9 This criterion guarantees the selection of the users who possess not only better power- gain product but also they offer less interference to the neighbor cells. The denominator ∑ L j =1 ,j = $_{l}$P$_{k,}$$_{max}$ g$_{n,k,lj}$ accounts for the maximum aggregate interference that the k th user in cell l , may cause to all cells. Even though this criterion is heuristic, it improves the performance compared to the traditional C/I scheme (which gives nearly similar results as our lower bound). Once the initial allocations are computed, we can calculate the initial throughput of the network C$_{o}$ using (1). • Maximize Throughput Iteratively until Convergence : In this step, we select any cell l and subcarrier n arbitrarily and re-perform the allocation at this subcarrier considering the other cell allocations fixed, i.e., I$_{n,l}$ remains fixed. More explicitly, we compute C$_{n,k,l}$ = log$_{2}$(1+ p$_{n,k,l}$h$_{n,k,l}$ σ $^{2}$+ I$_{n,l}$ ) for all users in cell l one by one and select the user which gives the maximum incremental throughput at subcarrier n , i.e., C$_{n,k,l}$ − C$_{o}$ . Note that, in order to compute C$_{n,k,l}$ , we need to compute p$_{n,k,l}$ which can be obtained simply by dividing P$_{k,}$$_{max}$ equally among all the fixed allocated subcarriers of user k and the new one which is currently under observation. Once the reallocation is done at subcarrier n , we move to the next subcarrier in cell l and so on. As the new allocations are computed for cell l , we calculate the new increased network throughput C$_{new}$ and move to another cell j . The whole process is repeated again with C$_{o}$ = C$_{new}$ until convergence to a desired accuracy is achieved. Once the subcarrier allocation is done, the optimal powers can then be calculated for the high SINR regime or for the general SINR regime through solving a series of GPs using successive convex approximation which is a provably convergent heuristic [14]. This approach is known to compute globally optimal power allocations in many cases. Thus, for given allocations, (1) can Phase II: Power Allocation DRAFT March 19, 2018