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Aalto University School of Electrical Engineering
ELEC-E4750 Radiowave Propagation and Scattering Session 10: Cellular links (3)
ELEC-E4750 24.11.2016
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Aalto University School of Electrical Engineering
Aalto University School of Electrical Engineering
Schedule
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Wk Date Location New topics, lectures and deadlines
43 Tue. 25 Oct. R037/TU3 1194-1195 Thu. 27 Oct.
44 Tue. 01 Nov. Topic 7: wireless and cellular systems Thu. 03 Nov. Clicker lecture 7
45 Tue. 08 Nov. Topic 8: cellular links (1) Thu. 10 Nov. Clicker lecture 8
46Tue. 15 Nov. Topic 9: cellular links (2) Thu. 17 Nov. Clicker lecture 9; threshold deadline of
topics 5-8
47 Tue. 22 Nov. Topic 10: cellular links (3) Thu. 24 Nov. Clicker lecture 10
• Suzan leads on 25 and 27 Oct. • Usman is away for 25.9-01.11. • Jan, Usman and Suzan lead on 24 Nov.
Aalto University School of Electrical Engineering
Books, Topics and Exercises § Books
§ Main books § S. Saunders, Antennas and Propagation for Wireless Communication Systems, Chapters 3, 5,
6-8, 10, 12 15, Wiley. § H. L. Bertoni, Radio propagation for modern wireless systems, Chapters 2-6, Prentice Hall. § A. . Molisch, Wireless Communications, Chapters 1 and 8, Wiley. § John A. Richards, Radio wave propagation, an introduction or the non-specialist, Chapter 3,
Springer. § Hardcover or paperback copies of both books are available in AaltoELEC and main
library. § Supplemental books:
§ D. M. Pozar, Microwave Engineering, Chapter 1, Wiley.
§ Topic 9: Cellular links (2) (Ch. 12, Ch. 2) § Exercise 1: Physical propagation modeling in microcells § Exercise 2: Pathloss and small-scale fading
§ Topic 10: Cellular links (3) (Ch. 10, Ch. 5) § Exercise 1: Small-scale fading models § Exercise 2: Characterization of small-scale fading (simulations)
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Aalto University School of Electrical Engineering
Aalto University School of Electrical Engineering
Contact Sessions for Topic 10• Goals of the present exercise problems are to
– Acquire the physical understanding of small-scale fading (problem 1) – Be able to characterize small-scale fading mathematically (problem
2) • During the contact sessions, you are
– solving the exercise problems by referring to relevant parts of the course books.
• A limited number of course books are available in the room. – encouraged to discuss with other students and teachers. – asked to contact teachers once your solutions are ready.
• If you prepare exercise solutions in an electronic format (recommended), upload the solution to MyCourses first and then contact teachers.
– asked to propose points for your ready solutions to the teachers. – not given exercise points without discussing with teachers.
• The discussions MUST happen in the contact sessions. – reminded that the threshold deadline topic 9-12 exercises and the
deadline of all exercises returns is December 15th.
Aalto University School of Electrical Engineering
Aalto University School of Electrical Engineering
Empirical Pathloss Estimation
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pathloss
Shadowing
Small-scale fading
Aalto University School of Electrical Engineering
Aalto University School of Electrical Engineering
Rayleigh Fading• Many propagation paths with
similar power
6 f (x + jy) = 1
2πσ 2 exp −x2 + y2
2σ 2
"
#$
%
&'
f (x) = 12πσ
exp −x2
2σ 2
"
#$
%
&'
Figs from Saunders,
Ch. 10.
Aalto University School of Electrical Engineering
Aalto University School of Electrical Engineering
PDF of Rayleigh fading
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f (x) = 12πσ 2
exp −x2
2σ 2
⎛
⎝⎜
⎞
⎠⎟
f (y) = 12πσ 2
exp −y2
2σ 2
⎛
⎝⎜
⎞
⎠⎟
PDF(r) = rσ 2 exp −
r2
2σ 2
⎛
⎝⎜
⎞
⎠⎟
Fig from Saunders,
Ch. 10.
Aalto University School of Electrical Engineering A. B. C. D.
0%
67%
33%
0%
Q1a:WhichstatementisincorrectaboutRayleighfadingofreceivedfieldstrength?A. Wecanobserveitinrichsca1ering
environments.B. Theircomplexamplitudeslooklike
whiteGaussiannoise.C. Wecanpredictwhereinspacewe
seelargeandsmallamplitudes.D. Correspondingphaseisuniformly
distributedover0to2π.
Aalto University School of Electrical Engineering A. B. C. D.
0% 0%
100%
0%
Q1b:WhichstatementisincorrectaboutRayleighfadingofreceivedfieldstrength?A. Wecanobserveitinrichsca1ering
environments.B. Theircomplexamplitudeslooklike
whiteGaussiannoise.C. Wecanpredictwhereinspacewe
seelargeandsmallamplitudes.D. Correspondingphaseisuniformly
distributedover0to2π.
