Generalized MGF of Beckmann Fading With Applications to Wireless Communications Performance Analysis

The Beckmann distribution is a general multipath fading model for the received radio signal in the presence of a large number of scatterers, which can thence be modeled as a complex Gaussian random variable where both the in-phase and quadrature components have arbitrary mean and variance. However,...

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Bibliographic Details
Published in:IEEE transactions on communications 2017-09, Vol.65 (9), p.3933-3943
Main Authors: Pena-Martin, Juan P., Romero-Jerez, Juan M., Lopez-Martinez, F. Javier
Format: Article
Language:English
Subjects:
Analytical models
Beckmann fading
Channels
Communication channels
Complexity
Computer simulation
energy detection
Fading
Mathematical analysis
maximal ratio combining (MRC)
Measurement
Performance measurement
Radio signals
Random variables
Rayleigh channels
receiver operating characteristic (ROC)
Rician channels
secrecy capacity
Signal to noise ratio
square-law combining (SLC)
Wireless communication
Wireless communication systems
Wireless communications
Wiretapping
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Summary:The Beckmann distribution is a general multipath fading model for the received radio signal in the presence of a large number of scatterers, which can thence be modeled as a complex Gaussian random variable where both the in-phase and quadrature components have arbitrary mean and variance. However, the complicated nature of this distribution has prevented its widespread use and relatively few analytical results have been reported for this otherwise useful fading model. In this paper, we derive a closed-form expression for the generalized moment-generating function (MGF) of the signal-to-noise ratio (SNR) of Beckmann fading, which permits to circumvent the inherent analytical complexity of this model. This is a new and useful result, as it is a key for evaluating several important performance metrics of different wireless communication systems and also permits to readily compute the moments of the output SNR. Thus, we obtain simple exact expressions for the energy detection performance in Beckmann fading channels, both in terms of the receiver operating characteristic (ROC) curve and of the area under ROC curve. We also analyze the outage probability in interference limited systems affected by Beckmann fading, as well as the outage probability of secrecy capacity in wiretap Beckmann fading channels. Monte Carlo simulations have been performed to validate the derived expressions.
ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2017.2688396