PDF of the Maximum of Two Correlated Random Variables with Applications to Fading Channels

Probability density function (PDF) of multiple random variables can be employed to analyze many parameters of multiple antenna wireless communication systems, such as bit error rate (BER), ergodic and secrecy capacity, selection combining (SC) scheme and higher-order statistics to compute average fade duration (AFD) and level crossing rate (LCR) of a faded signal envelope. In this paper, a new method to represent PDF of the maximum of two correlated Rayleigh, Weibull, Nakagami-m and α - μ variates is analyzed and closed form expressions are extracted. The derived PDFs are expressed in terms of conditional probability and there is no need to compute infinite series summations or hypergeometric functions presented in the literature. Then, the BER performance of binary phase shift keying (BPSK) modulation and secrecy capacity performance in a 2 × 1 transmit antenna selection with maximal ratio combining (TAS/MRC) system over correlated Rayleigh, Weibull, Nakagami-m and α - μ fading channels are analyzed. Theoretical results are verified by simulation.