Design a computer program (Matlab, but any program will do) to simulate the large-scale path loss and co-channel interferences in a cellular radio system. Here we consider a 7-cell reuse system with the hexagonal cell radius of R = 1,500 m, and three sectors. Using the Log-Normal shadowing, we can write the received power at a mobile at a distance * d* [m] from the base station antenna as where accounts for the received power at the reference distance and

*for path loss exponent. Assume the transmitter power 1W, the path loss exponent 3, and the reference distance =100m. Also assume that all the first-tier co-channel cells (sectors) are actively interfering those mobiles in the reference cell and sector. The r.v. is zero mean Gaussian with σ=4dB. Let us calculate SIR (Signal-to-Interference Ratio) of mobile phones in the reference cell. Assume =0 [dBm]. Assume there are 30 mobile phones in the reference sector.*

*n*

Hint: In MATLAB, you may use * rand* for a uniform number generation between 0 and 1 and

*σ*

*for Normal random number with the standard deviation σ.*

*randn*

Let us calculate and plot the SIR for a mobile in the reference sector whose position is denoted by (x,y) [note: you may use polar coordinate as well]. You may designate the position of the base station antenna with the coordinate (0,0). Note that the range of x: d_{0 }≤ x ≤ R. For y, you have to figure out the valid range of y by considering the sides of the reference hexagon (e.g., a linear function of x), which is an important part of the problem. In other words, be sure that all the mobiles so dropped are within the reference sector

First, derive the signal power for the mobile located at (x,y) in terms x and y in the reference sector.

Derive the interferences from co-channel sectors in terms of x, y, and R.

Write the equation for SIR of a representative mobile in terms of x, y, R, Be sure that the y value does not exceed the valid range.

Distribute randomly 30 mobiles in the reference sector and plot them.

List SIR values of all 30 mobiles and indicate the worst and the best SIR values and their positions respectively considering the shadowing. Draw 3D plot to show SIRs of all 30 mobiles respect to their (x,y) positions.

By maintaining the positions of 30 mobiles, change the standard deviation deviation σ =2 and 4 and discuss the effects.

Also, change n=2, and 4 and discuss the effect.

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**In your report:**

Answer all the questions above and include all the principles, equations, flowchart of the simulation code, and the source codes that you used.