(Out-of-cell interference averaging) Consider a cellular system with two adjacent single-dimensional cells along a highway, each of length d. The base-stations are at the midpoint of their respective cell. Suppose there are K users in each cell, and the location of each user is uniformly and independently located in its cell. Users in cell i are power controlled to the base-station in cell i, and create interference at the base-station in the adjacent cell. The power attenuation is proportional to r-a where r is the distance.

The system bandwidth is W Hz and the cb/I0 requirement of each user is /3. You can assume that the background noise is small compared to the interference and that users are maintained orthogonal within a cell with the out-of-cell interference from each of the interferers spread across the entire bandwidth. (This is an approximate model for the OFDM system in the text.)

1. Outage occurs when the users are located such that the out-of-cell interference is too large. For a given outage probability pout, give an approximate expression for the spectral efficiency of the system as a function of K, a and /3.

2. What is the limiting spectral efficiency as K and W grow? How does this depend on a?

3. Plot the spectral efficiency as a function of K for a = 2 and /3 = 7 dB. Is the spectral efficiency an increasing or decreasing function of K? What is the limiting value?

4. We have assumed orthogonal users within a cell. But in a CDMA system, there is intra-cell interference as well. Assuming that all users within a cell are perfectly power controlled at their base-station, repeat the analysis in the first three parts of the ques- tion. From your plots, what qualitative differences between the CDMA and orthogonal systems can you observe? Intuitively explain your observations. Hint: Consider first what happens when the number of users increases from K = 1 to K = 2.