8 D. A Motivating Example Consider an example with two cells, two users and two subcarriers. Each user can transmit with a maximum power of 1 W. Assume H$_{1}$ = [1 0.9; 0.8 0.7] and H$_{2}$ = [1 0.9; 0.8 0.7]. Single cell allocation strategies that aim to maximize the local throughput of each cell suggest A$_{1}$ , P$_{1}$ and A$_{2}$ , P$_{2}$ = [1 0; 0 1]. Computing the UB using (10) results in 1.7655 bps/Hz/cell where σ $^{2}$= 1 . Now, assume the knowledge of interfering link gains at each BS, i.e., G$_{12}$ = [0.9 0.2; 0.2 0.9] and G$_{21}$ = [0.7 0.1; 0.1 0.7]. Computing the throughput again while keeping the single cell allocations and taking into account the interfering gains leads to an average network throughput of 1.1137 bps/Hz/cell. However, better allocations are possible if we consider A$_{1}$ , P$_{1}$ and A$_{2}$ , P$_{2}$ = [0 1; 1 0] as per the criterion discussed in Section IV which enhances the resulting average network throughput to 1.5977 bps/Hz/cell. Considering the high intricacy of implementing the optimal solution, we develop a two-stage centralized scheme. In comparison to the centralized scheme presented in [12], the subcarrier allocation phase of the developed scheme is iterative and computationally intensive. However, the performance is better even without the power allocation phase and, thus, it can provide an effective benchmark for low complexity schemes. Compared to [12], we also discuss the power allocation phase for the general SINR regime. IV. SUB-OPTIMAL CENTRALIZED RESOURCE ALLOCATION SCHEMES A. Centralized Scheme A In the proposed scheme, we split the resource allocation procedure into two phases: subcarrier allocation phase and power allocation phase. It is important to note that the subcarrier allocation phase involves a power equalization step, thus, it is not totally independent of power allocation. • Initial Allocation : Firstly, we define the term for the allocation of resources t o the users as follows: Phase I: Subcarrier Allocation χ$_{n,k,l}$ = p$_{n,k,l}$h$_{n,k,l}$ ∑ L j =1 ,j = l P$_{k,}$$_{max}$g$_{n,k,lj}$ (11) DRAFT March 19, 2018