Coverage gain and Device-to-Device user Density: Stochastic Geometry   Modeling and Analysis
  Device-to-device (D2D) communication has huge potential for capacity and coverage enhancements for next generation cellular networks. The number of potential nodes for D2D communication is an important parameter that directly impacts the system capacity. In this paper, we derive analytic expression for average coverage probability of cellular user and corresponding number of potential D2D users. In this context, mature framework of stochastic geometry and Poisson point process has been used. The retention probability has been incorporated in Laplace functional to capture reduced path-loss and shortest distance criterion based D2D pairing. The numerical results show a close match between analytic expression and simulation setup. 
Hafiz Attaul Mustafa, Muhammad Zeeshan Shakir, Muhammad Ali Imran, Ali   Imran, and Rahim Tafazolli
cs.IT math.IT