Chapter 3 Mobile Radio Propagation: Large-Scale Path Loss 1. (a) Explain the advantages and disadvantages of the 2-ray ground reflection model in the analysis of path loss. (b) What insight does the 2-ray model provide about large-scale path loss that was disregarded when cellular systems used very large cells? 2 . In a 2-ray ground reflected model, assume that must be kept below 6. 261 radians for phase cancellation reasons. Assuming a receiver height of 2 m, and given a requirement that be less than 50 , what are the minimum allowable values for the T-R separation distance and the height of the transmitter antenna?

The carrier frequency is 900 MHz. 3. In the 2-ray path loss model with ? derive an appropriate expression far the location of the signal nulls at the receiver. 4 . Compare the received power for the exact expressions for the 2-ray ground reflection model. Assume the height of the transmitter is 40 m and the height of the receiver is 3m. The frequency is 1800 MHz, and unity gain antennas are used. Plot the received. 5. Referring to Figure P3. 3, compute d = d1, the first Fresnel zone distance between transmitter and receiver for a 2-ray ground reflected propagation path, in terms of and X.

This is the distance at which path loss begins to transition from d to d behavior. Assume 6 . If the received power at a reference distance d0 = I km is equal to 1 microwatt, find the received powers at distances of 2 km, 5 kin, 10 km, and 20 km from the same transmitter for the following path loss models: (a) Free space; (b) n = 3; (c) n = 4; (d) 2-ray ground reflection using the exact expression; (e) extended Hata model. Assume f=1800 MHz, ht = 40m, hr = 3m, Gt=Gr=0dB. Plot each of these models on the same graph over the range of 1 km to 20km. 7 .

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Assume the received power at a reference distance d0 = 1 km is equal to 1 microwatt, and f=1800 MHz, ht = 40m, hr = 3m, Gt=Gr=0dB. Compute, compare, and plot the exact 2-ray ground reflection model with the approximate expression. At what T-R separations do the models agree and disagree? What are the ramifications of using the approximate expression instead of the exact expression in cellular system design? 8 . A transmitter provides 15W to an antenna having 12 dB gain. The receiver antenna has a gain of 3 dB and the receiver bandwidth is 30 kHz.

If the receiver system noise figure is 8 dB and the carrier frequency is 1800 MHz, find the maximum T-R separation that will ensure that a SNR of 20 dB is provided for 95% of the time. Assume n = 4, dB, and d0 = 1 km. 9. Assume a SNR of 25 dB is desired at the receiver. If a 900 MHz cellular transmitter has an EIRP of 100 W, and the AMPS receiver uses a 0 dB gain antenna and has a 10 dB noise figure, find the percentage of time that the desired SNR is achieved at a distance of 10 km from the transmitter. Assume n=4, dB, and d0 = 1 km.

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