Joint Average Contiguous Duration of Correlated Fading Envelopes

RESUMO

Average contiguous duration (ACD) measures the mean time for which a fading envelope remains continuously inside a bounded amplitude interval. This letter extends the concept to two correlated observations by introducing joint average contiguous duration (JACD) and joint average fade duration (JAFD). Both metrics are expressed as joint-region occupancy probabilities divided by the corresponding inward boundarycrossing rates. For correlated Rayleigh fading, closed-form JACD and JAFD expressions are derived using the bivariate Rayleigh cumulative distribution function (CDF), Rayleigh level-crossing rates, and conditional Rician probabilities. As an application, reciprocal secret-key generation (SKG) is considered through JACD-based multilevel quantization and raw key generation rate (KGR) expressions. Numerical results show that JACD-balanced quantization improves the worst-bin joint duration, same-bin occupancy, and sample-wise raw KGR compared with marginalACD balancing.