content_image/295631.jpg content_image/295632.jpg
where ¯ K = P max C σ 2 , C is the path loss constant, r is the user distance from its serving BS, ψ and η denotes the shadowing and small scale fading coefficient between use r and BS on a given subcarrier, respectively, β is the path loss exponent, σ denotes the thermal noise at the receiver and ζ is the composite fading. Note that all users are assumed to be associated with their closest BS [6], [11], therefore r ≤ R . 

Each cell is divided into K concentric circular regions. Since path loss decays exponentially from cell center to cell edge, therefore, we consider discretization of cellular region in such a way that the path loss decay within each circular region remains constant or uniform. The main motivation for dividing the cell into a discrete set of circular regions relies on the fact that the channel statistics of the users located in a given circular region become relatively similar especially for large values of K . More explicitly, the characterization of the circular regions can be demonstrated as follows: 

<img src='content_image/295631.jpg'>

where κ is the path loss decay within each circular region [dB]. Due to the exponential nature of the path loss, it varies rapidly near the cell center than at the cell edge, therefore, (i) each of the k th circular region bounded by two adjacent rings, i.e., r$_{k}$ and r$_{k}$$_{−}$$_{1}$ possess non-uniform width Δ$_{k}$ = r$_{k}$ − r$_{k}$$_{−}$$_{1}$ ; (ii) the number of circular regions are high in the cell center than at the cell edge; (iii) the average number of users located within k th circular region bounded by ring r$_{k}$ and r$_{k}$$_{−}$$_{1}$ are considered to be located at r$_{k}$ . Note that, this is an approximation which is required for deriving the analytically tractable model of ICI and in any case it is not required for the Monte-Carlo simulations. The average number of users in each ring k (for analysis) can then be given as: 

<img src='content_image/295632.jpg'>

It is important to note that u$_{k}$ can be a fraction; therefore, we round off the fractional part of users. 

## B. Main Steps of the Proposed Framework 

In order to characterize the statistics of the uplink and downlink ICI for generalized fading channels and various scheduling schemes, the proposed framework mandates the following steps: 

i) Derive the distribution f$_{r}$$_{sel}$ ( r ) of the distance of the allocated user r$_{sel}$ in a given cell from its serving BS based on the deployed scheduling scheme. Without loss of generality, we assume the same scheduling scheme is implemented in all cells; therefore, f$_{r}$$_{sel}$ ( r ) remains the same for all cells. 

