Closed-Form Expressions for Secrecy Capacity over Correlated Rayleigh Fading Channels

We investigate the secure communications over correlated wiretap Rayleigh fading channels assuming the full channel state information (CSI) available. Based on the information theoretic formulation, we derive closed-form expressions for the average secrecy capacity and the outage probability. Simulation results confirm our analytical expressions.

💡 Research Summary

The paper addresses physical‑layer security in wireless communications by analyzing the classic Wyner wiretap model under correlated Rayleigh fading. Assuming that the transmitter (Alice) has perfect instantaneous channel state information (CSI) of both the legitimate link (Alice‑Bob) and the eavesdropping link (Alice‑Eve), the authors derive closed‑form expressions for two fundamental performance metrics: the average secrecy capacity and the secrecy outage probability for a given target secrecy rate.

The system model defines the received signals as (y = h_{sd}x + n_d) and (z = h_{se}x + n_e), where the complex Gaussian fading coefficients (h_{sd}) and (h_{se}) have zero mean, unit variance noise, and their instantaneous SNRs (\alpha = |h_{sd}|^2) and (\beta = |h_{se}|^2) follow exponential distributions with means (\lambda_1) and (\lambda_2), respectively. Crucially, (\alpha) and (\beta) are statistically correlated with coefficient (\rho). The joint PDF is expressed using the modified Bessel function (I_0(\cdot)). By expanding (I_0) into its infinite series, the joint PDF is decomposed into a weighted sum of separable terms (f_k(\alpha,\beta)) with coefficients (c_k = \rho^k /