Assume a downlink low-rate communication transmit 500 bits/second at carrier frequency of 2 GHz. If the mobile travels with 60 mph (miles per hour), does the reception incur any distortion? (No explanation, no points)
To determine if the reception incurs any distortion, we need to consider the Doppler effect caused by the relative motion between the transmitter (base station) and the receiver (mobile). The Doppler effect is the change in frequency or wavelength of a wave as perceived by an observer moving relative to the wave source.
The Doppler effect is given by the following equation:
f' = f(1 + v/c)
where f is the original frequency, f' is the received frequency, v is the relative velocity between the transmitter and the receiver, c is the speed of light.
In this case, the carrier frequency is 2 GHz, and the mobile is traveling at 60 mph. We need to convert the speed to meters per second, and then calculate the relative velocity between the transmitter and the receiver. Assuming a conversion factor of 0.44704 meters per second per mph, we get:
v = 60 mph x 0.44704 m/s per mph = 26.8224 m/s
Using the Doppler equation, we get:
f' = 2 GHz * (1 + 26.8224 m/s / 3e8 m/s) = 2.000000089 GHz
The received frequency is slightly shifted due to the Doppler effect, but the change is negligible compared to the carrier frequency. The distortion is typically significant when the relative velocity is a significant fraction of the speed of light, or when the carrier frequency is much higher than in this case. Therefore, we can conclude that the reception does not incur any significant distortion.
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