Consider a cellular system with a total of 120 channels. The system is modeled by a regular hexagonal grid with the base stations placed in the corners of each cell. The base stations use directional antennas. Assume that the base stations use ideal sectorized antennas with 60◦ lobe width, i.e. every cell is divided into two halves requiring two channel groups. The path loss exponent is 4. The SIR requirement for good signal quality is 15 dB and thermal noise can be neglected. Compare the capacity (measured as channels/unit area) of this system with the two following systems: 

a) A system with 120◦ sector antennas. 

b) A system with omni-directional antennas and base stations in the center of the cell.