Q1. Determine the received signal power observed by a user equipment (UE) at 4m and at a distance of 500 m from a 14 m high base station. The transmitter and receiver antenna gains are 10 dB and 5 dB, respectively. Transmitted power is 30 dBm. Do all calculations using dB.
Q2. With a subcarrier spacing of 10 kHz, how many subcarriers will be used in an OFDM system with 8 MHz channel bandwidth?
Q3. Let us consider an OFDMA system that uses the same carrier spacing irrespective of the channel bandwidth used. It employs 1024 subcarriers for 10 MHz channel. How many subcarriers will be used if the channel was (a) 1.25 MHz, (b) 5 MHz, (c) 8.75 MHz?
Q4. If 100 mW transmit power is used by a 2.4 GHz WiFi router, find the received power in dBm at a distance of 20 meter (assume free space path loss with unit antenna gains).
Q5. Repeat the previous question for a 60 GHz WiFi router:
(a) what is the received power at 20 m?
(b) what transmit power should be used by the router if the same received power of Q4 was to be achieved at 20 m?
(c) at what distance the same received power of Q4 could be achieved if the router still used 100 mW?
Q6. You have bought a 2.4 GHz WiFi router with two dipole antennas claiming effective antenna gain of 6 dB. Your laptop has a single dipole with 0 dB gain and it claims a receiver sensitivity of -64 dBm. Calculate the maximum distance from the router your laptop can receive data if the router always use a transmit power of 20 dB.
Q7. You have bought a 2.4 GHz WiFi router with antenna gain of 6 dB and default transmission power of 100 mW. Your laptop has a 0 dB antenna gain and claims a receiver sensitivity of -60 dBm. Can you connect your laptop to the router from a distance of 150 m? Why or why not?
Q8. What degrees of freedom we have for the following MIMO configurations:
(a) 2x2 MIMO
(b) 4x2 MIMO
(c) 10x4 MIMO
(d) 20x10 MIMO
(e) 20x20 MIMO
Q9. Inspired by the MIMO technology, you are committed to design new laptops with lots of antenna elements fitted to it. For a linear (1 dimensional) antenna array, how many antennas can you fit within a length of 15 cm for the following WiFi bands?
(a) 2.4 GHz
(b) 5.8 GHz
(c) 60 GHz
Q10. In future, we may be forced to use frequencies as high as 10 THz to transmit data superfast required for some yet-to-be invented applications. What size of antenna (full length) would we need for such devices?
