28 Gamma(3 / 2 , 2 / 3) . Firstly we will provide a brief overview of the Monte-Carlo simulation setup. 1) Generate U uniformly distributed users per cell. Each user has an instantaneous SNR given by (53). Select a user with maximum instantaneous SNR. Store the distance of the selected user, i.e., r$_{sel}$ from the serving BS. 2) Compute the distance of the selected user from the BS of interest, i.e., ˜ r$_{sel}$ using cosine law and finally generate the interference using (57). 3) Repeat all steps for a large number of iterations. Generate histogram for the discrete RV r$_{sel}$ with non-uniform bin widths. The CDF of the ICI for different transmit power budgets and different path loss exponents for greedy scheduling with and without PC is plotted in Fig. 10. High values of path loss exponents causes rapid In Fig. 9 the impact of the maximum transmit power limit is shown on the PMF of allocated user locations. The obtained PMF results fit well with exhaustiveMonte-Carlo simulations. Since the users located within the threshold region r$_{t}$ can compensate their distance based path loss, each user has on average equal probability of allocation within r$_{t}$ . The increasing trend of PMF within r$_{t}$ is therefore simply due to an increase in the number of users in each ring from cell center to the cell edge. It is important to note that the users located beyond r$_{t}$ transmit with their maximum power as they cannot compensate path loss. These users are therefore scheduled based on their relative channel gains which prioritizes close users over the far users and hence causes rapid decay of allocation probability beyond r$_{t}$ . In greedy scheduling [25], the cell center users have higher priority to be allocated over the cell edge users. On the other side, round robin scheduling provides equal probability of allocation to each user, hence high probability of allocation near the cell edge due to the large area and large number of users at the cell-edge. By observing the result, it can be concluded easily that greedy scheduling with power control (PC) follows the trend of round robin within r$_{t}$ whereas the trend of greedy scheduling beyond r$_{t}$ . The performance of greedy scheduling with PC is therefore expected to lie in between the two extremes. Two different transmit power limits are also studied in Fig. 9 which yields two threshold distances, i.e., r$_{t}$ = 400 m and r$_{t}$ = 260 m, respectively. It can be observed that the greater the maximum transmit power, the greater is the threshold distance and more users located farther from the BS become capable to compensate path loss which increases fairness and in turn the incurred ICI. The slight mismatch in the simulations and analysis demonstrates the impact of discretization which is dominant for channel based scheduling beyond r$_{t}$ . However, this error can be reduced by increasing the number of rings.