Question

Consider a vehicle moving away from the transmitter at 100km/h. Determine the coherence time and whether the fading is fast or slow for the 30 kHz bandwidth system, taking the bit rate to be equal to the bandwidth and the carrier frequency to be 900 MHz. a vehicle moving away from the transmitter at 100km/h. Determine the coherence time and whether the fading is fast or slow for the 30 kHz bandwidth system, taking the bit rate to be equal to the bandwidth and the carrier frequency to be 900 MHz.

Answer 1

The coherence time is 3.33 x 10^-5 s and the fading is slow.

Step-by-step explanation:

The coherence time can be calculated using the formula Tc = 1 / B, where Tc is the coherence time and B is the bandwidth.

In this case, the bandwidth is 30 kHz, so the coherence time is Tc = 1 / 30,000 Hz = 3.33 x 10^-5 s.

To determine whether the fading is fast or slow, we compare the coherence time with the time it takes for the vehicle to move one wavelength away from the transmitter.

The formula to calculate the time it takes for the vehicle to move one wavelength away is t = λ / v, where t is the time, λ is the wavelength, and v is the velocity of the vehicle.

Since the frequency is given as 900 MHz, the wavelength can be calculated using the formula λ = c / f, where λ is the wavelength, c is the speed of light, and f is the frequency.

Plugging in the values, we get λ = 3 x 10^8 m/s / (900 x 10^6 Hz)

= 0.333 m.

Now, substituting the values into the formula, we get t = 0.333 m / (100,000 m/s)

= 3.33 x 10^-6 s.

Since the coherence time (3.33 x 10^-5 s) is much larger than the time it takes for the vehicle to move one wavelength away (3.33 x 10^-6 s), the fading is considered to be slow.