One way to improve the capacity of cellular systems is to employ a two-channel bandwidth scheme, where a hexagonal cell is divided into two concentric hexagons as shown in Figure 5.19. The inner...

One way to improve the capacity of cellular systems is to employ a two-channel bandwidth scheme, where a hexagonal cell is divided into two concentric hexagons as shown in Figure 5.19. The inner hexagon is serviced by 15 kHz channels, while the outer is serviced by 30 kHz channels. Suppose that the 30 kHz channels require an 18 dB threshold to maintain acceptable radio link quality, while the 15 kHz channels require 24 dB. The path loss exponent is 4. a) Consider the downlink and assume a fourth-law path loss model. Determine the ratios, 0 = D/R0 and i = D/Ri. b) Determine the ratio of the inner and outer hexagonal areas, Ai/A0. c) Let Ni and N0 be the number of users allocated to the inner and outer portions of the cell respectively, and assume that the channels are allocated such that Ni/N0 = Ai/(A0 − Ai). Determine the increase in capacity (channel per cell) over a conventional one-channel bandwidth system that uses only 30 kHz channels, if the system uses a 7-cell reuse cluster. Consider only the first tier of interference and neglect the thermal noise.