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

Abstract

Abstract-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 inphase 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 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.

A Simple Evaluation for the Secrecy Outage Probability Over Generalized-K Fading Channels

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On the Performance of Quantum Key Distribution FSO Systems Under a Generalized Pointing Error Model

“…where E{•} represents the average operator. By setting some specific values for the parameters of the MGF of the Beckmann distribution in (6) of [12], the form of (1) can be also easily obtained.…”

DF Relayed Subcarrier FSO Links over Malaga Turbulence Channels with Phase Noise and Non-Zero Boresight Pointing Errors

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