Exponential Expression

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 243 Experts worldwide ranked by ideXlab platform

Pooi Yuen Kam - One of the best experts on this subject based on the ideXlab platform.

  • A Refinement to the Viterbi-Viterbi Carrier Phase Estimator and an Extension to the Case With a Wiener Carrier Phase Process
    IEEE Access, 2019
    Co-Authors: Tianyu Song, Pooi Yuen Kam
    Abstract:

    We provide a theoretical foundation for further analysis and optimization of the Mth-power (MP) carrier phase estimator for MPSK modulation. Also known as the Viterbi-Viterbi (VV) estimator, it is commonly used in practice because it leads to low-latency receiver implementations. The MP carrier phase estimator first raises the received noisy signal samples to the Mth-power to remove the unknown phase modulation, and then extracts the unknown carrier phase of the mid-symbol using a weighted sum of these modulation-wiped-off received signal samples over a symmetrical observation window. Our starting point is the single-term, complex Exponential Expression for a complex sinusoid received in complex, additive, white, Gaussian noise (AWGN), which leads to a great deal of simplicity in dealing with arbitrary powers of the noisy received signal sample when compared with the conventional approach of raising the sum of signal plus noise to higher powers. The single-Exponential Expression enables us to first optimize the weighting coefficients of the MP carrier phase estimator with respect to the statistics of the AWGN, in a manner much simpler than previous approaches. Then, it enables us to apply the linear minimum mean square error (LMMSE) criterion to optimize the MP estimator with respect to both the statistics of the AWGN and the carrier phase noise that we model here as a Wiener process. Although the LMMSE MP estimator is computationally intensive for online implementation, a much less complex version is suggested that can be efficiently implemented in real time. Extensive simulation results are presented to demonstrate the improved performance of the LMMSE MP estimator over the conventional MP estimator. By using a sufficiently long symmetrical observation window, the LMMSE estimator does not suffer from the block length effect, which leads to much performance gain over the VV/MP estimator especially at high signal-to-noise ratio (SNR) and high phase noise. A phase unwrapping algorithm is also presented for accurate unwrapping of the estimated carrier phase before it is used in data detection. The proposed LMMSE carrier phase estimator is suitable for implementing a coherent receiver at all SNRs.

Tianyu Song - One of the best experts on this subject based on the ideXlab platform.

  • A Refinement to the Viterbi-Viterbi Carrier Phase Estimator and an Extension to the Case With a Wiener Carrier Phase Process
    IEEE Access, 2019
    Co-Authors: Tianyu Song, Pooi Yuen Kam
    Abstract:

    We provide a theoretical foundation for further analysis and optimization of the Mth-power (MP) carrier phase estimator for MPSK modulation. Also known as the Viterbi-Viterbi (VV) estimator, it is commonly used in practice because it leads to low-latency receiver implementations. The MP carrier phase estimator first raises the received noisy signal samples to the Mth-power to remove the unknown phase modulation, and then extracts the unknown carrier phase of the mid-symbol using a weighted sum of these modulation-wiped-off received signal samples over a symmetrical observation window. Our starting point is the single-term, complex Exponential Expression for a complex sinusoid received in complex, additive, white, Gaussian noise (AWGN), which leads to a great deal of simplicity in dealing with arbitrary powers of the noisy received signal sample when compared with the conventional approach of raising the sum of signal plus noise to higher powers. The single-Exponential Expression enables us to first optimize the weighting coefficients of the MP carrier phase estimator with respect to the statistics of the AWGN, in a manner much simpler than previous approaches. Then, it enables us to apply the linear minimum mean square error (LMMSE) criterion to optimize the MP estimator with respect to both the statistics of the AWGN and the carrier phase noise that we model here as a Wiener process. Although the LMMSE MP estimator is computationally intensive for online implementation, a much less complex version is suggested that can be efficiently implemented in real time. Extensive simulation results are presented to demonstrate the improved performance of the LMMSE MP estimator over the conventional MP estimator. By using a sufficiently long symmetrical observation window, the LMMSE estimator does not suffer from the block length effect, which leads to much performance gain over the VV/MP estimator especially at high signal-to-noise ratio (SNR) and high phase noise. A phase unwrapping algorithm is also presented for accurate unwrapping of the estimated carrier phase before it is used in data detection. The proposed LMMSE carrier phase estimator is suitable for implementing a coherent receiver at all SNRs.

Jeremy N Drummond - One of the best experts on this subject based on the ideXlab platform.

