Wang, F. Dicesare, M. Zhou
    Abstract:

    The authors present a matrix Moment Generating Function based approach for performance analysis of extended stochastic Petri nets. Three fundamental structures that can be reduced into a single transition matrix are discussed. One example is given to illustrate the proposed approach for system performance evaluation.

M. Zhou - One of the best experts on this subject based on the ideXlab platform.

  • Integration of Petri nets and Moment Generating Function approaches for system performance evaluation
    Journal of Systems Integration, 1993
    Co-Authors: M. Zhou, F. Dicesare
    Abstract:

    This article integrates arbitrary stochastic Petri nets (ASPN) and Moment Generating Function approaches for performance evaluation of discrete event dynamic systems (DEDS). These systems include computer-integrated manufacturing systems, resource-shared distributed systems, and communication networks. ASPN can describe various DEDS in which the time duration for activities may be a random variable of arbitrary distributions. In ASPN models, transitions with firing delays of general distributions are used to model these activities. Using our proposed performance analysis methodology, we first represent a system as an ASPN model, then generate its reachability graph and convert it into a state machine Petri net, derive the transfer Functions of interesting performance measures through stepwise reductions, and finally obtain the analysis results. This method makes it possible to obtain analytical solutions of important performance indices. We use a robotic assembly system to illustrate the method. We obtain several important performance measures of a closed-form. Finally, we discuss the limitations of this approach and future research.

  • Moment Generating Function approach to performance analysis of extended stochastic Petri nets
    Proceedings. 1991 IEEE International Conference on Robotics and Automation, 1991
    Co-Authors: F. Dicesare, M. Zhou
    Abstract:

    A Moment Generating Function approach for performance analysis of extended stochastic Petri nets (ESPN) is proposed. In ESPN, firing delays of transitions can be either deterministic or stochastic with an extended distribution. Transfer Functions for transitions are first defined based on Moment Generating Functions of all transitions and then used to evaluate system performance. Three fundamental structures that can be reduced into a single transition are discussed. Two examples are given to illustrate the proposed approach for system performance evaluation. The advantages and limitations of such an approach are discussed, and future research directions are indicated.

  • ICRA - Moment Generating Function approach to performance analysis of extended stochastic Petri nets
    Proceedings. 1991 IEEE International Conference on Robotics and Automation, 1991
    Co-Authors: F. Dicesare, M. Zhou
    Abstract:

    A Moment Generating Function approach for performance analysis of extended stochastic Petri nets (ESPN) is proposed. In ESPN, firing delays of transitions can be either deterministic or stochastic with an extended distribution. Transfer Functions for transitions are first defined based on Moment Generating Functions of all transitions and then used to evaluate system performance. Three fundamental structures that can be reduced into a single transition are discussed. Two examples are given to illustrate the proposed approach for system performance evaluation. The advantages and limitations of such an approach are discussed, and future research directions are indicated. >

  • Matrix Moment Generating Function based approach for evaluating extended stochastic Petri nets
    Conference Proceedings 1991 IEEE International Conference on Systems Man and Cybernetics, 1991
    Co-Authors: Zhihuai Wang, F. Dicesare, M. Zhou
    Abstract:

    The authors present a matrix Moment Generating Function based approach for performance analysis of extended stochastic Petri nets. Three fundamental structures that can be reduced into a single transition matrix are discussed. One example is given to illustrate the proposed approach for system performance evaluation.

Adolfo V. T. Cartaxo - One of the best experts on this subject based on the ideXlab platform.

  • Moment Generating Function for the Rigorous Performance Assessment of Direct-Detection Baseband OFDM Communication Systems
    Journal of Lightwave Technology, 2012
    Co-Authors: João L. Rebola, Adolfo V. T. Cartaxo
    Abstract:

    A new Moment Generating Function (MGF) is proposed to assess rigorously the performance of optically preamplified receivers with direct-detection employing baseband orthogonal frequency division multiplexing (OFDM). By comparison with Monte Carlo simulation, the proposed MGF-based method shows very good accuracy when predicting the bit error probability for arbitrary optical and electrical filters, different numbers of OFDM subcarriers, and double sideband and single sideband optical OFDM signals. Its good accuracy when estimating the bit error probability in each individual subcarrier is also demonstrated. The new MGF-based method exhibits a significant improvement of accuracy when compared to the MGF-based method previously reported in the literature, especially for filter bandwidths not exceeding the OFDM signal bandwidth, which is the range corresponding to the optimum filter bandwidth.

  • Bit error probability evaluation in optically preamplified direct-detection OFDM systems using the Moment Generating Function
    IEEE OSA Journal of Optical Communications and Networking, 2012
    Co-Authors: João L. Rebola, Adolfo V. T. Cartaxo
    Abstract:

    A novel method that allows the evaluation of the performance of an optically preamplified direct-detection baseband orthogonal frequency division multiplexing (OFDM) system with arbitrary optical and electrical filtering at the optical receiver is proposed. The method is based on the Moment Generating Function of the symbol detected in each OFDM subcarrier after equalization and relies on the assumption that the noise samples at the fast Fourier transform (FFT) block input at the receiver side are practically uncorrelated. It is shown that, for typical filter bandwidths used in direct-detection optical OFDM systems (similar to or exceeding the OFDM signal bandwidth), the proposed method provides reasonably accurate estimates of the bit error probability for different electrical and optical filter types with various bandwidths, and for different numbers of OFDM subcarriers. For filter bandwidths smaller than the OFDM signal bandwidth, the proposed method becomes inaccurate due to the high correlation between the noise samples at the FFT block input.

  • Using the Moment Generating Function for the performance assessment of optically preamplified direct-detection OFDM systems
    2011 SBMO IEEE MTT-S International Microwave and Optoelectronics Conference (IMOC 2011), 2011
    Co-Authors: João L. Rebola, Adolfo V. T. Cartaxo
    Abstract:

    A new method based on the Moment Generating Function (MGF) is proposed to evaluate the performance of an orthogonal frequency division multiplexing (OFDM) system with optical preamplification and direct-detection at the optical receiver, which takes into account arbitrary optical and electrical filtering at the optical receiver. The accuracy of the proposed method is investigated by comparison of the bit error probability obtained from the MGF with the estimates obtained from Monte Carlo simulation, for different electrical filter types with various bandwidths and for a different number of OFDM subcarriers. It is shown that the proposed method has a good accuracy, for bandwidths of the electrical filter typically used in optical OFDM systems (larger than the OFDM signal bandwidth).