On the Bivariate Nakagami-m Cumulative Distribution Function: Closed-Form Expression and Applications

In this paper, we derive exact closed-form expressions for the bivariate Nakagami-m cumulative distribution function (CDF) with positive integer fading severity index m in terms of a class of hypergeometric functions. Particularly, we show that the bivariate Nakagami-m CDF can be expressed as a finite sum of elementary functions and bivariate confluent hypergeometric Φ₃ functions. Direct applications which arise from the proposed closed-form expression are the outage probability (OP) analysis of a dual-branch selection combiner in correlated Nakagami-m fading, or the calculation of the level crossing rate (LCR) and average fade duration (AFD) of a sampled Nakagami-m fading envelope.