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Sri Lanka Institute of Information Technology
B. Sc. Eng. (Honours) Degree
Final Examination
Year 4 - Semester 2 (20 17)
EC4671- Wireless Communications
Duration:
2 hours
October 2017
Instructions to Candidates:
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This is a closed-book exam. However, students are allowed to carry one A4 page handwritten reference sheet. No electronic devices are allowed.
This paper contains 5 pages including the cover page.
This paper has 3 questions. Each question has sub-questions. Answer all questions.
Write down your answers in the answer booklet ONLY.
All symbols, notation and terminologies are consistent with those in the course materials.
Question 1 (Total points:
35)
1) Suppose one needs to construct a maximal-length shift register (MLSR) to generate the
pseudo-noise (PN) sequence for a spread spectrum system. Here the primitive polynomial
(mod-2) of order 6 (shown below) is used:
a) (8 points) What is the length of the output sequence (from the MLSR) in one period?
b) (10 points) Construct the diagram of the corresponding maximal-length shift register.
(Hint: Indicate all the elements properly.)
c) (6 points) Suppose the maximal-length PN sequence generated here is used for
spreading. If the user bit rate is 20k bits/second, calculate the corresponding chip
rate.
d) (3 points) Let the initial state of the shift register be 101011. Find out the next 3
states of MLSR based on your construction.
2) (6 points) In a direct-sequence spread spectrum system, a user's information bits are
given as 0 1 0 1. The spreading code for this user is the second row of the 4 x 4
Walsh-Hadamard matrix H 4 . Find out the spread sequence, i.e., the chip sequence after
spreading. (Hint: Use bipolar form for all sequences.)
3) (2 points) Show that the 5-th row and the 7-th row of the 8 x 8 Walsh-Hadamard matrix
H 8 are orthogonal sequences. (Hint: Use bipolar form for all sequences.)
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Question 2 (Total points:
30)
Consider the frame structure and the uplink time slot structure of the IS-136 (D-AMPS) system
shown in Fig. 1. The time slot is for a traffic channel. The IS-136 system is a time-division
multiple-access (TDMA)/ frequency-division duplex (FDD) system. The upper part of Fig. 1
shows the frame structure, which consists 6 time slots. The lower part of Fig. 1 shows the
structure of a time slot. All frames have the same frame structure. All time slots have the same
slot structure. The bits used for G, R, sync, SACCH and CDVCC are NOT considered as user
data. They are considered as overhead. The details of G, R, sync, SACCH and CDVCC are not
specified, but this will not affect answering the questions.
40 msec frame
slots
---.
1
2
3
4
-....
bits
---.
6
6
16
G
R
data
28
324 bits
122
sync
data
6
5
~-
12
SACCH
12
CDVCC
122
data
uplink
Fig. I. Frame and time slot structures of the uplink traffic channel in the IS-136 system; 1 msec = 10- 3 seconds.
1) (6 points) Explain the meaning of FDD.
2) (8 points) Evaluate the frame efficiency. (Hint: The frame efficiency is defined as the ratio
of all user data bits over the total number of bits in one frame.)
3) (5 points) Evaluate the system transmission rate. (Hint: This is the raw data rate, i.e., the
total number of bits divided by the time used for their transmission.)
4) (5 points) In an IS-136 system, a full-rate user uses 2 time slots in one frame. Evaluate
a full-rate user's information/data rate. (Hint: This is the rate for the transmission of user
data ONLY.)
5) (6 points) Explain one advantage of TDMA over COMA in the uplink communications.
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Question 3
(Total points: 35)
A wireless receiver uses M(M > 1) rece1ve antenna elements. The antennas are placed
sufficiently apart from each others, so that the received signals at different antennas undergo
independent and identically distributed (i.i.d.) Rayleigh fading.
1) ( 5 points) Explain the use of diversity in wireless communications.
2) (5 points) Suppose you are to design a diversity receiver. What are the important factors to
be considered for making a choice out of selection diversity and maximal-ratio combining
(MRC)? Justify your answers.
3) For the rest of this question, consider the case where selection combining is used at the
receiver. It is shown that the average signal-to-noise ratio (SNR) after selection with M
antennas is given by
'Ysc =
r
(t ~) '
k=l
where r(> 0) is the average SNR per branch. In addition, the probability that the instantaneous SNR (after selection) drops below a given threshold B is given by
Probbsc :::; B]
= ( 1 - e-~) M
The values in the above two equations are the original values, not in dB.
a) (5 points) For this sub-question, consider M
= 4. Suppose the average SNR after
selection is 23.19 dB. Evaluate the average SNR per branch, i.e.,
r.
(Hint: Convert
the value in dB to its original value.)
b) (5 points) As in Sub-question a), suppose M
= 4 and the average SNR after selection
is 23.19 dB. Evaluate the probability that the instantaneous SNR after selection drops
below 23.01 dB. (Hint: Here B is given in dB. Convert it into its original value first.)
c) (2 points) The instantaneous SNR, denoted as {, of each branch (i.e., each link
between the transmit antenna to any of the receive antennas) has the following
exponential probability density distribution (pdf)
1 :l
p(r) = ye-r,{;?: 0,
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where f(> 0) is a given constant. Find out (or develop the formula for) the probability
Prob(r >C).
d) (3 points) For a random variable with the pdf given by (*) m Sub-question c),
calculate its variance.
e) (10 points) Consider a two-branch diversity system, i.e., M = 2. Denote the instantaneous SNRs from Branch 1 and Branch 2 as 1 1 and ')'2, respectively. Here 11, 12 are
assumed to be i.i.d. with the same distribution given by ( *) shown in Sub-question
c). Let min(/1 , 1 2 ) denote the minimum (or the smaller one) of /I and ')'2 . Find out
(or develop the formula for) the following probability
where C > 0 and
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r > 0 are
given constants.
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