Module title and code: Antenna, Propagation and Wireless Communications Theory, ES4D2 Assessment setter (module tutor): Dr Yunfei Chen
Assignment Weighting (10% module etc.) and typical hours work: 20% of module, 30 hours Learning outcomes assessed:
Interpret the basics of wireless channels
Advance knowledge of techniques to enhance efficiency
Design wireless receivers
Evaluate performances of wireless techniques
Comprehend communications organisation and spectrum techniques
Context/Introduction/Background to the assignment: Based on material of part 2 with further research required for some questions.
Requirements/Task: Please answer all questions (four questions).
Formatting requirements: Handwritten answers (provided they are legible) can be scanned submitted, or a combination of typed and scanned handwritten work. Marks may be deducted if the handwriting and scanned documents are not legible.
Submission date/deadline: Thursday week 16 (16/01/2020) at 20.00 via tabula (See assignment deadlines at: https://warwick.ac.uk/fac/sci/eng/eso/undergraduate_students/coursework/assignmentdeadlines/ )
Assessment criteria/mark scheme: Marking is out of 100% and the marks allocated to each question are shown at the end of each question.
Additional Useful Resources: Beyond the relevant books, from the reading list and those cited in moodle page/lecture notes, please note that you have access to the journal/conference research papers the University subscribes to and means to search for these, such as the database of Web of Science (also known as the Web of Knowledge) see databases at https://warwick.ac.uk/services/library.
Feedback format: Each submitted report will be marked electronically and answers to the questions will be provided.
2019-2020 ES4D2 Part 2 Assignment Question 1 (total 35 marks)
Statistical characterization of the fading process can be done as follows:
(a) Assume that the fading process is given byY X2 X2 X2 X2 , where X,i1,2,3,4, are
1234 i
independent Gaussian random variables each with mean 0 and variance 1. Generate 100 realizations of Y as data Y. Give your MATLAB code in the solution. (The MATLAB randn function gives a standard
Gaussian random number with mean zero and variance 1.) (5 marks) (b) Use measurements in (a) to find the empirical cumulative distribution function (CDF) ofY . Give your MATLAB code and a plot of the empirical CDF in the solution. (The MATLAB [F,W]=ecdf(Y) function
gives the value of the Kaplan-Meier CDF of data Y in vector F evaluated at vector W.) (c) Among the following candidate models:
The CDF of a lognormal distribution given by
The CDF of a Gamma distribution given by
P(x)(k,x/),x0, k,0 (k)
The CDF of a Rayleigh distribution given by
x2 P(x)1e 22 ,x0
(5 marks)
20log10(x) P(x)1Q L ,x0
2 L
where (,) is the incomplete Gamma function. Use measurements in (a) to estimate the parameters of L , L2 , k , and 2 by using the equations of
1 N
2 0 l o g 1 0 ( Y ) , 2 iL
1 N
2 0 l o g 1 0 ( Y ) 2 , 2 iL
1 N
Y 2 , k
3s (s3)2 24s 12s
L
parameters and plot the CDFs of all candidate models with the estimated parameters in one figure. If you want to use the built-in functions in MATLAB, note that some of their definitions are different from those above. (10 marks)
(d) Calculate the mean squared error (MSE) for each candidate model with the estimated parameters given
i1
, Y,whereslnN YN lnY andN100inthiscase.Givethevaluesofestimated
N i1
1N 1N1N
2N i1
kNi1 i1 i1
N 1 i1
i
i
i
i
by(c)inthesolution.(TheMSEisdefinedasEI [P(w) f ]2,where P(w) isthevalueoftheCDFof
iii
the candidate model at wi , fi is the i -th component of F, and wi is the i -th component of W.)
1/3
(10 marks)
(e) State the best candidate model in the solution. Plot the CDF of the best model and the empirical CDF in
one figure. (5 marks)
Question 2 (total 20 marks)
A mobile communications system allows a maximum power loss of 140 dB at the edge of the cell during the transmission. In the system, the path loss follows LP 40 lg r , where r is the distance between the receiver and the transmitter. The shadowing AS follows a lognormal distribution with location variability 8 dB. The fast fading A follows a Rayleigh distribution with mean fading power 2 2 20 .
F
(a) If the transmission power loss is caused by path loss only, one has L LP . Determine the radius of the cell. (5 marks) (b) If the transmission power loss is caused by path loss and shadowing only, one has L LP LS ,
where LS 20 lg AS . To achieve a minimum coverage fraction of 80% at the edge of the cell, determine the
radius of the cell. (5 marks) (c) Assume that shadowing is independent of fast fading. If the transmission power loss is caused by path loss, shadowing as well as fast fading, one has L LP LS LF , where LF 20lg AF and AF follows a
Rayleigh distribution with mean fading power 2 2 20 . Derive the empirical CDF of L L using 10000 SF
realizations and the randn function in MATLAB. Give your MATLAB code and a plot of the empirical CDF with the x-axis between -20 and +20 and y-axis between 0 and 1 in the solution. (10 marks)
Question 3 (total 25 marks)
Consider a wideband fast fading channel with three multipath taps: 1 t with mean amplitude , 2 t with mean amplitude 1, and 3 t with mean amplitude .
(a) Calculate the RMS delay of the channel. Assume that the mean power is the square of the mean
amplitude. Show all the procedures of calculation. (6 marks)
(b) Assume that B is the signal bandwidth. Determine the relationship between and B such that the
channel is frequency-non-selective. 1 (2 marks)
(c) Assume that the channel frequency response is | C ( f ) | 1 f W , | f | W with W=12.8 kHz. Assume 2
that the data rate equals the sampling rate. Choose the data rate such that ISI-free signal design is possible.
(5 marks) (d) Use a raised-cosine pulse with roll-off factor of 0.6 to design the pulse-shaping filer at the transmitter
and the receiving filter at the receiver. (12 marks)
2/3
Question 4 (total 20 marks)
Compare and discuss the diversity methods, the frequency bands and the modulation schemes used by different 5G standards.
3/3
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