The radius R of the cell is set to 500m and the cell is decomposed into non-uniform circular regions of width Δ$_{k}$ . The path loss variation within each circular region is set to κ = 2 dB. For each Monte-Carlo simulation trial, we generate U uniformly distributed users in a circular cell of radius R . Each user has instantaneous SNR given by (1) and short term average SNR (¯ γ ) . We allocate a user with maximum instantaneous SNR in the greedy scheme whereas in the proportional fair scheme we allocate a user based on the maximum normalized SNR. For the round robin scheme, we select any user arbitrarily. For location based round robin we select a user randomly from the w th ring in a time slot w whereas we select a user with maximum SNR without considering the users of the previously allocated w − 1 rings for the greedy round robin scheme. Next, we calculate the distances of the selected users, i.e., r$_{sel}$ , from their serving BS and compute the distances to the BS of interest, i.e., ˜ r$_{sel}$ for all scheduling schemes. The process repeats for large number of Monte-Carlo simulation trials. The distance data is then analyzed by creating a histogram whose bins are given by [1 , · · · r$_{k}$$_{−}$$_{1}$, r$_{k}$, r$_{k}$$_{+1}$, · · · R ] . Fig. 2 depicts the PMF of the location of the scheduled user in a given cell based on the proportional fair, greedy and round robin scheduling schemes. Since the proportional fair scheme exhibits some fairness among users in a cell, the PMF of the allocated user locations is expected to be more flat compared to the greedy scheme. Since the cell edge has more users due to the large area and each user has equal probability to be allocated on a given subcarrier, therefore the round robin scheme exhibits high probability at the cell-edge. It is important to note that the numerical results for the derived PMF in Fig. 2 nearly coincide with the exhaustive Monte-Carlo simulation results with a small number of rings K = 10 and κ = 2 dB. Moreover, it can also be noticed that the width of the circular regions tend to increase from cell center to cell edge which is due to the exponentially decaying path loss as mentioned in Section II. The number of required rings is expected to decrease by reducing β and increasing the amount of power decay within each circular region and vice versa. Another important point to explain with reference to Fig. 2 is that with the increase in the number of competing users on a given subcarrier, the PMF of opportunistic scheduling schemes tends to get skewed which is due to the fact that the higher the number of users in the cell center, the higher is the probability of allocating a subcarrier in the cell center. In order to get an integer number of users within a ring, A. Parameter Settings and Simulation Setup: B. Results and Discussions: 18