Stochastic Geometry Modeling of Cellular Uplink Power Control under Composite Rayleigh-Lognormal Fading

Power control for uplink transmission in a randomly laid-out cellular network operating over an environment with path loss and composite Rayleigh-lognormal shadowing is investigated. Each mobile station (MS) adjusts its transmit power to completely remove shadowing and to partially invert the effect of path loss. Using stochastic geometry tools, we derive an approximate coverage probability expression and validate it via simulations. With the power control scheme considered, shadowing with lower standard deviation improves the coverage probability. Also the severity of shadowing of local and surrounding environments has the same effect on the coverage probability. It was also observed that at low signal-to-interference-plus-noise ratio (SINR) thresholds, complete compensation of shadowing and partial compensation of path loss improves coverage, while at high SINR thresholds inverting only the effect of shadowing gives a better coverage probability.