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Numerical: FDMA channels (12.8 MHz)

Short answer

Number of channels N = (total bandwidth − 2 × guard bandwidth) / channel bandwidth = (12.8×10⁶ − 2×10×10³) / (30×10³) = 426. So 426 radio channels per simplex band.

Calculate the number of radio channels available in the FDMA system with following data. A US analog mobile phone system is allocated 12.8 MHz for every simplex band. The total spectrum allocated is 12.8 MHz, the guard bandwidth is 10 KHz and the channel bandwidth is 30 KHz.

In FDMA, the total band is divided into channels of equal width, after leaving a guard band at each edge of the allocated spectrum. The number of channels is

N = (B_t − 2·B_guard) / B_c

where B_t = total spectrum, B_guard = guard band at each edge, B_c = channel bandwidth.

Given: B_t = 12.8 MHz (per simplex band), B_guard = 10 kHz, B_c = 30 kHz.

 N = (12.8×10⁶ − 2 × 10×10³) / (30×10³)
   = (12 800 000 − 20 000) / 30 000
   = 12 780 000 / 30 000
   = 426

Answer: N = 426 radio channels (in each simplex band; these pair up to give 426 duplex channels in the forward and reverse bands).

This matches the AMPS (US analog) system, which uses 30 kHz channels with FDMA/FDD.

✓ Answer checked by Claude Opus 5.5 (high effort)

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