EEE6431 Broadband Wireless Techniques Practice Sheet 1 – Semester-1 2022
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EEE6431 Broadband Wireless Techniques
Practice Sheet 1 – Semester-1 2022
Note: (i) Free space pathloss: PL = #$2 ; (ii) Ground plane pathloss: PL ≈
1. A transmitter produces 17 W of RF power, express the transmit power in units of dBm.
(a) 42.3 dBm;
(b) 12.3 dBm;
(c) 84.6 dBm;
(d) 24.6 dBm.
2. Find the received power in dBm at a free space distance of 1000 m from a unity gain Tx antenna operating at 1800 MHz and 40 W radiated power. Assume the Rx antenna gain is also unity.
(a) -81.5 dBm;
(b) - 111.5 dBm;
(c) -51.5 dBm;
(d) - 141.5 dBm.
3. In the downlink of an 1800 MHz cellular system, a mobile station is located 1 km from a base station. If the transmit power is 40W, find the received power in dBm at the mobile using the 2-ray ground propagation model assuming Gt = Gr = 1, ht = 30 m and hr = 1.5 m.
(a) -66.4 dBm;
(b) -70.9 dBm;
(c) -57.5 dBm;
(d) -40.9 dBm.
4. An expression for the simplified pathloss model is given by: Pr = Pt K $% . The terms in d0 and g are defined as:
(a) d0 = antenna far field reference distance; g= median attenuation exponent; (b) d0 = antenna far field reference distance; g= pathloss exponent;
(c) d0 = free space pathloss constant; g = pathloss exponent;
(d) d0 = range; g= median attenuation exponent.
5. Using the simplified pathloss model, find the outage probability due to shadow fading at a range of
1500 m. Assume a 900 MHz radio carrier, a gof 4, a d0 of 10 m and a K of 2.65´10-3 . The standard deviation due to shadow fading is 4 dB, the transmit power Pt = 10 mW and the minimum receive power requirement Pmin = - 110 dBm: [Note Q(k) is provided below]
(a) 1.8%;
(b) 7.2%;
(c) 3.6%;
(d) 1.2%;
6. At a receiver with bandwidth Bu , two multipath components with delays T1 and T2 are resolvable if:
(a) |T1 − T2 | ≫ u ;
(b) |T1 − T2 | ≫ u ;
(c) |T1 − T2 | ≪ u ;
(d) |T1 − T2 | = u .
7. A radio Tx and Rx operating at 900 MHz have a LOS path of electrical length 250m and a single multipath of electrical length 500m. What is the phase difference between both signals at the receiver and is the multipath interference constructive or destructive (assume unity reflection coefficient):
(a) -p rad, Destructive;
(b) -p/4 rad, Constructive;
(c) 0 rad, Constructive;
(d) -5p/4 rad, Destructive
8. A time invariant Channel Impulse Response (CIR) consists of three multipaths: ej0 at delay 0s; ej冗/2 at delay 1µs; and e -j冗/2 at delay 5µs. Which equation best describes the CIR:
(a) 6 (T) + j6(T − 1us) + j6 (T − 5us);
(b) 6 (T) + j6(T − 1us) − j6 (T − 5us);
(c) 6 (T) + j6(T + 1us) − j6 (T + 5us);
(d) 6 (T) −j6 (T − 1us) − j6 (T − 5us).
9. Consider a channel with Rayleigh fading and average received power r = 23 dBm. Find the probability that the received power falls below 10 dBm:
(a) 10%;
(b) 1.25%;
(c) 2.5%;
(d) 5%.
10. The average fade duration in a Rayleigh fading channel is given by T̅R = , where p = ;PR ⁄PT
and fD is the maximum Doppler shift. What is the average fade duration if fD is 10 Hz and the
received signal power is below one quarter of its average value:
(a) 23 ms;
(b) 52 ms;
(c) 45 ms;
(d) 100 ms
Graphical Q-Function
2023-01-11