Secrecy Analysis of α-Beaulieu-Xie Fading Channel Under Selection Combining Diversity

Peta-Hertz (PHz) communication technology is envisioned to provide an enormously high data rate with true sense global coverage ranging from air to underwater deployment. However, both line-of-sight (LOS) and non-LOS (NLOS) components are needed to characterize the fading channels of the PHz communication system. Recently, the proposed α-Beaulieu-Xie fading distribution, with α as a modified parameter, appropriately characterizes wireless channels with multiple LOS and NLOS components simultaneously. In addition, α-Beaulieu-Xie distribution exhibits a high degree of trade-off between mathematical tractability and match with experimental data. This research presents various measures of physical layer security over α-Beaulieu-Xie fading channel under the SC diversity scheme. In particular, analytical expressions for Secrecy Outage Probability (SOP)(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">γ</sub>(γ)|<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Out</i>−<i>SC</i></sub>), Probability of Non-Zero Secrecy Capacity (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>nz</i>−<i>SC</i></sub>), and Average Secrecy Capacity (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>SAv</i>−<i>SC</i></sub>) are derived over α-Beaulieu-Xie fading channel under the SC diversity scheme. Further, asymptotic expressions for respective secrecy measures are presented as (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Out</i>−<i>SC</i></sub>(γ)|<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Aymp</i></sub><italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i>(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i>), <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>nz</i>−<i>SC</i></sub>|<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Aymp</i></sub>, and (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>SAv</i>−<i>SC</i></sub>|<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Aymp</i></sub>). Furthermore, the effect of various physical parameters, such as the overall severity parameter of both LOS and NLOS (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m_X</i>), the severity parameter of LoS (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m_Y</i>), and the fading parameter (α) on the presented secrecy measures, is quantified numerically. Numerical quantification reveals that the decrease in the value of (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">γ</sub>(γ)|<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Out</i>−<i>SC</i></sub>) with an increase in the value of α is proportional to the value of α for a lower regime of γ only. Whereas a decrease in the value of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m_x</i> with an increase in the value of α reflects that the value of (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">γ</sub>(γ)|<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Out</i>−<i>SC</i></sub>) depends more dominantly on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m_x</i> than that of α. In addition, it is noticeable that an increase in either <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m_x</i> or α increases the value of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>SAv</i>−<i>SC</i></sub>. However, an increase in the value of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m_x</i> and α by the same amount, say 0.2, results in a higher increase in the value of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>SAv</i>−<i>SC</i></sub> with an increase in the value of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m_x</i> than that of an increase in the value of α. In addition, each analytical expression is quantified numerically with respect to the respective asymptotic expressions.