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Numerical: coverage range of a 150 W base station

Short answer

Convert 150 W to 51.76 dBm; max allowed path loss = 155.76 dB. Using log-distance model PL(d) = 15 + 40 log(d) gives log(d) = 3.519, d = 10^3.519 = 3304 m. Coverage range ≈ 3.30 km.

Determine the radio coverage range of a base station that transmits a RF signal at 150 W, given the receiver threshold level is −104 dBm. Assume that the path loss at the first meter is 15 dB in a mobile radio propagation condition. (Path loss exponent = 4)

Given: P_t = 150 W, receiver threshold = −104 dBm, path loss at 1 m (d₀) = 15 dB, path loss exponent n = 4.

Step 1 – Transmit power in dBm

P_t = 10 log(150 W / 1 mW) = 10 log(150000)
    = 51.76 dBm

Step 2 – Maximum allowed path loss The signal can be received while P_r ≥ −104 dBm, so:

PL_max = P_t − P_r(min) = 51.76 − (−104)
       = 155.76 dB

Step 3 – Log-distance path loss model

PL(d) = PL(d₀) + 10 n log(d/d₀),   d₀ = 1 m
155.76 = 15 + 10 × 4 × log(d)
40 log(d) = 140.76
log(d) = 3.519
d = 10^3.519 = 3304 m

Answer: The radio coverage range of the base station is about 3.30 km (radius ≈ 3304 m).

✓ Answer checked by Claude Opus 5.5 (high effort)

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