17 In Fig. 1, Fig. 2 and Fig. 3, we present the performance of the centralized scheme A, centralized scheme B and the distributed scheme for two cells, four cells and seven cells, respectively. The results have been taken after averaging over 10,000 channel realizations and are shown for both simulation scenarios. The performance of all schemes is calibrated using the established upper and lower bounds. Since the centralized scheme A has computationally exhaustive power allocation phase, the results are presented for the subcarrier allocation phase of Algorithm 2 only. However, it can be observed that the scheme still has the capability to serve as a suitable benchmark for the developed low complexity schemes. In order to highlight the significance of the less complex GP problem defined in (14), we also present th e performance of the centralized scheme B without power control. For the two cell scenario, the performance gap between the centralized schemes is negligible and they give nearly similar results. However, as the number of cells increases the performance gain of the centralized scheme A is evident over all schemes even without power control. Moreover, it is also important to note the significant degrad ation in the performance of centralized scheme B without power control phase. This degradation is found to be increasing with the increase in number of cells. It is also worth to mention here that the proposed less complex GP problem (14) can be implemented in a distributed way using the techniques explained in [14] and can be used with any set of subcarrier allocations. Thus, in the distributed approach we use the near optimal single cell allocations in conjunction with the less complex GP problem (14). The significance of the power control phase can be obser ved easily from the results which becomes more evident for high number of cells . Moreover, the presented results depict the reduction in the average network throughput as the number of interfering cells increases. The performance gap of the proposed schemes increases with respect to the evaluated UB. Even though the UB is not tight and reflects an over optimistic average network throughput, it provides an idea on the performance gap between the proposed schemes and the optimal solution. In Fig. 4, we assume that the users in each cell are placed at equally spaced angles from 0 to 2 π . The performance evaluation of all schemes has been done by changing the user positions DRAFT March 19, 2018