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 non-integer 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 integer, are employed to obtain closed-form expressions for (i) the SOP (with an unknown passive wire-tapper's channel state information), and (ii) ergodic secrecy capacity (with partially-known active wire-tapper's channel state information under slow fading). The new secrecy results for non-integer m generalise (i) the proposed findings for integer m, and (ii) 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 real m. 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 improving wireless secrecy, but also achieving the eventual successful transmission from a Source to a Destination. The new SOP results for real m (i) can be employed as lower bounds, and (ii) 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.