Secrecy Analyses for Real $m$ Under Dual Correlated Nakagami-$m$ Fading Employing an Adaptive Encoder and a New Broadcasting Protocol

Using a well-known wire-tap model, novel wireless secrecy analyses under dual correlated Nakagami-m fading with a real fading parameter m are reported. Infinite summations for incomplete gamma functions are employed to derive compact expressions for secrecy capacity and secrecy outage probability (SOP) under noninteger m. Independently, using finite summations, corresponding closed-form findings for integer m are also derived. In the current literature, finite summations for the incomplete gamma functions, whose first arguments and hence m must be an integer, are employed to obtain closed-form expressions for, first, the SOP (with an unknown passive wire-tapper's channel state information), and second, ergodic secrecy capacity (with partially known active wire-tapper's channel state information under slow fading). The new secrecy results for noninteger m generalize the proposed findings for integer m, and existing findings under dual correlated Rayleigh fading for m = 1. The new findings can thus be comprehensively employed for wireless secrecy computation under dual correlated Nakagami-m fading for realm. Infinite-summation convergence and cross verification are also obtained for a finite number of terms, which shows the practicality and consistency of the new findings. For the first time, secrecy analyses employing an adaptive encoder with ON/OFF transmission are performed under dual correlated Nakagami-m fading for real m to not only improve wireless secrecy, but also achieve the eventual successful transmission from a source to a destination. The new SOP results for real m can be employed as lower bounds and complete theoretical secrecy analyses, for SOP under dual correlated Nakagami-m fading with integer m. Simulation results are employed to show matching between the proposed findings and existing findings.