EEE6431 Broadband Wireless Techniques Practice Sheet 2
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EEE6431 Broadband Wireless Techniques
Practice Sheet 2
1. Find the Shannon capacity of a wireless communications system with a SNR of 8 dB and a bandwidth of 8 MHz.
(a) 22.96 Mbit/s;
(b) 25.36 Mbit/s;
(c) 15.91 Mbit/s;
(d) 17.58 Mbit/s.
2. Find the SNR in dB required to achieve a Shannon capacity of 1 bit per channel use.
(a) 0 dB;
(b) 1 dB;
(c) 2.35 dBm;
(d) 9.54 dBm.
3. A wireless communications system experiences NB fading with two time-domain i.i.d. channel amplitudes ℎ" = 1 + j of probability 0.3 and ℎ' = 2 − j. If only the Rx knows the CSI, calculate the Shannon capacity for an average Tx power P+ = 2 W, N" = 1001 W/Hz and B = 20 MHz.
(a) 105.77 Mbit/s;
(b) 107.85 Mbit/s;
(c) 103.40 Mbit/s;
(d) 73.31 Mbit/s.
4. For the wireless communications system in Q3, find the optimum Shannon capacity when the transmitter knows the CSI as well as the receiver.
(a) 105.77 Mbit/s;
(b) 107.85 Mbit/s;
(c) 73.31 Mbit/s;
(d) 31.84 Mbit/s.
5. A wireless communications system experiences WB fading with two frequency domain channel coefficients H" = 1 + j and H' = 2 − j. Find the optimum Shannon capacity when the transmitter and receiver know the CSI for an average Tx power P+ = 2 W, N" = 1001 W/Hz and B = 20 MHz.
(a) 100.65 Mbit/s;
(b) 107.85 Mbit/s;
(c) 69.77 Mbit/s;
(d) 30.30 Mbit/s.
6. A wireless communications system uses multicarrier modulation with a total system bandwidth of 10 MHz. The system is located in an urban area with a channel RMS delay spread T9:; = 2 µs. Find the number of subchannels needed to obtain flat fading in each subchannel.
(a) 200;
(b) 256;
(c) 128;
(d) 400;
7. The CIR of a frequency selective RF channel is given by ℎ(T) = 6(T) + 6(T − 2T; ) + 6(T − 5T; ), where T; is the sample period. What is the length of the CP in samples?
(a) 5;
(b) 6;
(c) 4;
(d) 3.
8. In a 16-subcarrier OFDM system operating in a frequency selective fading channel, a particular transmitted OFDM data block is given by s = [s" s' sG sH sI sJ sK sL s1 sM s'" s'' s'G s'H s'I s'J ]O . If the CP length is equal to 3 samples, what is the CP for this data block.
(a) s0 s1 s2;
(b) s0 s2;
(c) s15 s14 s13;
(d) s13 s14 s15 .
9. Consider a 4 subcarrier OFDM wireless communications system. Find the transmitted OFDM symbol for a binary data vector [1 0 0 1]O assuming BPSK modulation and a CP of length one.
(a) [1 + j 0 1 − j 0 1 + j]O ;
(b) [0 0 1 − j 0 1 + j]O ;
(c) [1 − j 0 1 − j 0 1 + j]O ;
(d) [−1 + j 0 1 − j 0 1 + j]O .
10. Consider a 4 subcarrier OFDM wireless communications system. Find the FD channel coefficients for
a CIR given by ℎ = [1 1 + j 1 − j]O .
(a) [3 1 1 − 2j −1 + 2j]O ;
(b) [3 1 1 + 2j −1 − 2j]O ;
(c) [3 −1 + 2j 1 − 2j 1]O ;
(d) [3 −1 − 2j 1 + 2j 1]O .
11. For the CIR in Q- 10 find the received signal vector for the transmitted OFDM symbol in Q-9.
(a) [2j 3 − j 2 1 − j]O ;
(b) [2j 3 + j 2 1 + j]O ;
(c) [−2j 3 − j −2 1 − j]O ;
(d) [−2j 3 + j −2 1 + j]O .
2023-01-11