  • Solubility and Density for Cyanazine + Ethanol + Water
    Journal of Chemical & Engineering Data, 1995
    Co-Authors: Liam A Hurley, A G Jones, Jeremy N Drummond
    Abstract:

    The solubility of cyanazine in water (1) and ethanol (2) has been determined over the temperature range 10-30 o C and the whole range of solvent water mass fractions W 1 =0.0-1.0, and the densities of the resulting saturated solutions have also been measured. At each temperature, the solubility of cyanazine increases with increasing mole fraction x 2 of ethanol up to a local maximum at x 2 ≃ 0.9. The density of saturated aqueous ethanol solutions of cyanazine decreases with increasing ethanol content over the whole range. The solubility of cyanazine in aqueous ethanol at each temperature is correlated by polynomial (W 1 =0.3-1.0) and Exponential (W 1 =0.0-0.4) Expressions while the density results are fitted to an Exponential Expression

  • solubility and density for cyanazine ethanol water
    Journal of Chemical & Engineering Data, 1995
    Co-Authors: Liam A Hurley, A G Jones, Jeremy N Drummond
    Abstract:

    The solubility of cyanazine in water (1) and ethanol (2) has been determined over the temperature range 10-30 o C and the whole range of solvent water mass fractions W 1 =0.0-1.0, and the densities of the resulting saturated solutions have also been measured. At each temperature, the solubility of cyanazine increases with increasing mole fraction x 2 of ethanol up to a local maximum at x 2 ≃ 0.9. The density of saturated aqueous ethanol solutions of cyanazine decreases with increasing ethanol content over the whole range. The solubility of cyanazine in aqueous ethanol at each temperature is correlated by polynomial (W 1 =0.3-1.0) and Exponential (W 1 =0.0-0.4) Expressions while the density results are fitted to an Exponential Expression

A G Jones - One of the best experts on this subject based on the ideXlab platform.

  • SOLUBILITY AND DENSITY FOR CYANAZINE PLUS ETHANOL PLUS WATER
    Journal of Chemical & Engineering Data, 1995
    Co-Authors: La Hurley, A G Jones, Jn Drummond
    Abstract:

    The solubility of cyanazine in water (1) and ethanol (2) has been determined over the temperature range 10-30 degrees C and the whole range of solvent water mass fractions W-1 = 0.0-1.0, and the densities of the resulting saturated solutions have also been measured. At each temperature, the solubility of cyanazine increases with increasing mole fraction x(2) of ethanol up to a local maximum at x(2) similar or equal to 0.9. The density of saturated aqueous ethanol solutions of cyanazine decreases with increasing ethanol content over the whole range. The solubility of cyanazine in aqueous ethanol at each temperature is correlated by polynomial (W-1 = 0.3-1.0) and Exponential (W-1 = 0.0-0.4) Expressions while the density results are fitted to an Exponential Expression.

  • Solubility and Density for Cyanazine + Ethanol + Water
    Journal of Chemical & Engineering Data, 1995
    Co-Authors: Liam A Hurley, A G Jones, Jeremy N Drummond
    Abstract:

    The solubility of cyanazine in water (1) and ethanol (2) has been determined over the temperature range 10-30 o C and the whole range of solvent water mass fractions W 1 =0.0-1.0, and the densities of the resulting saturated solutions have also been measured. At each temperature, the solubility of cyanazine increases with increasing mole fraction x 2 of ethanol up to a local maximum at x 2 ≃ 0.9. The density of saturated aqueous ethanol solutions of cyanazine decreases with increasing ethanol content over the whole range. The solubility of cyanazine in aqueous ethanol at each temperature is correlated by polynomial (W 1 =0.3-1.0) and Exponential (W 1 =0.0-0.4) Expressions while the density results are fitted to an Exponential Expression

  • solubility and density for cyanazine ethanol water
    Journal of Chemical & Engineering Data, 1995
    Co-Authors: Liam A Hurley, A G Jones, Jeremy N Drummond
    Abstract:

    The solubility of cyanazine in water (1) and ethanol (2) has been determined over the temperature range 10-30 o C and the whole range of solvent water mass fractions W 1 =0.0-1.0, and the densities of the resulting saturated solutions have also been measured. At each temperature, the solubility of cyanazine increases with increasing mole fraction x 2 of ethanol up to a local maximum at x 2 ≃ 0.9. The density of saturated aqueous ethanol solutions of cyanazine decreases with increasing ethanol content over the whole range. The solubility of cyanazine in aqueous ethanol at each temperature is correlated by polynomial (W 1 =0.3-1.0) and Exponential (W 1 =0.0-0.4) Expressions while the density results are fitted to an Exponential Expression

Gregory S. Patience - One of the best experts on this subject based on the ideXlab platform.

  • An Exponential Expression for gas heat capacity, enthalpy, and entropy
    Experimental Thermal and Fluid Science, 2016
    Co-Authors: Charles Bruel, François-xavier Chiron, Jason Robert Tavares, Gregory S. Patience
    Abstract:

    Abstract Gas heat capacity, C P , is a fundamental extensive thermodynamic property depending on molecular transitional, vibrational and rotational energy. Empirical four-parameter polynomials approximate the sigmoidal C P trends for temperatures up to 1500 K and adding parameters extends the range. However, the fitted parameters have no physical significance and diverge beyond their range at high temperature. Here we propose an Exponential Expression for C P whose fitted parameters relate to the shape of the C P versus T curve and to molecular properties: C P  =  C P 0  +  C P ∞ [1 + ln( T )(1 +  T i / T )] exp(− T i / T ). It accounts for more than 99% of the variance with a deviation of ∼1% from 298 K to 6000 K for linear C 1 –C 7 hydrocarbons and N 2 , H 2 O, O 2 , C 2 H 4 , H 2 , CO, and CO 2 . We also provide an integrated form for enthalpy and an approximation to calculate entropy variations. This model replaces empirical polynomials with an Expression whose constants are meaningful.