Leveraging the Gaussian Q-Function Approximation for Error Metrics Assessment of Digital Modulation Schemes in α–κ–μ Fading Channel
Leveraging the Gaussian Q-Function Approximation for Error Metrics Assessment of Digital Modulation Schemes in α–κ–μ Fading Channel |
||
|
||
© 2024 by IJETT Journal | ||
Volume-72 Issue-7 |
||
Year of Publication : 2024 | ||
Author : Jyoti Gupta, Ashish Goel |
||
DOI : 10.14445/22315381/IJETT-V72I7P132 |
How to Cite?
Jyoti Gupta, Ashish Goel, "Leveraging the Gaussian Q-Function Approximation for Error Metrics Assessment of Digital Modulation Schemes in α–κ–μ Fading Channel," International Journal of Engineering Trends and Technology, vol. 72, no. 7, pp. 296-301, 2024. Crossref, https://doi.org/10.14445/22315381/IJETT-V72I7P132
Abstract
This research includes the application of a Gaussian Q-function approximation for the error metrics analysis of communication systems. The Bit Error Rate (BER) and Symbol Error Probability (SEP) are paramount metrics for assessing wireless communication systems. The inherent fluctuation in signal intensity induced by fading effects necessitates a thorough analysis of error performance. The Gaussian Q-function appears to be an effective mathematical tool for calculating error probability in the context of random changes in channel strength. The Gaussian Q-function approximation is crucial for dealing with fading channels in communication systems. Leveraging the Gaussian Q-function approximations simplifies computations, boosting the utility of the proposed methodology in real-world communication scenarios. The present work generates a more accurate and simple approximate solution for error rate analysis for numerous modulation techniques. In this paper, we used popular digital modulation techniques for the application of Gaussian Q-function approximation in α–κ–μ fading distribution. Monte-Carlo simulations validated the analytical results and accuracy of the proposed closed-form expression for various digital modulation schemes.
Keywords
Error metrics, α–κ–μ fading, Gaussian Q-function and Digital modulation schemes.
References
[1] Gustavo Fraidenraich, and Michel Daoud Yacou, “The α-η-μ and α-κ-μ Fading Distributions,” 2006 IEEE Ninth International Symposium on Spread Spectrum Techniques and Applications, Manaus, Brazil, pp. 16-20, 2006.
[CrossRef] [Google Scholar] [Publisher Link]
[2] Jules M. Moualeu et al., “Performance Analysis of Digital Communication Systems Over α - κ - μ Fading Channels,” IEEE Communications Letters, vol. 23, no. 1, pp. 192-195, 2019.
[CrossRef] [Google Scholar] [Publisher Link]
[3] Ehab Salahat et al., “Moment Generating Functions of Generalized Wireless Fading Channels and Applications in Wireless Communication Theory,” 2017 IEEE 85th Vehicular Technology Conference (VTC Spring), Sydney, NSW, Australia, pp. 1-4, 2017.
[CrossRef] [Google Scholar] [Publisher Link]
[4] J.W. Craig, “A New, Simple and Exact Result for Calculating the Probability of Error for Two-Dimensional Signal Constellations,” MILCOM 91 - Conference Record, McLean, VA, USA, vol. 2, pp. 571-575, 1991.
[CrossRef] [Google Scholar] [Publisher Link]
[5] M. Chiani, D. Dardari, and M.K. Simon, “New Exponential Bounds and Approximations for the Computation of Error Probability in Fading Channels,” IEEE Transactions on Wireless Communications, vol. 2, no. 4, pp. 840-845, 2003.
[CrossRef] [Google Scholar] [Publisher Link]
[6] George K. Karagiannidis, and Athanasios S. Lioumpas, “An Improved Approximation for the Gaussian Q-Function,” IEEE Communications Letters, vol. 11, no. 8, pp. 644-646, 2007.
[CrossRef] [Google Scholar] [Publisher Link]
[7] Pavel Loskot, and Norman C. Beaulieu, “Prony and Polynomial Approximations for Evaluation of the Average Probability of Error Over Slow-Fading Channels,” IEEE Transactions on Vehicular Technology, vol. 58, no. 3, pp. 1269-1280, 2009.
[CrossRef] [Google Scholar] [Publisher Link]
[8] Qinghua Shi, and Y. Karasawa, “An Accurate and Efficient Approximation to the Gaussian Q-Function and its Applications in Performance Analysis in Nakagami-m Fading,” IEEE Communications Letters, vol. 15, no. 5, pp. 479-481, 2011.
[CrossRef] [Google Scholar] [Publisher Link]
[9] Dharmendra Sadhwani, Ram Narayan Yadav, and Supriya Aggarwal, “Tighter Bounds on the Gaussian Q Function and its Application in Nakagami- m Fading Channel,” IEEE Wireless Communications Letters, vol. 6, no. 5, pp. 574-577, 2017.
[CrossRef] [Google Scholar] [Publisher Link]
[10] Yunfei Chen, and Norman C. Beaulieu, “A Simple Polynomial Approximation to the Gaussian Q-Function and its Application,” IEEE Communications Letters, vol. 13, no. 2, pp. 124-126, 2009.
[CrossRef] [Google Scholar] [Publisher Link]
[11] Jelena Nikolić, and Zoran Perić, “Novel Exponential Type Approximations of the Q-Function,” Facta Universitatis, Series: Automatic Control and Robotics, vol. 21, no. 1, pp. 47-58, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[12] Zoran Perić et al., “Two Interval Upper-Bound Q-Function Approximations with Applications,” Mathematics, vol. 10, no. 19, pp. 1-15, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[13] Aditya Powari et al., “Novel Romberg Approximation of the Gaussian Q function and its Application over Versatile κ − μ Shadowed Fading Channel,” Digital Signal Processing, vol. 132, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[14] Mehmet Bilim, and Dervis Karaboga, “Improved Chernoff Bound of Gaussian Q-function with ABC Algorithm and its QAM Applications to DB SC and MRC Systems over Beaulieu–Xie Channels,” Physical Communication, vol. 58, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[15] Ehab Salahat, and Ali Hakam, “Performance Analysis of α-η-μ and α-κ-μ Generalized Mobile Fading Channels,” European Wireless 2014; 20th European Wireless Conference, Barcelona, Spain, pp. 1-6, 2014.
[Google Scholar] [Publisher Link]
[16] Marvin K. Simon, and Mohamed-Slim Alouini, Digital Communication over Fading Channels, John Wiley & Sons, 2005.
[CrossRef] [Google Scholar] [Publisher Link]
[17] Amer M. Magableh, and Mustafa M. Matalgah, “Moment Generating Function of the Generalized α - μ Distribution with Applications,” IEEE Communications Letters, vol. 13, no. 6, pp. 411-413, 2009.
[CrossRef] [Google Scholar] [Publisher Link]
[18] Irene A. Stegun, and Milton Abramowitz, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, Dover Publications, pp. 1-1046, 1965.
[Google Scholar] [Publisher Link]
[19] A.P. Prudnikov, Yu. A. Brychkov, and O.I. Marichev, Integrals and Series, Vol. 3: More Special Functions, Gordon and Breach Press US, 1986.
[Google Scholar] [Publisher Link]
[20] Luca Rugini, “Symbol Error Probability of Hexagonal QAM,” IEEE Communications Letters, vol. 20, no. 8, pp. 1523-1526, 2016.
[CrossRef] [Google Scholar] [Publisher Link]