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Numerical: cellular vs non-cellular voice channels

Short answer

Coverage area per cell is 140 km² divided by 7, giving 20 km². Each cell reuses 30% of the 40 voice channels, i.e. 12 channels; total cellular channels = 7 × 12 = 84, versus 40 in non-cellular, a 2.1× capacity increase from frequency reuse.

Consider a single high-power transmitter that can support 40 voice channels over an area of 140 km² with the available spectrum. If this area is equally divided into seven smaller cells, each supported by lower power transmitters so that each cell supports 30% of the total voice channels, then determine i) Coverage area of each cell [1] ii) Total number of voice channels available in a cellular system compared to a non-cellular system. [3]

Given: single high-power transmitter: 40 voice channels over 140 km². Area divided into 7 equal cells; each cell supports 30 % of total channels.

i) Coverage area of each cell

A_cell = 140 / 7 = 20 km²

ii) Total voice channels: cellular vs non-cellular

Channels per cell:

k = 30 % of 40 = 0.3 × 40 = 12 channels per cell

Total channels in the cellular system (each cell uses its own 12 channels; channels are reused in non-adjacent cells):

C_cellular = 7 × 12 = 84 channels

Non-cellular system:

C_non-cellular = 40 channels

Ratio:

84 / 40 = 2.1

Answer: (i) 20 km² per cell; (ii) the cellular system provides 84 channels versus 40, i.e. 44 more channels or 2.1 times the capacity, because frequencies are reused in different cells.

✓ Answer checked by Claude Opus 5.5 (high effort)

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