Performance analysis of poisson cellular networks with lognormal shadowed Rayleigh fading

This paper analyzes downlink coverage probability and spectral efficiency of Poisson cellular networks with lognormal shadowed Rayleigh fading, provided each user is associated to the closest base station (BS). Both location-dependent and cell area wide aspects of the coverage probability and spectral efficiency metrics are presented. Performance impact of system parameters such as frequency reuse factor, transmission probability, and Signal to Interference Ratio (SIR) gap from Shannon capacity are characterized. Numerical results support the view that shadowing significantly degrades the performance. The cell area wide spectral efficiency decreases by 37% when the shadowing standard deviation increases from 0dB to 12dB. Finally, the derived results on location-dependent metrics are applied to Fractional Frequency Reuse (FFR) optimal partitioning in terms of system spectral efficiency, which is found dependent on system parameters such as SIR gap from Shannon capacity. It is also numerically shown that the FFR significantly improves the (link) spectral efficiency for cell edge users. For a user far away from its associated BS (at a distance 3 times the radius of average cell area) and considering SIR gap from Shannon capacity of 3dB, FFR(1,3) improves the (link) spectral efficiency by 239% compared to the universal reuse factor.