16 as follows: where d$_{ref}$ is the reference distance and is set equal to 0.05 km, d$_{k,l}$ is the distance of the k th user from the l th BS. The first term denotes the path loss where γ is the path loss exponent and is set equal to 3. The second term represents log-normal shadowing with a mean of 0 dB and a standard deviation of 8 dB. The last factor F$_{n,k,l}$ corresponds to Rayleigh fading. The bandwidth of the system is assumed to be 20 MHz with a noise power spectral density of 8 . 6455 × 10 − 15 W/Hz at each receiver. The channel conditions are assumed to be fixed during a frame. The interfering gains from the j th interfering cell to the cell of interest l are computed as follows: h$_{n,k,l}$ = ( − 122 − 10 γ log$_{10}$ d$_{k,l}$ ) − N (0 , σ $^{2}$) + 10 log$_{10}$ F$_{n,k,l}$ d > d$_{ref}$ h$_{n,k,l}$ = ( − 122 − 10 γ log$_{10}$ d$_{ref}$ ) − N (0 , σ $^{2}$) + 10 log$_{10}$ F$_{n,k,l}$ d < d$_{ref}$ g$_{n,k,jl}$ = ( − 122 − 10 γ log$_{10}$ d$_{k,l}$ ) − N (0 , σ $^{2}$) + 10 log$_{10}$ F$_{n,k,j}$ where d$_{k,l}$ is the distance between the k th user in the interfering cell j and the l th BS. We consider the following two simulation scenarios: In Table 1, we compare the performance and complexity of the centralized and distributed schemes with the derived bounds and the optimal solution in high SINR regime. The optimal solution is computed by the exhaustive search based subcarrier allocation phase detailed in Section II. All users are placed at equal distance d from the BS and at equally spaced angles (i.e., scenario A). The results are taken after averaging over 100 channel realizations. The simulation results show that the performance gap between the benchmark centralized scheme A (with power control) and the optimal solution is negligible compared to the low complexity centralized and distributed schemes. However, this observation may not remain valid for bigger network scenarios. Moreover, as d increases the degradation of the average network throughput is evident. • Scenario A: Users are equidistant from the BS and placed at equally spaced angles. • Scenario B: Users are assumed to be uniformly distributed across the whole cellular area. DRAFT March 19, 2018