In this homework you will have a chance to learn about cellular network planning using some simplified models. You need to use both MATLAB and AMPL. It is preferable to use MATLAB to create the models and data files that will then use in AMPL to do the optimization.
• First consider the following scenario. You are given the (x,y) coordinates of a set of base stations/towers/access points. The transmission power of each tower is fixed to P. For a successful communication with a mobile device /node the received power needs to be at least P_min. Using the Hata model for propagation determine the maximum radius R at which a mobile node can still communicate with a given AP. Now consider circles of radius R around each of the APs. Clearly some of these circles will intersect and some will not.
Your task is to assign frequencies to the various APs such that no two APs with intersecting circles will have the same frequency. The objective is to minimize the total number of frequencies used in the network. ( The rationale is that each frequency has to be obtained from the FCC by paying a licensing fees and hence minimizing the number of frequencies is equivalent to minimizing the cost for the network operator) For simplicity the frequencies are indexed as 1, 2, 3, …
The locations of the APs are given in file ap_locn.mat, which you can load into MATLAB. Clearly, the total number of frequencies that you need in the network is no greater than the total number of APs in the network; each AP can be assigned a different frequency; you can use this as a starting point in your formulation.
Once you obtain the result for the frequency assignment, import your results into MATLAB. Now plot on a 2-D graph the location of the APs and also indicate their frequencies next to it.
• Now we will consider an extension of the above problem to allow for different towers/APs to use different transmission powers. For simplicity assume that each tower can use one of two possible powers P1 and P2, where P1