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Doppler effect; cordless phone path loss

Short answer

Doppler effect is the change in received frequency due to relative motion, with maximum shift fm = v/λ. For the cordless phone at 52 MHz and 50 m, free space path loss is 40.7 dB.

Define Doppler's effect in small scale fading. (i) Given a cordless phone operating at 52000 kHz frequency which has a range of 50 m. Determine the free space path loss.

Doppler effect in small-scale fading

The Doppler effect is the apparent change in the frequency of a received signal due to relative motion between transmitter and receiver. A mobile moving at speed v receives a wave arriving at angle θ to its direction of motion with a frequency shift

fd = (v/λ)·cosθ

In a multipath channel, waves arrive from many angles, so each has a different Doppler shift. The received spectrum spreads over fc ± fm (fm = v/λ). This Doppler spread causes random frequency modulation and makes the channel time-varying; it decides whether fading is fast or slow (through coherence time Tc ≈ 0.423/fm).

Free space path loss of the cordless phone

Given: f = 52 000 kHz = 52 MHz, d = 50 m. Assuming unity gain antennas:

λ = c/f = 3×10⁸ / 52×10⁶ = 5.769 m

PL = 20 log(4πd/λ)
   = 20 log(4π × 50 / 5.769)
   = 20 log(108.91)
   = 40.74 dB
(check: 32.44 + 20 log 52 + 20 log 0.05
       = 32.44 + 34.32 − 26.02 = 40.74 dB)

Answer: Free space path loss ≈ 40.7 dB.

✓ Answer checked by Claude Opus 5.5 (high effort)

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