Digital Communication 4 (ENG4052)
Friday 14th May 2021
Q1. Table Q1 shows the range of mobile (cellular) network technologies in current deployment.
|
2G
|
2.5G
|
3G
|
4G
|
5G
|
|
GSM
|
GSM+GPRS
|
UMTS
|
LTE
|
NR
|
Table Q1: range of mobile (cellular) network technologies in current deployment
(b) State which of these network technologies have packet-switched elements.
(c) Indicate what provisions there are for voice calls where a network technology consists of only packet-switched elements.
(d) Two major network operators in the US have recently announced a deprecation of all circuit-switched elements. What are the motivations for the network operators in taking this action?
(e) Indicate what detrimental consequences could afect some users, if any.
Q2. Figure Q2 shows the carrier, the in-phase and in-quadrature components of a digitally modulated waveform.
0 25 50 75 100 125 150 175 200
0 25 50 75 100 125 150 175 200
100
Time/ns
Figure Q2: The carrier, the in-phase and in-quadrature components of a digitally modulated waveform.
(a) What is the carrier frequency?
(b) What is the modulation scheme?
(c) If there are no pairs of repeating symbols in Figure Q2, what is the symbol (baud) rate?
(d) The modulation scheme uses Gray coding. Provide a valid digital data string that results in this modulated waveform?
(e) Sketch a constellation diagram for the modulation with the Gray code labels corre-sponding to your answer to part (d).
Q3. The distribution of the major blood group types in Scotland’s population is given in Table Q3.
|
O+
|
A+
|
B+
|
AB+
|
O-
|
A-
|
B-
|
AB-
|
|
40 9%
|
28 8%
|
9 2%
|
2 7%
|
9 5%
|
6 3%
|
2 0%
|
0 6%
|
Table Q3: Major blood group distribution in Scotland’s population
(a) Treating this as a symbol set with the given probabilities, calculate the entropy in bits of the complete symbol set.
(b) A new database system is being devised. Determine an optimal Hufman preix code for the symbol set that minimises the required storage space for the major bloodgroup data.
(c) Compare the storage space requirements for your Hufman code with a simple 3 bit code for the 8 major blood groups and the calculated entropy.
(d) It is decided that, for simplicity, the database should use a simple 3 bit code for the 8 major blood groups, but there are concerns that the data could become corrupted due to single bit errors. Therefore additional parity bits must be included in the database. One of the block codes under consideration has a generator matrix in systematic form,
1 0 0 0 1 1ª
G = 0 1 0 1 0 1
«0 0 1 1 1 0¬
What does the term systematic mean in this context?
(e) Determine the 8 valid codewords for this block code.
(f) What is the minimum Hamming distance for this code?
(g) How many single bit errors can be detected in a codeword?
(h) How many single bit errors can be corrected in a codeword?
(i) Determine the parity check matrix for this code?
(j) The codeword 010011 is received. Is this a valid codeword? If not, what is the most likely correct codeword and corresponding input data?
(k) If a requirement of the system is that there should be a probability of 10-9 or less of an error in the blood group data after error correction and decoding, what is the maximum single bit error ratio in the database which can be tolerated.
Q4. A transmission channel of a digital communications system based on double sideband modulation has an available bandwidth of 12MHz.
(a) If the signal to noise ratio corresponds to 8.45dB, what does the Shannon-Hartley theorem give for the maximum rate at which information can be transmitted over this channel with an arbitrarily low error rate?
(b) Pulse modulation is considered for the communications format in this channel. By using matched iltering, the pulse spectrum is a raised cosine pulse with a roll-of of β = 0.5. Explain what is meant by the term matched ilter.
(c) Sketch the pulse spectrum.
(d) If the bandwidth of the pulse spectrum equals the available bandwidth, what is the minimum symbol separation time which suppresses inter-symbol interference?
(e) For the quadrature phase shift keying (QPSK) modulation format, what is the corre- sponding data rate (bits per unit time) for this communication link?
(f) Now Orthogonal Frequency Division Multiplexing (OFDM) with 4096 (complex co- efficient) subcarriers is considered for the same digital communications system with QPSK constellation mapping. Why is it advantageous to have a power of 2, i.e. 2N , for the total subcarriers, even if a number of them do not carry data?
(g) What is the subcarrier spacing for this OFDM example?
(h) Hence, or otherwise, what is the minimum useful symbol (time) length for this exam- ple?
(i) What is the corresponding maximum data (bit) rate?
(j) What practical considerations would result in a data rate somewhat reduced from the ideal case?
(k) Determine an achievable data rate for atypical practical example coniguration.