Consider a highway cellular system. Assume that the highway is exactly linear, the cells are of length 2R, and the cell width (i.e., the width of the highway) can be ignored. Frequencies can be reused in cells whose centers are D units apart. The base station in each cell is at its center, and has two directional antennas, one covering each half of the cell (i.e., the cells are "sectorized" into two sectors). a. Relate D, R, and the number of reuse groups N. b. Accounting only for first tier interferers, assuming that Rayleigh fading is averaged out, assuming independent log-normal shadow- ing for all the received signals, determine the minimum value so that the SIR falls below 12 dB with a probability of 1%. You must analyze both the forward and reverse channels. The standard deviation of log-normal shadowing is 8 dB. Take the power law path loss exponent to be 4. c. Explain why the SIR analysis is greatly simplified in this problem by assuming directional antennas; that is, by sectorization. d. Given that there are 200 traffic channels available (assume single channel per carrier) determine the maximum number of Erlangs that each cell can be offered.