content_image/296233.jpg content_image/296235.jpg content_image/296236.jpg
ii) Derive the distribution f$_{˜}$ $_{r$_{sel}$}$(˜ r ) of the distance between the allocated user in a neighboring interfering cell and the BS of the cell of interest ˜ r$_{sel}$ . 

iii) Derive the distribution f$_{X}$$_{l}$ ( x ) of the interference from the neighboring cell l . Finally, derive the MGF of the cumulative ICI, i.e., Y = ∑ L l =1 X$_{l}$ . 

## III. PART I: DISTRIBUTION OF THE SCHEDULED USER LOCATION 

Considering the high dependence of the uplink ICI on the location of the scheduled users in the neighbor interfering cells which in turn depends on the deployed scheduling schemes, we derive in this section the distribution of the distance between the scheduled user and its serving BS in a given cell (i.e., the probability mass function (PMF) of r$_{sel}$ ) considering the following five scheduling algorithms: gre edy scheduling, proportional fair scheduling, round robin scheduling, location based round robin scheduling, and greedy round robin scheduling. 

## A. Greedy Scheduling Scheme 

Greedy scheduling is an opportunistic scheme that aims at maximizing the network throughput by taking full advantage of multiuser diversity. However, it suffers from low fairness among users which makes it less attractive for network operators. The procedure for determining the PMF of r$_{sel}$ considering greedy scheduling is divided into two steps: 

Step 1 ( Selecting the user with the highest SNR in ring k ): Since the path loss decay within each circular region is considered to be uniform, we approximate the distance of all users located within k th circular region by ring r$_{k}$ for analytical tractability as we already mentioned in Section II. In this step, we select a user with maximum SNR in each ring k which posses u$_{k}$ users. Thus, selecting a user in a ring k is equivalent to selecting the user with maximum channel gain among all the users in ring k , i.e., 

<img src='content_image/296233.jpg'>

where ζ$_{i}$ is the composite fading channel gain between user i and its BS on a given subcarrier. The CDF and PDF of the maximum channel gain ζ$_{k}$ can be written as follows: 

<img src='content_image/296235.jpg'>

<img src='content_image/296236.jpg'>