Aalto University School of Electrical Engineering
Aalto University School of Electrical Engineering
Rice Fading• Rayleigh fading + dominant
propagation path, e.g., LOS
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−3 −2 −1 0 1 2 3−3
−2
−1
0
1
2
3
Real
Imaginary
f (x + jy) = 12πσ 2 exp −
(x − scosφ)2 + (y− ssinφ)2
2σ 2
"
#$
%
&'
s =1
φ =π2
Figs from Saunders,
Ch. 10.
Aalto University School of Electrical Engineering A. B.
22%
78%
Q2a:ThetwostandingwavecurvesrepresentRayleighandRicefading.WhichoneisRiceFading?A. CurveA.B. CurveB.
-10 -5 0 5 10Distance [6]
-30
-20
-10
0
10
Gai
n [d
B]
AB
A B
Aalto University School of Electrical Engineering A. B.
0%
100%
-10 -5 0 5 10Distance [6]
-30
-20
-10
0
10
Gai
n [d
B]
AB
Q2b:ThetwostandingwavecurvesrepresentRayleighandRicefading.WhichoneisRiceFading?A. CurveA.B. CurveB.
A B
Aalto University School of Electrical Engineering
Aalto University School of Electrical Engineering
Cumulative Distribution Function (CDF)
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CDF(r ') = prob(x ≤ r ') = PDF(r)−∞
r '∫ dr
-20 -10 0 10Gain [dB]
10-2
10-1
100
Cum
ulat
ive
prob
abilit
y-10 -5 0 5 10
Distance [6]
-30
-20
-10
0
10
Gai
n [d
B]
Aalto University School of Electrical Engineering
Aalto University School of Electrical Engineering
Q3: Derive the CDF of Rayleigh fading from the PDF on the paper you have. You can discuss with your peers.
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CDF(r ') = PDF(r)−∞
r '∫ dr
PDF(r) = rσ 2 exp −
r2
2σ 2
⎛
⎝⎜
⎞
⎠⎟
-30 -20 -10 0 10Envelope [dB]
0
0.1
0.2
0.3
0.4
0.5
Prob
abilit
y
PDF of Rayleigh
distribution
Aalto University School of Electrical Engineering A. B.
56%
44%
-20 -10 0 10Gain [dB]
10-2
10-1
100
Cum
ulat
ive
prob
abilit
yQ4a:ThetwoCDFcurvesrepresentRayleighandRicefading.WhichoneisRiceFading?A. CurveA.B. CurveB.
A
B
Aalto University School of Electrical Engineering A. B.
100%
0%-20 -10 0 10
Gain [dB]10-2
10-1
100
Cum
ulat
ive
prob
abilit
yQ4a:ThetwoCDFcurvesrepresentRayleighandRicefading.WhichoneisRiceFading?A. CurveA.B. CurveB.
A
B
Aalto University School of Electrical Engineering
Aalto University School of Electrical Engineering
Empirical Pathloss Estimation
17
pathloss
Shadowing
Small-scale fading
Aalto University School of Electrical Engineering
Aalto University School of Electrical Engineering
Shadowing
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Figs from Saunders,
Ch. 9.
Aalto University School of Electrical Engineering
Aalto University School of Electrical Engineering
Empirical Modeling of Shadowing
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Fig from Saunders,
Ch. 9.
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Shadowing: Physical Interpretation and Modeling • Caused by obstacles in propagation path between mobile
and base station.
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NAAAA ×××= …21
NLLLAL +++== …2110log10Central limit theorem à Normal distribution in the log-domain.
Aalto University School of Electrical Engineering A. B. C. D.
33%
22%22%22%
Q5a:Pathloss(P),shadowing(S),andsmall-scalefading(F).Whichstatementiscorrect?A. Typicaldynamicrangeofthe
receivedsignalisP>S>>F.B. Whatwecallstandingwaveis
equivalenttoF.C. TypicalspaJalrangeofSis
inverselyproporJonaltotheradiofrequency.
D. ThecentrallimittheoremdefinesthesignaldistribuJonsofP,SandF.
Aalto University School of Electrical Engineering A. B. C. D.
0% 0%0%
100%
Q5b:Pathloss(P),shadowing(S),andsmall-scalefading(F).Whichstatementiscorrect?A. Typicaldynamicrangeofthe
receivedsignalisP>S>>F.B. Whatwecallstandingwaveis
equivalenttoF.C. TypicalspaJalrangeofSis
inverselyproporJonaltotheradiofrequency.
D. ThecentrallimittheoremdefinesthesignaldistribuJonsofP,SandF.
Aalto University School of Electrical Engineering
Aalto University School of Electrical Engineering
Contact Sessions for Topic 10• Goals of the present exercise problems are to
– Acquire the physical understanding of small-scale fading (problem 1) – Be able to characterize small-scale fading mathematically (problem
2) • During the contact sessions, you are
– solving the exercise problems by referring to relevant parts of the course books.
• A limited number of course books are available in the room. – encouraged to discuss with other students and teachers. – asked to contact teachers once your solutions are ready.
• If you prepare exercise solutions in an electronic format (recommended), upload the solution to MyCourses first and then contact teachers.
– asked to propose points for your ready solutions to the teachers. – not given exercise points without discussing with teachers.
• The discussions MUST happen in the contact sessions. – reminded that the threshold deadline topic 9-12 exercises and the
deadline of all exercises returns is December 15th.